What is Fundamental

The goal of fundamental physics is to find a few simple concepts that can explain everything. One popular concept is the idea of a dynamical equation, which in prin­ciple explains one moment in terms of another moment.

Some physicists try to deny any special starting point, and just treat our universe as one possible string of events. In this account, the whole history of our universe could be like the outcome of some lottery machine, with no fundamental explanation as to why things are this way and not some other. But we know how to analyze such situations, using randomness, and it predicts a universe completely at odds with what we actually observe. Our universe is not random after all.

The solution to this dilemma is clear, as outlined in the previous section. At minimum, we need to add a fundamental boundary explanation to the dynamics— the ‘starting point’ from which the dynamics can finish the explanatory job. The typical form of boundaries in physics is exactly the form that we need at the Big Bang: smooth and boring, at least for half of the parameters in the microstate. If we accept this boundary as a given, we can not only explain what we see, but we can also explain the Second Law of Thermodynamics itself. And with it, an explanation of why our forward-time predictions are so successful, despite vastly incomplete knowledge.

Once one is willing to accept boundary explanations as being fundamental, other new perspectives become available. In classical physics, our dynamical equations are arguably less fundamental than the boundary-constrained Lagrangian density that generates them. In this “Lagrangian Schema”, it’s actually the boundary constraint and the Lagrangian density (and a globally extremized action) that are fundamental— dynamical laws are merely a consequence.

There’s a subtle but intriguing difference between the Lagrangian perspective and that of simply adding an initial boundary to classical dynamics. In the Lagrangian case, one puts a boundary around the whole of spacetime, not just in the past. Fur­thermore, when using a Lagrangian, one only constrains half the parameters on each boundary; the other parameters on the boundary are determined by the solution to the whole problem. If we took boundaries more seriously, this perspective might even indicate that dynamical explanations were not as fundamental as we might have thought; they might be subsumed by a deeper combination of boundary- and action-explanations.

And it really does matter which types of explanations are most fundamental, for that is the level of our most basic physical hypotheses, the level at which we should consider model modifications. Those who think that dynamical explanations are most fundamental routinely consider the form of those dynamics; they frame the debate between deterministic equations and stochastic equations, between linear and non-linear evolution. But the corresponding debates on boundary explanations have been sadly lacking, especially those framed in the Lagrangian Schema. Should we consider boundaries that allow for many possible global solutions, and then apply the equal a priori postulate exactly once, to all possible histories? [20] Or should we consider boundaries that determine everything else, down to the last exact detail? [21] Debates over modifications to action-explanations are also lacking, despite promising unexplored territory [22].

But even outside the Lagrangian Schema, dynamical explanations are not enough, and random explanations are no explanations at all. All known explanatory schemas need to utilize boundaries as a fundamental feature—without them, they fall apart. The conclusion is simple: Fundamental boundary explanations need to be taken seriously and literally. Instead of looking for some dynamical explanation of those boundaries—or worse, a random anthropic explanation—we should think about physics that uses boundaries as fundamental ingredients. Our cosmological bound­ary is as fundamental and non-random as anything we have yet discovered. Only by treating it that way can we move forward in developing even more fundamental explanations of our universe.

Acknowledgements The author would like to thank the Foundational Questions Institute, the Fetzer Franklin Fund, and the Peter & Patricia Gruber Foundation for hosting and sponsoring these always-interesting contests. Further thanks are due to those who led to improvements in this published version of the essay: Zeeya Merali, Alyssa Ney, Dean Rickles, and everyone else who commented on the original version.