Regarding the problem of the low entropy state at the big bang, people like Penrose, Page, Carroll etc. do not think that inflation solves the problem. I recently read and listen to Seth Lloyd and his explanations about the beginning of the universe from the point of view of entropy as information. In my layman-interpretation of Lloyd's proposal, the universe at the beginning (at the beginning of inflation) is small and very simple, containing only a few qbits of information. Being small, the energy it contains is also little so it doesn't need to be in a very uncommon low entropy configuration. In fact at this moment the universe is not smooth so almost all energy it contains must be used to describe the system, implying a high entropy state. During inflation, the inflation energy grows as potential gravitational energy grows. Being the universe still almost empty of particles and matter, and as it become bigger and thus smoother and ordered, the rise in energy is more substantial compared to the rise in the information needed to describe the system. So entropy is lower (the system has a lot of free energy not required to describe the system). This is the core of my question. It is possible that the process i just described leads to a temporary lowering of the entropy of the universe, untill reheating populate the universe with particles and the entropy goes high again, but, coming from a lower state, the time-asymmetry and the arrow of time emerge, and the subsequent interaction of particles with the gravitational field and the quantum fluctuations in energy density (cmb) give rises to galaxies, and all kind of lower entropy systems? I know the first law of thermodynamics states that energy is conserved, but, as in inflation, the positive energy is balanced by the negative gravitational energy. I also know the second law of thermodynamics, that says that entropy has to increase, both in the future as in the past. But that is a law based on statistics and probabilities, so it should be possible, given a process like the one i described above, to reach a lower entropy state from a higher one. I also know about Maxwell's demon, so i know that any attempt to do this NOW will result in a process that overall requires more information than it can produce, in the end increasing the entropy of the whole system. But conditions at the beginning of inflation were different from now, as i described above. Could not be it that a small system very simple to describe, injected with energy by an inflation field coupled with a gravitational field (preserving the first law of thermodynamics), would result in a decrease in entropy (interpreting entropy as the ratio between energy and the amount of information required to describe the system)?
Please refer us to your source of information so we can have some idea of what you're talking about. Does he have a paper on arxiv.org, for example?
the reference to Seth Lloyd mostly regarded the interpretation of entropy as information, these links on arxiv can be relevant to that (i haven't read them yet): http://arxiv.org/abs/quant-ph/9908043 http://arxiv.org/abs/quant-ph/9612034 i read about the implications of information theory for the initial state of the universe in Lloyd's book "Programming the Universe", i'll quote one of the relevant parts (page 37): "all at once, the universe sprang into existence. Time began, and with it, space. The newborn universe was simple; the newly woven fabric of quantum fields contained only small amounts of information and energy. At most, it required a few bits of information to describe[...] As soon as it began, though, the universe began to expand. As it expanded, it pulled more and more energy out of the underlying quantum fabric of space and time. Current physical theories suggest that the amount of energy in the early universe grew very rapidly (a process called “inflation”), while the amount of information grew more slowly. The early universe remained simple and orderly: it could be described by just a few bits of information. The energy that was created was free energy. This paucity of information did not last for long, however. As the expansion continued, the free energy in the quantum fields was converted into heat, increasing entropy, and all sorts of elementary particles were created. These particles were hot: they jiggled around with a vengeance. To describe this jiggling would take a lot of information. After a billionth of a second—the amount of time it takes light to travel about a foot—had passed, the amount of information contained within the universe was on the order of 100 million billion billion billion billion billion (1050) bits."
I was able to view the relevant page of the book on amazon, and I think there's information necessary to understand what he's saying in the part you cut out: This is an interesting idea, but as far as I know (I could be wrong) it is something completely idiosyncratic to Lloyd. I have never heard of anyone suggesting that "there is only one possible initial state of the universe." Since this section from his popularization doesn't give any specifics, it's impossible to know what theories he's referring to. Typically, the laws of physics determine the evolution of a physical system over time, but they say absolutely nothing about the initial conditions. As far as I know (and again, I could be wrong), the consensus view is precisely the opposite of what Lloyd is saying here. He's saying that it's completely natural to imagine the initial universe as having zero entropy. The typical argument is that one should expect the early universe to have maximum entropy, since low-entropy states are extremely improbable if you're choosing a state at random. I think the consensus view is that the early universe had a very large entropy (not zero!), but not nearly as large as the maximum entropy. We have a FAQ about this: https://www.physicsforums.com/showthread.php?t=509650 This isn't right. There is no such thing as conservation of energy, and no such thing as gravitational potential energy, in a cosmological spacetime. We have a FAQ about this: https://www.physicsforums.com/showthread.php?t=506985 The early universe was very dense. It was not almost empty of particles and matter. If you're using entropy as a measure of order, then it can't have gotten more ordered. That would violate the second law of thermodynamics. No, entropy has to go up, by the second law. One thing that seems sloppy to me about this popularization is that he talks about information as growing, and tries to make inferences about entropy from it, but he doesn't say anything about coarse-graining. The standard model of particle physics says that information is in some sense always conserved. Therefore you can't really talk about a connection between information and entropy without introducing some kind of coarse-graining. The two papers on arxiv that you linked to are, as far as I can tell, not really relevant to the subject of your original post.
Also, note that the interpretation of entropy as a measure of information content of a system dates back to the 40's and Claude Shannon's seminal paper A Mathematical Theory of Communication. Brillouin's book Science and Information Theory carefully lays out the equivalence of Shannon's information entropy and Boltzmann's thermodynamic entropy.
Also note that the small size of the universe prior to inflation, does not really explain the low entropy state of the early universe. See Page 6 of http://arxiv.org/abs/0711.1656:
sorry for my late reply but i haven't had the time to address the questions properly before. I know that people like Penrose and Carroll have issues regarding the apparent ability of inflation to explain the low entropy near big bang, i wrote it in the first line of my first post, my question is in fact just about this. I will try to be more precise. I am asking your opinion about the fact that a simple universe, as the inflating universe is, can mathematically be consistent with a low (meaning lower-than-now) entropy state (in the process creating an arrow of time and the chance for low entropy systems to emerge). In my view answering "no because the second law of thermodynamics doesn't permit it", it is not a fulfilling answer, as the observational evidence that entropy was lower in the past is anyway in clear violation of thermodynamics, and i currently know of no solutions to this problem that do not require multiple universes (not that i have anything against the idea but i would feel more confortable if there was a self-consistent explanation that doesn't need interactions with external systems to work). i think what Lloyd had in mind is some kind of old-school "ultimate theory" of the kind Einstein or Weinberg were looking for, with no variables, so that you don't need even a bit of information to make it start, as is completely defined and necessary in itself (no options, no bits). That was before many worlds, string landscapes and eternal inflations theories came to suggest that maybe it doesn't even exists a single theory of that kind. i cut it out because it doesn't matter to me for the present discussion if no bits as opposed to just a few bits of information are required at the beginning, the point is that the initial conditions are simple, and i think that is also the consensus view. But you also write in the link you provided that So we can at least agree that entropy in the past (near the beginning at least) was at least lower than now. But isn't it also a violation of the second law of thermodynamics, if we don't provide an explanation for this (since second law also applies in the past)? As you wrote, current models doesn't seem to Penrose to provide this explanation, and that is precisely what my understanding of Lloyd' proposal tries to do. As far as i understand it, the universe at the end of inflation, just before reheating, was dense with the energy of the inflation field, but beside it and the tiny quantum fluctuations, it was empty of standard model's particles. i think the consensus view is that inflation made the universe smoother and, in a word, simpler, that's one of the best features of inflation. In Lloyd view's as i understand it, a simpler universe means a universe that requires less information to be described, so that it has loads of available free energy. That's a universe with low entropy. It doesn't have to be in a low entropy state before inflation, initial conditions can be random as long as there's an inflation field that make homogeneus the structure of space-time and spreads the free energy at the end of the process. At the end of the process inflation energy is released and the second law instantly take charge and entropy increases hugely (as Lloyd points out) causing reheating, and the emergence of standard model's particles and the arrow of time. That's the point of my question. The universe during inflation became more simpler and that means, from the point of view of information, a universe meager to describe. The fact that less information is required seems to imply that there are fewer degrees of freedom describing the state of the system. This seems to violate unitarity, as Sean Carroll points out on page 15 (same argument as yenchin): http://arxiv.org/PS_cache/hep-th/pdf/0410/0410270v1.pdf "An obvious prerequisite for unitary evolution is the conservation of the set of degrees of freedom characterizing the system" but he also adds: "Whether one chooses to think of this process as truly non-unitary is to some extent a matter of choice, depending on one’s point of view toward collapse of the wavefunction; from a Copenhagen point of view it is truly non-unitary, while from a many-worlds perspective the evolution of the entire wavefunction is perfectly unitary. If unitarity is violated, degrees of freedom are brought into existence as the universe expands, so that our current universe has a much larger number of degrees of freedom than were present in the corresponding comoving volume at the beginning of inﬂation" So IF most degrees of freedom evolve during/just after inflation, that would be an explanation for the low entropy state near the beginning and the apparent violation of the second law. I know that decoherence in a relative states framework can account for the apparent violation of unitarity on the single branches (the appartent "collapse of the wave-function"). I also read that a decoherence process is present even before the end of inflation: http://www.sbfisica.org.br/bjp/files/v35_391.pdf section 4 So my question is, is it possible that the universe, from a coherent and very simple state, by undergoing decoherence gains additional degrees of freedom (at least in our relative apparently-non-unitary branch) that exponentially increase the entropy of (our branch of) the system? After all, Carroll himself writes that "there is an apparent violation of unitarity in the process of reheating, due to particle production" Couldn't that violation of unitarity, due to decoherence, explain the sudden increase in entropy? Or maybe a similar process happening during inflation even before reheating? In general, what is the effect on entropy of a system changing from a coherent state to a decohered state? i found this thread that can be useful to my question https://www.physicsforums.com/showthread.php?t=260539 in here they say that "Zurek states that entropy increases upon decoherence", could this be of any relevance to my arguments above?