Curt Jaimungal: Can Physics Explain Its Own Laws?
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Why do physical laws have the specific form they do?
Why do physical laws have the form that they do? Do we text the universe at two AM and say, hey, you up? Need to talk about fundamental constants. The question seems straightforward since physics ostensibly explains everything else, so what about its own foundations? Here's why I think this innocent query is beguiling and treacherous. Physicists love to point to our explanatory successes, so we have Wigner or Wigner's classification, however it's pronounced, telling us that particles are certain types of representations of certain types of groups. This quote unquote explains why particles have the properties that they do. They're just mathematical consequences of space-time symmetries, yo. And then we have Nother's theorem, which links, again, certain symmetries to conservation law.
Laws under some variational principles. For instance, you may have learned that spatial symmetry gives momentum conservation, and time symmetry gives energy conservation. It's all beautiful, no? Now Nother's theorem is said to quote unquote explain conserved quantities. Firstly, there are problems with defining energy in this manner, and you can click on this video here to watch what energy actually is in general relativity. But here's what many. Many tend to not think about. We're actually facing a Nothers inverse problem. So given a set of conservation laws, can we uniquely determine the symmetries? The answer is no. Multiple Lagrangians can give the same physics, thus the map from the symmetries to the conserved quantities is not invertible.
Now I should say there is actually an inverse Nother's theorem, see Harvey Brown's paper here, his recent work. The problem is that for these inverse Nothers theorems you do require additional constraints, and it doesn't fully resolve the uniqueness issues. Also, there are conservation laws that can exist without variational principles, such as with dissipative systems and conserved quantities that lack a Lagrangian formulation. All of this, of course, presumes we even know what we mean when we say law. Now, is the quote unquote law of the excluded middle is that a law? What if I then called it the rule of excluded middle? Does it lose its lawhood status and gain rulehood? Okay, getting back to it. So, when pressed about why do the laws exist, physicists tend to retreat to grander theories, because why not?
So we have Tegmark's mathematical universe hypothesis. Reality is mathematics to him. Laws are invertible because they're just mathematical structures that exist in some Platonic realm. And every self-consistent mathematical structure exists. As the universe somewhere. I'm not sure he believes this. I did speak to him here. Then there's Lee Smolin's cosmological natural selection. This is where the universe reproduces through black holes with slight mutations in their laws. We see our particular laws because they're going to be optimized for black hole production by following natural selection. And by the way, I've spoken to Lee here. And again, I'm not sure. That even he believes that either. Then there's Wheeler's It from Bit that says that laws somehow emerge from information.
Reality is fundamentally made of yes or no questions or answers to those yes or no questions, and physical laws are somehow patterns in this cosmic questionnaire. And I've spoken not to Wheeler, I've spoken to Amanda Gefter on this topic here, and John Norton himself has critiques here about physics. as information. Now you may think that some of these solve the problem, but in some manner it's probably not satisfying to you. It seems like each is just pushing the problem back. So Tegmark needs to explain, well, why these mathematical structures and not some others, and then Lee Smolin would need to have some meta laws governing the universe's reproduction, and Wheeler as well. So why this information or what governs the laws of information?
Is it just math? Then are we in a subset of the mathematical universe and we inherit all the problems from that? And then of course there's the circularity of did the observers come first?
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Chapters
4 chapters
1
Why do physical laws have the specific form they do?
0:00–5:33
2
What is the ‘justification problem’ for explaining physical laws?
5:33–9:18
3
How do Noether’s theorem and its inverse illustrate limits on explaining laws?
9:18–15:03
4
What philosophical positions (Humean vs. non‑Humean) define a physical law?
15:03–15:15
Speakers
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