Difference between revisions 5702388 and 5772174 on simplewikiThe idea of the heat death of the universe, proposed in 1851 by [[w:William Thomson, 1st Baron Kelvin|William Thomson]], stems from the [[second law of thermodynamics]], which states that [[heat]] tends to pass from hotter to colder bodies and eventually becomes uniformly distributed. As an elementary particle of matter (such as a proton) self‑gravitationally shrinks, its heat becomes intensified ("augmented") to a higher temperature and then radiated away into the ambient vacuum:
(contracted; show full)ond law of thermodynamics]], heat tends to pass from hotter to colder bodies. So, when a portion of the zero‑temperature heat self‑gravitationally shrinks to a nonzero temperature, a half of the resultant nonzero‑temperature heat becomes radiated into the colder ambient vacuum, at which moment the particle of nonzero‑temperature heat undergoes self‑gravitational shrinkage to a still higher temperature.<ref>Böhm-Vitense, Erika. [https://books.google.co
.ukm/books?id=msZMEvEpxG8C&pg=PA29 Introduction to Stellar Astrophysics]. CUP, 1992, p. 29. "After each infinitesimal step of collapse the star has to wait until it has radiated away a half of the released gravitational energy before it can continue to contract."</ref> Thus the temperature difference between the self‑gravitationally shrinking particle and the ambient vacuum increases, which increases the rate of heat loss and thereby accelerates the particle's self‑g(contracted; show full)
We walk the stage of life, performers of a drama for the benefit of the cosmic spectator. As the scenes proceed he notices that the actors are growing smaller and the action quicker. When the last act opens the curtain rises on midget actors rushing through their parts at frantic speed. Smaller and smaller. Faster and faster. One last microscopic blurr of intense agitation. And then nothing.
:—Eddington, Arthur. [https://books.google.co
.ukm/books?id=KHyV4-2EyrUC&pg=PA90 The Expanding Universe] CUP, 1933, pp. 90–92
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When the above-described exponentially accelerating shrinkage and radiative "evaporation" of positive‑actual‑energy protons into the negative‑potential‑energy ambient vacuum comes to an end, the universe again has the maximal (''i.e.'', zero) potential energy, and the minimal (''i.e.'', zero) actual energy. Such a universe is in a state of '''heat death''' and exists as a uniform blanket of zero-temperature heat. The 13.8‑billion‑year‑long gravitational life cycle then begins anew. And so ''ad infinitum''.
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For stable equilibrium the gravitational potential energy of the system must be a minimum.<ref>Barker, George Frederick. [https://books.google.co.ukm/books?id=bKEAAAAAMAAJ&q=%22for+stable+equilibrium+the+potential+energy+of+the+system+must+be+a+minimum%22 Physics: Advanced Course]. Henry Holt, 1893, p. 202</ref> In the case of multiple protons, the gravitational potential energy is proportional to the radius of a single proton and to the spatial separation of protons.<ref>Thomson, it will be remembered, stores his heat in the form of the potential energy of separation of the elements of the sun.</ref> Thus, the continuum's pro(contracted; show full)ely with time, so that the rate of heat loss exponentially decreased. This insouciant view was overturned by [[w:Jonathan Homer Lane|Jonathan Homer Lane]], who in 1870 discovered that the temperature of a self‑gravitating perfect-gas sphere is inversely proportional to its radius: ''rT''(''r'') = ''constant''. This equation is known as Lane's law.<ref>Reid, Neill I. Hawley, Suzanne L. [https://books.google.co
.ukm/books?id=04_aBwAAQBAJ&pg=PA84 New Light on Dark Stars: Red Dwarfs, Low-Mass Stars, Brown Dwarfs]. Springer, 2013, p. 84</ref> For example, when the sphere's radius (''r'') decreases tenfold, the sphere's temperature (''T'') increases tenfold:
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Lane reached the apparently paradoxical result that a star by losing heat and contracting actually grew hotter. A star shrinking under gravitation to half its linear size and remaining built on the same model, or "homologous" (i.e., the densities at two corresponding points at any two stages remaining the same fraction of the mean density) would be eight times as dense, and the internal pressures would be sixteen times as great as the overlying material is attracted four times as strongly and its weight is held up on only a quarter of the area. From the formula connecting temperature with pressure and density, given earlier in the chapter, it will be seen that the temperature in this example would be twice as great. By such reasoning, Lane concluded that as stars get smaller they grow hotter to withstand gravitation and resist collapse.
:—Doig, Peter. [https://www.archive.org/stream/outlineofstellar031648mbp#page/n95/mode/2up An Outline of Stellar Astronomy] Hutchinson, 1947, p. 76
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The [[Stefan–Boltzmann law]] (1879) dictates that the rate at which a unit surface area of the self‑gravitationally condensing sphere radiates away heat is proportional to the fourth power of the sphere's temperature. So, even after taking into account that the sphere's surface area decreases a hundredfold (as the square of the radius), Lane's law implies that, '''when the self‑gravitating sphere's radius shrinks tenfold, the sphere's total radiative heat loss per unit time increases a hundredfold'''.
In addition, the gravitational potential energy of a self‑gravitationally collapsing uniform sphere is proportional to its radius ''R'':
:<math>U=-\frac{3GM^2}{5R}</math>
That is why the tenfold decrease in the radius implies that the amount of generated collapse‑impeding actual energy decreases tenfold. Therefore, '''when the self‑gravitating sphere's radius shrinks tenfold, the speed of the sphere's collapse increases a thousandfold'''.
In 1983, numerical calculations on large computers predicted that as the temperature is raised the colour‑repelling physical vacuum should flip into the simple vacuum, of which protons consist, at a temperature of 2 × 10<sup>12</sup> K.<ref>Willis, Bill. [https://books.google.co.ukm/books?id=F0aIiC-z5_kC&pg=PA10 Collisions to melt the vacuum]. ''New Scientist'', 3 October 1983, p. 10</ref> From the [[Stefan–Boltzmann law]] it follows that a body as hot as the proton must be radiating away its energy at a frantic pace and shrink accordingly. To an observer consisting of such rapidly shrinking protons, intergalactic spaces must appear to be expanding with an exponential acceleration. In 1998, [[w:Adam Riess|Adam Riess]] and his team discovered that the appa(contracted; show full)*[[Minimum total potential energy principle]]
==References==
{{Reflist}}
[[Category:Cosmology]]
[[Category:Thermodynamics]]
[[Category:Universe]]
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