# I Time and entropy

1. Dec 23, 2016

### windy miller

Is there any way to measure time without reference entropy? i.e suppose the universe has maximum entropy , is there any way to define a sense of time "after" that?

2. Dec 23, 2016

Staff Emeritus
With a clock.

3. Dec 23, 2016

### BvU

Is the wrong answer. Unless you manage to wriggle yourself (and clock) outside the universe

out of time, out of place -- story of many lives

4. Dec 23, 2016

### windy miller

OK but what can you use as a clock in maximal entropy universe?

5. Dec 23, 2016

### Buzz Bloom

I am unclear on the concept of "maximum entropy". If the universe is expanding, in what sense it its entropy at a maximum? I am also unclear about the concept of measuring time as used in the original question. If the universe is expanding, then the universe itself "measures" time. If hypothetically our universe is finite and then contracts after a finite time, how is the total entropy of such a universe defined?

6. Dec 23, 2016

### Chalnoth

It's certainly possible to define time in the abstract as a distance between timelike events, but without entropy it's not possible for there to be a meaningful direction of time.

7. Dec 23, 2016

### Staff: Mentor

If the universe continues to expand forever, there is no maximal entropy; it can continue increasing without bound.

8. Dec 24, 2016

### SleepDeprived

Although many well known physicists have used entropy as the proof of the existence of time, I am not too convinced and the argument is more coincidental than intrinsic. Part of the reason it's so hard to talk about time is because I don't think there is a well agreed upon definition of time and until we can agree on what time is, it's impossible to say anything else about it as far as what it is.
It's possible to say that time is not fundamental but a by product of something which I don't really know. And there could be contradiction in our equations and theory. For example, the photon which based on our the Lorentz transformation has zero mass which means it can be everywhere at the same time. How can something has zero mass and can be everywhere at the same time? What is the definition of time when something can be everywhere at the same time?

Edit: Could time be defined something that is similar to, for example, "temperature"? That is temperature is not really fundamental but it's more of our human perception. I mean we have lots of equations dealing with temperature but it's all but a show of what's really going on.

Last edited: Dec 24, 2016
9. Dec 24, 2016

### Staff: Mentor

I would not put it this way. I would put it that many physicists use entropy to define an "arrow" of time, i.e., to define which direction of time is the "future" direction--namely, the direction in which entropy is increasing. But this definition assumes that we already have "time" as a concept.

What's wrong with the definition already given in this thread, that time is what a clock measures?

No, it doesn't. It means the concept of "proper time" does not apply to a photon. But a photon still has a well-defined worldline in spacetime; it certainly does not occupy all events in spacetime, which is what your claim amounts to.

I don't know what you mean by this.

10. Dec 24, 2016

### Buzz Bloom

Hi @windy miller:
I confess that I have some trouble understanding what kind of answer you are seeking for your original question:
My problem is that I see ambiguities regarding the terms you use. I am not an expert re thermodynamics, so my discussion below may well have errors, in which case i hope someone will correct me.
"Maximum entropy."​
The entropy for the entire universe is infinite because the universe is infinite. Using this context there is no time at which the total entropy is not already at its maximum value. Therefore, a different concept is needed. If a closed system is isotropic and in equilibrium, then there is no free energy that could be used to do work. There is the possibility that the free energy might be eliminated as the system achieves equilibrium. Even if we ignore numerical values, this state being isotropic and in equilibrium may be taken as the state of maximum energy. No measuring devices of any kind can exist in such a state. So in this context we can now address the question:
"Is there any way to define a sense of time" in such a state.​

This reveals another ambiguity. One possible approach is to consider what quantum mechanics might tell us. Any measurable quantity does not have a specific value until a measurement is made. Therefore, using this context, the concept of time ever having a specific value is not possible, since measurement devices cannot exist.

I might well be mistaken, but have made a guess that this is part of what you are considering as the context for your original question. I have in mind an alternative context for resolving the second ambiguity which leads to a different answer, but unfortunately I have to stop posting now. I will try to post a description of this alternative context as soon as I can.

Regards,
Buzz

Last edited: Dec 24, 2016
11. Dec 25, 2016

### Buzz Bloom

Hi @windy miller:
Continuing from my post #10.
The Friedman equation is given below
(from https://en.wikipedia.org/wiki/Friedmann_equations under “Density parameter”.)

This equation relates the relative scale of the universe as it expands, represented by the variable a, to four components of different kinds of mass-energy equivalents, and the Hubble constant, H. H is defined by
H = da/dt.​
A time is chosen as a reference time, t0, for which a = 1, and H = H0.

Each of the four mass-energy equivalent components have a coefficient represented by Ω and a subscript, and by a power of a. The four Ω coefficients add to 1.

Solving this equation for a(t) produces
a(t) = F(ΩR, ΩM, Ωr, t) .​
For the purpose of this discussion, we assume the Ω variables are known constants, so this can be written as
a(t) = F(t).​
t can then be calculated as a function of a:
t = F-1(a).
In this context t represents time relative to the reference time, t0. Therefore actual time equals t × t0. Although this time cannot be measured (because there are no measurement devices), time exists in the same sense that the scale of the universe, represented by a, exists.

Another physical value that exists in the same sense is temperature. The term ΩR/a4 represents the equivalent mass-energy for radiation (mostly photons). The Stephan-Boltzman law
shows that the radiant energy density is proportional to the fourth power of temperature, T. This means that in the universe we are discussing, temperature is inversely proportional to a, say
a = σ/T.​
Therefore time is calculable as t x t0 in terms of temperature T:
t = F-1(σ/T).​

Thus we see that time has the same kind of reality as temperature, even without measurement devises.

Hope this helps,

Regards,
Buzz

12. Dec 25, 2016

### rkastner

13. Dec 26, 2016

### julcab12

https://arxiv.org/pdf/1005.2985v5.pdf . According to Rovelli "The thermal time hypothesis. In nature, there is no preferred physical time variable t. There are no equilibrium states (rho sub zero) preferred a priori. Rather, all variables are equivalent; we can find the system in an arbitrary state (rho); if the system is in a state (rho), then a preferred variable is singled out by the state of the system. This variable is what we call time." -- Temperature T is, in fact, the ratio of thermal time to proper time.

The main idea is derived from mathematical result from the theory of von Neumann algebras where A quantum system's associated von Neumann algebra describes what you can observe about the system - the 'algebra of observables'. Be warned. Althougth the hypothesis of a purely mathematical result from the theory of von Neumann algebras (linked to the thermodynamic notion of time present in a specific mathematical framework of the quantum theory of many-body systems). Even if this hypothesis is on very solid ground mathematically, it is usually very difficult to tell when mathematical truth corresponds to physical truth.

Last edited: Dec 26, 2016
14. Dec 28, 2016

### windy miller

Consider a model like Rovellis loop quantum gravity. In the cosmological version the universe is contracting before its expanding. My understanding is that entropy of the contracting epoch is not thought to be carried through into the expanding branch. Lets not worry if that is realistic or not for the moment. But assume its correct. What are the implications of that? We are used to defining the notion of before and after as lower entropy in the past and higher entropy into the future. So lets assume we can watch video tape of the history of the universe in reverse. The universe is expanding so as we wind the tape back we see it contracting. We get to the bounce point and then see the universe expanding again. However can we say the contracting region is in the past? Its not necessarily lower entropy but on the other hand if we extend the timeline of our universe"before" the big bang according to this model there is still something there. So people in the LQC community will say the universe was expanding before it was contracting but from an entropy perspective how do we define that or can we define it without notions of entropy? very confusing.

15. Dec 28, 2016

### spacejunkie

There are a few models which display a symmetry around the point of lowest entropy - the so-called "one past, two futures" models. In these the arrow of time moves in "opposite directions" away from the bounce.

See for eg
Carroll and Chen
hep-th/0410270v1

Barbour, Koslowski and Mercati
gr-qc/1507.06498

Shani, Shtanov amd Toporenski
gr-qc/1506.01247v3

Last edited: Dec 28, 2016
16. Dec 29, 2016

### windy miller

Hi spacejunkie, thats certainly true in some models but not in all. Lac does not include a reversal of the arrow of time at the bounce, thats really where my question (post 14) was addressed.

17. Jan 1, 2017

### julcab12

... In LQC-LQG. There is no distinction of time or proper time. Time is not fundamental. It is a relational and a timeless universe (not exactly but treated differently). It is intrinsic observer-independent time variable--According to Rovelli. BTW Im not an expert. Clarifications sake : https://www.physicsforums.com/threads/global-emergent-time-how-does-tomita-flow-work.660941/. Kudos to the late Marcus.

18. Jan 1, 2017

### windy miller

Marcus died? Im so sorry to hear that, He will be sorely missed.

19. Jan 3, 2017

### Gerhard Mueller

Aren't all known physical processes, which depend on time, appropriate to determine the time difference between two events?
Not too exotic examples are: Radioactive decay, cooling down of a hot object, a sandglass ...

20. Jan 3, 2017

### windy miller

Imagine a universe that is just particles in thermal equilibrium, can there still be raidacotve decay in such a universe?

21. Jan 3, 2017

### Staff: Mentor

Sure, why not? The inverse reaction would just have to be proceeding at the same rate.

22. Jan 3, 2017

### windy miller

and you could use that to make a clock presumably so the notion of time ticking representing the movement from low entropy to high entropy is not a necessary one as long as there is some sort of mass that can decay? Is that right?

23. Jan 3, 2017

### Staff: Mentor

Not necessarily. Radioactive decay is normally viewed as increasing entropy: the entropy of the decay products is higher than the entropy of the original nucleus. Of course, if we're talking about an entire universe in thermal equilibrium, that view doesn't really apply.

But the more fundamental answer is that "the notion of time ticking representing the movement from low entropy to high entropy" is not correct to begin with. Increasing entropy does not define what "time" is. It just happens to be an empirical fact about our universe, or at least the portion of it (in spacetime) that we can observe, that we can use increasing entropy to define a direction of time, i.e., to distinguish the "future" from the "past". If we were in a universe in a complete state of thermal equilibrium, we would not be able to do this. In fact, in a universe in a complete state of thermal equilibrium, it is not clear that beings like us could even exist; our existence depends on our bodies being far out of thermal equilibrium. But there could still certainly be processes taking place in such a universe that could define a "rate of time flow"--cyclical processes or processes like radioactive decay.