Would a collapsing universe break the Law for entropy

[skeleton]

Given:
- Entropy is the measure of ordered states of a system.
- At the creation of the universe from the Big Bang event, all matter was in a more primitive form (eg: quarks instead of hadrons).
- Dark Energy is providing a mechanism by which the universe may forever expand.

Hypothetical scenario:
- Consider that Dark Energy not being as plentiful as estimated.
- The universe is observed to be decelerating in its expansion, which may eventually lead to a contraction.
- Then eventually the universe may lead to a Big Crunch.

Consequential conjecture:
- It might be presumed that matter will transform to primitives as had originated during the Big Bang.
- It might be presumed that all primitive matter is arranged into a more compacted volume.
- It could be imagined that this compacted volume would have fewer ordered arrangements (permutations) than how the current universe is arranged.
- Then one could conclude that the entropy of a Big Crunch is lower than the current state of the universe.

Questions:
- Would a collapsing (non-expanding) universe imply a reversal of the Second Law of Thermodynamics?
- Would a collapsing universe demonstrate that the mechanics of the universe is a reversible (thermodynamic) process.

 

[bill alsept]

Questions:
- Would a collapsing (non-expanding) universe imply a reversal of the Second Law of Thermodynamics?

Yes, and what if it was already collapsing like everything else we see.

 

[thebiggerbang]

Instead of focusing on the 'compaction of matter' only, do also look at what happens to the system (the universe) as a whole. Although I can't comment on how this would prevent the law from breaking down, we should possibly look at the work done (but on what?) during the compaction.

 

[Chalnoth]

Given:
- Entropy is the measure of ordered states of a system.

This isn't an accurate description. Entropy is a measure of the specific configuration of the system. Basically, it's a measure of how many possible ways the microscopic configuration of the system can be modified without the macroscopic measurable variables (e.g. pressure, temperature, density) changing. A higher-entropy system is one in which the same observables can be described by a larger number of microscopic configurations.

This is, fundamentally, why systems tend from lower-entropy configurations to higher-entropy configurations: there are many, many more high-entropy configurations than low-entropy configurations. So if you start with low entropy, as it moves to a different configuration, chances are the new configuration will be higher in entropy. If you actually run the numbers, the probabilities are so unbelievably strong that for most situations you are absolutely guaranteed to move to a higher-entropy configuration, just because nearly all of the possible configurations are higher in entropy.

- Then one could conclude that the entropy of a Big Crunch is lower than the current state of the universe.

That's either wrong or a statement that it almost certainly won't happen. Basically, you can having a collapsing universe increase in entropy just fine: as long as matter continues to get more and more clumpy as the universe collapses, it's going to increase in entropy. And if your specific model of the recollapse doesn't follow this and instead has a decrease in entropy, then it is almost certainly an incorrect model (basically, if your model has decreases in entropy, any slight perturbation of the model will lead to a situation where the entropy increases instead, probably meaning your model is unstable and will never happen like that).

 

[bill alsept]

This is, fundamentally, why systems tend from lower-entropy configurations to higher-entropy configurations: there are many, many more high-entropy configurations than low-entropy configurations. So if you start with low entropy, as it moves to a different configuration, chances are the new configuration will be higher in entropy. If you actually run the numbers, the probabilities are so unbelievably strong that for most situations you are absolutely guaranteed to move to a higher-entropy configuration, just because nearly all of the possible configurations are higher in entropy.

If you separated all matter down to a point that it could not be divided again as in quanta and say the universe was made and filled with these diffused particles. Wouldn't that be entropy at its highest level? As it accumulates into larger and larger matter (no matter how unorganized it looks to some) the entropy would have to drop. And at 100% density would be the lowest entropy.

 

[Chalnoth]

If you separated all matter down to a point that it could not be divided again as in quanta and say the universe was made and filled with these diffused particles. Wouldn't that be entropy at its highest level? As it accumulates into larger and larger matter (no matter how unorganized it looks to some) the entropy would have to drop. And at 100% density would be the lowest entropy.

I have no idea what you mean.

But I think this point may help: the fact of the matter is that when you start dealing with interactions between particles, whether gravity, electromagnetic, nuclear, or whatever, the calculations start to get horribly complicated and it becomes difficult to apply the "number of configurations" view directly. Basically, the "number of configurations" view is still completely accurate, but the way in which you calculate that number of configurations becomes horribly complicated, and you just can't use simple intuitive pictures.

The better rule of thumb is basically to say that if we see something happen going forward in time, then that process is either constant in entropy or represents an increase in entropy, whatever that process happens to be.

 

[dacruick]

I have no idea what you mean.

But I think this point may help: the fact of the matter is that when you start dealing with interactions between particles, whether gravity, electromagnetic, nuclear, or whatever, the calculations start to get horribly complicated and it becomes difficult to apply the "number of configurations" view directly. Basically, the "number of configurations" view is still completely accurate, but the way in which you calculate that number of configurations becomes horribly complicated, and you just can't use simple intuitive pictures.

The better rule of thumb is basically to say that if we see something happen going forward in time, then that process is either constant in entropy or represents an increase in entropy, whatever that process happens to be.

This is how I'm understanding the conversation. The OP is asking about a contracting universe, in which case configurations of particles will becomes more ordered. The problem that I see with this is that as you move to a lower entropy configuration, the number of higher entropy configurations increase, making it statistically even less likely to continue along the "decreasing entropy" trend.

I think that this process is a product of thermal energy flowing from high to lower temperature. So I think what the OP is actually asking(which is a cool question), if thermal energy flowed from low temperature to high temperature, would it be possible for the universe to contract all the way back to a singularity.

 

[Chalnoth]

This is how I'm understanding the conversation. The OP is asking about a contracting universe, in which case configurations of particles will becomes more ordered.

Except there is no reason whatsoever to believe that a collapsing universe would do this.

 

[dacruick]

Except there is no reason whatsoever to believe that a collapsing universe would do this.

So let me see if I'm understanding this; you're saying that reversing the thermodynamic laws shouldn't have an effect on the expansion of the universe?

 

[Chalnoth]

So let me see if I'm understanding this; you're saying that reversing the thermodynamic laws shouldn't have an effect on the expansion of the universe?

That statement doesn't make any sense to me.

Instead what I'm saying is that changing the sign of the expansion has no impact on thermodynamic laws. Basically, if our universe were such that at some point it started to recollapse, matter would still tend to form more and more clumps as the universe collapsed. The collapse, in other words, would not be the time reversal of the expansion: our universe started out extremely smooth, and has gotten lumpier with time as entropy has increased. A transition to collapse wouldn't slow this process down, let alone reverse it. Indeed, the recollapse would cause things to get lumpier even faster.

 

[dacruick]

That statement doesn't make any sense to me.

Instead what I'm saying is that changing the sign of the expansion has no impact on thermodynamic laws.

Hmm. I've always been told that there is a relationship between the expansion of the universe and entropy, but from what you're saying it sounds like they are independent.

 

[Chalnoth]

Hmm. I've always been told that there is a relationship between the expansion of the universe and entropy, but from what you're saying it sounds like they are independent.

Yes, absolutely.

Basically, the forward time direction is defined by the direction in which entropy increases. Increases in entropy are precisely what causes us to experience the sensation of time moving inexorably forward. Because the direction of time is set by entropy, it is a contradiction in terms to talk about anything at all causing entropy to decrease in the future.

There is a slight caveat here that entropy doesn't quite increase inexorably. It fluctuates slightly, but for most situations we can ignore the fact that entropy wiggles up and down in its overall trend upward.

 

[skeleton]

Perhaps the distant future of the universe would see all matter collected into black holes. Afterwards, there would be no intergalactic dust nor stars; there would eventually be only black holes. What remains are very cold objects. Black holes with mass equal to the Sun would have a temperature of 10^-5 oK. Larger black holes would be even colder.

Bose-Einstein condensates of atomic matter have been observed in temperature ranges from 2 oK to 14 oK. In this phase of matter, all the constituent atoms share an equal value to their properties. So the number of permutations for the amalgamation is unity instead of a larger number (which otherwise would be a function of its population N and available states).

My conjecture is that future black holes might behave something like a Bose-Einstein condensate within - with a single-value for each of its internal properties. This is somewhat consistent with the notion that black holes have no hair - they don't show their inherent features because they don't have any (or but one value for each parameter). If so, then these massive objects have perhaps only a few constitutive parameter that could permutate (vis a vie statistical mechanics - with attention to entropy). Despite their enormous mass, perhaps their permutable property of its mass is 'one' (its actual weight, but without any provision for spatial distribution). Likewise for the properties of charge and spin - a single value for each.

Now, let's go even further into the universe's future. Eventually, all those black holes may come together, as driven by their mutual gravitational attraction. (Remember, I was contemplating the scenario where there is insufficient Dark Energy to overcome the gravitational potential of the remaining black holes.)

Alas, the entire universe might coalesce into a single giant black hole. That terminal black hole would have perhaps only three state values: mass, charge and spin. There would be no permutations for spatial arrangement as the universe would consistent merely of a single singularity. Space might become meaningless and time would be irrelevant.

And what of the entropy of the terminal universe. Entropy, S = kB*ln(N_states) = kB*ln(1) = 0.

 

[bill alsept]

Perhaps the distant future of the universe would see all matter collected into black holes. Afterwards, there would be no intergalactic dust nor stars; there would eventually be only black holes. What remains are very cold objects. Black holes with mass equal to the Sun would have a temperature of 10^-5 oK. Larger black holes would be even colder.

Bose-Einstein condensates of atomic matter have been observed in temperature ranges from 2 oK to 14 oK. In this phase of matter, all the constituent atoms share an equal value to their properties. So the number of permutations for the amalgamation is unity instead of a larger number (which otherwise would be a function of its population N and available states).

My conjecture is that future black holes might behave something like a Bose-Einstein condensate within - with a single-value for each of its internal properties. This is somewhat consistent with the notion that black holes have no hair - they don't show their inherent features because they don't have any (or but one value for each parameter). If so, then these massive objects have perhaps only a few constitutive parameter that could permutate (vis a vie statistical mechanics - with attention to entropy). Despite their enormous mass, perhaps their permutable property of its mass is 'one' (its actual weight, but without any provision for spatial distribution). Likewise for the properties of charge and spin - a single value for each.

Now, let's go even further into the universe's future. Eventually, all those black holes may come together, as driven by their mutual gravitational attraction. (Remember, I was contemplating the scenario where there is insufficient Dark Energy to overcome the gravitational potential of the remaining black holes.)

Alas, the entire universe might coalesce into a single giant black hole. That terminal black hole would have perhaps only three state values: mass, charge and spin. There would be no permutations for spatial arrangement as the universe would consistent merely of a single singularity. Space might become meaningless and time would be irrelevant.

And what of the entropy of the terminal universe. Entropy, S = kB*ln(N_states) = kB*ln(1) = 0.

I have made this claim in a few other post but no one wants to discuss cold black holes and I'm told those discussion are not allowed on PF. I agree that any matter compacted to a finale density would not be able to have moving parts at least on the inside. I’ll also go out on a limb and say:

I would make changes to your final outcome. I believe that it is the substance of space that is slowly condensing into everything we see and in the end as long as there is still space the surface of the black holes will still stay active and hot. When all black holes have accumulated into one and the last bit of space has condensed onto the surface of the finale black hole, then the activity will stop and so will the effect of gravity. And with respect to the OP entropy would be at its lowest.

This final singularity will not have the effect of gravity and would be cold and motionless throughout. With no motion there could be no electromagnetic fields. If it were not for the motion of the last and final remnants of space condensing onto the surface of this singularity then the cycle would come to a stop.

But instead, as the last quanta hit the surface and bump unto quanta already on the surface small fields will continue to form. The fields repulse each other and because the effect of gravity has gone away a chain reaction begins. Starting on the surface the quanta push each other in an outward direction. Soon more and more quanta are forming repulsive fields and all moving in an outward direction. With everything moving the same outward direction there would be no resistance and no speed limit. Just a suggestion for the source of inflation.

 

[Chalnoth]

Perhaps the distant future of the universe would see all matter collected into black holes. Afterwards, there would be no intergalactic dust nor stars; there would eventually be only black holes. What remains are very cold objects. Black holes with mass equal to the Sun would have a temperature of 10^-5 oK. Larger black holes would be even colder.

Bose-Einstein condensates of atomic matter have been observed in temperature ranges from 2 oK to 14 oK. In this phase of matter, all the constituent atoms share an equal value to their properties. So the number of permutations for the amalgamation is unity instead of a larger number (which otherwise would be a function of its population N and available states).

My conjecture is that future black holes might behave something like a Bose-Einstein condensate within - with a single-value for each of its internal properties. This is somewhat consistent with the notion that black holes have no hair - they don't show their inherent features because they don't have any (or but one value for each parameter). If so, then these massive objects have perhaps only a few constitutive parameter that could permutate (vis a vie statistical mechanics - with attention to entropy). Despite their enormous mass, perhaps their permutable property of its mass is 'one' (its actual weight, but without any provision for spatial distribution). Likewise for the properties of charge and spin - a single value for each.

Now, let's go even further into the universe's future. Eventually, all those black holes may come together, as driven by their mutual gravitational attraction. (Remember, I was contemplating the scenario where there is insufficient Dark Energy to overcome the gravitational potential of the remaining black holes.)

Alas, the entire universe might coalesce into a single giant black hole. That terminal black hole would have perhaps only three state values: mass, charge and spin. There would be no permutations for spatial arrangement as the universe would consistent merely of a single singularity. Space might become meaningless and time would be irrelevant.

And what of the entropy of the terminal universe. Entropy, S = kB*ln(N_states) = kB*ln(1) = 0.

The problem is that these states are macrostates of black holes, not microstates. The entropy of a black hole is well-understood, and it is most definitely not zero (it's proportional to the area of the horizon). Our understanding of entropy tells us that the very small number of observable quantities for a black hole (specifically its horizon area, rotational velocity, and electromagnetic charge) are described by a tremendous number of configurations of the black hole. That is to say, there must be a very large number of degrees of freedom for each possible choice of area, charge, and rotation to explain the entropy of the black hole.

 

[bill alsept]

The problem is that these states are macrostates of black holes, not microstates. The entropy of a black hole is well-understood, and it is most definitely not zero (it's proportional to the area of the horizon). Our understanding of entropy tells us that the very small number of observable quantities for a black hole (specifically its horizon area, rotational velocity, and electromagnetic charge) are described by a tremendous number of configurations of the black hole. That is to say, there must be a very large number of degrees of freedom for each possible choice of area, charge, and rotation to explain the entropy of the black hole.

I would agree that the area from the event horizon down to surface of the black hole would be extreme and described by a tremendous number of configurations. At least until all space has been accumulated. But below the surface where particles are condensed to the point that nothing can move things would be completely ordered.

 

[Chalnoth]

I would agree that the area from the event horizon down to surface of the black hole would be extreme and described by a tremendous number of configurations. At least until all space has been accumulated. But below the surface where particles are condensed to the point that nothing can move things would be completely ordered.

Our rather firm grasp of the entropy of the black hole says otherwise. And furthermore, we now know that the black hole itself can be fully-described only by the degrees of freedom on its horizon. You don't need a large number of states inside the horizon: the large number of states are on the horizon itself.