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Original Message
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Here's a paper I wrote a few years ago, which deals with some of the "multiverse" ideas in quantum mechanics.
HYPOTHESIS:
So-called "Level I" (cosmological) and "Level III" (quantum mechanical) multiverses may in fact be differing conceptual models of the same physical reality.
BACKGROUND:
According to theoretical physicist Max Tegmark, an understanding of modern cosmology predicts that the overall multiverse (totality of all that exists) actually consists of several discrete "levels," each being considered a multiverse in and of itself. For the purposes of this article, a "multiverse" is understood to be a set of causally-connected domains. One such domain, in this context, would be our own observable universe, the cosmos with which we are familiar.
The first level multiverse, which is fairly uncontroversial, consists of individual Hubble volumes (observable universes like our own) existing within infinite space. If, as observations increasingly indicate, the overall geometry of space-time is "flat" (exhibiting no appreciable curvature at the largest scales), space itself must be infinite (or sufficiently large to be virtually so). In an infinite (or near-infinite) space, the edge of our observable universe would not be the edge of space itself - it would simply represent a limit to how much of space we can see from our vantage point. A hypothetical observer elsewhere in infinite space would be at the center of his own Hubble volume (observable universe). If this observer were located sufficiently far away from us, his observable universe would not include any part of our own.
Simple laws of probability clearly indicate that in an infinite space filled with an infinite number of such Hubble volumes, all possible physical configurations must be played out. There is no possible physical configuration which is not realized - not only once, but an infinite number of times. Some enormous distance from you, there is another person who is your exact double reading an article exactly identical to this one. At an enormous distance from him is another such doppelganger, and so on, without end. As mind-boggling as this multiplicity may seem, it is a direct consequence of modern physics.
Interestingly, this prediction is made not only by Big Bang cosmology, but by quantum mechanics as well. According to the increasingly well-accepted Everett interpretation of quantum mechanics, at the quantum level, all possibilities are played out. Through a process known as 'decoherence,' each time a quantum event occurs, the physical universe 'splits off' into any number of equally real histories - one for each possible outcome of the quantum event.
At the quantum level, there are no discrete 'particles' or objects in the conventional sense - instead, there is only a 'wave function' which is governed by a probabilistic mathematical concept known as the Schroedinger equation. The wave function essentially consists of a superposition of all possible states which any given subatomic particle might assume. Mathematically, all of this occurs within so-called Hilbert spaces, special conceptual analogues of normal space in which superpositions of this nature can occur.
At first glance, an idea such as Everett's may seem to multiply existence to an outrageous degree, yet it actually represents the simplest solution to quantum mechanics. Because this interpretation requires the least amount of intial information (it is simpler to create an equation describing all possible eventualities than an equation to describe any single specific eventuality), those who have hoped to cut away the quantum multiverse with Ockham's Razor have found the tool turned against them to good effect.
In the Copenhagen interpretation, chief rival of the Everett (multiverse) interpretation, a particle cannot assume any definite state until the wave function is forced to 'collapse' due to an observation (an act of extracting information from the system) having been made. When the wave function collapses, the particle or system in question assumes a single definite state from within the range of all possible states. However, it is not clear what qualifies as an 'observation,' nor is it clear why conscious observers (who are either directly or indirectly required for an observation to be made in any meaningful sense) should have the power to 'create reality' in this sense. Various apologetics have been made attempting to minimize or explain away these problems, but few have been particularly convincing. The core of the Copenhagen interpretation, at least in the eyes of its many critics, remains "magical." As a result, the majority of physicists now favor some form of mutiverse interpretation.
In the Everett interpretation, the Schroedinger equation is taken at face value, and there is no added postulate of 'wave function collapse.' Instead, the universal (overall) wave function evolves deterministically over time, but due to the process of decoherence (which simulates wave function collapse without violating quantum mechanical time unitarity), the individual 'histories' (parallel universes) become separated from their counterparts at the classical (macroscopic) level.
In simpler terms, it seems that everything is unified at the quantum level, but at the much more complex level of atoms, ants, and the Andes, things fall apart. Because the influence of nearby quantum systems tends to degrade the stability of superposed or 'entangled' quantum systems with which they come into contact, decoherence occurs as a natural consequence of the interaction of any given system with its environment. While some argue that it is not altogether clear how decoherence completely avoids reference to the observer, it is generally accepted that this view proceeds directly from the Schroedinger equation in a way that the Copenhagen interpretation (with its non-unitary postulate of wave function collapse) cannot. In the decoherent histories (multiverse) interpretation, the wave function doesn't collapse, it just gets confused. This results in a 'fallen' classical world where the unity of the microscopic quantum level is not experienced by macroscopic self-aware subsets such as human beings, who find themselves able to percieve only one history at a time.
The Everett interpretation, then, predicts a multiverse which, although derived from entirely different concepts, is strikingly similar to what we have previously described as a first level ("cosmological") multiverse. This "Level III" quantum multiverse, which is taken to be somehow 'co-substantial' with our own observable universe rather than distant in space-time as are the other Hubble volumes in the cosmological multiverse, is nonetheless functionally identical. In both the Level I and the Level III multiverse, we have the realization of every possible physical configuration. In fact, Tegmark points out, "As strange as this [the Everett multiverse] may sound, the exact same situation occurs even in the Level I multiverse... The only difference between Level I and Level III is where your doppelgängers reside. In Level I they live elsewhere in good old three-dimensional space. In Level III they live on another quantum branch in infinite-dimensional Hilbert space."
ARGUMENT:
I will here propose the speculative possibility that the cosmological (Level I) and quantum (Level III) multiverses are in fact one and the same. I shall further suggest that quantum mechanics itself may be derived from the existence of the Level I multiverse, and that the level III multiverse implicit in the Everett interpretation may not in fact be a discrete, individual multiverse in its own right, but simply another way of experiencing (or conceptualizing) the Level I cosmological multiverse of infinite space.
Tegmark astutely observes the following:
"...In other words, the Level III multiverse adds nothing new beyond Level I and Level II, just more indistinguishable copies of the same universes--the same old story lines playing out again and again in other quantum branches. The passionate debate about Everett's theory therefore seems to be ending in a grand anticlimax, with the discovery of less controversial multiverses (Levels I and II) that are equally large."
That this seems horribly redundant is not sufficient reason to conclude that it is not so - but it is a reasonable impetus to examine the possibility of reducing away the redundancy.
Traditionally, the essential randomness inherent to quantum mechanics is ascribed (within the Everett interpretation) to the the fact that at the quantum level (where there is a superposition of states), parallel universes which are 'close' to one another in terms of probability distribution interfere with each other, leading to a fundamental uncertainty regarding the state of any particular physical universe (quantum configuration). It is assumed that these parallel universes which are interfering with one another are co-substantial in terms of space-time, meaning that they are undetectable but infinitely close to our own universe, but what if this were not so? What if, instead, spatially-distant quantum configurations which are 'close' in terms of probability distribution (or, perhaps more appropriately, configuration) were (via non-locality) interfering with each other at the level of quantum superposition?
While examining this possibility, bear in mind that we have established the Level I (cosmological) multiverse to be an infinite space containing an infinite number of Hubble volumes in all possible physical configurations. The raw material for a multiverse-reducing scenario is already present here - we have only to establish that the cosmological universe might operate in accordance with the Everett interpretation on a quantum level, without reference to the existence of an actual quantum multiverse apart from the cosmological one.
It is not yet entirely clear to me how this might be established, but for purposes of argument, I would submit that non-locality is likely to be a key factor. Traditionally, non-locality is understood as arising from the existence of the quantum multiverse, but if the quantum multiverse is in fact identical to the cosmological one, then non-locality is a property inherent to space-time itself. If space-time is non-local, quantum events could interact with their duplicates and their close analogues within the cosmological multiverse despite the fact that these parallel universes are spatially separated by vast distances. The wave function of a given particle might be nothing more than a non-local superposition of states within infinite space - meaning that what is interfering with our universe is not an alternate universe which is undetectable but spatially co-substantial with our own, but an alternate universe many trillions of light years distant.
Conceptualizing space in non-local terms may seem troublesome, since we commonly view locality as that which defines space. The distance or 'intervening void' between objects A and B is dependent upon the location of said objects, which seems to implicate locality in the definition of space. Recent work, however, has suggested that a concept closely associated with space, that of time, may in fact be essentially 'non-local' in that there are no actual moments or 'instants' of time. Although seemingly couterintuitive, this new idea of time dispenses at once with Zeno's paradoxes and similar concerns which have troubled philosophers and theoretical physicists alike. If time is without 'locality' in terms of discrete instants, must not space be so as well? After all, physicists since Einstein rarely speak of either time or space as separate entities. Instead, a single "spacetime" is understood to encompass both aspects.
If time is non-local, then, so must be space. The fact that we experience space as local should not trouble us, for we also experience time as if it had directionality, discrete instants, and in fact a quantum structure, despite the fact that all of these perceptions may ultimately prove illusory. A non-local spacetime would at once explain quantum mechanics and its attendant 'Level III' multiverse by virtue of the fact that any part of the infinite cosmological (Level I) multiverse is in some sense spatio-temporally co-substantial with all other parts.
If this were true, it would eliminate the redundancy of postulating two discrete multiverse 'levels' which predict virtually identical physical consequences. The number of discrete 'types' of multiverse would be reduced from four to three - the level I (cosmological) multiverse, the level II (inflationary) multiverse, and the level IV (mathematical) multiverse. A very brief introduction to these other 'multiverse levels' follows.
The inflationary (Level II) multiverse consists of other infinite spaces such as the one in which our own Hubble volume is contained (other level I multiverses). According to many proponents of inflationary theory, at the largest scales, space itself is full of these multiverse 'bubbles' which have inflated to infinite size, and yet space (or 'hyperspace') can contain an infinite number of such 'bubbles,' perhaps because the space between them is expanding faster than the bubbles can fill it.
In contrast, the mathematical (Level IV) multiverse consists of other mathematical frameworks in addition to the familiar one which produces inflationary volumes such as our own. However, while the existence of the inflationary multiverse is fairly well-accepted, the mathematical multiverse (a pet of Tegmark) remains controversial. Disregarding the mathematical multiverse for the moment, reducing away the Level III quantum multiverse would leave us with a singular view of an infinite 'hyperspace' filled with individual infinite or near-infinite spaces (cosmological multiverses). There would be no redundancy, only a unified, unlimited system capable of actualizing all possible physical configurations in all possible ways. Even if we were to include the mathematical multiverse, we could still envision such a seamless continuum - reality would consist ultimately of 'mathspace,' which gives rise to the hyperspace mentioned above (among other possible configurations), which gives rise to inflationary bubbles, and so on.
CONCLUSION:
I realize that what I have suggested here may be seen as a speculative idea more than a genuine hypothesis, as I have not clearly shown a mechanism by which it might be possible to resolve the cosmological and quantum multiverses into a single entity, although I have suggested space-time non-locality as a possible area for inquiry. Some may argue that to think of non-locality in terms of space-time alone is meaningless, since it requires the very quantum multiverse we are trying to reduce away. However, in addition to the argument based on the possible non-locality of time, other evidence is emerging to indicate that spacetime may not be quantized, and therefore non-locality may be a precondition of quantum mechanics. For example, recent observations indicate that Hubble images of distant galaxies are 'too clear,' meaning that if spacetime were quantized, significantly more image distortion would be expected than was actually observed. If space-time is not quantized, how can it behave non-locally unless non-locality is one of its properties?
Note that despite its limitations, the hypothesis outlined in this article is falsifiable. If the cosmological and the quantum multiverses could be shown to be quantitatively different in terms of the configurations they allow for, the idea would be in trouble. In addition, evidence suggesting that our own spacetime is both non-infinite and also not sufficiently large to allow for an exhaustive array of physical configurations would be very damaging.
The idea also makes predictions. If it is true, it should be (in principle) possible to isolate the particular spatially-distant but probabilistically 'close' quantum parallels which are interfering with any particular quantum event in our own universe. Of course, it is virtually unimaginable that a process sophisticated enough to actually do this could ever be devised, but the prediction is made nonetheless.
Also, since non-locality is only one suggested area of inquiry rather than the only possible mechanism for the hypothesis, it is not crucial that it be what allows the reduction to take place. Perhaps other, and better, methods of showing the cosmological and quantum multiverses to be one and the same will appear. On the other hand, it may be that this speculation is simply mistaken - but if it is, then we live in a pretty redundant universe.
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