Can Physics Explain Its Own Laws?

Why do physical laws have the form they do? Do we text the universe at 2AM: “hey, u up? need to talk bout fundamental constantz.”

This question seems straightforward, since physics (supposedly) explains everything else, so why not its own foundations?

This innocent query is beguiling and treacherous. Let me show you why.

The Limits of Explanatory Power

Physicists love to point to our explanatory successes. We have Wigner’s classification telling us that particles are irreducible representations of the Poincaré group:

\( \lvert \psi \rangle \in \mathcal{H}_{\text{mass}, \ \text{spin}}\)

This “explains” why particles have the properties they do. Hey, they’re just mathematical consequences of spacetime symmetries, yo!

We have Noether’s theorem linking (variational principle derived) symmetries to conservation laws:

\(\delta S = 0 \;\Longrightarrow\; \partial_\mu j^{\mu} = 0\)

Spatial translation symmetry gives momentum conservation. Time translation symmetry gives energy conservation. Beautiful, no?

Curt’s aside: There are problems with defining energy in this manner. Watch this video on “what is energy, actually?” or read about it here.

But here’s what most physicists don’t think about: we’re actually facing Noether’s inverse problem. Given a set of conservation laws, can we (uniquely!) determine the symmetries? The answer is no. Multiple Lagrangians can give the same physics. The map from symmetries to conserved quantities isn’t invertible.

Curt’s aside: Though I should note there is an inverse Noether theorem—see Harvey Brown’s more recent work. The problem is that for inverse Noether theorems, you require additional constraints and it doesn’t fully resolve the uniqueness issues. Also, conservation laws can exist without variational principles such as dissipative systems with conserved quantities, but that lack a Lagrangian formulation.

Alternative Theories: Trying to Fill the Gaps

When pressed on why laws exist, physicists retreat to grander theories, because why not?:

Tegmark’s Mathematical Universe Hypothesis: Reality is mathematics. Laws are inevitable because they’re just mathematical structures that exist in some Platonic realm. Every self-consistent mathematical structure exists as a universe somewhere. I’m not sure even he believes this!

Smolin’s Cosmological Natural Selection: Universes reproduce through black holes, with slight mutations in their laws. We see these particular laws because they’re optimized for black hole production. I’ve spoken to him here, and I’m not even sure that he believes this either!

Wheeler’s It-from-Bit: Laws emerge from information. Reality is fundamentally made of yes/no answers to questions, and physical laws are just patterns in this cosmic questionnaire. I’ve spoken to Amanda Gefter on this topic here, and also here are critiques from John Norton.

You may think these solve the problem. Actually, each just pushes it back. Tegmark needs to explain why these mathematical structures and not others. Smolin needs meta-laws governing universe reproduction. Wheeler needs… well, see Norton’s critique I discussed previously. There’s also this article I wrote here on philosophers vs. physicists which has gone semi-viral.

Philosophical Challenges: The True Test of Laws

Here’s where philosophers earn their keep. Putnam’s model-theoretic argument shows that even if physics could derive all its laws from some fundamental principle, we couldn’t know if we’d found the “true” explanation.

The reasoning is that any theory T that explains our observations has multiple models. You can think of these different ways of mapping the theory’s terms onto reality. This was one of the reasons Putnam thought that the Lowenheim-Skolem theorem wasn’t a mere mathematical curiosity like most did/do. Here’s an article on that:

The real philosophical meat is in what we even mean by “law”… But you’re a clever chap, so you saw that coming… Darn. You make me work hard.

The Nature of Laws: Definitions Under Scrutiny

When physicists say “law,” they usually mean something like F = ma.

But philosophers have been sharpening their knives on this concept for decades:

Humean view: Laws are just patterns in the mosaic of events. They describe regularities but don’t govern anything. David Lewis championed this—laws are whatever gives us the best combination of simplicity and strength in systematizing facts.

Non-Humean view: Laws have genuine oomph. They’re not just descriptions but prescriptive constraints on what can happen. Armstrong argues laws are relations between universals that necessitate their instances.

The recent Chen (2023) paper on “Laws of Physics” frames fundamental laws as constraints on physical possibilities. I’ve spoken to him along with Barry Loewer on this exact topic of what constitutes the laws of physics here. But do you think this is recursive? Are we defining laws in terms of what’s physically possible, which is itself defined by… the laws? (By the way, there’s this article here on the unexamined “in principle.”)

Curt’s aside: I’m unsure if F=ma is more a definition of force than a result/law but that’s a story for another day. Subscribe to hear more about that.

Fundamental Explanations: The Quest for the Core

The problem isn’t that physics can’t explain its laws. It’s that the very concept of “explanation” seems to presuppose some regularity. Regularities also seem to be another word for “law” or at least “law-like.”

Curt’s aside: It’s like asking if “influencer” is a job or just unemployment with better photos.

Think about it. What does it mean to explain something? Generally speaking, you connect it to something else via some reliable pattern—a law. So, for instance, to explain why an apple falls, you invoke gravity. To explain gravity, you invoke curved spacetime. To explain why spacetime curves… you need more laws. It’s a Russian nesting doll made of disappointment.

Even distinguishing laws from “accidents” itself presupposes laws! Why? You can’t say “this is a law, not a mere accident” without already having criteria for what constitutes a law (philosophers call this “lawhood”), which themselves must be grounded in… laws.

I understand that Barry Loewer tried to escape this. Loewer’s “package deal account” says we get laws and natural properties together, bootstrapping our way out of circularity. Is this just pushing the problem back? Do you now need to explain why this package and not another? I don't know as I don't grasp the concept yet but I'm letting you know about it anyhow in case you're interested in learning more or filling in my benightedness!

Agrippa’s Trilemma: The Philosophical Deadlock

Part of the issue is that whatever justification you have will seemingly always have problems. This is just Agrippa’s trilemma (also known as Münchhausen’s trilemma) applied to physics:

1. Infinite regress: Each law explained by deeper laws, forever

2. Circular reasoning: Laws eventually explain themselves

3. Dogmatic assertion: Some laws are just brute facts

None of these are satisfactory to most people. At least most people that I talk to.

Most physicists either consciously or unconsciously choose option 3. “The universe just has these symmetries”—but is this an explanation? Or is this an admission of explanatory defeat dressed up as profundity?

Curt’s aside: It’s like asking why logic is logical. The question uses the very thing it’s questioning. You can’t stand outside logic to examine it objectively because your examination would itself need to be logical (or illogical, in which case, good luck with that—or you can be “extra”-logical, perhaps touching something theological where reason gives way to faith, as Kierkegaard would say). Note that I’ve spoken to Jonathan Pageau about this here, because Jonathan constantly asks the question of “from where do you stand?” when making a critique or a claim, whether against God, for God, for “science”, etc. Many of us think we stand from some objective place of nowhere, but Jonathan believes we always have assumptions and values which dictate any perspective.

There are actually ways of getting around this trilemma, but I’ll explore these more later. Feel free to subscribe to the Substack to get notified.

Modern Theories: Attempts and Failures

Recent papers/theories keep trying to square this circle:

“Law Without Law” appeals to emergent regularities from quantum mechanics. But QM itself has laws (Schrödinger equation, Born rule). “Law without law” is like “alcohol-free beer”—like, why are you even here?

QBist approaches say laws are features of our beliefs, not reality. This dissolves the problem by denying there’s anything to explain. Though I am glad it allows me to say “It’s not you, it’s quantum mechanics” as a valid breakup line.

There are more and I'll fill this in later. Feel free to help me out in the comments.

The Real Question: Beyond Physics

Perhaps asking physics to explain its own laws is like asking a system to step outside itself and justify its own foundations. Perhaps it’s asking English to explain why it has grammar (though Elan Barenholtz has some thoughts on this).

Does the concept of “explanation” itself presupposes lawhood? If explanation means “subsumption under laws,” then asking for an explanation of laws is asking laws to subsume themselves. PS: I’ve tried to subsume myself. It’s not pretty. Still hurts.

Anyhow, I’m deeply interested in this entire line of line of thinking because I believe it will lead us to revelations about what it means to explain and to understand in general. I think what explanation is itself, is actually at the heart of what one wants when one searches for a theory of everything, a theory of nature, or even purpose.

Thus, the impossibility of physics explaining its own laws isn’t a failure of physics. I view it more optimistically. I view it as a success of clear thinking about what explanation can (and can’t) do/be.

Implications for Theories of Everything

Basically, every theory of everything faces this problem. Even if we found unique mathematical structures that give our universe, we’d need to explain:

• Why mathematics at all?

• Why these mathematical structures have physical instantiation?

• Why the correspondence between math and physics? (NOTE: coming up shortly will be my critiques of the so-called unreasonable effectiveness of mathematics, so subscribe to my Substack if you’re interested)

• If anything else occurs to you, let me know in the comments below…

The usual move is to declare one of these “fundamental” and stop asking questions. That’s fine for doing physics. But it’s intellectual surrender for understanding reality. It may even be moral surrender, though I haven’t made up my mind on that one.

Perhaps the real lesson is that explanation has limits. Math has limits (in some Gödelian sense). Science has limits (in some Putnamian sense). Perhaps the same goes for explanation in general. Not because we’re cretinous or haven’t found the correct theory, but because explanation by its nature is a concept that only makes sense within a broader scaffolding of regularities.

Remember the opening question: “Why do physical laws have the form they do?”

The answer isn’t that we don’t know yet, or that we need a better theory. Any possible answer would itself be a law, requiring its own explanation. At least, this is my present deliberation. Subject to change pending new explanations.

I want to hear from you in the Substack comment section below. I read each and every response.

—Curt Jaimungal

PS: If you think you’ve found a way around this, ask yourself: does your solution assume any regularities, patterns, or consistencies? If yes, you’ve assumed what you’re trying to explain. If no, then how is it an explanation?

PPS: This connects to why consciousness is so puzzling. Explaining consciousness seems to require standing outside experience to view it objectively. It seems like any such viewing would itself be an experience. It’s Agrippa’s trilemma in phenomenological drag.

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