The idea of heat death stems from the second law of thermodynamics, which states that entropy tends to increase in an isolated system. If the universe lasts for a sufficient time, it will asymptotically approach a state where all energy is evenly distributed. In other words, in nature there is a tendency to the dissipation (energy loss) of mechanical energy (motion); hence, by extrapolation, there exists the view that the mechanical movement of the universe will run down in time due to the second law. The idea of heat death was first proposed in loose terms beginning in 1851 by William Thomson, who theorized further on the mechanical energy loss views of Sadi Carnot (1824), James Joule (1843), and Rudolf Clausius (1850). Thomson’s views were then elaborated on more definitively over the next decade by Hermann von Helmholtz and William Rankine.
History
The idea of heat death of the universe derives from discussion of the application of the first two laws of thermodynamics to universal processes. Specifically, in 1851 William Thomson outlined the view, as based on recent experiments on the dynamical theory of heat, that “heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect.” [1]
William Thomson (Lord Kelvin) - originated the idea of universal heat death in 1852.
In 1852, Thomson published his “On a Universal Tendency in Nature to the Dissipation of Mechanical Energy” in which he outlined the rudiments of the second law of thermodynamics summarized by the view that mechanical motion and the energy used to create that motion will tend to dissipate or run down, naturally.[2] The ideas in this paper, in relation to their application to the age of the sun and the dynamics of the universal operation, attracted the likes of William Rankine and Hermann von Helmholtz. The three of them were said to have exchanged ideas on this subject.[3] In 1862, Thomson published the article “On the age of the sun’s heat” in which he reiterated his fundamental beliefs in the indestructibility of energy (the first law) and the universal dissipation of energy (the second law), leading to diffusion of heat, cessation of motion, and exhaustion of potential energy through the material universe while clarifying his view of the consequences for the universe as a whole. The key paragraph is:[4]
The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping for ever.
In the years to follow both Thomson’s 1852 and the 1865 papers, Helmholtz and Rankine both credited Thomson with the idea, but read further into his papers by publishing views stating that Thomson argued that the universe will end in a “heat death” (Helmholtz) which will be the “end of all physical phenomena” (Rankine).[3][5]
Temperature of the universe
In a "heat death", the temperature of the entire universe would be very close to absolute zero. Heat death is, however, not quite the same as "cold death", or the "Big Freeze", in which the universe simply becomes too cold to sustain life due to continued expansion, though the result is quite similar.[6] For a "heat death" to occur, proton decay must take place.
Current status
Inflationary cosmology suggests that in the early universe, before cosmic expansion, energy was uniformly distributed,[7] and thus the universe was in a state superficially similar to heat death. However, the two states are in fact very different: in the early universe, gravity was a very important force, and in a gravitational system, if energy is uniformly distributed, entropy is quite low, compared to a state in which most matter has collapsed into black holes. Thus, such a state is not in thermal equilibrium, and in fact there is no thermal equilibrium for such a system, as it is thermodynamically unstable.[8][9] However, in the heat death scenario, the energy density is so low that the system can be thought of as non-gravitational, such that a state in which energy is uniformly distributed is a thermal equilibrium state, i.e., the state of maximal entropy.
The final state of the universe depends on the assumptions made about its ultimate fate, and these assumptions have varied considerably over the late 20th century and early 21st century. In a "closed" universe that undergoes recollapse, a heat death is expected to occur, with the universe approaching arbitrarily high temperature and maximal entropy as the end of the collapse approaches. In an "open" or "flat" universe that continues expanding indefinitely, a heat death is also expected to occur, with the universe cooling to approach absolute zero temperature and approaching a state of maximal entropy over a very long time period. There is dispute over whether or not an expanding universe can approach maximal entropy; it has been proposed that in an expanding universe, the value of maximum entropy increases faster than the universe gains entropy, causing the universe to move progressively further away from heat death.[citation needed] Finally, some models of dark energy cause the universe to expand in ways that result in some amount of usable energy always being available, preventing the universe from ever reaching a state of maximum entropy.[citation needed] The expectation of the scientific community as of 2007 is that the universe will continue expanding indefinitely.[citation needed]
Timeline for heat death
The Primordial Era, from the Big Bang to 155 million years after the Big Bang
The Primordial Era is the first Era of the Universe. There are no galaxies or stars in the Primordial Era. In this era, the Big Bang, the subsequent inflation, and Big Bang nucleosynthesis are thought to have taken place. Toward the end of this age, the recombination of electrons with nuclei made the universe transparent for the first time.
The Stelliferous Era, from 155 million years to 1014 (100 trillion) years after the Big Bang
This era, which we are currently inhabiting, is the time in which stars are formed from collapsing clouds of gas. About 155 million years after the Big Bang, the first star formed. After its formation, a star will begin to fuse some of its gas. Stars whose mass is very low will eventually exhaust all their fusible hydrogen and then become heliumwhite dwarfs.[10] Stars of low to medium mass will expel some of their mass as a planetary nebula and eventually become a white dwarf; more massive stars will explode in a core-collapse supernova, leaving behind neutron stars or black holes.[11] In any case, although some of the star's matter may be returned to the interstellar medium, a degenerate remnant will be left behind whose mass is not returned to the interstellar medium. Therefore, the supply of gas available for star formation is steadily being exhausted.
The Milky Way Galaxy and the Andromeda Galaxy merge into one galaxy: 3 billon years from now
The Andromeda Galaxy is currently approximately 2.5 million light years away from our galaxy, the Milky Way Galaxy, and is moving towards it at approximately 120 kilometers per second. Approximately three billion years from now, or approximately 1.7×1010 (17 billion) years after the Big Bang, the Milky Way and the Andromeda Galaxy may collide with one another and merge into one large galaxy. Because it is not known precisely how fast the Andromeda Galaxy is moving transverse to us, it is not certain that the collision will happen.[12]
Coalescence of Local Group: 1011 (100 billion) to 1012 (1 trillion) years
The galaxies in the Local Group, the cluster of galaxies which includes the Milky Way and the Andromeda Galaxy, are gravitationally bound to each other. It is expected that between 1011 (100 billion) and 1012 (1 trillion) years from now, their orbits will decay and the entire Local Group will merge into one large galaxy.[13], §IIIA.
Galaxies outside the Local Supercluster are no longer detectable in any way: 2×1012 (2 trillion) years
Assuming that dark energy continues to make the Universe expand at an accelerating rate, 2×1012 (2 trillion) years from now, all galaxies outside the Local Supercluster will be red-shifted to such an extent that they are no longer detectable in any way.[14]
The Degenerate Era, from 1014 (100 trillion) to 1040 years from now
Approximately 1014 (100 trillion) years from now, star formation will end, leaving all stellar objects in the form of degenerate remnants. This period, known as the Degenerate Era, will last until the degenerate remnants finally decay.[13], § III–IV.
Star formation ceases: 1014 (100 trillion) years
It is estimated that in 1014 (100 trillion) years or less, star formation will end.[13], §IID. The least massive stars take the longest to exhaust their hydrogen fuel (see stellar evolution). Thus, the longest living stars in the Universe are low-mass red dwarfs, with a mass of about 0.08 solar masses, which have a lifetime of between 1013 (10 trillion) and 2×1013 (20 trillion) years.[13] §IIA. Coincidentally, this is comparable to the length of time over which star formation takes place.[13] §IID. Once star formation ends and the least massive red dwarfs exhaust their fuel, nuclear fusion will cease. The low-mass red dwarfs will cool and become white dwarfs.[10] The only objects remaining with more than planetary mass will be brown dwarfs, with mass less than 0.08 solar masses, and degenerate remnants: white dwarfs, produced by stars with initial masses between about 0.08 and 8 solar masses, and neutron stars and black holes, produced by stars with initial masses over 8 solar masses. Most of the mass of this collection, approximately 90%, will be in the form of white dwarfs.[13] §IIE. In the absence of any energy source, all of these formerly luminous bodies will cool and become faint.
The Universe will become extremely dark after the last star burns out. Even so, there can still be occasional light in the Universe. One of the ways the Universe can be illuminated is if two carbon-oxygen white dwarfs with a combined mass of more than the Chandrasekhar limit of about 1.4 solar masses happen to merge. The resulting object will then undergo runaway thermonuclear fusion, producing a Type Ia supernova and dispelling the darkness of the Degenerate Era for a few weeks.[13] §IIIC;[15] If the combined mass is not above the Chandrasekhar limit but is larger than the minimum mass to fuse carbon (about 0.9 solar masses), a carbon star could be produced, with a lifetime of around 106 (1 million) years.[16], p. 91 Also, if two helium white dwarfs with a combined mass of at least 0.3 solar masses collide, a helium star may be produced, with a lifetime of a few hundred million years.[16], p. 91 Finally, if brown dwarfs collide with each other, a red dwarf star may be produced which can survive for over 1013 (10 trillion) years.[13] §IIIC.
Stellar remnants escape galaxies or fall into black holes: 1019 to 1020 years
Over time, brown dwarfs and stellar remnants will pass close to each other. When this happens, the trajectories of the objects involved in the close encounter change silghtly. After a large number of encounters, lighter objects tend to gain kinetic energy while the heavier objects lose it. Objects which gain enough energy will reach galactic escape velocity and depart the galaxy, leaving behind a smaller, denser galaxy. Since encounters are more frequent in the denser galaxy, the process then accelerates. The end result is that most objects are ejected from the galaxy, leaving a small fraction (approximately 1%) which fall into the central supermassive black hole. This process is expected to take from 1019 to 1020 years.[13], §IIIA;[16], pp. 85–87
The supermassive black holes are all that remains of galaxies once all protons decay, but even these giants are not immortal.
Protons start to decay: >1032 years
The subsequent evolution of the universe depends on the existence and rate of proton decay. Experimental evidence shows that if the proton is unstable, it has a half-life of at least 1032 years.[17] If a Grand Unified Theory is correct, then there are theoretical reasons to believe that the half-life of the proton is under 1041 years.[13], §IVA. If not, the proton is still expected to decay, for example via processes involving virtual black holes, with a half-life of under 10200 years.[13], §IVF The rest of this timeline assumes that the proton half-life is approximately 1037 years.[13], §IVA. Shorter or longer proton half-lives will accelerate or retard the process.
Half of all protons and neutrons decay: 1037 years
Given the above assumption on the half-life of the proton, one-half of all baryonic matter has now been converted into gamma radiation and leptons through proton decay.
All protons and neutrons decay: 1040 years
Given our assumption on the half-life of the proton, protons (and bound neutrons as well)[13], §IVA will have undergone roughly 1,000 half-lives by the time the universe is 1040 years old. To put this into perspective, there are an estimated 1080 protons currently in the Universe.[18] This means that the number of nucleons will be slashed in half 1,000 times by the time the universe is 1040 years old. Hence, there will be roughly ½1,000 (approximately 10–301) as many nucleons remaining as there are today; that is, zeronucleons remaining in the Universe at the end of the Degenerate Age. Effectively, all baryonic matter has been changed into photons and leptons.
The Black Hole Era, from 1040 years to 1.7x 10106 years from now
At about 1040 years, black holes will dominate the Universe. They will slowly evaporate via Hawking radiation. The lifetime of a black hole is proportional to the cube of its mass, so larger black holes take longer to decay.[19] A black hole with a mass of around 1 solar mass will vanish in around 2×1066 years, while a supermassive black hole with a mass of over 1011 solar masses (a typical galaxy mass) will evaporate in roughly 10100 years.[13], § IVG.
Hawking radiation has a thermal spectrum. During most of a black hole's lifetime, the radiation has a low temperature and is mainly in the form of massless particles such as photons and gravitons. As the black hole's mass decreases,
its temperature increases, becoming comparable to the Sun's by the time the black hole mass has decreased to 1019kilograms. The hole then provides a temporary source of light during the general darkness of the Black Hole Era. During the last stages of its evaporation, a black hole will emit not only massless particles but also heavier particles such as electrons, positrons, protons and antiprotons.[16], pp. 148–150.
The Dark Era, more than 1.7x 10106 years from now
The lowly photon is now king of the Universe as the last of the supermassive black holes evaporate.
After all the black holes have evaporated (and after all the ordinary matter made of protons has disintegrated, if protons are unstable), the universe will be nearly empty. Photons, neutrinos, electrons and positrons will fly from place to place, hardly ever encountering each other. It will be cold, and dark, and there is no known process which will ever change things.
By this era, with only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with very low energy levels and very large time scales. Electrons and positrons drifting through space will encounter one another and occasionally form positronium atoms. These structures are unstable, however, and their constituent particles must eventually annihilate.[13], §VF3. Other low-level annihilation events will also take place, albeit very slowly.
The Universe now reaches an extremely low-energy state. What happens after this is speculative. It's possible that a Big Rip event may occur far off into the future. Also, the Universe may enter a second inflationary epoch, or, assuming that the current vacuum state is a false vacuum, the vacuum may decay into a lower-energy state.[13], §VE. Finally, the Universe may settle into this state forever, achieving true heat death.
Alternative futures of the universe
Alternative times from Freeman Dyson's "Time Without End: Physics and Biology in an Open Universe"[20], from 101500 to 10(101100) years:
101500 years—the estimated time until all matter decays to 56Fe (if the proton does not decay). See isotopes of iron.
10(1026) years—low estimate for the time until all matter collapses into black holes, assuming no proton decay.
10(1076) years—high estimate for the time until all matter collapses into neutron stars or black holes, again assuming no proton decay.
10(101100) years—scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing a black hole with the estimated mass of our entire universe. This time assumes a statistical model subject to Poincaré recurrence. A much simplified way of thinking about this time is that in a model where our universe's history repeats itself arbitrarily many times due to the properties of statistical mechanics, this is the time scale when it will first be somewhat similar (for a reasonable choice of "similar") to its current state again.
The Last Question, a short story by Isaac Asimov which considers the inevitable oncome of heat death in the universe and how it may be reversed.
References
^Thomson, William. (1951). “On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule’s equivalent of a Thermal Unit, and M. Regnault’s Observations on Steam.” Excerpts. [§§1-14 & §§99-100], Transactions of the Royal Society of Edinburgh, March, 1851; and Philosophical Magazine IV. 1852, [from Mathematical and Physical Papers, vol. i, art. XLVIII, pp. 174]
^How Massive Single Stars End Their Life, A. Heger, C. L. Fryer, S. E. Woosley, N. Langer, and D. H. Hartmann, Astrophysical Journal591, #1 (2003), pp. 288–300.
^Life, the Universe, and Nothing: Life and Death in an Ever-expanding Universe, Lawrence M. Krauss and Glenn D. Starkman, Astrophysical Journal, 531 (March 1, 2000), pp. 22–30. doi:10.1086/308434. Bibcode:2000ApJ...531...22K.
^Solution, exercise 17, One Universe: At Home in the Cosmos, Neil de Grasse Tyson, Charles Tsun-Chu Liu, and Robert Irion, Washington, D.C.: Joseph Henry Press, 2000. ISBN 0-309-06488-0.
^ abParticle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole, Don N. Page, Physical Review D13 (1976), pp. 198–206. doi:10.1103/PhysRevD.13.198. See in particular equation (27).
^Time without end: Physics and biology in an open universe, Freeman J. Dyson, Reviews of Modern Physics51 (1979), pp. 447–460, doi:10.1103/RevModPhys.51.447.
.jpg)
