Entropy Real? End of Time? - Veritasium Video

Is entropy real? It seems like it's not real because it depends on how you group microstates together into a macrostate, and the way you group them can be arbitrary. For example (at 13:04 of the video below), there are 91,520 microstates in the macrostate “9 in left; 1 in right” but 627,264 microstates in the macrostate ‘5 in left; 5 in right”, meaning there are way much more microstates in the latter than in the former, so the latter macrostate is more probable. But the naming of "left" and "right" is in a sense “arbitrary” because I can always rename or regroup which atoms/positions I shall now consider as left and which as right, artificially. So my question is, if I can arbitrarily rename or regroup how I define my macrostates, then is entropy real?

My question is in relation to this YouTube video "The Most Misunderstood Concept in Physics" by Veritasium: www.youtube.com/watch?v=DxL2HoqLbyA

But in any case, you don't really need to watch the video to understand my question.

My second question is does time stop to exist in the future, suppose the ultimate fate of the universe is a heat death?

24:29 of the video: “In the distant future, after the last black hole has evaporated, the universe will be in its most probable state. Now, even on large scales, you would not be able to tell the difference between time moving forwards or backwards, and the arrow of time itself would disappear.”

It seems rather weird to me that time would stop existing in future (or stop existing in any meaningful way). So I think it would be the case that the universe can never achieve heat death completely; it will always get closer and closer to it but will never reach it, so time will never cease to exist, because that state is never reached. Anyway, I may be wrong. So please correct me if I am wrong.

Another related question would be, since time has a beginning (which is the start of the Big Bang), then does that mean time must have an end?

What is real?

Are forces real? Energy? Hamiltonians? Fields? Photons?

Vanadium 50 said:

What is real?

A physical cup, made of ceramic for example, on a table, is real. But the same cup appearing in your dream is not, because it does not exist in the physical world. It is only an image of the real cup that exists in the physical world. It is created by your brain, but seems real because of how information in your brain is being organised. It is an artefact or a by-product of how our brain processes information we get from the physical world.

Similarly, a digital image or video of the same cup is not real, because it is a result of how a computer processes the information stored in a computer file, in the form of ‘0’s and ‘1’s.

Microstates are real because they are what the real, physical world is. Macrostates are not real because they are a result of how we or how our brain groups certain information from the universe arbitrarily into certain artificial manners (aka macrostates) that allow us to make sense of the information (otherwise the information is too much and our brain would be overwhelmed), to make the information “useful” for our survival. In other words, our brain simplifies the vast amount of information in the physical world into a manner we can handle and can use for our day-to-day living.

So while we may classify microstates 1, 2 and 3 into macrostate A (and microstates 4-10 into macrostate B), because that is how we has evolved to be for survival, an alien civilisation or a cat’s brain may perceive the physical world differently and thus may classify all the even microstates as macrostate A’ (and the odd ones as B’). Therefore, since macrostates are a consequence of how we group or process information, and not what the physical world really is, macrostates are not real. And since entropy depends on how macrostates are defined, which can be done arbitrarily and differently and species-dependent, entropy is not real. Entropy is an artefact or a by-product of how we process information, but it is not a real thing in the physical world, like how a physical ceramic cup is. It is more like that cup in your dream or that cup in a photo or video.

Anyway, I do not know if what I am saying is right. But this is what makes sense to me at this point. So I am putting my thinking in the form of statements instead of questions, so that it flows better and it’s easier to read and for anyone to correct me by pointing out anything wrong somewhere in it.

Happiness said:

Is entropy real? It seems like it's not real because it depends on how you group microstates together into a macrostate, and the way you group them can be arbitrary. For example (at 13:04 of the video below), there are 91,520 microstates in the macrostate “9 in left; 1 in right” but 627,264 microstates in the macrostate ‘5 in left; 5 in right”, meaning there are way much more microstates in the latter than in the former, so the latter macrostate is more probable. But the naming of "left" and "right" is in a sense “arbitrary” because I can always rename or regroup which atoms/positions I shall now consider as left and which as right, artificially.

I'm not sure I understand what you're getting at. If there are 7 times more microstates in which each bar has 5 energy packets compared to the left bar having 9 packets and the right have 1, then the same is true if you say the right has 9 and the left has 1 (assuming the bars are identical). But that's really just missing the point. If we bring a warm bar into contact with a cool bar, it is statistically unlikely for all of the energy packets to rearrange themselves such that the warm bar heats up and the cool bar cools further.

If we increase the number of particles in the bars to realistic numbers then it goes from statistically unlikely to statistically impossible.

Happiness said:

My second question is does time stop to exist in the future, suppose the ultimate fate of the universe is a heat death?

Not as far as we know. What Veritasium is getting at in the video is that once the universe reaches heat death, we no longer have clearly delimited low and high entropy regions. There are no more hot and cold regions, no more stars turning one element into another and throwing out radiation, nothing but an endless soup or fog of radiation and matter that does nothing interesting. The only changes in the universe will be minor changes from one statistically likely state to another statistically likely state.

The arrow of time is a concept that explains why things occur one way but not the reverse. For example, if shatter a glass by dropping it you don't see the shards reforming into a whole glass later on. A piece of fabric left out in the Sun will fade, but the color doesn't just come back on its own later on. It doesn't 'unfade'. An apple left out will eventually rot, but a rotted apple will never turn back into a fresh apple. This is because all of those are processes that take an object from a low entropy state to a higher entropy state.

What Veritasium is saying is that once we reach maximum entropy in the universe, the arrow of time 'disappears'. But the arrow of time is not time itself. Physicists don't use the arrow of time in their formulas. They use time. If we could somehow track a particle moving in the universe in the far future after heat death, our equations of motion and interaction would still work just fine. The particle would still move and interact just as it should. Time still exists.

Happiness said:

Another related question would be, since time has a beginning (which is the start of the Big Bang), then does that mean time must have an end?

No, not really. First, we don't know if the universe had an absolute beginning. The Big Bang is just the name we give to the rapid expansion of the universe in the distant past. Any allusions to the Big Bang being the absolute beginning of the universe is just speculation. All we can really say is that the universe was much more dense and hot in the past and has expanded and cooled since then. Taking this process to its extreme gives us the eventual heat death of the universe.

Happiness said:

So while we may classify microstates 1, 2 and 3 into macrostate A (and microstates 4-10 into macrostate B), because that is how we has evolved to be for survival, an alien civilisation or a cat’s brain may perceive the physical world differently and thus may classify all the even microstates as macrostate A’ (and the odd ones as B’). Therefore, since macrostates are a consequence of how we group or process information, and not what the physical world really is, macrostates are not real. And since entropy depends on how macrostates are defined, which can be done arbitrarily and differently and species-dependent, entropy is not real.

I'm not sure what you mean. If we look at the two bars example, we get clearly defined states in each bar. There is no uncertainty about which states are real vs not real. The same is true for any of physically possible system. It has certain states that it can be in, all of which are real states.

You could take one configuration and call it Macrostate A, and another as Macrostate B, and you could swap the names around, but this doesn't physically do anything. The bar that is hot will still transfer heat to the bar that is cool, no matter what you call it or how you label it.

So electromagnetic fields are not real, even though they can move objects, store energy and even kill you if they get big enough? Or are they real too?

This looks like philosophy, and not very good philosophy at that, since two people may not even agree on what is "real".

Drakkith said:

we don't know if the universe had an absolute beginning...
Any allusions to the Big Bang being the absolute beginning of the universe is just speculation.

Since the age of the universe is 13.7 billion years, can we say that 13.7 billion years ago was the absolute beginning?

I remember Stephen Hawking said in his book that the Big Bang created space and time, time did not exist before the Big Bang or it is not allowed to ask what existed before the Big Bang, because at that "time", there was no time.

So how could I reconcile what you said (about there being no absolute beginning or our lack of knowledge thereof, and Big Bang being the absolute beginning is just speculation) with what Stephen Hawking said?

Happiness said:

So how could I reconcile what you said (about there being no absolute beginning or our lack of knowledge thereof, and Big Bang being the absolute beginning is just speculation) with what Stephen Hawking said?

Can you please cite the particular book by Hawking and quote here the specific passage you are referring to? Thanks.

Happiness said:

Since the age of the universe is 13.7 billion years, can we say that 13.7 billion years ago was the absolute beginning?

No, we can only say that our model stops predicting things 13.7 billion years ago because of singularities in the math. That is, the math leads to infinities in its answers if we wind back the clock this far. That's all a singularity is, a mathematical result that is infinite.

Happiness said:

I remember Stephen Hawking said in his book that the Big Bang created space and time, time did not exist before the Big Bang or it is not allowed to ask what existed before the Big Bang, because at that "time", there was no time.

I don't know what Stephen Hawking said, as I haven't read his book, but if he said this then he's simplifying a great many things to write a book the average reader can digest. What should be said is that we can only model space and time starting from a certain point in the past and going forward because of the infinity issues I just mentioned. One should be under no illusions that our current model is 'absolute' in any sense.

Happiness said:

So how could I reconcile what you said (about there being no absolute beginning or our lack of knowledge thereof, and Big Bang being the absolute beginning is just speculation) with what Stephen Hawking said?

You can understand that Hawking did not write a rigorous book that goes into detail about where and how our models break down. He wrote a book summarizing the Big Bang Theory and took some liberties when writing so that the average person would be able to read it.

To understand entropy maximization, look at https://en.wikipedia.org/wiki/Principle_of_maximum_entropy
Not knowing e.g. what percentage p of bits are "1", the safest assumption is p=1/2, because the number of possibilities binomial(n,pn) ~ exp(n*h(p)) is maximized for p=1/2: such "p=1/2 subsets" grow the fastest - they will dominate all the possibilities.

Statistical mechanics are effective models - replacing complex scenarios with statistical parameters like "p percentage of particles are in the left containment".
Such mean-field-like approximations, generally called stosszahlansatz, allows to prove entropy growth (e.g. https://en.wikipedia.org/wiki/H-theorem ) for approximations of time-symmetric models.

2 slides from https://www.dropbox.com/s/2tmp4cmrbvfjs4b/MERWsem.pdf :

Drakkith said:

but if he said this then he's simplifying a great many things to write a book the average reader can digest.

I read this in his last book "Brief Answers to the Big Questions" and for me he simply lied to the reader to support his view that "god does not exist, and we don't need one because we know how Universe came to existence - the Big Bang". Honestly, I stopped reading after that, and it was only the very first chapter... I guess his personal philosophies were more important than scientific truth.

Happiness said:

So my question is, if I can arbitrarily rename or regroup how I define my macrostates, then is entropy real?

This is a very good and often asked question. It is true that there is some freedom in how exactly to define entropy, but it doesn't mean that it's not real. Many things have a freedom in how exactly to define them, and yet they are real. Momentum depends on the choice of velocity of observer, gravitational potential energy depends on the choice of altitude where it is zero, angular momentum depends on the place of the origin. Out of physics, meaning of a text depends on the language, intelligence depends on how you measure it ... All these things are real, but when you speak of them you must specify these conditions on which they depend. In science things must be precisely defined, and definitions are something that humans choose at will. The choice of definition is a matter of convenience, sometimes one definition is more convenient, sometimes another definition is more convenient, it depends on the context. It's a general principle in science, valid for all things, including entropy.

Happiness said:

since time has a beginning

It is unfortunate that you feel you can state that as a fact, since it is NOT a fact. It is one hypothesis of many, and it may or may not be true.

That's the problem with students starting to learn directly statistical mechanics. Entropy is a well defined quantity in phenomenological thermodynamics like temperature or heat. The meaning of these concepts seems rather abstract if you start from statistical mechanics.

Everybody: I'm pretty sure Hawking is referring to the Hartle-Hawking no-boundary proposal. So he's neither grossly oversimplifying nor talking out of his back end. But he does seem to be overstating its relevance to the actual universe.