The Arrow of Time, Entropy, and Universe Origins

†The origin of time asymmetry in the physical universe has exercised the attention of many of the world's greatest physicists since the time of Maxwell and Boltzmann. The problem is easily stated. Almost all physical processes display a unidirectionality in time, yet the underlying laws of physics (with a minor exception in particle physics) are symmetric in time. How does asymmetry arise from symmetry? Most investigators conclude that the explanation can be traced to the initial conditions of the system concerned. Seeking the ultimate origin of time asymmetry in nature inevitably takes one back to the origin of the universe itself, and the question of the cosmic initial conditions. It seems reasonable to assume that the universe was born in a low-entropy state, like a wound clock, from which it is sliding irreversibly toward a high-entropy state, or heat death, like a clock running down.

Therein lies a puzzle. From what we know about the state of the universe at, say, one second after the big bang, it was very close to thermodynamic equilibrium. Evidence for this comes from the cosmic background heat radiation, which has a Planck spectrum. So at first sight the universe seems to have been born in a high, rather than a low, entropy state. However, first impressions are misleading, because it is necessary to take into account the thermodynamic effects of gravitation. Self-gravitating systems tend to go from smooth to clumpy, so the fact that the early universe was in an almost completely uniform state (disturbed only by the tiny ripples that triggered the growth of large scale structure) suggests that, gravitationally, the universe began in a low-entropy state. If so, then the arrow of time derives ultimately from the initial cosmological smoothness.

Naturally that conclusion begs an explanation: Why did the universe start out smooth and grow clumpy? What created the initial smoothness? One explanation is inflation. According to this theory, the universe jumped in size by a colossal factor in the first split second, a process that would effectively iron out any prior irregularities. However, the inflation process is a product of laws of physics that are symmetric in time, so plausible though this explanation may be, it appears to have smuggled in asymmetry from symmetry. Clearly there is still much room for disagreement on this historic and vexatious topic.

John Wheeler has contributed to the discussion of the arrow of time in a number of ways. Perhaps best known is the work he did in the 1940's with Richard Feynman, formulating a theory of electrodynamics that is symmetric in time. The arrow of time manifests itself in electromagnetic theory through the prevalence of retarded over advanced waves: a radio transmitter, for example, sends waves outwards (into the future) from the antenna. In the Wheeler-Feynman theory, a radio transmitter sends half its signal into the future and half into the past. Causal chaos is avoided by appealing to cosmology. It turns out that given certain cosmological boundary conditions - namely the ability of cosmic matter to absorb all the outgoing radiation and turn it into heat - a frolic of interference between the primary and secondary sources of electromagnetic radiation occurs. This serves to wipe out the advanced waves and build up the retarded waves to full strength. Thus the electromagnetic arrow of time derives directly from the thermodynamic arrow in this theory.

Few physicists and cosmologists can resist taking on the arrow of time problem at some stage, and Andreas Albrecht rises splendidly to the challenge in his Science & Ultimate Reality paper, a summary of which appears below. Personally this is the sort of paper I thoroughly enjoy, because it makes us think really hard about the fundamental basis of physical theory. I have little doubt that Albrecht's ideas will provoke a heated debate, and I greatly look forward to the responses.

†Paul Davies

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†Title: The arrow of time, entropy and the origins of the universe. Author: Andreas Albrecht

†Boltzmann taught us that for familiar physical systems the thermodynamic arrow of time is deeply linked with very special initial conditions: Systems that start out far from equilibrium have an arrow of time as they are drawn toward the equilibrium. Systems that already are in equilibrium do not. Things appear somewhat different on cosmic scales because equilibrium is more elusive for strongly gravitating systems. An isolated black hole may be a good example of a gravitating system in equilibrium, but not much of the matter in the universe is in black holes.† Still, the ultimate origin of the thermodynamic arrow of time in the Standard Big Bang (SBB) cosmology lies with the very special highly homogeneous initial state, which is far removed from the collapsed states to which gravitating systems are attracted.

But now we have inflation which seems to tell the opposite story: Inflation tells us that the initial conditions of the SBB, rather than being unusual, are the generic result of evolution toward an attractor...a kind of equilibrium.† Can we really have it both ways?

A careful analysis of the arrow of time gives a very interesting perspective on current issues in cosmology.† This perspective helps us evaluate what role inflation, holography, or other ideas might ultimately have in explaining the special initial conditions of the Big Bang, and how ideas such as inflation might fit into a global picture that includes the time before inflation and the full range of possible cosmic histories, as well as the cosmic acceleration observed today.

[In my work], I analyze current ideas about the universe in the context of the arrow of time, and discuss the implications of this analysis for our ultimate understanding of the origins of the universe.

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