Information, symmetry, and QM

1. Sep 24, 2004

Mike2

I'm considering how the 2nd law of thermodynamics (2LT) might necessitate quantum mechanics.

For it would seem that QM effects always consist of a superposition of states. Each state has a particular structure, and there is a number of these states that must be in quantum mechanical superposition.

Now if each alternative state has a structure, then there must be some information (negative entropy) associated with that structure. But then the number of alternative states increase which seems like an expansive increase in entropy, right? So I wonder if the 2LT requires alternative state to increase entropy in order to compensate for the decrease in entropy (the increase of information) associated with each structure of each alternative. Or perhaps the increased number of alternatives is compensating for the expectation state.

So along these lines I consider the types of structure possible. I remember that the more symmetrical a structure the less information associated with it because it is the least complex structure. So this raises the question for me as to the meaning of "symmetry breaking" processes. Is QM "the" symmetry breaking process? If added complexity developes, this represents more information than the perfectly symmetrical states. So must this be accompanied by a number of quantum mechanical alternatives to be in superposition in order to at least balance entropy? Thanks.

2. Sep 25, 2004

Staff Emeritus
Actually the information is more with a symmetrical ordered state because it has fewer thing to know in order to describe it (fewer parameters). A noisy, broken-symmetry state is less known because you have to evaluate more parameters to describe it, and that is why information is the negative of entropy. Order -> low entropy, high information, disorder -> high entropy, low information.

3. Sep 25, 2004

Mike2

I thought broken symmetry was caused by the choice of one option over many alternative, thus representing more information. For example a pencil standing straight up on its lead is in a perfectly symmetrical state, but it is unstable and will eventually fall in one direction or another. There is a probability distribution as to which way it will fall. And the final choice as to which way it will go represents a choice with a given probability, and this results in increased information with that choice of direction, right?

4. Sep 27, 2004

Mike2

OK. I may have had it backwards. I suppose now that the universe started with perfect symmetry (I still suspect this perfect state has zero information content). And I'm not sure what is being symmetrical; is it some sort of manifold, or is it the metric on the manifold? I don't know if the number of dimensions can present any information, or must it be some manifold embedded in the dimension that must carry the information. Or maybe it is some function on the manifold that presents the information. Anyway... Then this perfectly symmetrical object breaks and its entropy increases. But if information must be conserved, there must be other possibilities, or a superposition of alternative states, that must exist so that the choice of that particular state provides enough information to offset the entropy of that particular state. Is this the prescription for why alternative states are assigned an amplitude and phase and why they interfere? Is this the reason that the universe expands, to provide alternative quantum states in order to balance entropy?

Certainly no one would argue that any information could leak out of the universe or enter into the universe as a whole. For then that would simply redefine the universe to include that region to which the information leaks or from where it enters. So it would seem that conservation of information would have to be a global (universal) property and not a local one. This could mean that if the universe is expanding and dissipating almost everywhere else, there can arise structures within the universe somewhere where information can be stored and structure preserved.

Last edited: Sep 27, 2004
5. Sep 27, 2004

Chronos

It seems probable the universe was preceeded by a state of perfect symmetry. I have no idea if it is even possible to describe this initial condition. The BB, IMO, occured when gravity decoupled from the perfectly symmetrical state simultaneously releasing space, time and energy. At this point expansion, IMO, is the only option. The universe now has degrees of freedom and thermodynamics would insist they be exploited. The clock starts ticking and space unfolds like a broken spring. Expansion increases the number of available states for quantum transactions to occur, thus permitting entropy to increase as required by thermodynamics. I think it likely that expansion will continue indefinitely for this reason, albeit it may eventually slow to an infinitesimally slow pace.

6. Sep 28, 2004

Mike2

Can a singularity have perfect symmetry? If instant infinity is not a possibility, then the universe grew from a closed manifold of some sort. Or perhaps it is a quantum mechanical superposition of alternatively dimensioned closed manifolds. (would this be the dynamical triangulation effort?) So I guess the question is what information can a closed manifold have? I suppose there is some information involved in the topology of various manifolds. But then I wonder if one manifold is isomorphic, or diffeomorphic to another, then will they both contain the same information? Or does the same information describe them both?

7. Sep 30, 2004

Mike2

So what is the most fundamental characteristic of a manifold that may contain "information"? Would that be the genus (how many holes are in it)? Could it be whether the manifold has a boundary (though I hear that you can close those boundaries to a point. What morphism is that?)? Which characteristic is more drastic? I suppose that drastic topology changes would be more of a result than a first consideration? Perhaps the genus of a manifold, or perhaps the number of dimensions is more is more arbitrary requiring a superposition.

8. Oct 1, 2004

Chronos

I do not think the singularity has zero volume. The planck density limit requires it to have a finite volume. This, IMHO, is necessary to satisfy the uncertainty principle.

9. Oct 1, 2004

Mike2

The volume depends on the metric on the manifold. Can't a manifold exist with metric that gives zero volume?

I guess one question would be where the metric comes from to begin with.