Friday, August 12, 2011

Beyond Singularities: Other GR and QM inconsistencies.

I noted in an earlier post that one of the potential conflicts of quantum mechanics and general relativity is the potential of a point-like particle with rest mass to blow up into a singularity, since there is infinite density in a point-like particle with rest mass.

But, if fundamental particles are given volume, this problem disappears. If that volume is on the order of the Planck mass or greater, the distortion of the space-time continuum resulting from any given fundamental particle is far below the limits of experimental methods to detect, and that if the fundamental particles are sphere-like and have a radius on the order of 10^-41 meters, that you reach a size where the time dialation effects of gravity fields in general relativity could conceivably explain CP violation in quantum mechanics.

There are also other quite different disconnect between general relativity and quantum mechanics.

General relativity's equations observes locality, at least in "small" areas of space-time. Quantum mechanics does not, at least in the case of entangled quanta that were once interacting in a way that synchronized their quantum states.

Further, quantum mechanics can get from point A to point B over paths that would seem impossible by any path if a classical particle with a fixed mass and momentum and original location with values for those equal something in the middle of the range that were the fundamental particle is smeared by the uncertainty principle would lie (this is called quantum tunnelling, and while it isn't strictly an instance of non-locality, it is non-intuitive for similar reasons).

Reconciling these aspects is not easy, although the quantum mechanical effects usually become virtually invisible at the scales and in the circumstances where general relativity applies to deviate from special relativity in four dimensional Minkowski space, where the equations of quantum mechanics in the Standard Model are defined.

True non-locality requires either a rethinking of the meaning of causality in the context of Feynman diagram connected particles, or a concept a bit like fate or destiny for a quantum particle.

Entanglement experiements involve the separation of space of two particles that were once in contact, the triggering of the collapse of the wave function on one of them in a way that reveals its state, and the measurement of the collapsed wave function of the other, which always corresponds correctly to its entangled twin, even though the wave functions of neither quantum was collapsed when they were together as tested by proofs of wave-like behavior between the common point of origin and the point of wave function collapse.

I may be wrong (and need to check), but my understanding is that entangled prticles don't necessary have collapsed wave functions at the same time, the second one collapsed is simply observed to have a state corresponding to the state of the first one collapsed when the second collapse eventually happens.

One way for this to happen is for a chain of causality to ride backwards in time along the particle whose wave function collapses first to the point of entanglement and then forward in time again to the entangled particle at the point when it collapses, passing continuously through space-time at no more than the speed of light, but involving causation that counterintuitively involves backward motion in time.

Another way for this to happen is for the entangled particles upon separating and while they are in a wave-like uncollapsed state to have an already defined but unexpressed collapse state that they are destined to take whenever a collapse happens in either case, if this "collapse destiny property" is set at the moment of entanglement, even though it isn't expressed until much later. Indeed, perhaps every quantum particle has a destined collapse state at the moment it comes into being as an uncollapsed quantum entity, that expresses when that collapse actually takes place. This destiny would be fundamentally and theoretically impossible for an observer to determine, not just experimentally impossible to determine, until the wave function of at least one of the entangled particles collapsed.

Note that this "destiny" concept is not deterministic in the overall sense. A particles collapse state is deterministic as of the time of collapse, but an exactly equivalent randomness to the conventional description takes place at the time that the particle becomes wave-like and uncollapsed. Quantum mechanics is just as random as it is under the conventional explanation, but the dice are rolled sooner and each quanta makes its way to the point of its ultimate wave function collapse with an invisible property that describes what will happen at that point - thus a uncollapsed wave function state of a quantum particle contains more information than is conventionally attributed to it. It carries a secret set of instructions about what to do when it arrives at its destination with it that is never revealed unless a co-conspirator rats out this information to the observer.

Similarly, maybe while every W boson acts exactly the same, a W boson's decay products are randomly determined when it is born, rather than when it decays. But, this does pose a problem, because the decay products of a W boson or an energetic photon that spontaneously gives rise to a particle and its antiparticle, must observe mass energy conservation, and the energy of a boson can change before it decays into something else or is absorbed. Hence, a quanta's destiny, if there is one, can be fixed no earlier than at the last time that it interacts with another quanta, rather than at its birth, and if this is the destiny rule, then the existence or non-existence of gravitons matters a great deal, as gravity could in theory change a particle's destiny by imparting momentum to it that make it possible to decay to a higher energy set of products and thus change the options in its desinty. Otherwise, gravitationally induced momentum shouldn't play a part in matter-energy conservation in decay products, yet surely, momentum of one kind shouldn't act differently than momentum of another under the equivalence principle.

Since this hidden destiny property of quanta doesn't manifest physically at all during the uncollapsed wave-like state of a quanta, it also shouldn't impact quantum mechanical phenomena like quantum tunnelling which are necessary to make such common devices as transistors work.

As long as this exact information doesn't have any impact on how the wave function propogates, this secret destiny idea could resolve epistomological and mathematical issues with non-locality without actually changing anything about how quanta behave in the physical world and might help improve our intuition about how to describe precisely what it is that triggers wave function collapse. This interpretation would also circumvent the ugliness of the many worlds interpretation of quantum mechanics, while not resorting to the full fledged pilot waves of Bohmian interpretations.

I'm sure that there are many ways that what I am saying could be wrong or ruled about empirically in quantum mechanics, but if that is the case then there must be some detail of it that I am misformed about and misunderstand, which as I am a layman, coulud certainly be the case. Also, like other "interpretations" of quantum mechanics this doesn't in and of itself change anything about what the equations predict in the real world.

But, this interpretation, if it works, might make it easier to mathematically formulate an integration of quantum mechanics and general relativity that does not require true non-locality, or true backwards in time causality.

It is also worth noting that while the working excellently fit to the data theory of quantum mechanics is that it is truly stochastic, that if the seemingly random results were actually the function of a highly sensitive to initial conditions chaotic function (e.g. the nth root of the moduli of location in a Klein-Kaluza suppressed dimension of space-time of a scale much less than 10^-41 meters at the place where "the dice are rolled") that it could appear perfectly random while actually being deterministic. Since the experimental results that we are currently capable of generating aren't any different under either scenario, this isn't very interesting. But, if some other aspect of the theory suggested a topology of space-time that would motivate this kind of deterministic function, it might become attractive as a means of unifying equations into some deeper theory.


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Andrew Oh-Willeke said...

"Believe" is a strong word in this context. I'm certainly not ideologically or dogmatically committed to any of my own suggestions and innovations, simply exploring them, just as theoretical physicists often proposed many contradictory theoretical possibilities in different papers that are not motivated by new evidence.

I'm really more publicly organizing my thoughts and thinking and reading than I am making any assertions about what the laws of physics actually say and exploring possibilities that I do not know to be contradicted. One of my hopes is that if I say something that is clearly wrong that someone could come along and make a comment that explains that fact.