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 ?
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.
Now, if you define information as being the product of the attributes of an object x the probability that the object will exist in the state you perceive it in, (where I think you are headed, logically ) you will have to assign an infinite negative probablility to the existence of the BB singularity in order to be able to conserve information over the course of the Universe. 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.
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.
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?
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.
Yes, there's a book or two on information theory kicking around.
I have to say it. that is one helluva profound question. space may itself require some kind of energy in order to exist.
there may be no such thing as an absolute, inert, space which can exist in a purely static way
and if space arises dynamically---that means it involves energy
this question you asked is confusing to think about----maybe I am going about it wrong----maybe you meant to ask something very simple
However I think the question has to be addressed in the context of some theoretical framework that gives a little bit more definition to the ideas of energy and volume.
In Gen Rel, space is the gravitational field and the gravitational field is what gives meaning to things like areas and volumes.
if the field is zero in some region, then that region could not have any volume
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?
Also, for example, We can calculate the entropy (therefore information) of a black hole. And we understand that black holes can produce particles. Therefore, it would seem that we can calculate the entropy of particle creation, right? All we need do is calculate the entropy/information of a black hole that would immediated dissipate into particles. Or something like that.
I'm getting a Browser bug report from amazon. Could you supply titles please? Thanks.
Separate names with a comma.