tag:blogger.com,1999:blog-85949795532380869272024-02-19T00:48:39.805-08:00PhysicSpacePhysics Space is the best home for the world's Physicist. This is a world where only Physics Matters. So this is the best site, where you will find the latest researches and publication explaining the physical nature of the world from different respective fields of Physics(such as Classical Mechanics, Relativistic Physics, Quantum Mechanics, AstroPhysics etc.) by the most known Great Physicist(Albert Einstein, Newton, Stephen Hawking, Galileo, Planks and our current 21th centuries physicist).Anonymoushttp://www.blogger.com/profile/12948124948045044887noreply@blogger.comBlogger60125tag:blogger.com,1999:blog-8594979553238086927.post-65946753845794031422019-02-22T02:01:00.005-08:002019-02-22T02:01:43.820-08:00 Galaxy and Structure Formation 2<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmCxVd1C9Ejo4UMTfXqGdMCOmb6ApQJkp9T9WuSjrNTkH6v_X6NSUvp9tQiiO8GAGUODDggDdX0LI2IqO28uo-djEYOsNyDdc48GhD99_6Rm4CEn1F1fR0-MsvFA3AcdkYjbGJ6iC_LKU/s1600/Slide48.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="540" data-original-width="720" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmCxVd1C9Ejo4UMTfXqGdMCOmb6ApQJkp9T9WuSjrNTkH6v_X6NSUvp9tQiiO8GAGUODDggDdX0LI2IqO28uo-djEYOsNyDdc48GhD99_6Rm4CEn1F1fR0-MsvFA3AcdkYjbGJ6iC_LKU/s400/Slide48.JPG" width="400" /></a></div>
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In 1968, Joseph Silk showed that, during the pre-recombination epochs, sound waves in the radiation-dominated plasma were damped by repeated electron scatterings (Silk, 1968). The effect of this damping was to dissipate fluctuations with masses less than about 10 12 M , a mass known as the Silk mass, by the epoch of recombination. Consequently, all fine-scale structure would be wiped out and only large-scale structures on the scale of large galaxies and clusters of galaxies could form after recombination. In the early 1970s, Zeldovich and Edward Harrison independently put together information about the spectrum of the initial fluctuations on different physical scales and showed that observed structures in the Universe could be accounted for if the mass fluctuation spectrum had the form Δ(M) ∝ M −2/3 in the very early Universe, corresponding to a power spectrum of initial fluctuations of the form |Δ k | 2 ∝ k n with n = 1. The amplitude of this scale-free power spectrum, known as the Harrison–Zeldovich spectrum of initial perturbations, was inferred to be ∼ 10^−4 (Harrison, 1970; Zeldovich, 1972).</div>
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A key test of these models was provided by the fact that density fluctuations at the epoch of recombination should leave some imprint upon the intensity distribution of the Cosmic Microwave Background Radiation on the sky. In the simplest picture, if the process of recombination were instantaneous, adiabatic perturbations would be expected to result in temperature fluctuations ΔT/T = 1/3 Δφ/c^2 = 1/3 Δ / on large physical scales associated with large-scale gravitational perturbations, an ef- fect known as the Sachs–Wolfe effect (Sachs and Wolfe, 1967). In fact, the problem is somewhat more complicated than this, partly because the process of recombination is not instantaneous and because other physical processes come into play on angular scales of about 1 ◦ and less. These include the adiabatic compression of the perturbations and first-order Doppler scattering due to the collapse of the primordial perturbations. These predictions provided a challenge for the observers since the amplitudes of the temperature fluctuations in these early theories were in the range ΔT/T ∼ 10%−3 − 10^−4 , well within the capability of sensitive anisotropy measurements of the Cosmic Microwave Background Radiation.</div>
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In the 1970s, these concepts gave rise to two principal scenarios for the formation of structure in the Universe. The first, known as the adiabatic model, was based upon a picture in which the perturbations were adiabatic sound waves before the epoch of recombination and structure in the Universe formed by the fragmentation of large-scale structures which reached amplitude δ / ∼ 1 at relatively late epochs. A realisation of this scenario was described by Andrei Doroshkevich, Sunyaev and Zeldovich in 1974 (Doroshkevich et al., 1974).</div>
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An alternative picture was one in which the perturbations were not sound waves<br />but isothermal perturbations in pressure balance with the background radiation in the pre-recombination plasma. Small mass perturbations were not damped in this picture and so perturbations on all scales survived to the recombination epoch. After that epoch, the Jeans’ mass dropped to about 10^6 M corresponding roughly to the masses of globular clusters. Galaxies and clusters of galaxies then formed by the process of hierarchical clustering under the influence of perturbations on larger physical scales.</div>
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Both models predicted similar amplitudes for the density perturbations at the epoch of recombination on large physical scales and consequently similar temperature perturbations in the Cosmic Microwave Background Radiation. Their subsequent behaviour was, however, quite different. The adiabatic picture could be thought of as a ‘top-down’ process of galaxy formation in which the largest scale structures formed first and then smaller scale structures formed by a process of fragmentation. In contrast, the isothermal picture corresponded to a ‘bottom-up’ process in which small-scale objects came together to form larger structures by hierarchical clustering. In the adiabatic picture, galaxies, stars and the chemical elements all formed atrelatively late epochs, whereas in the isothermal picture, they could begin to form at very much earlier cosmic epochs.</div>
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Throughout the 1970s increasingly sensitive searches were made for temperature fluctuations in the Cosmic Microwave Background Radiation, these observations being analysed critically by Bruce Partridge in his review of 1980 (Partridge, 1980a). His own observations had reached sensitivities of ΔT/T ≈ 10 −4 or slightly better by that time (Partridge, 1980b). Models with low density parameters were in serious conflict with these upper limits because, in these, there is relatively little growth of the perturbations after the epoch of recombination. Thus, by the early 1980s, the upper limits to the intensity fluctuations in the Cosmic Microwave Background Radiation were beginning to constrain severely purely baryonic theories of structure formation. Furthermore, the limits to the density parameter in the form of baryons from primordial nucleosynthesis arguments showed that, if the density of matter in the Universe were close to the critical density, most of the matter in the Universe would have to be in some non-baryonic form.</div>
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<a href="http://www.hausapost.com.ng/"><span style="font-size: xx-small;">www.hausapost.com.ng </span></a></div>
Algebrahttp://www.blogger.com/profile/11440946058125679273noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-62842444841109268302019-02-17T04:03:00.001-08:002019-02-17T04:03:23.297-08:00Galaxy and Structure Formation<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSwA8ugEHJwJapjDVxVbt7KnbuFSD8FvMDgaNXsi-keoMu2sqQvtCuxWoaLsSNtH1BlBl-3DruwZBuQx9L3iVtMhfw5o3K-_AIYtR32dv7VR-KZPrnKCrE2uhJAPngQck3eJ1wBIgxtPc/s1600/Slide48.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="540" data-original-width="720" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSwA8ugEHJwJapjDVxVbt7KnbuFSD8FvMDgaNXsi-keoMu2sqQvtCuxWoaLsSNtH1BlBl-3DruwZBuQx9L3iVtMhfw5o3K-_AIYtR32dv7VR-KZPrnKCrE2uhJAPngQck3eJ1wBIgxtPc/s400/Slide48.JPG" width="400" /></a></div>
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The Friedman world models are isotropic and homogeneous and so the enormous diversity of structure we observe in the Universe today is absent. The next step in developing more realistic models of the Universe is to include small density perturbations into the homogeneous, isotropic models and study their development under gravity. For the case of a stationary medium, this problem was solved by James Jeans in 1902 (Jeans, 1902). The criterion for collapse is that the size of the perturbation should exceed the Jeans’ length λ J = c s /(G 0 /π) 1/2 , where c s is the speed of sound in the medium and 0 its density. On scales greater than the Jeans’ length, the instability grows exponentially. The physical meaning of the instability criterion is that, on large enough scales, the gravitational force of attraction by the matter of the perturbation exceeds the pressure gradients which resist collapse.<br /> </div>
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The analysis was repeated for the case of an expanding medium in the 1930s by<br />Lemaître and by Richard Tolman for the case of spherically symmetric perturbations(Lemaître, 1933; Tolman, 1934) and the solution for the general case was found by Evgenii Lifshitz in 1946 (Lifshitz, 1946). Lifshitz found that the condition for gravitational collapse is exactly the same as the Jeans’ criterion at any epoch but, crucially, the growth-rate of the density perturbations is no longer exponential but only algebraic. For a Universe with the critical density, Ω 0 = 1 or 0 = 3H 0 2 /8πG, the density contrast Δ = δ / grows with time as Δ ∝ t 2/3 . The implication of this result is that the fluctuations from which the large-scale structure of the Universe formed cannot have grown from infinitesimal random perturbations. For this reason, Lemâitre, Tolman and Lifshitz inferred that galaxies could not have formed by gravitational collapse.</div>
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<br />From the early 1960s onwards, other authors took the point of view that the<br />solution to the problem was to include finite perturbations into the model of the early Universe and then follow in detail how their mass spectrum would evolve with time. The Moscow school led by Yakov Zeldovich, Igor Novikov and their colleagues and James Peebles at Princeton pioneered this approach to the study of the development of structure in the Universe. If perturbations on a particular physical scale are tracked backwards into the past, at some large redshift, the scale of the perturbation is equal to the horizon scale, that is r ≈ ct, where t is the age of the Universe. In 1964, Novikov showed that, to form structures on the scales of galaxies and clusters of galaxies, the density perturbations on the scale of the horizon had to have amplitude Δ = δ / ∼ 10 −4 in order to guarantee the formation of galaxies by the present epoch (Novikov, 1964). These were certainly not infinitesimal perturbations and their origin had to be ascribed to processes occurring in the very early Universe. </div>
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The discovery of the Cosmic Microwave Background Radiation in 1965 had an<br />immediate impact upon these studies since the thermal history of the pregalactic<br />gas could be worked out in detail and this was essential in order to determine<br />how the speed of sound, and hence the Jeans’ length, varied with cosmic epoch. If there is no energy input into the background radiation, the temperature of the thermal background radiation changes with scale factor a as T = T 0 /a = T 0 (1+z), where z is redshift, exactly as in the adiabatic expansion of a photon gas. Therefore, at redshifts z ∼ 1500, the temperature of the radiation was about 4000 K, at which temperature there were sufficient photons in the Wien region of the Planck distribution to ionise all the intergalactic hydrogen. This epoch is referred to as the epoch of recombination and at earlier epochs the hydrogen was fully ionised; at a correspondingly earlier epoch, the primordial helium was ionised as well. Somewhat earlier than the epoch of recombination, the inertial mass density of the radiation was equal to the mass density of the matter, c 2 = aT 4 , and so, at times earlier than the epoch of matter and radiation equality, the dynamics of the Universe were radiation-dominated. </div>
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The coupling of matter and radiation by electron scattering was worked out by Ray Weymann in 1966 and in much more detail by Zeldovich and Rashid Sunyaev in 1969 (Weymann, 1966; Zeldovich and Sunyaev, 1969). The pioneering papers by Zeldovich and Sunyaev were based upon the theory of induced Compton scattering which had been published by Aleksander Kompaneets in 1956, long after this remarkable classified work had been completed (Kompaneets, 1956). What these papers showed was that, during the radiation-dominated epochs, the matter and radiation were maintained in very close thermal contact by Compton scattering as long as the intergalactic gas remained ionised. This enabled the speed of sound to be determined at all epochs before the epoch of recombination. Therefore, the evolution of the Jeans’ length and the mass of baryonic matter within this length, what is known as the Jeans’ mass, could be evaluated. </div>
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<span style="font-size: x-small;">to be continue</span></div>
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<a href="http://www.hausapost.com.ng/"><span style="font-size: xx-small;">hausapost.com.ng </span></a></div>
Algebrahttp://www.blogger.com/profile/11440946058125679273noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-18738055171705634732019-02-14T11:53:00.000-08:002019-02-14T11:53:01.542-08:00The Big Bang<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxuGsq0OwInepCt5nJMyULEXZPsZN-yCWMXFebHq1tXnJp6B52RLglZKFfEnGkszjQyULNF024yyUHJjujJM0nqWz7aBvH5GKk7gaKhnvbNTzg6ZlZt4Fpt1Yla0cWjlTZjOyDc2elJko/s1600/bigbang.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="1280" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxuGsq0OwInepCt5nJMyULEXZPsZN-yCWMXFebHq1tXnJp6B52RLglZKFfEnGkszjQyULNF024yyUHJjujJM0nqWz7aBvH5GKk7gaKhnvbNTzg6ZlZt4Fpt1Yla0cWjlTZjOyDc2elJko/s640/bigbang.jpg" width="640" /></a></div>
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The next major advance occurred soon after the Second World War when George Gamow realised that, in an expanding Universe, the early stages must have been very hot indeed – the temperature was so high that the dynamics of the expansion were dominated by the energy density of thermal radiation rather than by its matter content, in other words, the Universe was radiation-dominated. Following an earlier suggestion of Lemaître, he attempted to explain the origin of the chemical elements by primordial nucleosynthesis, that is, by nuclear fusion processes as the Universe cooled down from its very hot initial stages. The reasons for adopting this picture were twofold. Firstly, following the work of Cecilia Payne, the abundances of the chemical elements in stars seemed to be remarkably uniform and secondly it was thought that the central temperatures of the stars were not high enough for nucle-osynthesis to take place. Gamow’s programme was not successful because of the problem of synthesising elements heavier than helium – there are no stable isotopes<br />with atomic mass numbers 5 and 8. Therefore, in the short time-scales available<br />in the hot early phases of the expansion, there was not time to synthesis elements heavier that helium. Gamow’s coworkers Ralph Alpher and Robert Herman showed that only deuterium, helium-3 and helium-4 were created in significant quantities(Alpher and Herman, 195).</div>
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n the course of their calculations, Alpher and Herman worked out the thermal<br />history of the Universe in some detail and predicted that there should be present in the Universe today a diffuse background of black-body radiation with temperature about 5 K, the cooled remnant of its very hot early phases (Alpher and Herman, 1948). The detection of this background radiation was far beyond the capabilities of the technology of the 1940s and the lack of success of Gamow’s programme of primordial nucleosynthesis resulted in the neglect of this key prediction for many years. Furthermore, in the 1950s, Fred Hoyle discovered the triple-α resonance, which leads to the formation of carbon from three helium nuclei (Hoyle, 1954). Soon after, he and his colleagues, Margaret Burbidge, Geoffrey Burbidge and William Fowler, showed how the heavy elements could be accounted for by nucleosynthesis in stars(Fig. 1) (Burbidge et al., 1957).</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYc_Z_-y35nhlwWMw6MFaicJlPYb0js8APRSV_Pua4f8aqi5GsK9Ao1iHD4lzOQSmWcKPRfYC6ug51KYwAhcKCFrKZRAW9mZsx7nWCtI_6f5kHx6BRxXy6msgL5NOBNRfcM-yN82ehO-w/s1600/bigbang.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1064" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYc_Z_-y35nhlwWMw6MFaicJlPYb0js8APRSV_Pua4f8aqi5GsK9Ao1iHD4lzOQSmWcKPRfYC6ug51KYwAhcKCFrKZRAW9mZsx7nWCtI_6f5kHx6BRxXy6msgL5NOBNRfcM-yN82ehO-w/s320/bigbang.png" width="212" /></a></div>
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<span style="font-size: x-small;">Fig. 1.6. The evolution of the fraction (by number) of the light nuclei in a radiation-dominated Universe, according to calculations by Fermi and Turkevich and published by Alpher and Herman in 1950 (Alpher and Herman, 1950). The models began with 100% of the material in the form of neutrons. The tritium 3 H and neutrons shown surviving to 2000 seconds decay radioactively with half-lives of 12.46 years and 10.25 minutes respectively</span></div>
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Interest in what is now referred to as the Big Bang model of the Universe grew<br />steadily through the 1950s and early 1960s as evidence was found for cosmological evolutionary effects in the distribution of faint radio sources (Ryle, 1955, 1958). On the theoretical side, interest was rekindled in the question of the synthesis of elements in the early Universe, not now with a view to creating all the elements, but rather to account for the cosmic abundance of helium. By 1964, it was appreciated that, wherever helium could be observed in the Universe, it is present with a very high chemical abundance, about 24% by mass. This figure far exceeded what could be explained by stellar nucleosynthesis. I remember vividly attending a course of post-graduate lectures given by Fred Hoyle in Cambridge in 1964 entitled Problems of Extragalactic Astrophysics in which this problem was discussed. During the lecture course, Hoyle, Roger Tayler, and John Faulkner carried out detailed computations of the expected abundance of helium produced by primordial nucleosynthesis. Within a week of the topic being raised, they had shown that about 23 to 25% of helium by<br />mass is created by this process and that the percentage is remarkably independent of the precise initial conditions. The paper by Hoyle and Tayler was published in Nature in 1964 (Hoyle and Tayler, 1964). Subsequent more detailed calculations by Robert Wagoner, Fowler and Hoyle confirmed these conclusions and suggested that other elements which are difficult to account for by stellar nucleosynthesis, the light isotope of helium, 3 He, deuterium, D, and lithium, 7 Li, could also be accounted for in this way (Wagoner et al., 1967). Equally important, the success of these computations resulted in an upper limit to the mean baryon mass density of the Universe of about one tenth the critical density – if the density were any higher, less than the observed abundances of deuterium and helium-3 would be created primordially.</div>
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By the early 1960s, as the sensitivity of receivers for centimetre wavelengths<br />improved, it became feasible to search for the cool background radiation left over from the early stages of the Big Bang. The predicted remnant of the Big Bang was discovered, more or less by accident, by Arno Penzias and Robert Wilson in 1965 (Penzias and Wilson, 1965). The Cosmic Microwave Background Radiation was the second key discovery of twentieth century observational cosmology. Observations by the Cosmic Background Explorer (COBE), launched in 1989, showed that, away from the Galactic plane, the radiation is uniform over the sky to better than one part in 100,000 on angular scales greater than 7 ◦ and that its spectrum is of black-bod form with a quite remarkable precision (Smoot et al., 1992; Fixsen et al., 1996). These observations provided compelling evidence that our Universe went through a very hot, dense phase when the matter and radiation were in thermal equilibrium in its early stages.</div>
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The upshot of these discoveries was that there were four independent pieces of<br />evidence for the Big Bang picture of the origin and evolution of our Universe. Firstly, the expansion of the distribution of galaxies discovered by Hubble; secondly, the black-body spectrum and isotropy of the Cosmic Microwave Background Radiation; thirdly, the formation of the light elements by primordial nucleosynthesis; and fourthly, the fact that the ages of the oldest stars and nucleochronology ages were of the same order as the expansion age of the Universe. Thus, the Big Bang provided a natural framework within which to tackle the problems of galaxy and structure formation.</div>
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Algebrahttp://www.blogger.com/profile/11440946058125679273noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-63778598608349409992019-02-13T01:35:00.003-08:002019-02-13T01:35:50.170-08:00The Physics of Fertilizer<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEb-tu2656tzUVH8InP-uUnXsTqh1uJSQKoCimuYMOJknescWbdrWjGY2UvjP8RwZZ_p8qWRYEpmaiaoHtDmcWtFhx7wrIwd9Fu0H6RItyvCcZLDPqxSn5jv_ZFqYEZ_WlNs3062YbYzU/s1600/fertilizers.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="420" data-original-width="750" height="223" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEb-tu2656tzUVH8InP-uUnXsTqh1uJSQKoCimuYMOJknescWbdrWjGY2UvjP8RwZZ_p8qWRYEpmaiaoHtDmcWtFhx7wrIwd9Fu0H6RItyvCcZLDPqxSn5jv_ZFqYEZ_WlNs3062YbYzU/s400/fertilizers.png" width="400" /></a></div>
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Fertilizers or fertilisers are compounds given to plants with the intention of promoting growth; they are usually applied either via the soil, for uptake by plant roots, or by foliar spraying, for uptake through leaves.</div>
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In this live Grade 12 Physical Sciences show we take a look at Fertilizers. In this case we discuss primary nutrients, we discuss the production of nitrogen containing fertillizers, we discuss the production of potassium and phosphorus containing fertilizers, we explain how to calculate the nutrient content in fertilizers using N:P:K rations and finally we discuss the negative impact of nutrients on the environment. </div>
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<b>WHAT HAPPENS TO FERTILIZER IN SOIL?</b></div>
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<b> </b><span style="color: #212100;">A lot of careful consideration goes into selecting which fertilizer should be added to a crop.</span><b><span style="color: #212100;"> </span></b><span style="color: #212100;">After
all the decisions have been made, little thought is then given to what
actually happens next. A brief review of some important fertilizer
reactions can help you get the most benefit from these valuable
resources. </span><b><span style="color: #212100;"><br />
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There are five major processes that happen to applied fertilizer. <br />
• </span></b><span style="color: #212100;">It is taken up by the crop </span><b><span style="color: #212100;"><br />
• </span></b><span style="color: #212100;">It reacts with soil minerals and organic matter to become part of the soil reserve </span><b><span style="color: #212100;"><br />
• </span></b><span style="color: #212100;">It can leach from the root zone with water </span><b><span style="color: #212100;"><br />
• </span></b><span style="color: #212100;">It can be lost to the atmosphere as a gas </span><b><span style="color: #212100;"><br />
• </span></b><span style="color: #212100;">It can move from the field through soil erosion and water runoff </span><b><span style="color: #212100;"><br />
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Nitrogen fertilizer </span></b><span style="color: #212100;">can be subject to
all five of these processes and may be the most difficult to manage of
all nutrients. Nitrogen fertilizer is most commonly added in the form of
nitrate, ammonium or urea. Their behavior is quite different and they
need to be managed with their specific properties in mind. </span><u><span style="color: #212100;"><br />
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Nitrate </span></u><span style="color: #212100;">(NO</span><sub><span style="color: #212100;">3</span></sub><sup><span style="color: #212100;">-</span></sup><span style="color: #212100;">):
Nitrate is very soluble in soil and moves freely with water in the
soil. Excessive rainfall or irrigation can easily move nitrate below the
root zone. In wet soils, bacteria may convert nitrate to nitrous oxide
(N</span><sub><span style="color: #212100;">2</span></sub><span style="color: #212100;">O), causing a loss of a valuable resource and the production of a greenhouse gas. Nitrate can also be converted to inert N</span><sub><span style="color: #212100;">2</span></sub><span style="color: #212100;"> </span><span style="color: #212100;">gas. </span><u><span style="color: #212100;"><br />
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Ammonium </span></u><span style="color: #212100;">(NH</span><sub><span style="color: #212100;">4</span></sub><sup><span style="color: #212100;">+</span></sup><span style="color: #212100;">):
As a positively charged cation, ammonium is largely held on soil cation
exchange sites. In warm aerated soils, ammonium is converted to nitrate
within a few days or weeks. In flooded soils, ammonium can persist for
long periods of time. When left on the soil surface, ammonium is in
equilibrium with ammonia gas and can be lost to the atmosphere. </span><u><span style="color: #212100;"><br />
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Urea </span></u><span style="color: #212100;">(CO(NH</span><sub><span style="color: #212100;">2</span></sub><span style="color: #212100;">)</span><sub><span style="color: #212100;">2</span></sub><span style="color: #212100;">):
As an uncharged molecule, urea moves freely with water in the soil. In
warm soils, urea is decomposed to ammonium within a week or two by an
enzyme (urease) that is present in almost all soils and plants. When
urea is left on the soil surface, a portion of the ammonium will be lost
as ammonia gas. If urea is placed beneath the soil surface or washed
into the soil by rainfall, ammonia losses are very low. <br />
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All added N fertilizer is accessed by soil microorganisms before the
plant roots have a chance for uptake. Since there are between 100
million and 1 billion bacteria in a single teaspoon of soil, their
numbers in an entire acre are almost unimaginable. When conditions are
optimal (warm temperature and adequate carbon), microorganisms will
immobilize some of the added N in their cells and it will become part of
soil organic mater. </span><b><span style="color: #212100;"><br />
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Phosphate fertilizer </span></b><span style="color: #212100;">quickly reacts in
soil to form many new compounds and remains very close to where it is
applied. The most common phosphate fertilizers are diammonium phosphate
(DAP; 46% P</span><sub><span style="color: #212100;">2</span></sub><span style="color: #212100;">O</span><sub><span style="color: #212100;">5</span></sub><span style="color: #212100;">, pH 7.5 to 8) and monoammonium phosphate (MAP; 48 to 61% </span><span style="color: #212100;">P</span><sub><span style="color: #212100;">2</span></sub><span style="color: #212100;">O</span><sub><span style="color: #212100;">5</span></sub><span style="color: #212100;">, pH 4 to 4.5). <br />
<br />
Phosphate fertilizers are initially soluble in water and thus readily
used by plants, but they quickly react with clays and other elements in
the soil to become less soluble. These newly formed compounds will
slowly dissolve and release soluble P over many months or years. These
chemical reactions can be influenced by modifying the fertilizer
properties or by minimizing fertilizer contact with soil with banded
fertilizer application. </span><br />
<span style="color: #212100;"><br />
Phosphorus movement in agricultural soils is quite limited, with
diffusion occurring in the range of a few millimeters to less than an
inch. In very sandy soils or where application rates greatly exceed
agronomic needs, P movement through the soil can be greater. <br />
<br />
Since P fertilizer is tightly bound to soil particles, erosion from the
field in runoff water can be a pathway of loss. Conservation practices
should be implemented to minimize erosion losses. Added phosphate
fertilizer is incorporated into microbial biomass and soil organic
matter, but in smaller amounts than N.</span><b><span style="color: #212100;"><br />
<br />
Potassium fertilizer </span></b><span style="color: #212100;">is most commonly added as potassium chloride. However, all forms of K fertilizer contain the identical chemical form (K</span><sup><span style="color: #212100;">+</span></sup><span style="color: #212100;">).
Other K-containing fertilizers may contain nitrate, sulfate,
thiosulfate, or phosphate, but the behavior of the K will be the same. <br />
<br />
Potassium is simpler to manage than N or P since it is not involved in
biological transformations. Most K fertilizers dissolve quickly in the
soil and the K will either immediately displace another cation on the
clay surface or move with water until it displaces another cation. </span><b><span style="color: #212100;"><br />
<br />
To get the most value from fertilizers, it is important to know what happens after they are added to the soil. </span></b><span style="color: #212100;">Many
people have little appreciation for the complex task of delivering the
right nutrition to growing plants. Integrating knowledge of soil
chemistry, soil microbiology and soil physics will go a long way in
helping improve fertilizer management. </span></div>
Algebrahttp://www.blogger.com/profile/11440946058125679273noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-11185755323099420972019-01-11T01:40:00.000-08:002019-01-11T01:40:36.540-08:00Education ::: Here’s How to Teach Yourself Physics and Math<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUvDStDLSGiTEI8oPK7mNVshkmIKEtGpi9fQpS8mP6fS0STIPopYmFHjpNNsHgf22OpUu8SHzljdieOW-7-8lxxE-lS0huBZS0drFbmE49J06L-zpvG0Vd4lo-oQwHqxtsGt9fTIyratE/s1600/images.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="61" data-original-width="126" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUvDStDLSGiTEI8oPK7mNVshkmIKEtGpi9fQpS8mP6fS0STIPopYmFHjpNNsHgf22OpUu8SHzljdieOW-7-8lxxE-lS0huBZS0drFbmE49J06L-zpvG0Vd4lo-oQwHqxtsGt9fTIyratE/s1600/images.png" /></a></div>
Physics and Mathematics are extremely important subjects. Actually, that’s a bit of an understatement.<br />
Physics and Mathematics allow us to peer out into the cosmos and understand the inner workings of the universe. At once, they show us our insignificance and our remarkable potential; they give us a hint of the vast possibilities that exist—of what we could (and may) one day accomplish. They allow us to see the world and to see ourselves anew.<br />
That begins to scratch the surface of these subjects.<br />
No one can deny their importance; however, it is also a fact that many people don’t know where to begin investigating these topics…what books to study, what themes to begin with. On top of this, many feel intimidated by physics and math—they seem to think that they are things which only the sharpest individuals are able to understand.<br />
But nothing could be farther from the truth.<br />
True, these subject areas might not be the easiest that you will ever happen across, but they are far from impossible. So. If you want to be a physicist or a mathematician, or if you just want to understand the subjects, here’s where to start.<br />
Huge thanks to the wonderful Moinak Banerjee for his work on this.<br />
<br />
Physics<br />
Here is professor John Baez advice on how to learn physics and mathematics. He mentions the books you should read, and they are conveniently listed according to increasing levels of difficulty.<br />
This is the list of books that Berkeley recommends for people who want to teach themselves physics.<br />
And yet another list that is pretty good , which was compiled on Physics Stack Exchange.<br />
Nobel laureate professor Gerard ‘t Hooft has recommended some learning sources that are all free, and he also has advice related to how to earn your own Nobel prize.<br />
Here is some great advice from a physicist on Physics Forums regarding what you should do if you want to do more than just learn physics—on what to do if you want to actually have a career in physics.<br />
To supplement these, check out our<br />
extensive list of online physics lecture videos.<br />
Math<br />
Mathematician Terence Tao, who is also a Fields medalist and a Breakthrough prize winner, gave some beautiful advice on pursuing a career in math here .<br />
If you are looking for mathematics books you should read, here is an extensive list by Berkeley .<br />
The aforementioned should probably be followed up by the compilation from the Math Stack Exchange .<br />
Also, there’s an extensive list of what you should read on the Georgia Institute of Technology website, and all of the texts that they link to are online and free.<br />
You can access more free math texts<br />
here and here .Bestarewahttp://www.blogger.com/profile/08979536370613290333noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-46233439003382065722019-01-10T01:56:00.000-08:002019-01-10T01:56:04.327-08:00Quantum particles :: When photons spice up the energy levels of quantum particles<div class="separator" style="clear: both; text-align: center;">
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Quantum particles behave in mysterious ways. They are governed by laws of physics designed to reflect what is happening at smaller scales through quantum mechanics. Quantum state properties are generally very different to those of classical states. However, particles finding themselves in a coherent state are in a kind of quantum state which behaves like a classical state. Since their introduction by Erwin Schrödinger in 1926, coherent states of particles have found many applications in mathematical physics and quantum optics.<br />
Now, for the first time, a team of mathematical physicists from Togo and Benin, call upon supersymmetry -- a sub-discipline of quantum mechanics -- to explain the behaviour of particles that have received a photon. These particles are subjected to particular potential energies known as shape-invariant potentials.<br />
In a paper published in EPJD , Komi Sodoga and colleagues affiliated with both the University of Lomé, Togo, and the University of Abomey-Calavi, in Cotonou, Benin, outline the details of their theory. These findings are relevant to scientists working on solving quantum optics and quantum mechanics applications.<br />
The authors show that their new states are not distributed in a classical way. The way the number of photons is distributed is different from the distribution in conventional coherent states. Their work can be applied to all models satisfying shape invariance conditions for which an exact solution exists, such as three-dimensional harmonic oscillator, Coulomb or Morse potentials, etc.Bestarewahttp://www.blogger.com/profile/08979536370613290333noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-87869483292405493972019-01-10T01:49:00.000-08:002019-01-10T01:49:43.903-08:00Quantum mechanics. ::: Introduction to quantum mechanics<div class="separator" style="clear: both; text-align: center;">
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Quantum mechanics is a physical science dealing with the behaviour of matter and energy on the scale of atoms and subatomic particles / waves.<br />
It also forms the basis for the contemporary understanding of how very large objects such as stars and galaxies, and cosmological events such as the Big Bang, can be analyzed and explained.<br />
Quantum mechanics is the foundation of several related disciplines including nanotechnology, condensed matter physics, quantum chemistry, structural biology, particle physics, and electronics.<br />
The term "quantum mechanics" was first coined by Max Born in 1924.<br />
The acceptance by the general physics community of quantum mechanics is due to its accurate prediction of the physical behaviour of systems, including systems where Newtonian mechanics fails.<br />
Even general relativity is limited -- in ways quantum mechanics is not -- for describing systems at the atomic scale or smaller, at very low or very high energies, or at the lowest temperatures.<br />
Through a century of experimentation and applied science, quantum mechanical theory has proven to be very successful and practical.<br />
The foundations of quantum mechanics date from the early 1800s, but the real beginnings of QM date from the work of Max Planck in 1900.<br />
Albert Einstein and Niels Bohr soon made important contributions to what is now called the "old quantum theory."<br />
However, it was not until 1924 that a more complete picture emerged with Louis de Broglie's matter-wave hypothesis and the true importance of quantum mechanics became clear.<br />
Some of the most prominent scientists to subsequently contribute in the mid-1920s to what is now called the "new quantum mechanics" or "new physics" were Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, and Erwin Schrödinger.<br />
Later, the field was further expanded with work by Julian Schwinger, Sin-Itiro Tomonaga and Richard Feynman for the development of Quantum Electrodynamics in 1947 and by Murray Gell-Mann in particular for the development of Quantum Chromodynamics.<br />
The interference that produces colored bands on bubbles cannot be explained by a model that depicts light as a particle.<br />
It can be explained by a model that depicts it as a wave.<br />
The drawing shows sine waves that resemble waves on the surface of water being reflected from two surfaces of a film of varying width, but that depiction of the wave nature of light is only a crude analogy.<br />
Early researchers differed in their explanations of the fundamental nature of what we now call electromagnetic radiation.<br />
Some maintained that light and other frequencies of electromagnetic radiation are composed of particles, while others asserted that electromagnetic radiation is a wave phenomenon.<br />
In classical physics these ideas are mutually contradictory.<br />
Ever since the early days of QM scientists have acknowledged that neither idea by itself can explain electromagnetic radiation.<br />
Despite the success of quantum mechanics, it does have some controversial elements.<br />
For example, the behaviour of microscopic objects described in quantum mechanics is very different from our everyday experience, which may provoke some degree of incredulity.<br />
Most of classical physics is now recognized to be composed of special cases of quantum physics theory and/or relativity theory.<br />
Dirac brought relativity theory to bear on quantum physics so that it could properly deal with events that occur at a substantial fraction of the speed of light.<br />
Classical physics, however, also deals with mass attraction (gravity), and no one has yet been able to bring gravity into a unified theory with the relativized quantum theory.<br />
Note: The above text is excerpted from the Wikipedia article "Introduction to quantum mechanics ", which has been released under the<br />
GNU Free Documentation License .Bestarewahttp://www.blogger.com/profile/08979536370613290333noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-15646141457727730312019-01-09T04:15:00.001-08:002019-01-09T04:15:38.058-08:00Esoteric Theory of Everything<b>Phases of Matter</b><br />
<b> </b><br />In addition to the four phases of physical matter (solid, liquid, gas and plasma) recognisedby modern science, the alchemists of old recognised a fifth element. They believed everything was created from the five elements: Earth (solid), Water (liquid), Wind (gas), Fire (plasma) and Aether (ether). They recognised aether as a phase of subtle matter that filled all space and supported the propagation of electromagnetic waves (e.g. light and magnetism). According to Leadbeater there are actually seven phases of physical matter; and where that ends different kinds of even subtler matter begin. The three lowest phases<br />of physical matter (1:1, 1:2 and 1:3) broadly correspond to solid, liquid and gas. The four higher phases of physical matter (1:4, 1:5, 1:6 and 1:7) are etheric, and are what science refers to as subatomic particles or dark matter. 1-atoms belong to the 1:7 phase and combine in many different molecular permutations to produce the hundreds of sub-atomic particles and chemical elements known to science.<br />
<br />
Figure 5 depicts the subatomic structure of a hydrogen atom as described by Leadbeater a hundred years ago. The nucleus is composed of six units (in two groups of three), and each unit is composed of three 1-atoms. According to conventional science the nucleus of a hydrogen atom is composed of only three units called quarks.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqtbjv6fIco9028dSu4EZuDdFy-UlWI1Fo-gObVwkAefUDwntFDcMGg16V_jSEVmFT_uWvkUw-O-XSTcMeRZhyHhiMSJ35ltefrHRkVTh6m0d6XqFow6_qIZubt1zG_U7Q11h-6fG8IbM/s1600/Screenshot+from+2019-01-09+13-13-20.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="181" data-original-width="340" height="340" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqtbjv6fIco9028dSu4EZuDdFy-UlWI1Fo-gObVwkAefUDwntFDcMGg16V_jSEVmFT_uWvkUw-O-XSTcMeRZhyHhiMSJ35ltefrHRkVTh6m0d6XqFow6_qIZubt1zG_U7Q11h-6fG8IbM/s640/Screenshot+from+2019-01-09+13-13-20.png" width="640" />Figure 5 – The subatomic structure of a hydrogen atom (not to scale)<br />Figure 6 shows that Leadbeater’s model has precisely twice as many particles as the<br />standard model suggests. This is because 50% of the 1-atoms in Leadbeater’s model are<br />negatively charged (antimatter).</a></div>
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<br />Anonymoushttp://www.blogger.com/profile/06916675492369629161noreply@blogger.com1tag:blogger.com,1999:blog-8594979553238086927.post-23822499637792987252019-01-09T01:56:00.000-08:002019-01-09T04:09:19.667-08:00Esoteric Theory of Everything 3<b>Even More Fundamental</b><br />
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1-atoms are far from being the ultimate fundamental particle from which everything in the universe is composed. Each 1-atom is composed of ten separate “strings” (closed loops) which are in turn composed of coiled loops of even smaller particles – see figure 3.<br />
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1-atoms are the fundamental particles of the physical plane (plane 1), 2-atoms are the fundamental particles of plane 2, 3-atoms are the fundamental particles of plane 3, etc. According to Leadbeater, each 1-atom is composed of forty nine 2-atoms, each 2-atom is composed of forty nine 3-atoms, each 3-atom is composed of forty nine 4-atoms, etc. The matter of the lower planes is composed of the matter of the higher planes, so all the planes can interpenetrate each other and occupy the same space. Figure 3 shows the number of fundamental atoms from the various planes that make up one fundamental atom of the<br />
physical plane.<br />
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<br />Anonymoushttp://www.blogger.com/profile/06916675492369629161noreply@blogger.com1tag:blogger.com,1999:blog-8594979553238086927.post-38379779612339055282019-01-09T01:45:00.000-08:002019-01-09T01:45:48.155-08:00Esoteric Theory of Everything 2<span style="font-size: large;">String Theory and the Standard Model</span><br />
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According to Leadbeater these particles are composed of 10 vibrating strings, which are in turn composed of even smaller particles, which are in turn composed of even smaller strings, etc... This suggests that the seemingly incompatible standard model and string theory may in fact be two sides of the same coin.<br />
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String theory proposes that everything is composed of incredibly minute strings or loops of energy-matter vibrating in ten (or more) dimensions. Our brains can only comprehend four dimensions – the three spatial dimensions (length, width and height) plus one temporal dimension (time). So according to string theory, six (or more) hidden spatial dimensions must exist beyond our perception. It is interesting to note that the ancient cosmologies of eastern religions are based on seven planes of existence, with our physical plane being the lowest.<br />
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According to Leadbeater the fundamental particle shown in Figure 1 is merely the fundamental particle of our physical dimension (plane 1) – for this reason I will refer to it as the 1-atom. 1-atoms are so small that modern science has not yet detected them, but they were theorised back in 1974 by Jogesh Pati and Abdus Salam, who referred to them as “preons”. According to Leadbeater, two varieties of 1-atom exist (positive and negative), each with the same basic structure but the spirals spin the other way in the negative variety (see Figure 2). This is due to zero point energy flowing down through the negative atoms and up through the positive atoms.<br />
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The negative particles are not electrons; they are antiparticles. A particle of antimatter has the same mass and magnitude as an equivalent particle of regular matter but an opposite charge. For example, the antiparticle of an electron is a positron. A positron is identical to an electron in every way except that it has a positive charge. The existence of antimatter was not predicted by conventional science until 1928 and confirmed experimentally in 1932, yet Leadbeater knew about it over 30 years earlier. Anonymoushttp://www.blogger.com/profile/06916675492369629161noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-22055309051539413162019-01-08T03:02:00.001-08:002019-01-08T03:02:12.148-08:00Esoteric Theory of Everything<b>Introduction</b><br />
<b> </b><br />For many decades, scientists have been trying to devise a single unified theory to explain all known physical phenomena, but a model that appears to unite the seemingly incompatible String Theory and Standard Model has existed for 100 years. It described baryons, mesons, quarks and preons over 50 years before conventional science. It stated that matter is composed of strings 80 years before string theory. It described the existence of anti-matter 30 years before conventional science. It described the Higgs field over 50 years before Peter Higgs. It described the existence of isotopes 5 years before conventional science. Could this be the beginning of a Theory of Everything – the holy grail of modern physics?<br />
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<b>Quantum Foam</b><br />
Quantum foam, also known as space-time foam, is a concept in quantum physics<br />proposed by Nobel physicist John Wheeler in 1955 to describe the microscopic sea of bubbling energy-matter. The foam is what space-time would look like if we could zoom in to a scale of 10 -33 centimetres (the Planck length). At this microscopic scale, particles of matter appear to be nothing more than standing waves of energy. Wheeler proposed that minute wormholes measuring 10 -33 centimetres could exist in the quantum foam, which some physicists theorise could even be hyper-spatial links to other dimensions. The hyper- spatial nature of the quantum foam could account for principles like the transmission of light and the flow of time. Some scientists believe that quantum foam is an incredibly<br />powerful source of zero-point energy, and it has been estimated that one cubic centimetre of empty space contains enough energy to boil all the world’s oceans.<br />
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So, if we could describe a microscopic standing wave pattern that appeared particle-like and incorporated a vortex within its structure, we might have the basis for a theory that could unite all the current variants in modern physics. Figure 1 appears to meet these criteria – it is a drawing of a subatomic particle reproduced from Occult Chemistry by Charles Leadbeater and Annie Besant, which was first published in 1909, although a similar diagram was published in a journal in 1895. Leadbeater explains that each subatomic particle is composed of ten loops which circulate energy from higher dimensions. Back in 1895, he knew that physical matter was composed from “strings” – 10 years before Einstein’s theory of relativity and 80 years before string theory.<br />
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<br />Anonymoushttp://www.blogger.com/profile/06916675492369629161noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-3864692021447306862018-12-31T11:20:00.001-08:002018-12-31T11:20:26.704-08:00An Introduction to Chaos Theory with the Lorenz Attractor<iframe allowfullscreen="" frameborder="0" height="344" src="https://www.youtube.com/embed/nNZzoMOf_CQ" width="459"></iframe>Ahmad Abdulnasir Shu'aibhttp://www.blogger.com/profile/09884233041414547192noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-55986286829104811472018-12-09T10:56:00.001-08:002018-12-09T11:08:24.267-08:00How does the Universe Expands?<div class="separator" style="clear: both; text-align: center;">
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In Newton’s Principia Mathematica, he emphatically took the position that all motion takes place with respect to a system of absolute space and time. He fiercely rejected the idea that the motion of a body could only be described relative to those of other bodies. This position was challenged by Bishop Berkeley, Christiaan Huygens and others but, at least until the late nineteenth century, Newton’s view prevailed. The issue was revived by Ernst Mach who argued that motion can only be defined relative to other bodies. Specifically, he took the view that the local inertial frame of reference is determined by the frame of the distant stars, or galaxies in modern parlance. Thus, a freely swinging Foucault pendulum swings in a reference frame which is fixed relative to the distant galaxies. Albert Einstein gave the name Mach’s principle to this idea.</div>
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During the late eighteenth century, non-Euclidean geometries began to be taken seriously by mathematicians who realised that the fifth postulate of Euclid, that parallel lines meet only at infinity, might not be essential for the construction of a self-consistent geometry. Proposals that the global geometry of space might not be Euclidean were discussed by Girolamo Saccheri and Johann Lambert. In 1816, Carl Friedrich Gauss repeated this proposal in a letter to Christian Gerling and was aware of the fact that a test of the local geometry of space could be carried out by measuring the sum of the angles of a triangle between three high peaks, the Brocken, Hoherhagen and Inselberg. In 1818, Gauss was asked to carry out a geodetic survey of the state of Hanover and he devoted a large effort to carrying out and reducing the data himself. He was certainly aware of the fact that the sum of the angles of the triangle was 180 degrees within the limits of geodetic measurements. </div>
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<a href="http://www.physicspace.com.ng/2018/12/how-is-structure-of-our-galaxy.html">How is the Structure of our Galaxy?</a></div>
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The fathers of non-Euclidean geometry were Nikolai Lobachevsky, who became rector of Kazan University in Russia in 1827, and János Bolyai in Transylvania, then part of Hungary. In the 1820s, they independently solved the problem of the<br />
existence of non-Euclidean geometries and showed that Euclid’s fifth postulate could not be deduced from the other postulates (Lobachevsky, 1829, 1830; Bolyai, 1832). In his papers entitled On the Principles of Geometry, Lobachevsky also proposed an astronomical test of the geometry of space. If the geometry were hyperbolic, the minimum parallax of any object would be </div>
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θ = arctan(a/R)</div>
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where a is the radius of the Earth’s orbit and R the radius of curvature of the<br />
geometry. He found a minimum value of R ≥ 1.66 × 10^5 AU = 2.6 light years,<br />
using an observational upper limit of 1 arcsec for the parallax of bright stars. In<br />
a prescient statement which will warm the hearts of observational astronomers, he remarked:</div>
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<i>There is no means other than astronomical observations for judging the exactness which attaches to the calculations of ordinary geometry.</i></div>
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<i> </i>Non-Euclidean geometries were placed on a firm theoretical basis by Bernhard Rie-mann, who also discovered closed spherical geometries. The English-speaking world was introduced these ideas through the works of William Clifford and Arthur Cayley. Until Albert Einstein’s discovery of the General Theory of Relativity, considerations of the geometry of space and the role of gravity in defining the large-scale structure of the Universe were separate questions. After 1915, they were inextricably linked. </div>
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In that year, after a titanic intellectual struggle, Einstein discovered the definitive<br />
version of his General Theory of Relativity which describes how space–time is distorted by the presence of matter and how, in turn, matter moves along trajec- tories in bent space–time (Einstein, 1915, 1916). For the first time, a relativistic<br />
theory of gravity was available which enabled self-consistent models of the Uni-<br />
verse as a whole to be constructed and, characteristically, Einstein did not hesitate to do so.</div>
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In seeking a solution of his field equations for the Universe as a whole, Einstein had explicitly in mind that Mach’s principle should be incorporated into any model of the large-scale structure of the Universe. He had, however, a major problem. Without modification, the field equations predicted that the Universe was unstable. He could only find static solutions by introducing what is now known as the cosmical or cosmological constant λ, which appears as a constant in Einstein’s field equations. In his great paper of 1917, Einstein showed that the introduction of the cosmological constant resulted in static solutions for the Universe as a whole which had closed, spherical geometry and a finite size (Einstein, 1917). He also believed that he had incorporated Mach’s principle into General Relativity, in the sense that no solution of the equations would exist if there were no matter present. In the same year, this was, however, shown to be incorrect by Willem de Sitter, who found solutions of the equations even if there were no matter present in the Universe (de Sitter, 1917).</div>
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For many decades, the status of the cosmological constant was the subject of debate. In 1919, Einstein realised that a term involving the cosmological constant would appear in the field equations of General Relativity, quite independent of its cosmological significance (Einstein, 1919). In the derivation of the field equations, the λ-term appears as a constant of integration which is normally set equal to zero in the development of standard General Relativity. Einstein was not enthusiastic about the term, remarking that it ‘detracts from the formal beauty of the theory’. Willem de Sitter wrote in 1919 that the term</div>
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<i>. . . detracts from the symmetry and elegance of Einstein’s original theory, one of whose chief attractions was that it explained so much without introducing any new hypotheses or empirical constant.</i></div>
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<i> </i>Others regarded it as a constant which appears in the development of the General Relativity and its value should be determined by astronomical observation.</div>
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The irony of the situation is that this debate took place before it was realised that the Universe is in fact non-stationary. In 1922, Aleksander Friedman published the first of two classic papers in which he discovered both static and expanding solutions of Einstein’s field equations. In the first paper, Friedman found solutions for expanding universes with closed spatial geometries, including those which expand to a maximum radius and eventually collapse to a singularity (Friedman, 1922). In the second paper of 1924, he showed that there exist expanding solutions which are unbounded and which have hyperbolic geometry (Friedman, 1924). These solutions correspond exactly to the standard world models of general relativity and are known as the Friedman world models.</div>
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In 1925, Friedman died of typhoid in Leningrad before the fundamental sig- nificance of his work was appreciated. The neglect of Friedman’s work in these early days is somewhat surprising since Einstein had commented, incorrectly as he admitted, on the first of the two papers in 1923. It was not until Georges Lemaître independently rediscovered the same solutions in 1927, and then became aware of Friedman’s papers, that the pioneering nature of Friedman’s contributions was appreciated (Lemaître, 1927).</div>
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Einstein’s field equations without the cosmological constant contain perfectly satisfactory solutions in which the Universe is uniformly expanding. According to George Gamow, when the expansion of the Universe was discovered, Einstein regarded the introduction of the cosmological constant as ‘the biggest blunder of my life’ (Gamow, 1970). The cosmological constant was not consigned to oblivion for long however. As Yakov Zeldovich remarked:</div>
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<i>The genie is out of the bottle and, once he is out, he is very difficult to put<br />back in again.</i></div>
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As the standard models of General Relativity became better understood, a major thrust of cosmological research became the determination of the large-scale dynamical and geometrical properties of the Universe – its rate of expansion, its deceleration, its mean density, its geometry and its age. These remained among the most difficult programmes of modern observational cosmology until, in the first years of the twenty-first century, precise estimates became available using techniques undreamt of by the pioneers of geometrical cosmology.</div>
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<a href="http://www.physicspace.com.ng/2018/12/how-is-structure-of-our-galaxy.html">How is the Structure of our Galaxy?</a></div>
Anonymoushttp://www.blogger.com/profile/12948124948045044887noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-13707509850567935082018-12-08T05:10:00.001-08:002018-12-08T05:19:18.427-08:00How is the Structure of our Galaxy? 2<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja3P_wjwxBn_HD3s8ryMDhSuE6Mejkh23wTzR5TsTG0kLTOUGQ3alk6PSRv2M503DrdR1DOBUEeFeN2xARiidpvKMNC4UowBtDFMH7VSppTkTyJ1jt-kvNnRBLRxL9ayv4tqeNbe4mBkA/s1600/galaxy.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="207" data-original-width="368" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja3P_wjwxBn_HD3s8ryMDhSuE6Mejkh23wTzR5TsTG0kLTOUGQ3alk6PSRv2M503DrdR1DOBUEeFeN2xARiidpvKMNC4UowBtDFMH7VSppTkTyJ1jt-kvNnRBLRxL9ayv4tqeNbe4mBkA/s640/galaxy.jpeg" width="640" /></a></div>
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<a href="http://www.physicspace.com.ng/2018/12/how-is-structure-of-our-galaxy.html"> How is the Structure of our Galaxy? 1</a><br />
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Even before the discovery of the telescope, it had been realised that there exist ‘nebulous’ objects which differ from the stars in having a diffuse or fuzzy appearance. Kant, Lambert, Swedenborg and Wright argued that these objects were ‘island universes’ similar to the Milky Way, but too distant to be resolved into stars. There was, however, no observational basis for this hypothesis. Herschel also inferred that the nebulae were island universes similar to our Galaxy. A test of this picture was to show that the nebulae could be resolved into stars and he believed that this had been achieved in a number of cases. In others, he assumed that the nebulae were too distant to be resolved into individual stars. This picture came into question, however, when he discovered that, among the nebulae were the planetary nebulae, which consist of a central star surrounded by a shell of gas. Herschel recognised that these nebulae were unlikely to be resolved into stars but rather consisted of ‘luminous fluid’ surrounding the central star.</div>
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The cataloguing of the bright nebulae was begun by Charles Messier whose catalogue of 109 objects was compiled during the years 1771 to 1784. Messier’s</div>
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interest was primarily in comets and his objective in compiling the catalogue was to enable him to distinguish between diffuse nebulae and comets. The catalogue contains a mixture of what we now know are the brightest Galactic and extra-galactic nebulae and they are still commonly referred to by their Messier, or M, numbers.</div>
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The systematic cataloguing of the nebulae was begun by William Herschel and his sister Caroline and was continued through the first half of the nineteenth century by his son John Herschel. The results of these huge endeavours was the publication by John Herschel in 1864 of the General Catalogue of Nebulae and Clusters of Stars containing 5079 objects. These catalogues were based upon visual observations long before photography became a standard tool of the astronomer. In 1888, John Dreyer published an expanded catalogue which was known as the New General Catalogue of Nebulae and Clusters of Stars which, together with the two supplementary Index Catalogues of 1895 and 1908, contain some 15,000 objects. Objects in these catalogues are still commonly referred to by their NGC or IC numbers.</div>
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While the cataloguing of the nebulae proceeded apace, their nature remained a mystery. Undoubtedly, some of them were gas clouds, as demonstrated by William Huggins’ pioneering spectroscopic observations of diffuse nebulae in the 1860s (Huggins and Miller, 1864). The big question was whether or not the ‘spiral nebulae’ were objects within our own Galaxy or were more distant systems. These nebulae were beyond the distances at which conventional techniques of distance measurement could be used. This problem culminated in what became known as ‘The Great Debate’ and concerned two related issues. Firstly, what is the size of our own Galaxy and, secondly, are the spiral nebulae members of our Galaxy or are they separate ‘island universes’, well beyond the confines of our Galaxy? This key episode in the history of modern astronomy should be required reading for all observers and theorists (Sandage, 1961b; Hoskin, 1976; Smith, 1982; Trimble, 1995).</div>
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To illustrate the nature of the problem, by 1920, Jacobus Kapteyn had determined the luminosity function of stars near the Sun and so, from star counts in different directions, determined the structure of the Galaxy which he found to be highly flattened with dimensions 1500 pc perpendicular to the plane and about 8 times that size in the Galactic plane (Fig. 1.2) (Kapteyn, 1922).</div>
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Meanwhile, Harlow Shapley had adopted a quite different approach to the de- termination of Galactic structure. In 1912, Henrietta Leavitt had discovered the remarkable period–luminosity relation for Cepheid variable stars in the Magellanic Clouds (Fig. 1.3). This discovery provided a powerful means of measuring astronomical distances because the Cepheid variables are intrinsically luminous stars and their distinctive light curves can be recognised in stars in distant systems. The Cepheid variables were the tools used by Harlow Shapley to determine the structure of the Galaxy through his studies of globular clusters. He found the scale of the</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEvjOC12XVHtbI7neKqdqKXbJ7wfDTTb2K2PgcUb85L0cSDBigy_VGb2ZRg7wt2CagB6R_ifIrwsWwgsX9DVe5bHwxSC_k7S8omUdMnuR0JUse_8G32rwU-m5hl4tPLyw-cDI4ZbmlPM8/s1600/pic.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="369" data-original-width="1600" height="91" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEvjOC12XVHtbI7neKqdqKXbJ7wfDTTb2K2PgcUb85L0cSDBigy_VGb2ZRg7wt2CagB6R_ifIrwsWwgsX9DVe5bHwxSC_k7S8omUdMnuR0JUse_8G32rwU-m5hl4tPLyw-cDI4ZbmlPM8/s400/pic.png" width="400" /></a></div>
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Fig. 1.2. Kapteyn’s model for the distribution of stars in the Galaxy (Kapteyn, 1922). The diagram shows the distribution of stars in a plane perpendicular to the Galactic plane. The curves are lines of constant number density of stars and are in equal logarithmic steps. The Sun S is slightly displaced from the centre of the system globular cluster system to be enormous, the most distance globular cluster having a distance of 67 kpc. Furthermore, the globular cluster system was not centred upon the Solar System, but rather most of the globular clusters were found in a direction centred upon the constellation of Sagittarius (Fig. 1.4) (Shapley, 1918).</div>
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The course of the debate was complex, but the issues were resolved finally and conclusively in 1925 by Edwin Hubble’s observations of Cepheid variables in the Andromeda Nebula. Using the period–luminosity relation for Cepheid variables, he established to everyone’s satisfaction that the spiral nebulae are distant extragalactic systems.</div>
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Within a year, Hubble had published the first major survey of the properties of galaxies as extragalactic systems. In his remarkable paper (Hubble, 1926), he introduced an early version of his classification of galaxies into ellipticals, spirals and irregulars, estimated mass-to-light ratios for these different types of galaxies used number counts of galaxies to show that they are uniformly distributed in space and hence estimated the mean density of matter in the Universe in the form of galaxies. Adopting Einstein’s static model of the Universe, he found that the radius of curvature of its spherical geometry was 27,000 Mpc. He estimated that, with the</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz8Cq6fOqgu__DDR0feRoeOsD_YwxZbKqJ-wCLRQb5jZu1_gOZAU6dGZmfwoETAfpe07lWgmKvkdDSXXAKXQD4NEvmZmFKGgYVAhB1T1jON8VPxi6QFazIERcEUdV8ecpEt23m1EC1zNQ/s1600/pic2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="398" data-original-width="532" height="239" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz8Cq6fOqgu__DDR0feRoeOsD_YwxZbKqJ-wCLRQb5jZu1_gOZAU6dGZmfwoETAfpe07lWgmKvkdDSXXAKXQD4NEvmZmFKGgYVAhB1T1jON8VPxi6QFazIERcEUdV8ecpEt23m1EC1zNQ/s320/pic2.png" width="320" /></a></div>
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Fig. 1.4. The distribution of globular clusters in the Galaxy according to Shapley’s distance measurements (Shapley, 1918). The scales on the abscissa and ordinate are in units of 100 pc and correspond to distances in and perpendicular to the Galactic plane respectively. The Sun, located at zero coordinates on the abscissa and ordinate, lies towards one edge of the globular cluster system</div>
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<i>100-inch Hooker telescope, he could observe typical galaxies to about 1/600 of the<br />radius of the Universe. He concluded with the remark that<br />. . . with reasonable increases in the speed of plates and sizes of telescopes,<br />it may become possible to observe an appreciable fraction of the Einstein<br />universe.</i></div>
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This paper marked the beginning of extragalactic astronomy. It comes as no surprise to learn that George Ellery Hale began his campaign to raise funds for the Palomar 200-inch telescope in 1928 – before the year was out, he had secured a grant of $6 million from the Rockefeller Foundation for the telescope, the construction of which was completed in 1949.</div>
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In 1929, Hubble made his second fundamental contribution to cosmology. He showed that the extragalactic nebulae are all moving away from our own Galaxy and that their recessional velocities v are proportional to their distances r from our Galaxy (Fig. 1.5a) (Hubble, 1929). It is remarkable that he was able to deduce this key result from such a small sample of nearby galaxies but, within five years, he and Humason had extended the relation to very much greater velocities and distances using the apparent magnitudes of the fifth brightest members of clusters of galaxies as distance indicators (Fig. 1.5b). The velocity–distance relation v = H 0 r is commonly referred to as Hubble’s law and H 0 as Hubble’s constant. The significance of this discovery was that, combined with the isotropy of the Universe, Hubble’s law demonstrates that the whole system of galaxies is partaking in a uniform expansion.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLZXVROdIo9_8HXXFISr1hw8k9Mc7Mj9kqNflyucbXqe3s4hRIMHtKy3-pkALIjDfuvfiaFYs_RPhgpBoUUNndyqL5pdXMsTB3Bb1dduKgZHEPnXS3jQkPZ8Z1S2fIeUfk3yL7n3WIrr0/s1600/pic3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1136" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLZXVROdIo9_8HXXFISr1hw8k9Mc7Mj9kqNflyucbXqe3s4hRIMHtKy3-pkALIjDfuvfiaFYs_RPhgpBoUUNndyqL5pdXMsTB3Bb1dduKgZHEPnXS3jQkPZ8Z1S2fIeUfk3yL7n3WIrr0/s320/pic3.png" width="227" /></a></div>
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<span style="font-size: x-small;">Fig. 1.5. a Hubble’s first velocity–distance relation for nearby galaxies (Hubble, 1929). The filled circles and the full line represent a solution for the solar motion using the nebulae individually; the open circles and the dashed line represent a solution combining the nebulae into groups. The cross is an estimate of the mean distance of the other 20 galaxies for which radial velocities were available. b The velocity–apparent magnitude relation for the fifth brightest member of clusters of galaxies, corrected for galactic obscuration (Hubble and Humason, 1934). Each cluster velocity is the mean of the various individual velocities observed in the cluster, the number being indicated by the figure in brackets.</span></div>
Anonymoushttp://www.blogger.com/profile/12948124948045044887noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-16633311923167714162018-12-06T15:40:00.000-08:002018-12-06T15:40:57.659-08:00How is the Structure of our Galaxy?<div class="separator" style="clear: both; text-align: center;">
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In his extraordinary text of 1610, the Sidereus Nuncius or The Sidereal Messenger, Galileo Galilei demonstrated that the Milky Way can be resolved into stars when observed through the telescope. These observations led to the earliest speculative cosmologies of the modern era. The ‘island universe’ model of René Descartes, published in The World of 1636, involved an interlocking jig-saw puzzle of solar systems. In 1750, Thomas Wright of Durham published An Original Theory or New Hypothesis of the Universe, in which the Sun was one of many stars which orbit the ‘Divine Centre’ of the star system. Immanuel Kant in 1755 and Johann Lambert in 1761 took these ideas further and developed the first hierarchical, or fractal, models of the Universe. Kant also made the prescient suggestion that the flattening of these ‘island universes’ was due to their rotation. The problem with these early cosmologies was that they lacked observational validation.</div>
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Towards the end of the eighteenth century, William Herschel was one of the first<br />astronomers to attempt to define the distribution of stars in the Universe in some<br />detail on the basis of careful astronomical observation. To determine the structure of the Milky Way, he counted the numbers of stars in different directions. Then, assuming that they all have the same intrinsic luminosities, he derived his famous picture for the structure of our Galaxy which consisting of a flattened disc of stars with diameter about five times its thickness, the Sun being located close to its centre(Herschel, 1785).</div>
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<a href="https://www.physicspace.com.ng/2018/11/is-length-contraction-real.html"> IS LENGTH CONTRACTION REAL </a></div>
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<br /></div>
<div style="text-align: justify;">
John Michell had already warned Herschel that the assumption that the stars have a fixed luminosity was a poor approximation. In his remarkable pioneering paper of 1767, Michell introduced statistical methods into astronomy in order to show that binary and star clusters must be real physical systems and not random associations of stars on the sky (Michell, 1767). Consequently, there must be a dispersion in the absolute luminosities of the stars from their observed range of apparent magnitudes in bright star clusters, such as the Pleiades. Despite this warning, Herschel proceeded to produce a number of different versions of his model for the structure of our Galaxy, adding appendages to account for various features of the star counts in different directions.</div>
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<div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw-m98Cz9bJ3jQTki3i_6A3uf2e_DF5ZgQHLKlFRw8Zl9OIVoZbvzLBd5R121hDzJY45159yn6NjXyi80Rf1KHCWM7D_1woBB71bY7OLAYPLEVrcEo5iGcRw2pE6RM06Hz-J_W-6436vg/s1600/How+is+the+Structure+of+our+Galaxy%253F.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="486" data-original-width="691" height="281" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw-m98Cz9bJ3jQTki3i_6A3uf2e_DF5ZgQHLKlFRw8Zl9OIVoZbvzLBd5R121hDzJY45159yn6NjXyi80Rf1KHCWM7D_1woBB71bY7OLAYPLEVrcEo5iGcRw2pE6RM06Hz-J_W-6436vg/s400/How+is+the+Structure+of+our+Galaxy%253F.png" width="400" /></a></div>
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In 1802, Herschel measured the magnitudes of visual binary stars and was forced to agree with Michell’s conclusion about the wide dispersion in the luminosities of the stars (Herschel, 1802). Equally troubling was the fact that observations with his magnificent 40-foot telescope showed that, the fainter he looked, the more stars he continued to find. There seemed to be no edge to the Galaxy and Herschel gradually lost faith in his model. In addition, the importance of interstellar extinction by dust was not appreciated – it was only in the 1930s that its central importance for studies of our own and other galaxies was fully appreciated.</div>
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<span style="font-size: x-small;">To be continue</span></div>
Anonymoushttp://www.blogger.com/profile/12948124948045044887noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-65030368729870254882018-11-04T10:18:00.002-08:002018-12-05T18:14:49.907-08:00Sharing Life Could Be Easy<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxIHxNEyvmzOae4Htzn4WfiWGSMZWLCXXtsgo0TwqfFl9UCxWY22HwUD4cRQmA_9eO4NFxZ8sKehdHzBXl9lIf8fDV8vNuakpu7djwdB8qvmnnRffHSFlxTf5FLlRR9bsiJA3zObYqjM8/s1600/Expanding.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="900" data-original-width="1600" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxIHxNEyvmzOae4Htzn4WfiWGSMZWLCXXtsgo0TwqfFl9UCxWY22HwUD4cRQmA_9eO4NFxZ8sKehdHzBXl9lIf8fDV8vNuakpu7djwdB8qvmnnRffHSFlxTf5FLlRR9bsiJA3zObYqjM8/s640/Expanding.jpg" width="640" /></a></div>
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How could life be shared between planets in close proximity to one
another? This question has received a greater insight thanks to new
analytics based on previously known and new calculations. <span style="color: black;">The findings</span>
from this new research are helping scientists understand how likely
life would be on a given planet in such tight-knit systems if that world
shows signs of habitability. This approach began with a blasphemous-at-the-time idea: that life
exists throughout the universe and can travel without supernatural
interference. Anaxagoras, a 5th-century B.C. Greek philosopher, called
this concept "panspermia."
Kelvin, Helmholtz and Arrhenius advanced the idea in the 19th and 20th
centuries by examining how life could be carried to and from Earth. In
2009, Stephen Hawking went beyond our solar system with the idea when he
suggested that "life could spread from planet to planet or from stellar
system to stellar system, carried on meteors." [5 Bold Claims of Alien Life] Dimitri Veras, an astrophysicist at the University of Warwick in
England and lead author of a recent paper on the subject, said, "Within
the last century, [panspermia] has been focused on life transport within
the solar system, including Earth." The TRAPPIST-1 solar system,
which is 39 light-years from Earth and includes seven planets packed
into an orbit smaller than Mercury's, changes this Earth-centric idea.
This system's sun is an ultracool red dwarf. So, even though the seven
nearby planets orbit closely, they are possibly all still in the
habitable zone, to varying degrees depending upon the makeup of their
atmospheres. That makes this system a perfect model for exploring the
idea of panspermia, per Hawking, anywhere in the universe. </div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
</div>
<div style="text-align: justify;">
use and are general enough to be applicable to a wide variety
of systems." [Exoplanet Discovery: The 7 Earth-Size Planets of TRAPPIST-1 in Pictures] But back to our solar system, where the "foundation for
panspermia-related processes has been established," Veras' paper said.
That includes evidence that life can survive the three stages of
traveling from one planet to another: initial ejection, the journey
through space between planets and impact onto a new planet. Each stage presents challenges to the survival of life. </div>
Veras wanted to create an analytical system to quantify each of these
parts to create a better understanding of the probability of the whole
process occurring.
<br />
<div style="text-align: justify;">
He had some information to start with: Microbes can survive ejection
from a planet with life on it, as per previous studies, and even a
voyage through interplanetary space, if shielded from the radiation and
cold. Less is known about how well a microbe that endured space travel
could survive impact on a new planet, which would be necessary for life
to complete the voyage from one planet to another. </div>
Because impact includes more unknowns than ejection and transit between
planets, Veras had less-detailed information to work with in this area
of his calculations.
<br />
<div style="text-align: justify;">
</div>
<div data-jwplayer-id="LKo1uFRn" style="text-align: justify;">
</div>
<div style="text-align: justify;">
"The physics of re-entry features complexities that are not present
with the ejection and voyage phases through space," he said. "For
example, frictional heating during re-entry can lead to the formation of
a fusion crust [the outer layer of the meteorite that melts and ablates
during atmospheric entry] on the surface of the meteorite."</div>
<div style="text-align: justify;">
To figure out how to calculate the tricky physics of atmospheric entry
onto a new planet, Veras turned to some already-available math. He told
Astrobiology Magazine that "Equations regarding the physics of impact
have already been established and used for solar system applications,
[so] we converted those for use in a general extrasolar system." </div>
<div style="text-align: justify;">
To understand the probability of ejected material traveling from one
planet to another, Veras combined his equations into analytics. This
way, he could figure out the whole system of panspermia, not just parts
of it. </div>
<div style="text-align: justify;">
"Usually, the dynamics of panspermia is studied with numerical
simulations. However, these can be slow to run and must be tailored to
an individual system," Veras said. "Alternatively, analytics are much
faster to use and are general enough to be applicable to a wide variety of systems."</div>
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</div>
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</div>
Anonymoushttp://www.blogger.com/profile/12948124948045044887noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-14269354352223630352018-11-04T09:46:00.000-08:002018-12-05T18:15:18.306-08:00IS LENGTH CONTRACTION REAL<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlvu8MmP45hrZLXfZDAwXHbW3RhgESr6bj140HUiafKy0O59TrQkNWUHHUo8czL3_rdht6LYWKS6WVX1MYygO6PSwMrNJWkXEwby3yShljk6RqATbL9le048h6bc5evRnmBUakQjp6LN0/s1600/cosmic-adventure-55-relativistic-length-contraction-17-638.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="442" data-original-width="638" height="440" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlvu8MmP45hrZLXfZDAwXHbW3RhgESr6bj140HUiafKy0O59TrQkNWUHHUo8czL3_rdht6LYWKS6WVX1MYygO6PSwMrNJWkXEwby3yShljk6RqATbL9le048h6bc5evRnmBUakQjp6LN0/s640/cosmic-adventure-55-relativistic-length-contraction-17-638.jpg" width="640" /></a></div>
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<div style="text-align: justify;">
One important relativistic effect remains to be derived: the change in length of an object that is moving relative to the observer. This effect, like time dilation, can be linked to the relativity of simultaneity.</div>
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<div style="text-align: justify;">
To measure the length of an object, one marks the positions of its end points on some scale and subtracts one reading from the other. If the object is at rest, those measurements can be carried out at leisure. If the object is moving, however, the two position measurements must be carried out simultaneously; otherwise, the result will surely be in error. As we have seen, simultaneity depends on the motion of the observer. If ground observers measure the position of the front and rear ends of a moving train simultaneously according to their clocks, these measurements take place at different times according to train clocks. According to train observers, therefore, the length measured by ground observers is incorrect.</div>
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<br /></div>
<div style="text-align: justify;">
The easiest way to determine the magnitude of the effect is to analyze a somewhat less direct, though equally legitimate, method of determining the length of an object moving at a known (uniform) speed, namely, by measuring the time required for the object to pass a stationary observer. The product of that time and the speed of the object is its length.</div>
Anonymoushttp://www.blogger.com/profile/12948124948045044887noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-24583832426847530152018-10-27T05:58:00.000-07:002018-12-05T18:15:42.705-08:00THE DECAY OF MUONS<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgovw_vYcuD_JIWslO2OW7JxNyQK7pTgyg56eP4Vjnb2nspV3h8P89CjfVd1k-1kj5_gLiDozdbw5fUBXsrCTFQBU-Jn0gGMnLTQXmvMxMViQqY6PcGqJJukM1qakqQ7bMxp4t_AyfgUXQ/s1600/MuonDecayTraces.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="370" data-original-width="528" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgovw_vYcuD_JIWslO2OW7JxNyQK7pTgyg56eP4Vjnb2nspV3h8P89CjfVd1k-1kj5_gLiDozdbw5fUBXsrCTFQBU-Jn0gGMnLTQXmvMxMViQqY6PcGqJJukM1qakqQ7bMxp4t_AyfgUXQ/s1600/MuonDecayTraces.png" /></a></div>
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<div style="text-align: justify;">
Real experiments have been performed, however, which provide striking confirmation of time dilation. In this section, I describe an experiment based on the decay of muons-unstable particles that were first discovered among the cosmic rays that continuously bombard the earth.</div>
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<br /></div>
<div style="text-align: justify;">
Muons decay according to the scheme</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: center;">
muon = electron + neutrino + antineutrino</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The details of the decay process are irrelevant; the only feature we need be concerned with is that muon decay, like any radioactive decay, is a probabilistic process characterized by a half-life, T. Out of any group of identically prepared muons, approximately half will have decayed within a time interval T. After another interval T has passed, half the survivors will have decayed and only a quarter of the original number remain, and so on. The half-life of muons at rest is about 1.5 microseconds.</div>
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<br /></div>
<div style="text-align: justify;">
The question at issue concerns the half-life of muons in motion. According to Galilean relativity, the motion should have no effect on the probability of decay; moving muons should have the same half-life as muons at rest.</div>
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<br /></div>
<div style="text-align: justify;">
Special relativity predicts a quite different outcome. Consider a beam of muons, all moving at the same speed v. The first postulate implies that in the muons' rest frame their half-life must be 1.5 microseconds. That is, after 1.5 microseconds have elapsed according to clocks that move with the muons, half of them will have decayed. The 1.5 microseconds is a proper time interval.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
For earth observers, the corresponding time interval is improper. The time interval during which half the muons decay, as measured by earth clocks, is therefore y(v) times 1.5 microseconds, where y(v) is the time<span style="font-size: x-small;"> </span>dilation factor that corresponds to the speed v. Letting To denote the rest half-life and T(v) the half-life for muons moving at velocity v, we conclude that according to special relativity,</div>
<div style="text-align: justify;">
<br />
T(v) = y(v) To (3.7)</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The faster the muons move, the longer they should survive according to clocks at rest in the laboratory. We may regard the group of muons as a specialized clock that "ticks" once every 1.5 microseconds in its own rest frame; at each tick, half the muons decay. According to observers in the laboratory, for whom that clock is in motion, it (like any other moving clock) runs slow: it "reads" 1.5 microseconds when the true elapsed time, measured by clocks at rest in the laboratory, is longer by the factor y(v). This prediction is subject to direct experimental test.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The first experiment was carried out in 1940 by Bruno Rossi and D. B. Hall, who used the cosmic ray "beam" that was then beginning to be studied and was known to contain many muons moving at speeds very close to c. If the half-life of those muons were equal to To, the beam should advance a distance cTo, some 450 meters, by the time half the muons had decayed. According to special relativity, with the half-life given by equation (3.7), the distance should be greater.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Rossi and Hall measured the attenuation of the cosmic ray muon beam as it proceeds down through the atmosphere; the attenuation is caused primarily by the decay of muons en route. They designed an array of Geiger counters that would register a count whenever a muon passed vertically through it and not when any other type of particle passed through. They took their equipment to several stations in Colorado, at different elevations. At each elevation, they measured the average number of counts per second. Figure 3.13 is a schematic view of the experiment, showing one trial with the detector at Echo Lake (elev. 3,200 m) and an-other at Denver (elev. 1,600 m).</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In addition to decays, another effect depletes the muon beam as it passes through the atmosphere: some of the muons collide with oxygen or nitrogen atoms in the atmosphere and are absorbed. The experimenters corrected for this effect by placing a layer of iron above the detector at the higher elevation. Since iron is much denser than air, about 20 centimeters of iron absorbs as many muons as does all the atmosphere between the two elevations. Any difference in the measured counting rates at the two stations could therefore be attributed to the decay of muons in the in-tervening region.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: right;">
<span style="font-size: x-small;">To be continue </span></div>
Anonymoushttp://www.blogger.com/profile/12948124948045044887noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-4470497074194980412018-10-24T22:31:00.001-07:002018-12-05T18:16:03.107-08:00 The Postulates of Relativity and Their Implications 3<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhriP6DzErI5_JrJCnCmKVTNVOLDA183EDMjy4fhuvFmTxWbd3muK1X-wzM2yqYtBJDut1sITntRUkIUou6jAp8XGPc_U7FvzJRYYPpnhQg8xOWMMz8B-9h16YK7F_NlXtbuDuoZDvB5PQ/s1600/relativity-implication.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="339" data-original-width="602" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhriP6DzErI5_JrJCnCmKVTNVOLDA183EDMjy4fhuvFmTxWbd3muK1X-wzM2yqYtBJDut1sITntRUkIUou6jAp8XGPc_U7FvzJRYYPpnhQg8xOWMMz8B-9h16YK7F_NlXtbuDuoZDvB5PQ/s1600/relativity-implication.png" /></a></div>
<br />
<br />
<h3>
THE RELATIVITY OF TIME: SIMULTANEITY</h3>
<div style="text-align: justify;">
The most profound conceptual implication of special relativity is the change it has brought about in our perception of the nature of time. Relativity requires us to reject the notion of absolute time, which was taken for granted by Newton and by all the thinkers who followed him.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
In a world in which time is absolute, the following proposition is surely valid: <i>if observers in different inertial frames measure the time interval between two events, using identically constructed clocks, the measured time intervals will in every instance be equal</i>. The proposition is (at least in principle) subject to experimental test. Although our intuition strongly suggests that the result of all such tests must be positive, it is conceivable that the measured time intervals might sometimes turn out to be different. In that case, absolute time would have to be abandoned. Einstein's postulates predict just such an outcome, and the prediction is confirmed (albeit indirectly) by experimental evidence. All the major conceptual consequences of special relativity can be related to the relativity of time.</div>
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<br /></div>
<div style="text-align: justify;">
I introduce the relativity of time by analyzing the concept of simultaneity. If tin1e is absolute, two events that occur at the same time according to one set of observers must be simultaneous as well for any other set. The second postulate leads inescapably to a contrary conclusion: other observers find that the events are not simultaneous. This result suffices to establish the relativity of time.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
One bit of reassurance can be offered the reader. If two events occur simultaneously at the same place, a single observer can directly experience both: she can see them happen together. Such events are simultaneous in any frame even according to special relativity. In fact, since an event is characterized by its space and time coordinates, two events that occur at the same time and at the same place can be regarded as parts of a single event.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
If, however, two events take place at different locations in a particula frame of reference, no single observer in that frame can experience both. Determination of simultaneity in such a case is a complicated procedure, as has already been discussed in chapter 1. Two observers are required, one at the location of each event; each observer records the reading of a clock on the scene, and the two readings are subsequently compared. If the readings are the same (and if the clocks are properly synchronized), the observers conclude that the events in question were simultaneous.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
After all that exchange. of information, however, simultaneity at a distance must be regarded as an inference rather than a sensory observation. Special relativity predicts that if observers belonging to a different inertial frame record the times of the same two events on their (separated) clocks, those clock readings will be unequal. That prediction, although counter-intuitive, does not contradict any sensory experience </div>
Anonymoushttp://www.blogger.com/profile/12948124948045044887noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-71661416269321166982018-10-21T22:15:00.000-07:002018-12-05T18:16:19.297-08:00The Postulates of Relativity and Their Implications 2<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW5rWHrY8g5IV1F9mC6f-H76RqvdGVnX6CeOio_T2sXC8Q9cw7cuRCGH1Mkj1Mt1vR3mlyDBP02wxzycibNePb6epy99oOy_BHQWGEx1so5mMRPMdnPbsNw1OFweYUynZAqVbr15d0RUA/s1600/relativity-implication.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="339" data-original-width="602" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW5rWHrY8g5IV1F9mC6f-H76RqvdGVnX6CeOio_T2sXC8Q9cw7cuRCGH1Mkj1Mt1vR3mlyDBP02wxzycibNePb6epy99oOy_BHQWGEx1so5mMRPMdnPbsNw1OFweYUynZAqVbr15d0RUA/s1600/relativity-implication.png" /></a></div>
<br />
<br />
<h3>
TIlE ROLE OF TIlE MICHELSON-MORLEY EXPERIMENT IN THE GENESIS OF RELATIVITY</h3>
<div style="text-align: justify;">
Special relativity appears to be a classic case of a theory constructed expressly to explain a puzzling experimental finding. The second postulate, the heart of the theory, seems to be based directly on the result of the Michelson-Morley experiment. This indeed is the way the story is presented in much of the literature. Robert Millikan, in an article written in honor of Einstein's seventieth birthday, put it as follows:</div>
<br />
<div style="text-align: center;">
That unreasonable, apparently inexplicable experimental fact [the<br />
result of Michelson-Morley] was very bothersome to 19th-century<br />
physics, and so for almost twenty years physicists wandered in the<br />
wilderness in the disheartening effort to make it seem reasonable.<br />
Then Einstein called out to us all, "Let us merely accept this as an<br />
established experimental fact and from there proceed to work out<br />
its inevitable consequences," and he went at that task himself with<br />
an energy and a capacity which very few people on earth possess.<br />
Thus was born the special theory of relativity.</div>
<div style="text-align: center;">
<br /></div>
<br />
<div style="text-align: justify;">
Millikan's account paints a dramatic (and credible) picture. Yet in his own writings Einstein suggests that Michelson's experiment played at most a minor role in the genesis of special relativity. The 1905 paper makes no mention of the experiment, although Einstein does refer to "unsuccessful efforts to discover any motion of the earth relative to the 'light medium,' " without identifying those efforts. 6 The Michelson-Morley experimentwas only one of them.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
There is some question as to whether Einstein even knew about the experiment when he wrote his paper. In an interview conducted in 1950, Einstein told Robert Shankland that he became aware of the Michelson-Morley result through the writings of Lorentz, but only after 1905. "Otherwise," he said, "I would have mentioned it in my paper." He added that the experimental results that had influenced him most were the observations on stellar aberration and Fizeau's experiment on the speed of light in moving water. "They were enough," he said.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
When Shankland raised the question again two years later, Einstein gave a different response. "This is not so easy, he said. "I am not sure when I first heard of the Michelson experiment. I was not conscious that it had influenced me directly during the seven years that relativity had been my life." He added that in the years 1905-1909 he thought a great deal about Michelson's result. He then realized that he had also been conscious of the re'sult before 1905, partly from the papers of Lorentz and more because he had "simply assumed this result of Michelson to be true."</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Abraham Pais, who knew Einstein well and wrote his scientific biography, is certain that Einstein did know about the Michelson experiment before 1905. 9 He points out that Einstein was in his seventies and not in good health when he talked to Shankland; at the first interview he probably did not remember that Michelson's experiment was discussed in Lorentz's 1895 monograph, which he had definitely read before 1905.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Even if Einstein was aware of Michelson-Marley's result, we must accept his assertion that it was not a major motivating factor in the genesis of relativity. He repeatedly uses terms like "negligible," "indirect," and "not decisive" to describe the influence of Michelson's experiment on his thinking. In his penetrating analysis of the issue, Gerald Holton concludes that "the role of the Michelson experiment in the genesis of Einstein's theory appears to have been so small and indirect that one may speculate that it would have made no difference to Einstein's work if the experiment had never been made at all." In light of this assessment, Einstein's achievement looms all the more remarkable.</div>
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If he was not influenced by Michelson's experiment, how did Einstein arrive at the second postulate? That is the intriguing question. Einstein's paper provides little guidance. In it he presents the second postulate with no explanatory remarks or motivation, as though it were a commonly accepted proposition instead of a daring departure from conventional notions. An illuminating passage is found in the autobiographical notes writ- ten by Einstein in 1949.</div>
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By and by I despaired of the possibility of discovering the true<br />
laws by means of constructive efforts based on known facts. The<br />
longer and the more despairingly I tried, the more I came to the<br />
conviction that only the discovery of a universal formal principle<br />
could lead us to assured results.... After ten years of reflection<br />
such a principle resulted from a paradox upon which I had already<br />
hit at the age of sixteen: If I pursue a beam of light with the veloc-<br />
ity c, I should observe such a beam as a spatially oscillatory electro-<br />
magnetic field at rest. However, there seems to be no such thing,<br />
whether on the basis of experience or according to Maxwell's equa-<br />
tions. From the very beginning it appeared to me intuitively clear<br />
that, judged from the standpoint of such an observer, everything<br />
would have to happen according to the same laws as for an ob-<br />
server who, relative to the earth, was at rest. For how, otherwise,<br />
should the first observer know, i.e., be able to determine, that he is<br />
in a state of fast uniform motion?</div>
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The seed of the theory of relativity had evidently been planted when Einstein was only sixteen years old! The idea that light has the same speed in all inertial frames, so difficult for an ordinary mind to grasp, was a quite natural one for Einstein. He was prepared to accept it even without strong experimental evidence. In the years following 1905, the postulates of relativity have been con firmed by ample experimental evidence, including refined versions of the Michelson-Morley experiment. But the genesis of the theory, apparently, lay in Einstein's inspired intuition.</div>
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Anonymoushttp://www.blogger.com/profile/12948124948045044887noreply@blogger.com1tag:blogger.com,1999:blog-8594979553238086927.post-13104788065556828682018-09-26T23:51:00.002-07:002018-12-05T18:16:46.541-08:00The Postulates of Relativity and Their Implications<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCwXJcceonMt4_-J4RTaSDh9wFvk_dL8pR_AGZyfd9Nfg1ckNAu465sKTKFQtMLB-n_cNmZy9UNUf7tzwJZAfBuKTorywvcpX_WPj9_IAhQDdXBbkNJ7YUV-p_nrKIx3j8Gi5QHTQSDKs/s1600/relativity-implication.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="339" data-original-width="602" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCwXJcceonMt4_-J4RTaSDh9wFvk_dL8pR_AGZyfd9Nfg1ckNAu465sKTKFQtMLB-n_cNmZy9UNUf7tzwJZAfBuKTorywvcpX_WPj9_IAhQDdXBbkNJ7YUV-p_nrKIx3j8Gi5QHTQSDKs/s640/relativity-implication.png" width="640" /></a></div>
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<br />
<h3>
THE POSTULATES</h3>
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In 1905 Albert Einstein, a twenty-six-year-old technical expert third class at the Swiss patent office in Bern, published three monumental papers in the Annalen der Physik. One of those papers set forth the theory now known as special relativity.l The theory is based on two postulates, which</div>
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I paraphrase as follows:</div>
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Postulate 1 (Principle of Relativity): The laws of nature are the same in all inertial frames.</div>
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Postulate 2 (Constancy of the Velocity of Light): The speed of light in empty space is an absolute constant of nature and is independent of the motion of the emitting body.</div>
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All of special relativity follows by logical deduction from these two postulates. The only other assumption required is that space is homogeneous and isotropic, that is, no region of space is intrinsically different from any other and there are no preferred directions in space. A principle of relativity had been propounded in the seventeenth century by Galileo but for a long time was believed to apply only to the laws of mechanics. Einstein's first postulate is simply the extension of Galileo's principle to encompass all the laws of physics, including those of electromagnetism and optics? Such a generalization had great intuitive appeal for Einstein. In his popular exposition of the theory, he says that a principle of such broad generality should hold with exactness in one domain of phenomena, and yet should be invalid for another, is a priori not very probable." 3 The quest for generality and for unifying principles guided Einstein in all his research.</div>
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The second postulate is the revolutionary part of special relativity. As Einstein says in the introduction to the 1905 paper, the second postulate is only apparently" irreconcilable with the first. What he means is that the two postulates are irreconcilable only if one insists on retaining the Galilean transformation, which implies that the speed of light (like that of anything else) should be different when measured by two sets of observers in relative motion. It also implies that the Galilean transformation, self evident though it may appear, must be rejected. The principal conceptual consequences of special relativity can, however, be demonstrated directly from Einstein's two postulates without employing the Lorentz transformation.</div>
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As noted, the second postulate provides a simple explanation for the null result of the Michelson-Morley experiment: if the speed of light is an absolute constant, the light travel times along the arms of the interferometer are always equal, no matter how the instrulnent is oriented. Hence, no fringe shift is to be expected as the interferometer is rotated. The Michelson-Morley experiment therefore provides strong (though indirect) support for the second postulate.</div>
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Direct experimental confirmation of the second postulate came only many years afterward. The most convincing data were provided by Alvager's experiment on the decay of neutral pions, in connection with Ritz's emission theory. In that experiment, pions moving at O.9998c were observed to decay into two photons (light pulses). One photon was emitted in nearly the forward direction (the direction of the decaying pion) and the other in nearly the opposite direction. According to Galilean relativity, the forward-moving photon should travel at speed 1.9998c and the other at only 0.0002c. Instead, both photons were observed to travel at speed c to within about three parts in 10^5 .</div>
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Demise of the Ether</h4>
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In nineteenth-century electromagnetism, the ether played a central role. It provided a unique frame of reference in which Maxwell's equations hold and the speed of light is the same in all directions. According to Einstein's postulates, every inertial frame has that property. There remains no role for the ether to play in the description of natural phenomena; it has becoine superfluous.</div>
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Many physicists, including both Lorentz and Michelson, were reluctant to abandon the ether. Although Lorentz quickly accepted Einstein's relativity, he continued to maintain that a medium of some kind is needed as the carrier of the electromagnetic field. In his Theory of Electrons, published in 1909, he said, "I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter." 4 Michelson expressed similar views. References to the ether continued to appear in the literature long after relativity had gained general acceptance. Gradually, however, the ether faded from discussion. </div>
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Special relativity dispenses also with the notions of absolute rest and absolute motion. So long as an ether was believed to exist, its rest frame provided a standard with respect to which absolute motion nlight be defined. A body could be said to be in a state of absolute rest if it was at rest relative to the ether. With the demise of the ether, all inertial frames are completely equivalent. There is no way to define absolute rest or absolute motion.</div>
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The first postulate implies that no experiment can have a result that favors one inertial frame over another. Nature imposes strict democracy among inertial observers; this rule dictates the outcome of many experiments. For example, consider two uniformly moving trains that approach each other on a straight track. The trains are equipped with identical speed-measuring devices, such as the radar employed by traffic patrols. Observers on each train aim their device at the other train and measure its</div>
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speed of approach. How are the results of the two measurements related? In a world governed by Galilean relativity, it is easy to show that the two measured speeds must be equal. Suppose one train moves at 30 m/sec and the other at 40 m/sec relative to the ground. The distance between the trains diminishes by 70 m each second, and both speed indicators must read 70 m/sec.</div>
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In special relativity, this simple argument is not valid. As we shall presently discover, space and time have many unexpected properties. Observers on each train find that the other train is contracted and its clocks run slow. Hence it is not at all obvious that the two speed measurements should yield identical results. That outcome is demanded by the first postulate, however, for any other would violate the requirement of equality among inertial observers. If the two radars were to register unequal readings, which speed should be the greater? There is nothing in the problem to distinguish between the two trains, other than that they are moving in opposite directions; the isotropy of space assures us that this cannot make any difference. The only outcome consistent with Einstein's first postulate is that the two measured speeds are equal.</div>
Algebrahttp://www.blogger.com/profile/11440946058125679273noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-72762707154734064322018-09-26T23:32:00.003-07:002018-12-05T18:17:05.076-08:00THE MICHELSON-MORLEY EXPERIMENT<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEji6S_gZxOgovId7Vc7xOBb7wFMxmD0aUpUWJsmeXOusrMPM6yKbmOC7OaXLtAfQiz36DikDw4zr39nXdmjVV4K7kq8WKFduIyd83Y3MGXoUJwa13GNaCo814zXwSnR4FHYYN5OPVrvheQ/s1600/morley-experiment.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="1100" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEji6S_gZxOgovId7Vc7xOBb7wFMxmD0aUpUWJsmeXOusrMPM6yKbmOC7OaXLtAfQiz36DikDw4zr39nXdmjVV4K7kq8WKFduIyd83Y3MGXoUJwa13GNaCo814zXwSnR4FHYYN5OPVrvheQ/s640/morley-experiment.jpg" width="640" /></a></div>
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<br />
<h3>
THE ETHER</h3>
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The Michelson-Morley experiment occupies a special niche in the pantheon of relativity. Contrary to many accounts, the experiment did not strongly influence Einstein's discovery of special relativity.l It nonetheless provides strong experimental underpinning for the theory and was instrumental in promoting its widespread acceptance. Albert A. Michelson's experiment was rooted in late-nineteenth-century ideas concerning the nature of light. I begin therefore with a brief exposition of those ideas.</div>
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That the speed of light is very great had been known for a long time. Galileo had tried to measure it but did not succeed. The first determination of the speed of light was obtained in 1676 by Ole Romer from his observations of the eclipses of one of Jupiter's moons. Because the earth-Jupiter distance changes, the interval between successive eclipses varies; the variation measures the time required for light to travel the additional distance. Romer's result for the speed of light, 2.2 X 10^8 m/sec, was about 25 percent low. 2 The best modern value is 2.998 X 10^8 m/sec.</div>
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During the eighteenth century a lively controversy raged over the question, Does light consist of tiny particles or is it a wave phenomenon? Expert opinion was divided; Newton, for example, favored the particle hypothesis. Many properties of light, such as reflection and refraction, can be explained in either view.</div>
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Strong evidence in favor of the wave hypothesis was provided by experiments performed by Thomas Young, Augustin-Jean Fresnel, and others, which showed that light exhibits interference and diffraction. These characteristic wavelike phenomena are well-nigh impossible to explain on the basis of a particle description. Although the wave character of light seemed firmly established by the early 1800s, the nature of the waves was not at all clear. The model favored at first was that light waves, like all other known waves, are a mechanical oscillation of some material medium. (A sound wave in air, for example, consists of longitudinal vibrations of air molecules.) The light medium was called the "luminiferous ether"; I shall refer to it simply as the ether.</div>
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The ether, if it exists, has quite unusual properties. It must pervade all space, even where no matter is present. (Unlike sound, light propagates readily through the best vacuum.) It must be extremely tenuous, in as much as the earth and all other astronomical bodies pass through etherfilled space with no detectable loss of speed. Finally, the ether must be capable of vibrating at extremely high frequencies. (The frequency of visible light is more than 10 14 cycles per second, much higher than that of any known mechanical oscillation.)</div>
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Important progress took place when James Clerk Maxwell showed that the equations of electricity and magnetism have solutions that consist of traveling waves, whose speed can be calculated in terms of known constants. The calculated speed of those electromagnetic waves turned out to be almost exactly equal to the measured speed of light. This was convincing evidence that light is in fact an electromagnetic phenomenon. After Maxwell's work, the mechanical model of light was abandoned. No material substance vibrates when an electromagnetic wave propagates; the oscillation is in the magnitudes of the electric and magnetic fields, which are only mathematical quantities. If no mechanical oscillation takes place, no medium is required. Most physicists were nonetheless unwilling to accept the notion that electromagnetic disturbances can propagate through an absolute vacuum. The ether thus lived on, viewed now as a medium that somehow "supports" the oscillations associated with the propagation of light even though it does not itself vibrate. The nature of that medium became even more mystifying.</div>
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<h3 style="text-align: justify;">
PRELUDE TO MICHELSON-MORLEY</h3>
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Numerous attempts were made during the late nineteenth century to confirm the existence of the ether. The Michelson-Morley experiment is the best known of those attempts. The experiment is described in the next section; here I indicate its basic idea by sketching an analogous experiment using water waves. The discussion is entirely within the framework of Galilean relativity.</div>
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In a wave phenomenon that involves a medium, the rest frame of the medium is a unique frame of reference. Observers in any frame can carry out experiments to determine their velocity relative to the medium. Suppose a ship is at rest in still water. Observers on the ship measure the speed of water waves moving in various directions. Because the medium is isotropic (the water looks the same in all directions), the measured speeds must all be equal. Let c denote that common speed.</div>
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An identical experiment carried out on a moving ship has a quite different outcome: the wave speed in that case varies with direction. A wave traveling in the same direction as the ship moves more slowly than one traveling in the opposite direction. In fact, if the ship's speed is c, a wave traveling in the same direction as the ship does not appear to move at all. By measuring the speeds of water waves in all directions, then, ship-borne observers can determine the velocity of their ship relative to the water. The direction in which waves travel slowest must be the ship's heading, and the magnitude of the minimum speed is c - V, where V is the speed of the ship. If all waves are found to travel at the same speed, the ship must be at rest relative to the water.</div>
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The same argument can be applied to the propagation of light, with the ether in place of the water and the earth playing the part of the ship. In the rest frame of the ether light travels at the same speed c in all directions, whereas in the earth frame the speed of light should vary with direction; the magnitude of the variation depends on V, which now denotes the speed of the earth relative to the ether. Michelson proposed to determine the value of V by detecting the difference in travel times of light rays traversing a given distance in different directions.</div>
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One does not have to believe in the ether to conclude that the speed of light measured on earth should vary with direction. The Galilean velocity transformation implies that light can travel at the same speed in all directions only in one reference frame; we may call that the isotropic frame" if we are not committed to the existence of an ether. Unless the earth happens to be at rest in the isotropic frame (which is highly improbable a priori), the speed of light in the earth's frame must depend on its direction.</div>
Algebrahttp://www.blogger.com/profile/11440946058125679273noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-81466245639360256552018-09-26T08:06:00.002-07:002018-12-05T18:27:37.960-08:00GALILEAN RELATIVITY 2<div class="separator" style="clear: both; text-align: center;">
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<h3>
EVENTS, OBSERVERS, AND FRAMES OF REFERENCE</h3>
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We begin by defining some important terms. In relativity an event is any occurrence with which a definite time and a definite location are associated; it is an idealization in the sense that any actual event is bound to have a finite extent both in time and in space.</div>
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A frame of reference consists of an array of observers, all at rest relative to one another, stationed at regular intervals throughout space. A rectangular coordinate system moves with the observers, so that the x, y, and z coordinates of each observer are constant in time. The observers carry clocks that are synchronized: each clock has the same reading at the same time.</div>
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Each observer records all events that occur at her location. Each event has four coordinates: three space coordinates and a time. By definition, the space coordinates are the coordinates of the observer who detected the event and the time of the event is the reading of her clock when it occurs.</div>
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A second frame of reference consists of another array of observers, all at rest relative to one another and all moving at the same velocity relative to the first set. They have their own coordinate system and their own (synchronized) clocks, and they also record the coordinates of events. The coordinates of a given event in two frames of reference are, in general, different. The central problem of relativity is just to determine the relation between the two sets of coordinates; this turns out to be not so simple a matter as it first appears.</div>
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<h3 style="text-align: justify;">
THE PRINCIPLE OF RELATIVITY AND INERTIAL FRAMES</h3>
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The principle of relativity was first enunciated by Galileo in 1632. Galileo's argument is clear and graphically put.</div>
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<i>Salviatus</i>: Shut yourself up with some friend in the main cabin below decks on some large ship and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle which empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something toward your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you</div>
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have observed all these things carefully (though there is no doubt that when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will</div>
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discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still. In jumping, you will pass on the floor the same spaces as before, nor will you make larger jumps toward the stern than to-</div>
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ward the prow, ... despite the fact that during the time that you are in the air the floor under you will be going in a direction opposite to your jump.... Finally the butterflies and flies will continue their flights indifferently toward every side, nor will it ever happen that they are concentrated toward the stern, as if tired out from keeping up with the course of the ship, from which they will have been separated during long intervals by keeping themselves in the air.... The cause of all these correspondences of effects is the fact that the ships' motion is common to all the things contained in it.</div>
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Galileo is asserting, in effect, that the laws of nature are the same in any two frames of reference that move uniformly with respect to one another. If identical experiments are carried out by two sets of observers, with identical initial conditions, all the results will be the same. It follows that there is no way to determine by means of experiments carried out in a given frame of reference whether the frame is at rest or is moving uniformly. Only the relative velocity between frames can be measured. This set of assertions is called the principle of relativity.</div>
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Galileo's motivation was to refute Aristotle's argument that the earth must be standing still. If the earth were moving, Aristotle had claimed, a stone dropped from the top of a tower would not land at its base, since the earth would have moved while the stone was falling. Galileo argues that the earth plays a role entirely analogous to that of the ship in his example; just as a stone dropped from the top of a mast lands at its foot whether the ship is moving or at rest, so does one dropped from a tower on earth. And just as observations carried out within the ship cannot be used to decide whether the ship is standing still or moving uniformly, so the observed motion of objects on earth implies nothing about the motion of the earth other than that it is (approximately) uniform.</div>
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Although Galileo may not have carried out all the ship experiments, he definitely performed the falling rock experiment as well as many others on falling bodies. In a famous letter replying to Francesco Ingoli, who had attacked his views and sided with Aristotle, Galileo says, "whereas I have made the experiment, and even before that, natural reason had firmly persuaded me that the effect had to happen in the way that it indeed does."</div>
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Several remarks are in order concerning Galileo's principle of relativity. First, the observations on which the principle was based were necessarily limited to quite slow speeds. Perhaps if the ship were moving very rapidly, shipborne observers might detect unusual effects that would enable them to conclude that their ship was indeed in motion. If that were to happen, the relativity principle would be only approximately valid. The laws of nature might be (very nearly) the same in two frames of reference that move slowly relative to one another but quite different in two frames whose relative velocity is great. Galileo's observations obviously could not exclude such a possibility, and even today the direct evidence from physics in moving laboratories is limited to fairly low velocities. Indirect evidence, however, strongly supports the hypothesis that the relativity principle holds for any speed.</div>
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Galileo's experiments all deal with phenomena in what is nowadays called mechanics; on the basis of those experiments, therefore, one can conclude only that a principle of relativity applies to the laws of mechanics. Perhaps other experiments, involving different phenomena, can distinguish among frames. Nineteenth-century physicists believed that electromagnetic and optical phenomena provide just such a distinction. According to the view prevalent during that period, there exists a unique frame of reference in which the laws of electromagnetism take a particularly simple form. If that were so, the principle of relativity would not apply to electromagnetic phenomena: the results of some experiments would depend on the observer's motion relative to the special frame. Many experiments were performed with the aim of determining the earth's motion relative to the special frame, but they all failed to detect any effect of that assumed motion. The most important was the Michelson-Morley experiment.</div>
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For Einstein, it was aesthetically unsatisfying that a principle of relativity should hold for one set of phenomena (mechanics) but not for another (electromagnetism.) He postulated that Galileo's principle applies to all the laws of nature; this generalization forms the basis for special relativity. The relativity principle has an important philosophical implication. If there is no way to distinguish between a state of rest and a state of uniform motion, absolute rest has no meaning. Observers in any frame are free to take their own frame as the standard of rest. Shore-based observers watching Galileo's ship are convinced that they are at rest and the ship is in motion, but observers on the ship are equally entitled to regard them selves as being at rest while the shore along with everything on it moves. The question, Which observers are really at rest? has no meaning if there is no cqnceivable experiment that could answer it. (According to observers in an airplane flying overhead, both shore observers and ship observers are in motion.)</div>
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In sum, the principle of relativity denies the possibility of absolute rest (or of absolute motion). Motion can be defined only relative to a specific frame of reference, and among uniformly moving frames strict democracy prevails: any frame is just as good as any other. Any reference to a body "at rest" should be understood to mean at rest in a frame of reference fixed on the earth" (or in some other specified frame).</div>
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The distinguishing feature of uniformly moving frames is that in any such frame the law of inertia holds: a body subject to no external forces remains at rest if initially at rest, or if initially in motion, it continues to move with constant speed in the same direction. In an accelerated frame, the law of inertia does not hold. Instead bodies seem to be subjected to peculiar forces for which no agent can be identified. Those forces, called inertial forces, have observable consequences. Observers in a given frame can determine whether their frame is inertial by carrying out experiments to test whether the law of inertia holds. A frame of reference fixed on earth satisfies the criterion fairly closely; for most purposes such a frame can be regarded as inertial. Because of the earth's rotation, however, an earthbound frame is not strictly inertial. Even a frame of reference fixed at the pole, which does not partake of the earth's rotation, is not strictly inertial because the earth is moving in a curved orbit around the sun. And the sun is itself in orbit about the center of the galaxy. An inertial frame is an idealization in the sense that no experiment can assure us that our frame is strictly inertial, that is, that</div>
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a body subject to no forces does not experience some tiny acceleration.</div>
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Algebrahttp://www.blogger.com/profile/11440946058125679273noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-12643594476863989212018-09-26T07:37:00.003-07:002018-12-05T18:27:55.714-08:00Galilean Relativity<div class="separator" style="clear: both; text-align: center;">
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<h3>
RELATIVITY AND COMMON SENSE</h3>
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A child walks along the floor of a moving train. Passengers on the train measure the child's speed and find it to be 1 meter per second. When ground-based observers measure the speed of the same child, they obtain a different value; observers on an airplane flying overhead obtain still another. Each set of observers obtains a different value when measuring the same physical quantity. Finding the relation between those values is a typical problem in relativity.</div>
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<i>According to Einstein, common sense is "that layer of prejudice laid down in</i></div>
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<i> the mind prior to the age of eighteen."</i></div>
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There is nothing at all startling about these observations; relativity was not invented by Albert Einstein. Einstein's work did, however, drastically change the way such phenomena are understood; the term "relativity" as used today generally refers to Einstein's theory.</div>
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The study of relativity began with the work of Galileo GaHlei around 1630; Isaac Newton also made important contributions. The ideas described in this chapter, universally accepted until 1900, are known as "Galilean relativity."</div>
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Galilean relativity is fully consistent with the intuitive notions that we call common sense." 1 In the example above, if the train moves at 30 meters per second (m/sec) in the same direction as the child, common sense suggests that ground-based observers should find the child's speed to be 31 m/sec; Galilean relativity gives precisely that value. Einstein's theory, as we shall see, gives a different result. </div>
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In the case of the child, the difference between the two theories is minute. The speed measured by ground observers according to Einstein's relativity differs from the Galilean value 31 m/sec only in the fourteenth decimal place; no measurement could possibly detect such a tiny difference. This result is characteristic of Einsteinian relativity: its predictions are indistinguishable from those of Galilean relativity whenever the observers, as well as all objects under observation, move slowly relative to one another. That realm is generally called the nonrelativistic limit, although Galilean or Newtonian limit would be a more apt designation. "Slowly" here means at a speed much less than the speed of light.</div>
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The speed of light plays a central role in Einstein's theory; whenever any speed in the problem approaches that value, Einsteinian relativity departs dramatically from that of Galileo and Newton. Because the speed of light is so great, however, most commonly observed phenomena are adequately described by Galilean relativity.</div>
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The special" theory of relativity, which is the principal subject of this book, is restricted to observers who move uniformly, that is, at constant speed in the same direction. If observers move with changing speeds, or along curved paths, the problem of relating their measurements is much more complicated. Einstein addressed that problem as well, in his general" theory of relativity. Because the general theory involves quite advanced mathematics. The special theory, in contrast, requires only elementary algebra and geometry and can be presented with full rigor.</div>
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Many of the conclusions of special relativity run counter to our intuition concerning the nature of space and time. Before Einstein, no one doubted that time is absolute. Newton put it as follows in his Principia: "Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external." </div>
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Special relativity obliges us to abandon the absolute nature of time. We shall see, for example, that the time order of two events can depend on the relative motion of the observers who view them. One set of observers may find that a certain event A occurred before another event B, whereas according to a second set of observers, who are moving relative to the first, B occurred before A. This result is surely difficult to accept.</div>
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In some cases, a reversal of time ordering would be truly bizarre. Suppose that at event A a moth lands on the windshield of a moving car; the car clock reads 12:00. At event B another moth lands; the car clock now reads 12:05. For the driver of the car, the order of those events is a direct sensory experience: she can see both events happen right in front of her and can assert with confidence that A happened first. If observers on the ground were to claim that event B happened first, they would be denying that sensory experience; moreover, the car clock would according to them be running backward! (It would read 12:05 before it reads 12:00.)</div>
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As we shall see, special relativity implies that moving clocks run slow. That is itself a strange result, but clocks running backward would be too much to swallow. No such disaster arises, however. In the case of the moths, event A happens first according to all observers. A reversal of time ordering can occur only for events spaced so far apart that no single observer (and no single clock) can be present at both. The order of such events is not a direct sensory experience for anyone; it can be determined only by comparing the readings of two distinct clocks, one present at event A and the other present at B. If two sets of observers disagree on the order of those events, no one's sensory experience is contradicted and no one sees any clock running backward. The proof of this assertion, depends on the fact that nothing can travel faster than light, one of the important consequences of special relativity.</div>
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A logical requirement of any theory is causality. If event A is the cause of event B, A must occur before B: the cause must precede the effect. We will see in chapter 5 that special relativity is consistent with the causality requirement. Whenever a cause-and-effect relation exists between two events, their time order is absolute: all observers agree on which one happened first.</div>
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Figure 1.1 shows a hypothetical experiment to illustrate the relativistic reversal of time ordering. Event A takes place in San Francisco and event B in New York. According to clocks at rest at those locations, A occurs before B. The same events are monitored by observers on spaceships moving from west to east at equal speeds; one ship is over San Francisco when event A occurs, and the other is over New York when event B occurs. Special relativity predicts that if the ships are moving fast enough, their clocks can show event B happening before A. Notice that no single clock is present at both events; the relevant times in the problem are recorded by four distinct clocks, two on the ground and two on the spaceships.</div>
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I hasten to add that no such experiment has ever been performed. The fastest available rockets travel a few kilometers per second, only about one hundred thousandth the speed of light. At that speed, the events of figure 1.1 would have to be separated in time by less than a millionth of a second</div>
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if a reversal of time order were to be detectable. Moreover, the speeds of the two spaceships would have to be equal to within a very small tolerance. The experiment is just too hard to carry out. But we can be confident that if faster rockets were available and if other technical requirements were met, the effect could be detected.</div>
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<span style="font-size: x-small;">Fig. 1.1. Hypothetical experiment to demonstrate </span><span style="font-size: x-small;">the reversal of time ordering predicted by special </span><span style="font-size: x-small;">relativity. Event A occurs in San Francisco, event B </span><span style="font-size: x-small;">in New York. Each event is detected by two sets </span><span style="font-size: x-small;">of observers-one set fixed on earth and the other </span><span style="font-size: x-small;">located on spaceships flying at equal (constant) </span><span style="font-size: x-small;">speeds. Each set of observers measures the times of </span><span style="font-size: x-small;">the two events on its own clocks, which have been </span><span style="font-size: x-small;">previously synchronized. According to earth clocks, </span><span style="font-size: x-small;">event A happens before B, whereas according to </span><span style="font-size: x-small;">spaceship clocks, B happens before A. The time in</span><span style="font-size: x-small;">tervals shown on the clocks are much exaggerated.</span></div>
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<span style="font-size: x-small;"> </span>The evidence that confirms special relativity comes principally from atomic and subatomic physics. In many experiments particles move at speeds close to that of light, and the effects of special relativity are dramatic. Particles are created and annihilated in accord with the famous Einstein relation E = mc^2 . No understanding of such phenomena, or of the kinematics of high-energy particle reactions, would be possible without relativity. Thus Einstein's theory is confirmed daily in every high-energy physics laboratory. Particle reactions are not within the realm of everyday experience, however; in the latter realnl, everything moves fairly slowly and relativistic effects are not manifested. If the speed of light were much smaller, the effects of special relativity would be more prominent and our intuition concerning the nature of time would be quite different.</div>
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Algebrahttp://www.blogger.com/profile/11440946058125679273noreply@blogger.com0tag:blogger.com,1999:blog-8594979553238086927.post-58646352212786648422018-09-25T05:53:00.001-07:002018-10-03T06:41:50.375-07:00EPILOGUE: THE PROSPECT AHEAD<div class="separator" style="clear: both; text-align: center;">
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THE UNIVERSE will certainly go on expanding for a while. As to its fate after that, the standard model gives an equivocal prophecy: It all depends on whether the cosmic density is less or greater than a certain critical value.</div>
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If the cosmic density is less than the critical density, then the universe is of infinite extent and will go on expanding forever. Our descendants, if we have any then, will see thermonuclear reactions slowly come to an end in all the stars, leaving behind various sorts of cinder: black dwarf stars, neutron stars, perhaps black holes. Planets may continue in orbit, slowing down a little as they radiate gravitational waves but never coming to rest in any finite time. The cosmic backgrounds of radiation and neutrinos will continue to fall in temperature in inverse proportion to the size of the universe, but they will not be missed; even now we can barely detect the 3° K microwave radiation background.</div>
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On the other hand, if the cosmic density is greater than the critical value, then the universe is finite and its expansion will eventually cease, giving way to an accelerating contraction. If, for instance, the cosmic density is twice its critical value, and if the presently popular value of the Hubble constant (15 kilometers per second per million light years) is correct, then the universe is now 10,000 million years old; it will go on expanding for another 50,000 million years, and then begin to contract. The contraction is just the expansion run backward: after 50,000 million years the universe would have regained its present size, and after another 10,000 million years it would approach a singular state of infinite density.</div>
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During at least the early part of the contracting phase, astronomers (if there are any) will be able to amuse themselves by observing both red shifts and blue shifts. Light from nearby galaxies would have been emitted at a time when the universe was larger than it is when the light is observed, so when it is observed this light will appear to be shifted toward the short wavelength end of the spectrum, i.e., toward the blue. On the other hand, the light from extremely distant objects would have been emitted at a time when the universe was still in the early stages of its expansion, when the universe was even smaller than it is when the light is observed, so when it is observed this light will appear to be shifted toward the long wavelength end of the spectrum, i.e., toward the red.</div>
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The temperature of the cosmic backgrounds of photons and neutrinos will fall and then rise as the universe expands and then contracts, always in inverse proportion to the size of the universe. If the cosmic density now is twice its critical value, then our calculations show that the universe at its maximum dilation will be just twice as large as at present, so the microwave background temperature will then be just one-half its present value of 3° K, or about 1.5° K. Then, as the universe begins to contract, the temperature will start to rise.</div>
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At first no alarms will sound—for thousands of millions of years the radiation background will be so cool that it would take a great effort to detect it at all. However, when the universe has recontracted to one-hundredth its present size, the radiation background will begin to dominate the sky: the night sky will be as warm (300° K) as our present sky at day. Seventy million years later the universe will have contracted another tenfold, and our heirs and assigns (if any) will find the sky intolerably bright. Molecules in planetary and stellar atmospheres and in interstellar space will begin to dissociate into their constituent atoms, and the atoms will break up into free electrons and atomic nuclei. After another 700,000 years, the cosmic temperature will be at ten million degrees; then stars and planets themselves will dissolve into a cosmic soup of radiation, electrons, and nuclei. The temperature will rise to ten thousand million degrees in another 22 days. The nuclei will then begin to break up into their constituent protons and neutrons, undoing all the work of both stellar and cosmological nucleosynthesis. Soon after that, electrons and positrons will be created in great numbers in photon-photon collisions, and the cosmic background of neutrinos and antineutrinos will regain thermal communion with the rest of the universe.</div>
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Can we really carry this sad story all the way to its end, to a state of infinite temperature and density? Does time really have a stop some three minutes after the temperature reaches a thousand million degrees? Obviously, we cannot be sure. All the uncertainties that we met in the preceding chapter, in trying to explore the first hundredth of a second, will return to perplex us as we look into the last hundredth of a second. Above all, the whole universe must be described in the language of quantum mechanics at temperatures above 100 million million million million million degrees (1032 ° K), and no one has any idea what happens then. Also, if the universe is not really isotropic and homogeneous, then our whole story may have lost its validity long before we would have to face the problems of quantum cosmology.</div>
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From these uncertainties some cosmologists derive a sort of hope. It may be that the universe will experience a kind of cosmic "bounce," and begin to reexpand. In the Edda, after the final battle of the gods and giants at Ragnorak, the earth is destroyed by fire and water, but the waters recede, the sons of Thor come up from Hell carrying their father's hammer, and the whole world begins once more. But if the universe does reexpand, its expansion will again slow to a halt and be followed by another contraction, ending in another cosmic Ragnorak, followed by another bounce, and so on forever.</div>
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If this is our future, it presumably also is our past. The present expanding universe would be only the phase following the last contraction and bounce. (Indeed, in their 1965 paper on the cosmic microwave radiation background, Dicke, Peebles, Roll, and Wilkinson assumed that there was a previous complete phase of cosmic expansion and contraction, and they argued that the universe must have contracted enough to raise the temperature to at least ten thousand million degrees in order to break up the heavy elements formed in the previous phase.) Looking farther back, we can imagine an endless cycle of expansion and contraction stretching into the infinite past, with no beginning whatever.<br />
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Some cosmologists are philosophically attracted to the oscillating model, especially because, like the steady-state model, it nicely avoids the problem of Genesis. It does, however, face one severe theoretical difficulty. In each cycle the ratio of photons to nuclear particles (or, more precisely, the entropy per nuclear particle) is slightly increased by a kind of friction (known as "bulk viscosity") as the universe expands and contracts. As far as we know, the universe would then start each new cycle with a new, slightly larger ratio of photons to nuclear particles. Right now this ratio is large, but not infinite, so it is hard to see how the universe could have previously experienced an infinite number of cycles.<br />
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However all these problems may be resolved, and whichever cosmological model proves correct, there is not much of comfort in any of this. It is almost irresistible for humans to believe that we have some special relation to the universe, that human life is not just a more-or-less farcical outcome of a chain of accidents reaching back to the first three minutes, but that we were somehow built in from the beginning. As I write this I happen to be in an airplane at 30,000 feet, flying over Wyoming en route home from San Francisco to Boston. Below, the earth looks very soft and comfortable—fluffy clouds here and there, snow turning pink as the sun sets, roads stretching straight across the country from one town to another. It is very hard to realize that this all is just a tiny part of an overwhelmingly hostile universe. It is even harder to realize that this present universe has evolved from an unspeakably unfamiliar early condition, and faces a future extinction of endless cold or intolerable heat. The more the universe seems comprehensible, the more it also seems pointless.<br />
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But if there is no solace in the fruits of our research, there is at least some consolation in the research itself. Men and women are not content to comfort themselves with tales of gods and giants, or to confine their thoughts to the daily affairs of life; they also build telescopes and satellites and accelerators, and sit at their desks for endless hours working out the meaning of the data they gather. The effort to understand the universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy.</div>
Algebrahttp://www.blogger.com/profile/11440946058125679273noreply@blogger.com0