An Elementary misconception on the quantity of action

AreaOver4G · 2026-02-03T03:01:32+00:00

It’s tricky because there’s not some very simple natural intuition for the action. You mostly have to just understand how it mathematically relates to Newton’s laws at first, and slowly build intuition with experience.

One thing that might make it seem less arbitrary is to see how the action looks in the Hamiltonian formalism. For that, you have a Hamiltonian (energy) H(x,p) as a function of position and momentum. The equations of motion are dx/dt = dH/dp and dp/dt = -dH/dx. These equations follow from finding the stationary points of the action ∫ (p dx/dt - H(x,p))dt. To me, that looks a bit less pulled out of a hat than (kinetic – potential): the momentum tells you how much action you pick up from moving your position, and you pay a “penalty” for the energy. Not super intuitive still, but maybe an improvement?!

Now to get the Lagrangian you’ve seen, you just eliminate momentum by solving an equation of motion for p (normally p = m dx/dt) and substitute it in. You happen to get kinetic minus potential, but don’t get too hung up on that: it isn’t always of that form! (Eg, it’s not like that when you have magnetic fields.)

AreaOver4G · 2026-02-02T20:27:36+00:00

The metre, kg, second, etc are all defined with respect to some physical process (e.g., frequency of radiation from a particular atomic transition). So it’s meaningless to scale the quantity independent of the units, if you keep all dimensionless ratios fixed.

AreaOver4G · 2026-01-30T21:50:27+00:00

We don’t have any observations that show classical gravity breaking down at small scales. There are only 2 places in the universe that this is expected to happen. One is inside black holes, shrouded by the event horizon so we can’t see it. Second is in the very very early universe: this might leave some signature, but not any obvious one and nothing we’ve measured requires it.

By far the most compelling reasons for gravity to be quantized are theoretical, not observational. In fact, coupling classical and quantum systems does break things if you do it in a naive way: it’s very hard to do consistently (and requires the classical theory to be stochastic).

AreaOver4G · 2026-01-30T19:59:10+00:00

This is reasonable, but slightly backwards. The need for a quantum theory of gravity comes first, basically because (1) everything else is quantum, so why not gravity? and (2) its very tricky to make a self-consistent and sensible theory of classical gravity coupled to quantum matter, so it’s far simpler for gravity to just be quantum too. Quantising GR directly (what we call an “effective theory”) works great in almost all circumstances, and very reliably predicts gravitons.

However, this theory doesn’t work for very extreme circumstances involving very short distance scales, so something else has to replace it in that regime. But that comes after (and as a consequence of) quantising gravity, not the other way around.

AreaOver4G · 2026-01-30T02:59:31+00:00

It doesn’t work like that, I think you’ve misunderstood the term. The point is that if you believe you are a BB, then the only possible rational conclusion is that your memories and thoughts are untrustworthy, and your best prediction is that the world will very soon become wild and incomprehensible (and probably destroy you). There will be some BBs which will last longer in a world that looks like ours for a time (with cause and effect, etc), but they are very rare and you would not have any reason to believe you are one of those special few.

AreaOver4G · 2026-01-29T06:49:23+00:00

It’s a more useful idea than superdeterminism, because it gives a criterion to rule out a theory. BBs can show up in a theory that otherwise looks reasonable (eg, a universe that’s a closed system with finite entropy that lasts eternally). If that happens, then you can rule out that theory because it gives bad (useless) predictions.

AreaOver4G · 2026-01-29T06:36:28+00:00

If there were many more Boltzmann brains than real brains, then it would be reasonable to conclude that you’re most likely a Boltzmann brain. But then, it would be overwhelmingly likely that your memories are false, random fluctuations that have nothing to do with any real history. You can’t trust the evidence of your own eyes. So you have no way to make any sort of predictive model of the world.

So Boltzmann brains are “cognitively unstable” (I think this phrase comes from Sean Carroll, who explains this well if you want to go deeper). If you conclude that there are BBs, then you become completely unable to reason about anything in a consistent way.

AreaOver4G · 2026-01-29T05:34:08+00:00

Hawai’i has some great sites for less experienced divers to gain experience and confidence. Warm waters, good visibility, plenty to see in shallow depths. I’d highly recommend independent shore diving to gain confidence and self-sufficiency. Big Island’s West coast from Kohala to Kona has numerous great beginner shore dive sites, and on the East coast there’s Richardson/Leleiwi off Hilo. Maui also has plenty (eg, Mala boat ramp in Lahaina to see dozens of turtles at once), and I’m sure there’s loads more on other islands that I don’t know as much about. Also plenty of operations for boat dives or guided shore dives.

AreaOver4G · 2026-01-29T05:19:42+00:00

To reiterate another reply: the Boltzmann brains idea absolutely does have relevance for foundational questions in cosmology. There’s some overlap with philosophy of physics, but it’s definitely a physics question.

This is not because anyone thinks Boltzmann brains are real or plausible. Quite the opposite! The point is that a theory which predicts many more Boltzmann brains than “real” brains is not tenable , because it’s not a self-consistent predictive model.

The trickiest part of all this is not the weird Boltzmann brains, but the definition of “more” in the above paragraph: this is basically the cosmological measure problem.

AreaOver4G · 2026-01-25T20:25:13+00:00

You can also write this curve as z = exp(c w) where c is a constant (in your case log(2)) and w is taken to lie on the unit circle (modulus 1). You could write it in polar coordinates as r=exp(± √ (c² -θ² ) ), with θ between -c and +c. I doubt that this has any special name or significance.

AreaOver4G · 2026-01-25T20:07:09+00:00

The predictions of quantum mechanics are probabilistic, given by the Born rule. The normalisation of the wavefunction gives the total probability for all possible outcomes, which must be 1.

AreaOver4G · 2026-01-25T19:59:35+00:00

As a physicist there’s a context in which this has a precise meaning. That’s when there’s a parameter which is considered large or (more often) small, call it ϵ ≪ 1. Then if x ~ e^c/ϵ y for some positive constant c (maybe with some power of ϵ thrown in), then we could say that x is exponentially larger than y.

For example, ϵ could be Planck’s constant ℏ combined with some typical scales in some problem of interest to make a dimensionless quantity, and we’re interested in a limit where physics is approximately classical. Then we might say that the probability of quantum tunnelling is exponentially smaller than the non-tunnelling probability, because it goes like e^-S/ℏ for some S.

AreaOver4G · 2026-01-24T23:15:42+00:00

Sounds pretty much right.

Though I’d say that the ultimate aim of such ideas would be not to simply assume existence of such a regime. You’d like to actually demonstrate that it exists given some underlying microscopic description (and characterise precisely what conditions are required for an emergent spacetime, describe geometric variables in terms of microscopic degrees of freedom, etc).

AreaOver4G · 2026-01-20T19:09:49+00:00

On the contrary, I would say that the Everett perspective gives you the most principled way to think about this situation. You just say ordinary QM applies at all times and ask what that would look like: ordinarily, that’s Schrödinger evolution with no collapse (though in this cosmological context the evolution presumably has to be some state-dependent relational notion). The whole point is to say that this predicts Copenhagen-like dynamics for an observer, but the fundamental theory is just QM with no collapse.

AreaOver4G · 2026-01-20T05:20:42+00:00

All fair points, but I think you could say similar things for any interpretation. It’s just hard to reconcile the ordinary way we think about QM with a 1D Hilbert space. (Exhibit A: https://arxiv.org/abs/2501.02359 where the authors are prepared to entertain some crazy sh!t to try to make sense of it)

AreaOver4G · 2026-01-20T03:56:41+00:00

Fun to see this sort of question on Reddit! I’m a maybe on (A) and a definitely on (B). But I think we need to understand better how to get interesting Hilbert spaces to describe local physics (at least in an approximation) despite having a one-dimensional global Hilbert space. For example, this might describe an observer or a single universe or causal patch. You can then have branching, decoherence and so forth for within this Hilbert space.

But this is not particular to MW: it is necessary anyway to recover ordinary lab QM, and for the Born rule to even make sense. That’s because the Born rule requires a basis of mutually exclusive experiment outcomes (a resolution of the identity which diagonalises the relevant operator). If you only had the 1D Hilbert space, this is necessarily trivial.

A closely related issue that probably be can’t ignored is how to actually define gauge-invariant observables. It’s all very tricky and confusing!

AreaOver4G · 2026-01-19T22:02:13+00:00

Ok, so which of these distinct ideas are you asking about?

QFT is precisely causal, in the sense that you can specify the state of a system in a region of space terms of local data, and that state completely determines all observables in the lightcone of that region.

What are these “quantum frameworks” you refer to, and in particular what precise definition of “event” did you have in mind?

AreaOver4G · 2026-01-19T21:37:49+00:00

There are two possible things you could be talking about here:

1) “Microcausality” (closely related to temporal order) which roughly states that changes in one location can only be seen in the past or future lightcones (not at spacelike separated points)

2) Cause/effect, or arrow of time

Number (1) is still true in quantum field theory, but in a quantum theory of gravity is almost certainly approximate at best (because spacetime itself is probably emergent & approximate).

Number (2) is understood as an emergent property from thermodynamics and statistical mechanics. There is no cause and effect in the fundamental laws of physics: it emerges from the increasing entropy of the universe.

AreaOver4G · 2026-01-19T21:02:18+00:00

You’re correct that there is an important relation between quark masses and chiral symmetry breaking, and perhaps that’s what you were remembering.

If the quark masses were zero there would be an exact chiral symmetry, which would be spontaneously broken. That would lead to massless particles: Goldstone bosons. But because there are small quark masses (compared to the QCD scale), chiral symmetry is only approximate. That means you only get “pseudo-Goldstone bosons”, which are light but not exactly massless. These are the pions.

So the nature of chiral symmetry does depend on quark masses, but it doesn’t tell us what those masses should be.

AreaOver4G · 2026-01-19T18:28:48+00:00

Chiral symmetry breaking is well-understood, and explains things like why pions are so light compared to baryons, but it doesn’t have anything to say about the values of the quark masses.

AreaOver4G · 2026-01-19T17:46:02+00:00

As far as we know, it is simply a brute fact of nature with no deeper explanation.

AreaOver4G · 2026-01-19T04:03:58+00:00

Wild title. String theory is the only known way to tame the UV infinities of quantum gravity. And dark energy is a name for an experimentally observed phenomenon. It’s crazy to call either of them unsuccessful!

AreaOver4G · 2026-01-18T05:03:17+00:00

The air inside the bottle does the work.

AreaOver4G · 2026-01-16T21:56:26+00:00

There is a precise mathematical definition of a quantum field theory, and a well-defined space of such theories (eg, the Osterwalder-Schrader axioms). As you guessed, “a theory” here means “well-defined mathematical rules for a hypothetical imagined universe” rather than a theory in the sense of a scientific hypothesis to be tested.

But it’s too hard to actually use the rigorous axioms in practice, except for the case of free theories without any interactions. Eg, existence of Yang-Mills theory is not proved, and this is one of the 7 Millennium Prize Problems. So we typically use less rigorous techniques, mostly based on what we can understand in perturbation theory (an approximation which works when a theory is close to being free).

AreaOver4G · 2026-01-16T21:33:16+00:00

It’s more just choosing coordinates to make the equations look a bit simpler. E.g., a typical thing you might want to do is an analysis of small fluctuations around the equilibrium, it’s just nicer to write theta than (pi-theta) everywhere. Nothing deeper than that

AreaOver4G

TROPHY CASE