Can a volume of space exist without the presents of some form of energy?
It has been experimentally shown that "empty" space is a seething sea of particle-antiparticle pairs that arise and self-annihilate. These virtual particles have opposite spins, charges, and time-lines, but each of the members has MASS. There is therefore a baseline amount of mass populating every speck of "empty space". This ground state is called Zero Point Energy.
If you do a Google search on "Casimir Effect", you will find lots of interesting links, including explanations of how ZPE has been experimentally verified.
I assume this idea is widely accepted in mainstream thinking.
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.
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?
Here is a nice read that is not very technical
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.
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.
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?
Good point. ZPE is thought to be responsible for the expansion of the universe. That is where the entropy increases.
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.
It would seem that all entities of reality of any physical concern are assumed to be describable by some mathematical structure, be it stars, molecules, particles, or even dimensions. All represent some sort of structure, and there should be some sort of entropy or information associated with their form and their dynamics. I'm considering a hypothesis that the universe as a whole conserves entropy/information. Perhaps it is zero to begin with as well. I wonder if starting with this assumption can guide us in understanding (mathematically) how the universe was constructed from scratch (nothing?) I would think that such a starting premise would also be able to account for any superposition of quantum effects (such as in quantum geometry of gravity, etc.) since that premise is so closely linked to probabilities.
Any thoughts gentlemen?
Plus there's the Cosmic Microwave Background radiation that permeates throughout the universe.
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 accomodate 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 accomodate cosmological expansion.
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.
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?
Let's see. What would be the classical limit of this "etropic universe"? As I understand it, classic physics is deterministic so that everything happens with a probability of 1. So there is no information added by new events.
But what is the link between information and QM? Didn't they do some work on this in regard to black holes? What is the information content of the fundamental quantum mechanical situation where each measurement is a choice from an ensemble? 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?
Let's see. IIRC, the probability distribution across quantum states is normalized to 1. So there is no information in the existence of the distribution itself. But when the wave function collapses to one choice from the possibilities, there is an increase of information associated with that. Where then is the entropy at least balanced if entropy decreases with a choice from an ensemble.
IIRC, it was partly because of these entropy, ZPE, etc thingies that Hawking lost his recent bet!
While I'm sure all those who've posted to thread are clear about what's within the bounds of observationally validated theory and what's not, it may help some readers to have a summary (if this is significantly incorrect, I'm sure folk will amend it):
- the Casimir effect is well-established, experimentally, and the observations are consistent with theory
- 'dark energy' or the 'cosmological constant' is ascribed as the cause of the observed acceleration of the expansion of the universe; however, while the observations are now much more clear cut than five years ago, IMHO they are still not as definitive as many portray them. The 'explanation' of the observations as ZPE/cosmological constant/dark energy/whatever is a topic of great energy and excitement among cosmologists; IMHO it's far too soon to say that there's a consensus on this
- no region of space is 'pure vaccuum'; not only are there gravitational fields (everywhere, not just near the Earth), but also a very significant neutrino flux (both relict and of more recent origin), the CMBR (as Phobos said; it's everywhere except regions that are opaque to microwaves), and cosmic rays (a hollow sphere deep underground may be relatively free of these; most of the universe is not). None of this is 'theory'; there are good observational results for all (except the relict neutrinos).
- 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'.
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.
There are experiments in the wings to probe the structure of space-time using cosmic rays and gamma ray bursts. We will learn something about discretization of space-time (and its coarseness) either way. String and LQG may be fringe, but if they show any promise in reconciling gravity with the other forces, the scientific community must explore them.
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?
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.
What is the information value of a pre-SN star? Now what is its information value after it goes SN and blasts its matter all over?
To revisit something from earlier in the thread, zero point energy exists as the ground state of "empty" space. Does ZPE have an information value in your U, or do you assign information value only to "real" things (things that are detectable to you because they exist above the ground state)?
One last example - a new unshuffled deck of cards may represent a highly entropic state to you because you personally understand the significance of the suits and numbers, but does it really contain more information (in your Universe) than any of the quasi-random states that the deck might end up in after being shuffled?
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.
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 ?
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