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ryokan
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What's the actual status of the Weyl curvature hypothesis?
Is there any best explanation to the early low entropy?
Is there any best explanation to the early low entropy?
Thank you, meteor.meteor said:Hi,
try this:
http://arxiv.org/abs/gr-qc/0408065
it exposes the problem of how the universe can evolve starting from its initial state, and the solution given by Penrose, by introducing the concept of "gravitational entropy"
I do not understand this argumentation. This state of maximal entropy mentioned (during nucleosynthesis), did correspond to a specific volume (Vo) and to a specific phase space (No). In a later time the universe expanded, the volume under consideration grew, Vi > Vo, and the phase space became larger Ni > No. Although the entropy So was indeed maximal for the state during nucleosynthesis with its phase space No, the later states had a greater maximal entropy (Si > So) because of new phase spaces Ni (Ni > No) in bigger volumes (Vi > Vo). For me there is no apparent contradiction between evolution of the universe and the second law. Probably I am missing something.In terms of classical thermodynamics, this means that the early universe must have been in a state of (near) thermodynamic equilibrium. From the usual definition of entropy, we can state equivalently that the early universe must have been one of (near) maximal entropy. Thus, according to the second law of thermodynamics, the universe could not have evolve beyond the initial state, since any such evolution would mean a reduction in entropy.
But, nevertheless, we know that matter eventually breaks up due to gravitational attraction and ends up forming structures such as galaxies, stars, planets, planetary clouds etc. This is an evolution in the direction of a less homogeneous distribution of matter, and hence towards a lower entropy state. It appears therefore as if the evolution of structures in the universe breaks the second law of thermodynamics.
A possible solution to this problem was suggested by Penrose [2] in 1977 by introducing the concept of gravitational entropy…
Since beyond the Universe we cannot talk on any phase space, I don't think that your argument be correct because of, although the Universe expand, the whole of phase space would be ever included in it from the beginning. If the early Universe is in thermodynamic equilibrium,it would remain near maximal entropy forever, with independence of expansion.hellfire said:In the introduction of the paper it is written:
I do not understand this argumentation. This state of maximal entropy mentioned (during nucleosynthesis), did correspond to a specific volume (Vo) and to a specific phase space (No). In a later time the universe expanded, the volume under consideration grew, Vi > Vo, and the phase space became larger Ni > No. Although the entropy So was indeed maximal for the state during nucleosynthesis with its phase space No, the later states had a greater maximal entropy (Si > So) because of new phase spaces Ni (Ni > No) in bigger volumes (Vi > Vo). For me there is no apparent contradiction between evolution of the universe and the second law. Probably I am missing something.
I'm still curious... if we take an system inside a volume with a particular entropy, how fast can it change? I assume that no information can leave or enter the light cone. So is the maximum amount that entropy can change governed by surface area change whose radius expands with the speed of light? So what would happen then if one starts low or zero entropy of a system in a small volume?hellfire said:Every next state in time will have a greater maximal S (which corresponds to thermal equilibrium). May be there is something completely wrong in what I am writing here, or may be there is some subtlety if one takes into account gravitation... some guesses?.
Are you claiming that the definition of entropy makes only sense withtin causally connected volumes? I think one can always consider a ‘bigger’ volume and ask which grade of order/disorder/entropy it contains, regardless whether it is causally connected or not. (I may be wrong because I am guessing). Anyway, I do not see how this could help to understand why there is a conflict between 2nd law and evolution of the universe.Mike2 said:I'm still curious... if we take an system inside a volume with a particular entropy, how fast can it change? I assume that no information can leave or enter the light cone. So is the maximum amount that entropy can change governed by surface area change whose radius expands with the speed of light? So what would happen then if one starts low or zero entropy of a system in a small volume?
hellfire said:ryokan, I am not sure to understand your point about the phase space, but let's forget the phase space and focus on the entropy and the volume. If one assumes a ideal gas with N particles at thermal equilibrium at a temperature T one has an entropy (afaik):
S ~ N (ln V + ln N)
Thus, if N remains constant and V increases S must increase assuming the next state is also in thermal equilibrium. If the relation above is correct and can be applied at least in a rough approximation, then I fail to see the problem with the second law. Every next state in time will have a greater maximal S (which corresponds to thermal equilibrium).
Good remark. Yes, according to this formula it would. Any closed and gravitationally bound system which obeys this formula would decrease its entropy (its volume would always decrease). It seams to me that if one wants to save the 2nd law one has to take into account gravitation. But I do not know how gravitation has to be considered in this case and in case of expansion.ryokan said:If so, in an hypothetical Universe evolution to a big crunch (if critical density were enough) it would have a reduction of entropy following a reduction in the Universe volume, with all its consequences, one of which would be a change in the time's arrow.
The Weyl's curvature hypothesis wants to solve this problem. That was the reason for this thread.hellfire said:Good remark. Yes, according to this formula it would. Any closed and gravitationally bound system which obeys this formula would decrease its entropy (its volume would always decrease). It seams to me that if one wants to save the 2nd law one has to take into account gravitation. But I do not know how gravitation has to be considered in this case and in case of expansion.
Let's see, I think entropy compares the order of a state compared to that order of that state at a different time, right? It certainly sounds like causally connected regions to me. What use is it to compare the order of some state compared to some other that is not at all causally connected to it?hellfire said:Are you claiming that the definition of entropy makes only sense withtin causally connected volumes? I think one can always consider a ‘bigger’ volume and ask which grade of order/disorder/entropy it contains, regardless whether it is causally connected or not.
"evolution"... How can we consider how things change without considering how it state of order changes. Evolution is how entropy changes things.hellfire said:Anyway, I do not see how this could help to understand why there is a conflict between 2nd law and evolution of the universe.
Only entropy do not seems to induce biological evolution. Rather it is the biological information which conducts evolution although increasing the entropy.Mike2 said:Evolution is how entropy changes things.
And if the entropy inside 3D sphere of a 4D light-cone is governed by the surface area of that 3D sphere, then what would be the entropy of a sphere shrunk down to the size of that Plank scale?Mike2 said:I'm still curious... if we take an system inside a volume with a particular entropy, how fast can it change? I assume that no information can leave or enter the light cone. So is the maximum amount that entropy can change governed by surface area change whose radius expands with the speed of light? So what would happen then if one starts low or zero entropy of a system in a small volume?
Which problem? According to the formula given above there is a problem for isolated systems which decrease in volume. But the universe expands, and expansion implies a growth of the maximal entropy (entropy in thermal eq.) Obviously I am missing something but I do not see what. It would be nice if someone could explain or give a link to an explanation of the problem which leads to this hypothesis. I just want to understand.ryokan said:The Weyl's curvature hypothesis wants to solve this problem. That was the reason for this thread.
If in any time after the Big-Bang, the Universe's entropy is maximal because it is near its thermal equilibrium (although this maximal entropy were increased by increase of V in expansion, following the formula in your post), what would be the origin of low entropy? It seems that in our solar system, Sun is the basic source of low entropy. It seems, then, that gravitation have a role in the origin of an early low entropy. But also bacause of gravitation, entropy will increase when stars age. There is so a time's arrow in the role of gravitation on entropy that, if I understand well, would be due to a different status of Weyl's tensor along time.hellfire said:Which problem? According to the formula given above there is a problem for isolated systems which decrease in volume. But the universe expands, and expansion implies a growth of the maximal entropy (entropy in thermal eq.) Obviously I am missing something but I do not see what. It would be nice if someone could explain or give a link to an explanation of the problem which leads to this hypothesis. I just want to understand.
hellfire said:Good remark. Yes, according to this formula it would. Any closed and gravitationally bound system which obeys this formula would decrease its entropy (its volume would always decrease). It seams to me that if one wants to save the 2nd law one has to take into account gravitation. But I do not know how gravitation has to be considered in this case and in case of expansion.
ryokan said:If in any time after the Big-Bang, the Universe's entropy is maximal because it is near its thermal equilibrium (although this maximal entropy were increased by increase of V in expansion, following the formula in your post), what would be the origin of low entropy? It seems that in our solar system, Sun is the basic source of low entropy. It seems, then, that gravitation have a role in the origin of an early low entropy. But also bacause of gravitation, entropy will increase when stars age. There is so a time's arrow in the role of gravitation on entropy that, if I understand well, would be due to a different status of Weyl's tensor along time.
The Weyl Curvature Hypothesis is a conjecture in theoretical physics that suggests the existence of a fundamental, quantum-mechanical connection between the curvature of spacetime and the entropy of a black hole. It proposes that the Weyl curvature tensor, which measures the intrinsic curvature of spacetime, is directly related to the entropy of a black hole.
The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. The Weyl Curvature Hypothesis provides a possible explanation for this law by suggesting that the Weyl curvature, which is a measure of the disorder or randomness of spacetime, is inextricably linked to the entropy of a black hole.
Currently, the Weyl Curvature Hypothesis is still a conjecture and has not been proven. However, some evidence from theoretical calculations and observations of black holes supports this hypothesis. For example, studies have shown that the entropy of a black hole can be calculated from the Weyl curvature tensor, and the results are consistent with the predictions of the Weyl Curvature Hypothesis.
If the Weyl Curvature Hypothesis is proven to be true, it could have significant implications for our understanding of the relationship between gravity, quantum mechanics, and thermodynamics. It could also provide a deeper understanding of black holes and their role in the universe.
Some scientists have raised concerns about the validity of the mathematical framework used to support the Weyl Curvature Hypothesis. Others argue that the hypothesis may not be testable with current technology and may require further advancements in theoretical physics. Additionally, some researchers propose alternative theories that could potentially explain the relationship between spacetime curvature and entropy without invoking the Weyl Curvature Hypothesis.