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It makes even more sense when you take the law of large numbers into account. The scale we're experiencing most things on is /so/ far removed from the scale on which these probabilities are being expressed.

There are more molecules in a cup of water (on the order of 10^24) than there are cups of water in the ocean. If you have a cup of water's worth of matter, you aren't just rolling 10 dice (or even 1000 dice) and looking for mostly 6s. You're rolling a few septillion dice and hoping for a significantly non-normal distribution. It just isn't feasible.

I don’t buy it. You can’t say entropy is probability and then say but we don’t know what probability really is. It’s both foundational to physics and computer science. I could say probability is really just entropy just as easily. I would go farther and say that time is entropy as we measure time by observing entropy.

you don't buy it? This is foundational. This isn't something I'm making up. It's the formal definition of entropy.

https://www.labxchange.org/library/items/lb:LabXchange:ac117....

I think his point is that it is not clear why every microstate is equally probable.

It's an assumption we make due to imperfect knowledge of a system. We assume all microstates have equal probability.

Just like rolling 6 dice. We assume all configurations of the 6 dice have equal probability.

What's the probability of rolling exactly 1,1,2,6,3,5? It's the exact same probability as rolling 6,6,6,6,6,6. We instinctively assign these probabilities based of of assumption because we also assume each number has a 1/6 probability so rolling exactly a certain number for each roll yields (1/6)^6

It's the macrostates that are subjectively grouping these microstates in various ways. If I pick the macrostate where all dice are the same there's only 6 microstates for that. If I make up the macrostate for at least one dice is different that's every possible microstate except 6 microstates where they are all the same.

Thanks for linking that. My point really was that entropy is many things and probability is among them.

this is great and it does make perfect sense to me, someone with no stat thermo background. but it makes me wonder

how is it then, that things are becoming more spread out over time?

what is the property about the past, that it seems have a lot of uncommon states and not a lot of the common ones?

if common states are mathematically more likely to be common, why is it that the future has them and the past does not, in general?

like, why hasn't heat death happened? the probability thing seems to be almost proof-like, you cannot really argue against it. but clearly, the universe did, to a great degree, at some point in the past. why?

>how is it then, that things are becoming more spread out over time?

It's more likely for things to spread out then to concentrate in one corner when you randomly move all particles in a box. If all particles moved to one corner of a box you would assume there's an intelligence at work moving the particles because such movement is too low of a probability to happen without intelligent intervention.

>if common states are mathematically more likely to be common, why is it that the future has them and the past does not, in general?

Common states are called "common" because their are more of them in general. Think in terms of things with a few states like rolling dice. You have a machine that rolls rice continuously and checks the result. Use this as an analogy of particles of gas moving around in a box and then use that as an analogy of the universe.

Nobody knows why probability works this way. Probability is what differentiates the arrow of time.

>like, why hasn't heat death happened? the probability thing seems to be almost proof-like, you cannot really argue against it. but clearly, the universe did, to a great degree, at some point in the past. why?

Entropy is just a phenomenon of probability. Don't let the concept of entropy rule your brain and override what's going on. Heat death hasn't happened because entropy can be frozen. You freeze ice then the particles stop moving.

Additionally all of what I said above doesn't apply to things with gravity like black holes. With gravity things begin to automatically self organize into circular orbits or spherical planets. Why? It's because entropy isn't measuring disorder. That's a mistake. Entropy is just saying that systems drift towards high probability macrostates. In systems with gravity, spherical shapes and circular orbits ARE a higher probability macrostate then one where the particles disordered. In this system a higher entropic state is actually MORE ordered then a lower entropic macrostate.

I don't know if there's going to be a "heat" death, but for sure we are moving towards higher entropy as the law says. But this does not necessarily mean more disorder or things getting spread out.

That's it. I think the word entropy just confuses everyone. It's just someone observed these weird phenomenon with heat and called it entropy. Then we realized it's just a bunch of particles moving into high probability patterns.

But that's a semantics game. Sub probability for entropy. Why do we live in a world where low probability states were in the past and high probability ones are in the future? What intrinsic property of the universe causes this asymmetry? One can imagine a symmetric k-negative universe where high probability macrostates trend towards low probability macrostates. Or a k-zero universe where the dice never rolls.

None of such questions follow definitionally from the second law ^H^H^H probability.

Yes. It is a semantics game. I feel people understand probability but they don't understand entropy hence it's easier to just use the term probability state.

And yes the questions you pose don't follow from the 2nd law. But they are the big question.

> how is it then, that things are becoming more spread out over time?

This may help: https://www.researchgate.net/figure/Classical-evolution-in-p...

If we knew the present we could predict the future - at least in classical physics. We have a very approximative knowledge of the present though, based on a macroscopic description. We can still predict a range of outcomes and see what it means in macroscopic terms. The initial set of states consistent with what we know “spreads out” as time goes by. We “lose” information by keeping only a “coarse” macroscopic description.

> what is the property about the past, that it seems have a lot of uncommon states and not a lot of the common ones?

This is called as Past hypothesis.

https://en.wikipedia.org/wiki/Past_hypothesis

> Why does probability seem to follow an arrow of time, it doesn't seem symmetrical like the rest of physics.

One cannot really oppose probability to "the rest of physics". Probability is not "a part of" physics. Probability is what we use to describe imperfect knowledge of a physical system - and we know more about the past than we do about the future.

No, probability is a mathematical game with axioms and theorems.

Why the rules of this game happens to describe systems where we have imperfect knowledge... nobody knows.

Another thing is all of these systems have probability travel in a single direction. Things with high probability are more likely to happen. If time were to go backwards, low probability events will start to spontaneously occur.

Ok, so we agree that probability is not a part of physics. I also agree that the question of how to apply probability in physics is interesting.

I’m not sure about the “nobody knows” though. I would say that statistical mechanics has been quite successful in “knowing”: https://arxiv.org/pdf/cond-mat/0501322

Haven't you heard of quantum mechanics. The probability wave makes it a foundational part and not just a macro phenomena.

Statistical mechanics is just a study of the application of probability to that macro phenomena. We still don't know why all of it works.

> Haven't you heard of quantum mechanics.

Haven't you looked at the article I sent which says "quantum" in every other page. Haven't you heard of its author Roger Balian and his (two-volume) book From microphysics to macrophysics: methods and applications of statistical physics.

> Statistical mechanics is just a study of the application of probability to that macro phenomena. We still don't know why all of it works.

"We" may "know" different things - and have a different view on the relative importance of what is known and what it isn't.

> Another thing is all of these systems have probability travel in a single direction. Things with high probability are more likely to happen. If time were to go backwards, low probability events will start to spontaneously occur.

If I shoot a pool ball to strike a heavier second ball which is at rest they will end up moving in opposite directions. If "time were to go backwards" - whatever that means - they would approach at the end one would be at rest. That's seems indeed unlikely with "time going forwards" because we wouldn't be able to do that if we tried (at least not systematically).

I don't think there is a conceptual problem or anything surprising there: we know how balls move given their initial conditions but we cannot control those initial conditions with the precision required to obtain a precise outcome.

There are also cases were we can prepare systems in the right configuration and produce "low probability" events even with "time going forwards": https://en.wikipedia.org/wiki/Spin_echo

>If I shoot a pool ball to strike a heavier second ball which is at rest they will end up moving in opposite directions. If "time were to go backwards" - whatever that means - they would approach at the end one would be at rest. That's seems indeed unlikely with "time going forwards" because we wouldn't be able to do that if we tried (at least not systematically).

in a vacuum no ball will ever go to rest if it's moving. It will move forever because there is no resistance.

What's happening in the pool table is that the ball is losing it's movement energy to the table. Table is absorbing it, the air is resisting it and slowly that vibrational energy becomes more and more spread out until it's basically imperceptible heat (which is also technically atoms vibrating).

What happens when time goes backwards is a bunch of tiny low probability events start happening. Heat from the background vibrating atoms by pure random luck happen to align and happen to produce motion that's noticeable. This happens from several places and by pure luck all of this vibrational motion concentrates on one place, the pool table and the ball. The kinetic vibrations just happen to push the ball slowly in one direction more and more with all kinetic vibrations by pure luck speeding up the ball. The ball being picking up speed until you with the tip of the pool cue catch the ball and ease it into a perfect stop, absorbing all the kinetic energy into the stick and your body.

All within the laws of physics but all extremely low probability events.

>There are also cases were we can prepare systems in the right configuration and produce "low probability" events even with "time going forwards": https://en.wikipedia.org/wiki/Spin_echo

When you put an intelligence in the system it's sort of cheating as you can manipulate random events to be non random and thus violate the laws of probability by intelligent choice. There's some computational theory here that states that the act of thinking itself produces entropy thus it's sort of conserved in a way but that' some other theory stuff that's another rabbit hole to dive into.

> In a vacuum no ball will ever go to rest if it's moving.

When a moving ball hits another massive ball that was in its way it’s pretty safe to assume that it was not moving in a vacuum.

>they would approach at the end one would be at rest.

I'm referring to this. This doesn't happen in space. It's on a table on earth.

If in “time going forwards” a ball hits another one at rest and you “reverse time” right after the collision won’t the “time going backwards” get that ball in rest again? (You’re the one who mentioned physics being symmetrical.)

The point is that with just two things interacting with “time going backwards” you “predict” unlikely things to “happen” and we know that it’s because the “initial” conditions are the exact ones that would make such things happen. It doesn’t seem a big mystery.

In the “many, many, many, we-don’t-even-know-how-many” things interacting case we would encounter something similar. The “initial” conditions if we had “time going backwards” are much more unlikely and the “outcome” much more unexpected because in reality we don’t know almost anything about the state of the system. But we know that those “initial” conditions are “special” - it’s not more mysterious than the simpler case.