Lately, in between the despair of the modern world and deciding what to eat, my mind found for itself another source of uncertainty to obsess over. This one’s a holdover from my physics days: why are the laws and constants of physics such as they are? I used to subscribe to the Weak Anthropic Principle: if the laws of physics were different, we wouldn’t be around to ask the question, so don’t worry about it. This is in contrast to the Strong Anthropic Principle which states that any universe must allow for intelligent observers. (I still hold that this is a weird leap of faith.) As I read bits of different metaphysics, the WAP is becoming less and less satisfying.

If you accept the WAP, then since we have no evidence that the parameters of our universe couldn’t have been different (unless you believe in a grand creator which renders all of this moot), you have to accept that either:

  1. We got really, really, extraordinarily lucky that the universe ended up being one that supports intelligent life as we know it.
  2. There are a multitude or infinity of universes with all manner of laws and/or constants of nature, and we are, naturally, in one that supports intelligent life as we know it.

Extremely improbable outcomes realistically only occur if there are extremely many rolls of the hyper-dice. So in grad school, I rejected the first alternative, but the second was enough for me. These days I have to wonder, why should we believe in multiverse or big bounce theories aside from the fact they make the WAP believable? They’re only a subset of many valid models that accurately account for our best tests and observations. So we actually can’t rely on it for supporting the WAP.

So what’s my take now? I hold out hope (faith?) that there’s a theory of everything to be discovered that would prove that the laws of nature are necessary – any other form would have inconsistencies. And a corollary: the constants in those laws are necessary. Any other values would lead to inconsistencies. And these values are going to be constrained by the laws, not because there are arbitrary magic values.

General relativity serves as an illustrative example here as it’s a complete theory of gravity. It’s a theory that derives from a simple proposition: the universe is geometric. Super-obvious, right? It’s just that curvy geometry wasn’t well-explored at the time, so Einstein had to invent new math. And what popped out was a beautiful theory of a form that is necessary given its basic assumptions, and this force called gravity emerges with all its nuances and surprising predictions which are continually being validated by experiments.

So why do we have gravity, and why does it behave as it does? Because space-time is geometric. It has to be. I love that. I want to think a similar route from axioms to theory can exist for the basic laws of physics, i.e. reality. In other words, instead of physics built on descriptive models, physics starting from basic axioms and necessary laws emerging from those.

There are still problems, of course. If there’s one consistent theory of everything for a set of axioms, there are probably many. Maybe infinitely many. So we’d still be left pondering one of them anthropic principles, and I’d still be left annoyed. Also, even if reality is consistent (and I really believe that it is) is there a consistent language of mathematics complete enough to accommodate all of reality? If no, what does that mean for math, physics, or reality?

Shoot, is math even the right model for expressing physics? Plenty of derivations in physics go, “there are two solutions to this equation, but this one isn’t physical so we’ll ignore it.” Math is definitely useful for producing predictions, but maybe reality is more subtle.

Also, finding this theory of everything wouldn’t actually be terribly useful. The world we play in is complex enough that we’re still going to rely on statistical and approximate models to do anything practical. Plus the interesting stuff is usually the emergent behavior that doesn’t derive directly from the basic laws.

So why does this question matter? Well, it just seems so remarkable that we live in a universe with such a wealth of phenomena as we have. How beautiful would it be to show that reality is as it uniquely must be? I would find deep comfort if for all the contradictions inherent in being human, at least the universe is consistent and whole.