Perhaps, in these tempestuous days, it is comforting to speculate that somewhere in the multiverse a parallel universe exists with another Earth in which there is no threat of global warming, alternative fuels provide most of the energy, the population is below carrying capacity and has all its needs met, and oh yes....politicians can conduct civil debates and the government always works on behalf of all citizens.

Perhaps such a place exists, but before such ruminations can be taken seriously, it would behoove us to first at least demonstrate that a parallel universe can be even remotely detected from within the confines of our own. Before considering such experiments - a bit of background.

Note that the "parallel universes" being considered here I regard as actual, separable PHYSICAL cosmi - and likely incepted from the selfsame primordial vacuum state (via cosmic inflation) as our own universe. Thus, an actual primordial vacuum - not a human observer or consciousness "making observational choices" (as in the case of the Hugh Everett 'Many worlds' interpretation of quantum theory) is the source of the real parallel universes. Thus, all putative parallel universes plausibly emerged from the primordial vacuum the way ours did, e.g. from the Big Bang.

Regarding inflation, most current standard theories propose inflation starting at about 10

^{-35}s and doubling over a period of anywhere from 10

^{-43}to 10

^{-35 }s after the initial inception. Estimates are that at least 85 such 'doublings' would be required to arrive at the phase where entropy rather than field resident energy dominates. The initial size (radius) of our universe would have been likely less than a proton's - maybe 1 fermi (fm) or 10

^{-15}m, by the time the doubling process began. By the time it ended (after 90 'doublings') it would have been around 1.25 x 10

^{12 }m. This is roughly eight times the distance of Earth from the Sun. In effect, the role of inflation is to give cosmic expansion a huge head start or boost, without which our universe would be much smaller. Other parallel universes emerging around the same time might have been larger or smaller depending upon their specific values for their fundamental physical constants (e.g. alpha, the "fine structure constant", h - the Planck constant, G, and eta the permittivity of free space).

In the graphic, I show an "idealized multiverse" replete with parallel universes, each occupying longitudinal geodesics specified under a coordinate φ, and separated by uniform angular measure Θ from adjacent universes. The whole represents a 5-dimensional manifold in a toroidal topology. The topological space of the hypertoroid cosmos can therefore be represented by the global state space, a product of absolute hypertorus coordinate time (Θ) and 'all-space'(φ):GL = Θ X φ

Now, I repeat, this is an idealized model which assumes that N-cosmi were incepted at equal intervals of time - as manifested by the equal spacing in Θ. In principle, we don't know a priori how "close" in complex time another parallel universe may be to our own. When one uses the assumption of "equal time intervals" between inceptions in our idealized multiverse, one isn't stating what those times are, and so they could be minuscule - and the smallest time unit imaginable is the unit tau, τ. (About 10

^{-43}s, and note Θ = f(τ).)

If we specify such an exact parallel universe time displacement we might be able to show how one parallel universe can be "mapped" topologically onto an adjacent one. As an example, let two parallel universes be distinguished by a 1-τ difference in fundamental time parameter, viz. [1 + 2τ] and [1 + 3τ], then we would require for connection, a mapping such that:

(Universe 'A'): f:X -> X = f(Θ,φ) = (Θ, 2φ)

(Universe 'B'): f:X -> X = f(Θ,φ) = (Θ, 3φ)

which means the absolute coordinate φ is mapped onto itself 2 times for [Universe A] and mapped onto itself 3 times for [Universe B]. Clearly, there’ll be coincidences for which: f(Θ,2φ) = f(Θ,3φ) wherein the two universes will 'interweave' a number of times.

For example, such interweaving will occur when φ = π/2 in [A] and φ = π/3 in [B]. The total set or system of multiple points obtained in this way is called a Synchronous temporal matrix. The distinguishing feature of this matrix is that once a single point is encountered, it is probable that others will as well. If one hyperspace transformation can occur linking parallel universes, A and B, then conceivably more such transformations can occur, linking A and C, D and E etc.

What if both absolute toroidal coordinates (Θ,φ) map into themselves the same number of times? Say, something like:

f:X -> = f(Θ, φ) = (2Θ, 2φ): Universe A

f:X -> = f(Θ, φ) = (3Θ, 3φ): Universe B

For example, given the previous conditions for coordinate φ, now let 2Θ = 3Θ for discrete values of Θ (e.g. 2π). For all multiples of 2π, the same toroidal cosmos will be experienced - if the absolute time coordinates are equal (e.g. π/2 = φ in A, and π/3 = φ in B) then we will have: Universe A = Universe B.

What does this equality mean? I conjecture that it implies a briefly inter-phased chaotic state prevails in both A and B where the fundamental physical constants are not fixed (in a future blog I will appeal to quantum chaos to describe this). For all intents and purposes it is as if a "portal" of sorts exists between them, though that doesn't mean it'd be accessible to humans. We say that there exists "an interpenetration of different parallel universes" but not necessarily entailing transfer of bodies from one to the other. Note that though the physical state spaces (e.g. with constants h, G, e/m, etc. )may be alike, they can still differ in dimensionality! And we cannot disregard fractal dimensionality.

IF one has this condition, THEN it is feasible that the (David) Deutsch experiment (See:

**The**

**Fabric of Reality**) to detect the interphasing of a parallel universe can be carried out, and the penetration of our universe by a parallel one validated.

In his book(pp. 38-47), Deutsch adopts the setup (Fig. 2-4) of a monochromatic light beam that passes through successive screens with single holes. The image presented on the screen is a central bright spot with darker penumbra around it. With a two slit pattern for the screens (p. 41) the experiment becomes more interesting in that successive barriers to generate the patterns engenders what Deutsch calls "shadow photons".

He acknowledges (p. 45) that "tangible" (i.e. measurable) photons are grounded in our tangible, current universe, but also that shadow photons can be thought of as collectively coming from a parallel universe. He then clarifies this in mind-blowing fashion (p. 45):

"For it turns out that the shadow particles are partititoned among themselves in exactly the same way as the universe of tangible particles is partitioned from them. In other words, they do not form a single, homogeneous parallel universe vastly larger than the tangible one, but rather a huge number of parallel universes, each similar in composition to the tangible one, and each obeying the same laws of physics, but differing in that the particles are in different positions in each universe."

In other words, using the graphic I've shown, we would need multiple ordered pair angles (Θ, φ) to actually lead to an incomprehensible number, thereby denoting all the shadow photons in one of Deutsch's experiments. But the existence of this multiplicity is what Deutsch uses to justify the term "multiverse" with which I concur. A final challenge to be met, is - I think - reconciling the physical multiverse with the (Hugh Everett III) 'Many worlds' interpretation of QM. I believe this requires using separate wave functions for each inflation-based parallel universe but exactly how each of these would be described is left to future QM workers. (They'd also need to ponder how 'many worlds' can be revamped if each wave state also coincides with a genuine, inflation-generated parallel universe. Also: Is the wave function a wholly physical representation (analogous to David Bohm's real de Broglie waves) , a statistical artifact or a combination of each?)

In the meantime, we've lots to ponder, including whether unknown to us sporadic interpenetrations can occur, say between a 'Universe A' and 'Universe B' and what effects they might have in our real world - say if our universe is denoted B. What physical factors might lead to such interpenetration or interphasing? Can any anomalous terrestrial events - like deja vu- which physicist Michio Kaku has speculated might occur in specific or unusual cases and not be merely memory short circuits - arise from "flipping between universes? Perhaps before we go there we need to nail down the properties of these "shadow particles" more rigorously first!

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