B Is time a consequence of 2nd law of thermodynamics?

[Ebi Rogha]

TL;DR Summary

Does time exist independently or it is a consequence of 2nd law of thermodynamics (the arrow of time, entropy)?

I have heard from a knowledgeable physics proffessor, time exists independently and it is not a consequence of arrow of time. Could some body explain this?

 

[anuttarasammyak]

How do you distinguish these two cases ? May we prepare the world without 2nd law of thermodynamics to investigate it ?

 

[FactChecker]

How can you even state the 2nd law without already having a concept of time? It seems that the dimension must exist before laws can be stated that use it.

 

[Dale]

Summary:: Does time exist independently or it is a consequence of 2nd law of thermodynamics (the arrow of time, entropy)?

I think it does. We have several theories of physics that have time besides the second law of thermodynamics.

 

[andresB]

In the physics of small systems we can see random fluctuations where the 2nd law is violated. Do time goes backward in those cases?

 

[Nugatory]

In the physics of small systems we can see random fluctuations where the 2nd law is violated. Do time goes backwards in those cases?

No.

 

[Lord Jestocost]

Summary:: Does time exist independently or it is a consequence of 2nd law of thermodynamics (the arrow of time, entropy)?

Sir Arthur Stanley Eddington in “THE NATURE OF THE PHYSICAL WORLD” (Cambridge, At the University Press (1929)):

“Without any mystic appeal to consciousness it is possible to find a direction of time on the four-dimensional map [space-time map, LJ] by a study of organization. Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointed towards the future; if the random element decreases, the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone.”

 

[bob012345]

In the physics of small systems we can see random fluctuations where the 2nd law is violated. Do time goes backward in those cases?

Let's be very careful about using the word violated. The fluctuations for small systems are not violations of anything. They are the allowable random occupation of a small number available states. Time has to go forward to occupy those available states.

 

[Dale]

Let's be very careful about using the word violated. The fluctuations for small systems are not violations of anything.

I agree with @andresB word choice here. The 2nd law says entropy never decreases and indeed in small enough systems it has been observed to occasionally decrease. This is an observation which is contrary to what is predicted by the 2nd law, which is what is meant by “violation”.

 

[bob012345]

I agree with @andresB word choice here. The 2nd law says entropy never decreases and indeed in small enough systems it has been observed to occasionally decrease. This is an observation which is contrary to what is predicted by the 2nd law, which is what is meant by “violation”.

Ok, I'm a bit surprised though. Would you argue the $2^{nd}$ Law just doesn't apply for very small systems then?

 

[Dale]

Ok, I'm a bit surprised though. Would you argue the $2^{nd}$ Law just doesn't apply for very small systems then?

Yes, the domain of applicability for classical thermodynamics does not include such small systems. The fluctuation theorem is more general. It applies to such small systems and it reduces to the 2nd law of thermodynamics in the appropriate limit

 

[bob012345]

Yes, the domain of applicability for classical thermodynamics does not include such small systems. The fluctuation theorem is more general. It applies to such small systems and it reduces to the 2nd law of thermodynamics in the appropriate limit

I see what you are saying. I had thought that since the $2^{nd}$ Law was statistical that possible violations for very small systems were always implied. But the Fluctuation Theorem removes ambiguity.

 

[Dale]

I see what you are saying. I had thought that since the $2^{nd}$ Law was statistical that possible violations for very small systems were always implied. But the Fluctuation Theorem removes ambiguity.

I agree with you that it was known to be statistical for a long time, so it is unsurprising that it fails for small systems. But the mathematical statement of the 2nd law of thermo is $dS/dt\ge 0$, and there is no ambiguity that that statement does not hold for small systems over short times.

 

[bob012345]

I agree with you that it was known to be statistical for a long time, so it is unsurprising that it fails for small systems. But the mathematical statement of the 2nd law of thermo is $dS/dt\ge 0$, and there is no ambiguity that that statement does not hold for small systems over short times.

I see. Thanks.

 

[bob012345]

I think it does. We have several theories of physics that have time besides the second law of thermodynamics.

What, if any, would be considered the most fundamental? Also, do we have time to talk about time or is this not the right time?** Shamelessly borrowed from here;

 

[Dale]

What, if any, would be considered the most fundamental?

I don’t know how to objectively measure fundamentalness, but maybe relativity?

 

[atyy]

I have heard from a knowledgeable physics proffessor, time exists independently and it is not a consequence of arrow of time. Could some body explain this?

Time exists in what we consider the fundamental laws of physics, eg. Newtonian mechanics, special relativity, and general relativity. Time is just a specific parameter in the equations. However, there is no direction of time in the sense that a glass dropping and breaking, and its time reversal in which the broken pieces fly up and reassemble into the glass, are both consistent with the fundamental laws of phsyics.

However, we do know that time has a direction in that the glass dropping and breaking is a more plausible physical situation than its time reverse. This is one arrow of time that is given by the second law of thermodynamics.

Another possible arrow of time is the expansion of the universe.

Here are is a discussion of how an arrow of time can arise, even though it is not present in the fundamental laws.