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How can we make headway through this mess? A space-time foam of wormholes is tough. It seems almost blindingly difficult to proceed with a mathematical analysis. Yet we try anyway on another web page.
Note that the probabilities of quantum wave functions are re-interpreted as the possible future geometrical arrangements of the Planck-scale foam. Some arrangements are very likely, some are very unlikely. There are no hidden variables here: all one can talk about is possible future arrangements based on a knowledge of the current/past history. (Question to be answered: if the past is not known, who does this affect the prediction? i.e. how would we envision a (non-relativistic) electron propagating in free space? What is happening to this 'wave' as this Planck-scale foam 'freezes' along? Generically, how does one derive the idea of a propagater from the foam? There are similarities to diffusion eqn, but how can one get more specific?) Next, let us imagine what this world of geodesics implies for quantum measurement. There is a strong sense of non-locality that is induced by this foam. Imagine the classic spin-EPR experiment, where a singlet decays into a pair of spin-1/2 particles, whose spins are then measured, and found to be correlated. This is where, I think, my handwaving reaches a crux, and all the best stuff falls out. Here goes (this is a bit rocky): Imagine that the spin-1/2 state is described by a collection of geodesics propagating on this foam. As this data propagates through the foam, a pair of measurements are made, and the data from these measurements are brought back together to roughly the same point in spacetime, where the experimenter can compare them and verify that e.g. Bell's theorem, has not been violated. Hypothesis: the geodesics in the space-time foam can only be made self-consistent in the backwards light cone. In particular, the geodesics from one measurement cannot be reconciled with those from the other until that have both entered into a common backwards light cone (i.e. the measurements have been brought together). When these paths are brought back together, the outcome 'freezes', i.e. become a part of the 'past'. This act of coming together defines not only the arrow of time, but defines time itself (or rather, distinguishes time from space). The Past is Manifest Destiny. (Newtonian ...) The claim is that this is no accident. The creation of the past is what happens when geodesics are reconciled on a space-time foam.
Note that inflation (a la big-bang inflation) seems to add an important ingredient to the above scenario. Without inflation, the wave of ice-9 freezing would have engulfed the entire universe in short order. With inflation, large space-like separations are introduced between all parts of the universe, thus requiring far, far more 'passage of time' to patch those parts back together into the frozen past.
- Hand-waving for quantum numbers and 'elementary particles'. Quantum numbers find expression in being certain twisted configurations of geodesics. That is, elementary particles, such as the electron or neutrino, might just be topologically stable arrangements of the Planck-scale space-time foam: solitons of some sort. In other words, they might be analogous to the 'particles' seen in solid-state physics: bosonic 'phonons', or fermionic crystalline dislocations/defects. Particle masses would then presumably be functions of the number of handles, or some other topological integer. Anti-particles would presumably be some reversed topological knots that, when brought near a particle, can be slipped to untie the knots. I don't know enough of topology to argue that the Pauli exclusion principle may be topological in nature: some (anti-)symmetrical exchange of handles between two configurations.
The topological interpretation avoids the silly questions such as 'why do all electrons look alike'? They all look alike because they are all represented by the same set of self-consistent twists in the space-time foam. Asking 'why do all electrons look alike' is tantamount to asking 'why are all instances of the number two alike?' Or maybe better yet: 'why do all single-point dislocations of a lattice look alike?' Physical particles are configurations of an underlying relativistic 'ether'. The above considerations would seem to dictate a program of topological research. However, this alone doesn't seem sufficient to resolve the issue of the arrow of time, or of the second law of thermodynamics. Topological arrangements would seem to be time-symmetric. Its too static in itself. If we are to view the past as 'fixed', and the future as 'indeterminate', then we need a language of topology where the past is fixed, the present is a mad scramble to arrange a topology so that it is consistent with everything that came in the past. I know of no topology that acts like this. There is no study that asks and answers the question: 'how do I tie the knot right here, so that the strands 'back there' don't have to be rearranged'. Topological stability in crystal lattice dislocations is independent of time, and are arrangements in 3D space. Instead, we need to ponder the evolution of topological entities as they are brought 'close' to each other in space. The other problem is that we still have no insight into what free-will might be all about. Clearly, free-will is a phenomenon of the present: I have no free-will in the past, nor in the future. At best, I can try to control what I am doing 'right now'. Topological arguments seem to be deterministic, however fanciful they may get. It seems to me that any theory of the flow of time is somehow incomplete until it also somehow addresses the question of free-will. - Re-emphasize that no matter how silly all of this sounds, it does indeed avoid both 'many-worlds' and the 'Schroedinger cat paradox' and all that baggage. No doubt, for some philosophers, 'many worlds' or quantum-indeterminate brain cells sound like more fun, but I think that my handwaving is less looney than the alternatives.
- There are two ways of dealing with Clauser Horne Shimony etal correlations. One way is to view this as a bizarre kind of interferometric experiment, where macroscopic indeterminism exists until the results of both space-time measurements are brought to the same general area of space-time. i.e. the cat is both dead and alive until the experimenter brings both measurements together to discover that correlations exist. But this violates our macroscopic intuition about locality.
Another possibility is that upon wave function collapse in one location, an influence travels 'backwards in time', along one arm of the experiment, and thence forwards along the other, precipitating a change there. What is the form of this influence? Why, precisely that which can carry no information: a gauge-like rotation of the phase of the wave function. For space-like separated measurements, this communication via backwards-traveling geodesics helps keep each side in perfect correlation with the other, so that any interaction with a macroscopic, stochastic tank of particles that is the measuring instrument is 'simultaneously' echoed in the other arm. Might it be possible to test this hypothesis experimentally, by placing two devices at space-like separations, blasting correlated particles into both of them, and then looking to see if they've achieved thermodynamic equilibrium? For, if the hypothesis is correct, then faster-than-light signalling is disallowed, but thermodynamic interaction is not. This might be experimentally testable. However, this is tricky, and has a (fatal?) flaw: we can still do faster-than-light signalling. Lets say that experimenter at location A measures the temperature of a container that is getting getting correlated photons being shot into it. Experimenter at location B can put one of two containers in the path of the photons: a hot tank, and a cold tank. If quantum correlations could act to bring the two containers into thermodynamic equilibrium, then experimenter A would see the temperature rise, or drop, over time. With sufficient space-like separation, this could be used to perform faster-than-light signalling. (Equally disturbing is to think of the situation in terms of entropy.) - Point out some obvious similarities between closed geodesics and (super-) strings. Note that if the spacetime foam has to wiggle around to close up inconsistent (grandfather-paradoxish) geodesics, that this could well resemble vibrations of strings. Add the weasel words to state that we may not be talking about four dimensions here. Maybe add some super-symmetric handwaving.
- Say something about the future. How the future is sort-of predictable, in the sense that I can predict the path of a baseball, although I cannot predict that the baseball stadium will not be suddenly wiped out by a meteorite or other unexpected event. It is this essence: the merging of all events into the past light cone, that distinguishes the future from the past. Emphasize that quantum uncertainty is a sum over all states is really what this is all about: the uncertain future can only be expressed over all possible quantum states precisely because the precise arrangement of the spacetime foam won't be known until it becomes the past. Emphasize also the oxymoron: the arrangement of the past affects the future.
- Explore how things like chaos theory have implications for the predictability of the future, and in particular, how positive-Lyapunov exponent spacetime foams.
- Explore things like 'Hausdorff measure', Serpinski carpets, etc. are relevant to the conversation. Explore to see how classical chaos manifesting itself at the Planck scale may explain certain quantum phenomena. I dunno, this is pretty far out there.
- Consciousness as a quantum phenomenon.
Arrow of Time We experience time to go forward, even though virtually all equations used in physics don't make a distinction between time moving forward, and time moving backwards. If the equations don't seem to care, then why does time move forward? This is the conundrum of the "Arrow of Time". Butterfly Effect A popular term in chaos theory. Best understood through and old litany: For want of a nail the shoe was lost, for want of a shoe the horse was lost, for want of a horse the rider was lost, for want of a rider, the message was lost, for want of a message the battle was lost, all for want of a nail. It is a statement that small differences in initial conditions can lead to drastically different final outcomes. See also 'Positive Lyapunov Exponent'. EPR (Einstein Podolsky Rosen) Paradox A famous paper where a conundrum of the Heisenberg Uncertainty Principle is explored ... Feynmann Path Integral Gestalt of Determinism When one places oneself outside the context of time ... Grandfather Paradox If you had a time machine, could you go back and kill your own grandfather while he was just a child? And if you had, where would that leave you? Time travel is filled with paradoxes. Hidden Variables, Bell's Theorem The idea that the probabilistic outcomes of quantum mechanics can't be accounted for by assuming the existence of some as-yet undetermined (hidden) controlling variables. Anthropocentric Universe These are physical facts that can be deduced from the existence of mankind and/or of the self. In particular, we can deduce that that the past is different than the future, because, well, that is just how we all experience time. Inflation Inflation for Beginners Light Cone Many Worlds Hypothesis PhD Thesis, 1957, Hugh Everett, Princeton University Pre-destination The idea that ones actions cannot change the future, that events will unfold in a certain way despite ones best efforts. Planck Length Platonic A concept advocated by Julian Barbour, arguing that time doesn't exist, and that instead one should view the universe as a giant configuration space, consisting of the positions of all particles relative to one-another. (In my opinion, the fact that this hypothesis has trouble explaining history, or at least, the human perception that there is a past, rather invalidates the whole thing. I am not happy about a theory that explains less, rather than more.) Quantum Entanglement Quantum Measurement Schreodinger's Cat Paradox Second Quantization Supersymmetry Superstring Wormhole |