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force5
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Can a volume of space exist without the presents of some form of energy?
Yes, ZPE is widely accepted, and the predicted forces have been experimentally measured. Just run a Googlesearch on "Casimir Effect". I'm not sure that this ground state "mass of vacuum" has been adequately incorporated into cosmology yet, but ZPE is non-controversial.force5 said:I assume this idea is widely accepted in mainstream thinking.
If space can be curved so that there is some sort of structure to spacetime, then it would seem that it should be possible to evaluate the Shannon information of that structure, and therefore associate and entropy to this curvature of spacetime. Is there more information associated with more or less curvature? Does this entropy mean that there is a certain emount of energy in empty space?force5 said:Can a volume of space exist without the presents of some form of energy?
The ZPE model says that there certainly is a ground state level of energy in empty space (vacuum energy). If that empty space is distorted by the presence of local mass, will the ZPE manifest differently? I think it is likely, (and I have posted inquiries to this forum looking for clues) with no positive feedback.Mike2 said:If space can be curved so that there is some sort of structure to spacetime, then it would seem that it should be possible to evaluate the Shannon information of that structure, and therefore associate and entropy to this curvature of spacetime. Is there more information associated with more or less curvature? Does this entropy mean that there is a certain emount of energy in empty space?
Your suspiscion is well founded. A 'pure' vacuum state [which does not exist in nature] would have no interacting fields and behaves differently than normal space, which has all sorts of interacting fields [e.g. gravitaty, EM]. If you are interested in a thorough [and I mean thorough] treatise on quantum field theory, try here.turbo-1 said:The ZPE model says that there certainly is a ground state level of energy in empty space (vacuum energy). If that empty space is distorted by the presence of local mass, will the ZPE manifest differently? I think it is likely, (and I have posted inquiries to this forum looking for clues) with no positive feedback.
Particles themselves are a form of structure which should have an accompanying information and/or entropy. That these particles can form spontaneously from empty space in the form of virtual particles would seem to correspond to a decrease in entropy. I would suppose that somewhere there should be a corresponding increase in entropy to at least balance things. If particles are forms of structure (as they surely are in string theory), then where is the corresponding increase in entropy for the decrease in entropy represented by particle creation?Chronos said:Your suspiscion is well founded. A 'pure' vacuum state [which does not exist in nature] would have no interacting fields and behaves differently than normal space, which has all sorts of interacting fields [e.g. gravitaty, EM]. If you are interested in a thorough [and I mean thorough] treatise on quantum field theory, try here.
http://arxiv.org/abs/hep-th/9912205
Good point. ZPE is thought to be responsible for the expansion of the universe. That is where the entropy increases.Mike2 said:Particles themselves are a form of structure which should have an accompanying information and/or entropy. That these particles can form spontaneously from empty space in the form of virtual particles would seem to correspond to a decrease in entropy. I would suppose that somewhere there should be a corresponding increase in entropy to at least balance things. If particles are forms of structure (as they surely are in string theory), then where is the corresponding increase in entropy for the decrease in entropy represented by particle creation?
Mike2 said:Particles themselves are a form of structure which should have an accompanying information and/or entropy. That these particles can form spontaneously from empty space in the form of virtual particles would seem to correspond to a decrease in entropy. I would suppose that somewhere there should be a corresponding increase in entropy to at least balance things. If particles are forms of structure (as they surely are in string theory), then where is the corresponding increase in entropy for the decrease in entropy represented by particle creation?
So is the increase in entropy (which at least balances the decrease in entropy associated with the creation of particle structures) come from the uncurling of large dimensions as the universe expands? Or does it come from the added space as the universe expands. I would thing that both are dissipative processes. Though perhaps adding space is adding structure/information.Chronos said:Good point. ZPE is thought to be responsible for the expansion of the universe. That is where the entropy increases.
Here is another question - they are a lot easier to come up with than answers! As our Universe expands, do the discrete fundamental units of space-time simply expand and remain constant in numbers? If not, do new units of space-time self-create to accommodate the expansion? This may sound goofy, but if the Loop Quantum Gravity folks are on the right track, space-time comes in discrete units quantized at the Planck level, and they will either have to distort or spontaneously arise to accommodate cosmological expansion.Mike2 said:So is the increase in entropy (which at least balances the decrease in entropy associated with the creation of particle structures) come from the uncurling of large dimensions as the universe expands? Or does it come from the added space as the universe expands. I would thing that both are dissipative processes. Though perhaps adding space is adding structure/information.
So if you add a unit of spacetime, what does that do to the entropy of the universe? Would that just add another state that a particle could be found in? (I suppose even stretching space continuously also may add more states where a particle could go) You may have to remind me again, what happens to the overall entropy in a closed container of gas if the volume is simply increased?turbo-1 said:Since we know that mass can distort space-time, I'm prepared to accept elasticity over continuous creation, but I could be wrong about that. It could even be a combination - perhaps there is a limit as to how much these discrete units can be distorted, at which point they break and form two new units... Pure speculation only, but there will be serious consequences for your entropic model in any event.
String and LQG are models that might allow GR to be reconciled with QED. For this to happen, gravity has to be modeled at the quantum scale. This is where the rubber meets the road. These are all mathematical models, by the way. The universe as conceived by Ptolomy, Copernicus, Kepler, Newton, Einstein, etc are only approximations. They are not real, in any sense. As inconsistencies arise, new models are developed that better explain observations, and they must evolve. Ultimately the failures of one model will spur the development of a successor that is more accurate and robust.Nereid said:- anything at all coming from String/M Theory or LQG is pure theory (some would say pure speculation); there are *no* observations or experiments which constrain either theory in any significant way; this includes anything to do with 'string-related entropy', or 'discrete fundamental units of space-time'.
OK, let's see,... Think with me,... Let's go all the way back to the very instant of creation, or at least to the first distinguishable entity, be it a particle or spacetime, etc. Wouldn't the rise of anything (from possibly nothing) constitute a form of structure. Whatever that first "thing" is, isn't the fact that it is distinguishable mean that it presents a particular amount of information? Wouldn't this represent an increase in information. Wouldn't this be a decrease in the entropy of the universe contrary to the 2nd law of thermodynamics? I would suppose that there would have to be balance somewhere so that at least the total entropy is zero. If that first entity follows from logic so there is no alternative, then the probability that it exist is 1 and the information is zero. Can there be alternatives with the first article? Or do alternatives only exist when there is more instances of something, for example, more than one point of spacetime, etc?Mike2 said:Does the collapse of the wave function represent an increase in information, or decrease of entropy? Does the creation of possible states represent an increase of entropy? Are the two always balanced?
Universal conservation of information is going to be really tough to define for lots of reasons, not the least of which is how you measure the information value of an object in its various states.Mike2 said:OK, let's see,... Think with me,... Let's go all the way back to the very instant of creation, or at least to the first distinguishable entity, be it a particle or spacetime, etc. Wouldn't the rise of anything (from possibly nothing) constitute a form of structure. Whatever that first "thing" is, isn't the fact that it is distinguishable mean that it presents a particular amount of information? Wouldn't this represent an increase in information. Wouldn't this be a decrease in the entropy of the universe contrary to the 2nd law of thermodynamics? I would suppose that there would have to be balance somewhere so that at least the total entropy is zero. If that first entity follows from logic so there is no alternative, then the probability that it exist is 1 and the information is zero. Can there be alternatives with the first article? Or do alternatives only exist when there is more instances of something, for example, more than one point of spacetime, etc?
I think this all constitutes a proof that the universe as a whole conserves information, right?
I only meant to suggest that such a conservation of information law (if it exists) might just be the mechanism that necessitates quantum superpositions of alternative structures. The structure represents an increase in information, the increase in the number of alternatives represents an increase in entropy, or something like that.turbo-1 said:Universal conservation of information is going to be really tough to define for lots of reasons, not the least of which is how you measure the information value of an object in its various states.
So as an entity (let's take the dimensionality for example) arises, which represents some sturcture, then with it also comes alternatives. Yes it would be hard to calculate the entropy of a certain n-dimensional sturcture. But could it be that the negative entropy of that structure will equal the information associated with choosing that structure among the alternatives? Is the information of any structure equal to the choice of it over the alternatives? Does this give a prescription of how to assign a probability (or an amplitude and phase) to a given structure ?Mike2 said:I only meant to suggest that such a conservation of information law (if it exists) might just be the mechanism that necessitates quantum superpositions of alternative structures. The structure represents an increase in information, the increase in the number of alternatives represents an increase in entropy, or something like that.
Let's look at the Universe in standard cosmology. We will assume that the Big Bang happened and that the Universe is expanding and will eventually cool to darkness. The existence of the singularity can be viewed as posessing a very high potential (low entropy) and low information content. Extrapolate out to the present (and assume our universe is expanding and cooling), and you will see that although the Universe is now headed to a more entropic state, it has a much higher information content.Mike2 said:So as an entity (let's take the dimensionality for example) arises, which represents some sturcture, then with it also comes alternatives. Yes it would be hard to calculate the entropy of a certain n-dimensional sturcture. But could it be that the negative entropy of that structure will equal the information associated with choosing that structure among the alternatives? Is the information of any structure equal to the choice of it over the alternatives? Does this give a prescription of how to assign a probability (or an amplitude and phase) to a given structure ?
Thanks for the reply. I'm thinking (no proof yet) that the expansion of the universe itself is a dissipative, entropy increasing balance to the information increasing development of structures within it. The interference of the quantum mechanical phases of various alternatives describes a kind of existence to these alternatives, since they interfere. The number of possible states must increase so that the information contained in a choice of some structure will equal the information content considered for that structure alone. For certainly any structure we may consider has information inherent in that structure. This is true simply because it was distinguishable from every other structure that could be considered but which it is not.turbo-1 said:Since we are here discussing this, the chance of the existence of the singularity cannot be infinitely small, but must in fact be unity. For this reason, if for no other, conservation of information does not "play well" with the standard model. If you envision a steady-state Universe of some type, you might be able to make the case for COI, but not for the Big Bang U.
That is a tautology, and is impossible to refute. Nor does it enlighten. The problem is "how will you define information such that it can be quantified and compared?" If you want to search for a mechanism that will conserve information, you first have to define "information" in a quantifiable way, so you can measure it.Mike2 said:Isn't information equal to information no matter how you look at it?
Yes, there's a book or two on information theory kicking around.Mike2 said:Do you know if there is any book about all this?
force5 said:Can a volume of space exist without the presence of some form of energy?
No it is not a tautology. I was equating extrinsic to intrinsic versions of information/entropy. The intrinsic version is obtained by the usual integration procedure. The extrinsic was obtained by the associated probabilities for alternatives. It is a tautology only when looking at the functions that describe probability distributions. But when we turn to look at other kinds of structure in the universe, such as one of many paths of a particle, then a single path has a structure/function of its own. There is information inherent in the structure of that path all by itself. And I was considering how this compares to the information associated with chosing that path over the alternatives that are suggested by the "path integral" formulation of QM. Are both kinds of information equal? That would be interesting and might suggest the necessity of QM. Does this help?turbo-1 said:That is a tautology, and is impossible to refute. Nor does it enlighten. The problem is "how will you define information such that it can be quantified and compared?" If you want to search for a mechanism that will conserve information, you first have to define "information" in a quantifiable way, so you can measure it.
I'm getting a Browser bug report from amazon. Could you supply titles please? Thanks.Yes, there's a book or two on information theory kicking around.
Interesting, I get that when following the link I posted! Just go to Amazon and search on information theory and you'll get lots of suggestions. You might wander over to a college bookstore near you and browse the used textbooks - probably a lot cheaper, and you'll get to see if the subject is presented in a manner that you're comfortable with.Mike2 said:I'm getting a Browser bug report from amazon. Could you supply titles please? Thanks.
That last paper may be "a bit off subject" but it is apropriate. Pseudo-scientists like William Dembski love manipulating information theory to "prove" Creationism - leave it to Davies to provide a cogent retort.Chronos said:Application of information theory to cosmological modeling is fairly common. Here are some links. The last paper is a bit off subject, but, you may find it interesting.
http://arxiv.org/abs/gr-qc/0402076
http://arxiv.org/abs/astro-ph/0310522
http://arxiv.org/abs/astro-ph/0309435
http://arxiv.org/abs/hep-th/0308165
http://arxiv.org/abs/cond-mat/0207707
http://arxiv.org/abs/gr-qc/0312078
http://arxiv.org/abs/astro-ph/0408014
turbo-1 said:This may sound goofy, but if the Loop Quantum Gravity folks are on the right track, space-time comes in discrete units quantized at the Planck level, and they will either have to distort or spontaneously arise to accommodate cosmological expansion.
Frustrating, is it not? I often wonder how big the mountain must be before even the Sherpa's question the possibility of conquering a new peak.Nereid said:The inspiring (depressing?) thing about good ol' Uncle Al is that the ever-growing body of experimental results continues to be consistent with GR! Or, saying the same thing in another way, the domain in which GR and QM will clearly show their mutual inconsistency remains beyond that which we can (and are likely to be able to) probe.
Appropriate to what? Mike2 asked for some information relevant to his questions. I missed the part where anyone brought up 'creationism' as an issue.turbo-1 said:That last paper may be "a bit off subject" but it is apropriate. Pseudo-scientists like William Dembski love manipulating information theory to "prove" Creationism - leave it to Davies to provide a cogent retort.
Appropriate in the sense that information theory (which was being discussed) is used to "prove" lif is emergent. Information theory is the tool of choice for Dembski, and to make it work for him, he puts some interesting constrants on what can be construed as information. Davies used the same tool with entirely different results, to "prove" life is emergent. If you Google "conservation of information" you will see some interesting links, and you will see why I emphasized the importance of defining "information".Chronos said:Appropriate to what? Mike2 asked for some information relevant to his questions. I missed the part where anyone brought up 'creationism' as an issue.
Use of information theory in quantum physics is surprisingly sophisticated. There are, of course, some inherent difficulties, but, less so than you might imagine. I don't know of any books, offhand, but there sure are some good papers. I have a couple more links that might be closer to the heart of your questions. Here is a old one.Mike2 said:I assume that every physical structure can be described mathematically with equations. And it would seem that there is a procedure for extracting the information in a function. Normally, information is calculated for probability distributions with an integral functional. So I suppose that the same technique could be used on any function as long as it were possible to normalize it by dividing it by the average. This means that the functions involved would have to be well behaved, not going to infinity, or at least integrable if they do. And I think this is true for any formulas of physics. Is this right?
What is remarkable about this hypothesis is that it may predict the "existence" of quantum mechanical alternatives so that the choice of some structure would equal the inherent information of that structure. Could it be any other way? Can you say that some structure has inherent information value without also saying that this mean that there must have been alternatives somewhere to chose it from? Is this a kind of extrinsic information equals intrinsic information law? Isn't information equal to information no matter how you look at it?
Do you know if there is any book about all this?