Introduction

The question of what is meant by a “fundamental” physical theory is more easily answered in the negative—after all, anyone can dream up a theory that clearly isn’t fundamental. Suppose some physicists thought they had discovered the ultimate theory, and could boil it down to a few sentences.

Obviously, no one would hail such a proposal as a breakthrough in fundamen­tal physics. Far from explaining everything, it would explain absolutely nothing. Besides, we already know it’s not true. Our best physical theories have revealed beau­tiful symmetries and mathematical patterns that are at least approximately encoded in the mathematical version of the rules that govern our universe—symmetries that belie any plausible claim of random-rule-generation.

Another group of physicists might try to incorporate these symmetries into a sim­ilar claim. “Of all the possible rules that respect these symmetries,” they might argue, “our universe has picked some at random, and those are the rules we observe!” Again, not a very impressive claim for a fundamental breakthrough. The next sections will

K. Wharton (B)

Department of Physics and Astronomy, San Jose State University, San Jose, CA 95192-0106, USA

e-mail: kenneth.wharton@sjsu.edu © Springer Nature Switzerland AG 2019

A. Aguirre et al. (eds.), What is Fundamental?, The Frontiers Collection, https://doi.org/10.1007/978- 3- 030-11301- 8_14 explore why we don’t find such explanations satisfying on a fundamental level, but the main reason should be broadly obvious: random explanations are necessarily the absence of fundamental explanations. Our most fundamental explanations purport to be non-random, to explain “Why this, and not that?”.

This point might hardly seem worth developing into an entire essay. A few string theorists might take a position similar to that of the previous paragraph, but they would be in the minority. And yet many physicists, I will argue, have fallen into an essentially similar line of reasoning. Certain aspects of our universe, it is commonly thought, should only be explained via randomness—and to the extent that such “random explanations” are not available, it is thought to be a serious problem.

This essay takes the opposing view, arguing that the very concept of a “random explanation” is as meaningless as the above suggestions concerning random laws of physics. Randomness is only a useful rule of thumb if there is nothing fundamental to explain. If there is something fundamental or interesting to explain, randomness cannot possibly do the job.

These are probably ‘fighting words’ for many people familiar with statistical mechanics, a branch of physics essentially built upon randomness. Its fundamental starting point, after all, is something often called the “equal a priori probability postulate”: when you don’t know any better, all possibilities are equally probable. It is commonly accepted that statistical mechanics explains the laws of thermodynamics, which would seem to be a clear counter-example.

But is this explanation really coming from randomness? The First Law of ther­modynamics is essentially just a statement of energy conservation. And we have excellent non-random explanations for this feature of our universe. Thanks to Emmy Noether, we know it nicely follows from a time-translation-symmetry. The essential use of the equal a priori probability postulate is to explain the Second Law of ther­modynamics, the fact that entropy always increases. And, to the eternal concern and seeming bemusement of many physicists, the logical steps from randomness to the Second Law are known to be faulty! They fail without the addition of something to break the time-symmetry, something to single out the future as being different from the past—specifically, the “Past Hypothesis” that entropy was much lower near the Big Bang [1-3].

In response to this failure, many physicists argue that some other “random expla­nation” is required to complete the derivation of the Second Law. This essay argues that this is neither possible nor desired. First, we will delve into different types of explanation, where randomness makes sense and where it fails. It works best when aligned with the Second Law, a fact that makes it particularly ill-suited to explaining the Second Law itself. For that, we need the Past Hypothesis: something true about our universe that is essentially the opposite of random, pointing us towards another type of fundamental explanation. Following this logic leads to the conclusion that we should take a much closer look at boundary constraints, one of our best non-random explanations, and arguably one of the most fundamental.

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