# B Why does time pass in an isolated vacuum?

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1. Oct 6, 2018

### Alec Hewitt

I read a little bit on the arrow of time and how some physicists think that it points in the direction of increasing entropy. This made sense until I thought about a vacuum. From what I read, entropy does not increase nor decrease in a vacuum so if we used this definition on the "arrow of time" then why does time pass in a vacuum?

2. Oct 6, 2018

### Staff: Mentor

If your whole universe is purely vacuum then the passage of time could be a meaningless concept - and there is nothing that could measure it anyway. As soon as you have things in the universe you don't have that problem any more.

3. Oct 6, 2018

### Alec Hewitt

What if there was electromagnetic radiation in this vacuum, would the entropy change? Also, do quantum fluctuations in the vacuum have anything to do with entropy?

4. Oct 6, 2018

### jambaugh

There are a couple of issues I must raise with your question. Firstly, there is also no increase nor decrease of entropy for any system in a "sharp state" as given by a wave-function (rather than a density operator). The vacuum is not unique in this respect. So by the reasoning you put into this question you should also ask about time's passage for any sharply defined quantum state.

As to how time relates to quantum systems, note that time is not a physical observable. It is not something "in the system" but rather is associated with the measuring devices in the classical (thermodynamic) realm. Time is still a "c-number" a classical parameter an part of the episystemic framework which defines the quantum system.

Finally as to the question of the arrow of time, that is a question about the asymmetry of time reversal on the macroscopic scale when the microscopic dynamics is apparently symmetric under time reversal. In both the symmetric and asymmetric scenarios there is no question of time passing between events. The question is about the discrete reversal transformation which looks so different in both cases. In quantum, there is a fundamental thermodynamic aspect to measurement. It is an irreversible process breaking the symmetry in specific ways. This is one of the places where the time asymmetry can "sneak into the picture" when one is trying to understand the emergence of a distinction between past an future.

Now your question is still a good question even with the issues I point out. It is a good question because it forces one to consider these issues. Its a thinking question not a "how to build a bridge" question. I have a few other questions for you to consider alongside yours.
• How do you know your system is in a vacuum state? Especially how do you know it is in such over a span of time?
• Can you verify a system is in vacuum without breaking that vacuum?
• Supposing I gave your question the simple answer "It (time) doesn't pass!". What empirical facts would confirm or dispute my claim?

5. Oct 7, 2018

### Staff: Mentor

A state in which all the photons are at the same place has less entropy than when they are spread out.

6. Oct 7, 2018

### jambaugh

No! That is not correct. Any sharp state, whether its with the photons in the same place or spread out to the 4 corners or all absent... any such state has zero entropy.

Non-zero entropy quantum systems must be described with density operators instead of hilbert space vectors/wave functions.

A better way to understand entropy in the quantum world is as entanglement of the system with its environment (especially with phenomena which are beyond event horizons and thus not reversible without some previously planned means of returning the outfleeing information.)

7. Oct 7, 2018

### Staff: Mentor

I disagree, unless you use a strange definition of sharp. Do you consider the cosmic background sharp?

Generally we presume that as things spread out from an ordered state, that we gradually lose track of their exact state, knowledge becomes fuzzy and entropy increases.

If all we know is that particles are contained in a volume, then a smaller volume corresponds to smaller entropy. I meant that a small volume and "the same place" are synonymous.

8. Oct 7, 2018

### Mister T

So far, so good.

You're pointing out that in a vacuum you couldn't use entropy as an arrow of time. That's also correct. For entropy to have meaning, in the sense that you're using it, you'd need collections of large numbers of particles.

Where you seem to have gone off the rails is claiming that time doesn't exist in certain places, like in vacuums, where you can't define an arrow of time. All the arrow of time tells you is the direction, it doesn't tell you that time exists. In other words, without an arrow of time we'd have no way of telling whether time was passing forwards or backwards. And in a vacuum there would indeed be no way to tell. There would be no way to observe energy spreading out.

9. Oct 7, 2018

### jambaugh

A sharp description is a description represented by a single Hilbert space vector. In field theories that would be an element of the Fock space. In all such cases the Von Neumann entropy is zero. The corresponding density operator is a single dimensional projection operator with trace 1 and thus $S = -k Trace(\rho \ln(\rho)) = 0$.

Entropy is not about the spatial arrangement of the photons or their number (in this particular example) excepting that there is typically only one zero particle state thus the vacuum typically has S=T=0. Entropy is about the degree to which one has a system which is less than maximally specified. It is a "measure of ignorance".

I've written three times as much as this and erased it multiple times. I'd be happy to discuss this in a different thread but fear I'll get far afield of the OP.