TIME SLIPS (2): Flights of Fancy or Temporal Displacements Based on Real Physics?

In the diagram directly above there appears a two-slit  diffraction pattern  and also an associated intensity pattern showing the relative light intensity for the pattern -obviously with the central portion amplitude above the rest.

David Deutsch's arguments on p. 44 of his monograph ('The Fabric of Reality") basically contend that:

"there is no intrinsic difference between tangible and shadow photons: each photon is tangible in one universe and intangible in all the other parallel universes"

In his representation on p. 41 (Fig. 2.7), we see a similar pattern to the one given above, along with an additional pattern in which the dark interference fringes are much wider. He infers that "something must be coming through the second pair of slits (bear in mind two, 2-slit arrangements are set up in sequence) to prevent the light from the first pair reaching X? But what? We can find out with further experiments."

After a lengthy bit of reasoning, including successive tweaking of thought experiments, Deutsch arrives at "shadow photons from a parallel universe". He infers (p. 44) for at least one arrangement "at least a trillion shadow photons accompanying each tangible one."

He also is careful to distinguish the respective properties: (ibid.)

"Thus, we have inferred the existence of a seething, prodigiously complicated, hidden world of shadow photons. They travel at the speed of light, bounce off mirrors, are refracted by lenses, and are stopped by opaque barriers or filters of the wrong color. Yet they do not trigger even the most sensitive detectors. The only thing in the universe that a shadow photon can be observed to affect is the tangible photon it accompanies. That is the phenomenon of interference. Shadow photons would go entirely unnoticed were it not for this phenomenon."

In light of the above, we now return again to the experience of Charlotte Moberly and Eleanor Jourdain in experiencing a time slip transferring them from the year 1901 to 1789. (Previous blog). Moberly described a flat and lifeless terrain in her report and most importantly declares: "There were no effects of light and shade, and no wind stirred the trees".  What do we infer?

If there really were "no effects of light and shade" then it must mean that their surreal domain was in fact an inter-phased one for two parallel universes. In this domain we surmise that if they could have performed the sequential two slit diffraction experiment cited by Deutsch they'd have found instead a central large dark area and bright fringes. As opposed to a central bright region and dark fringes. In addition, we may infer this interphased domain was dominated by shadow photons over tangible ones but at different angles.  This is why "everything suddenly looked unnatural, therefore unpleasant; even the trees behind the building seemed to have become flat and lifeless ".

It is important to reiterate here, that according to the standard multiverse theory (based on cosmic inflation), there are basically an infinite number of parallel universes. In the hyper-toroid geometry (graphic shown in the previous blog)  these separate universes can be regarded as lines of longitude, since an infinite number of them can be fit around the circumference of the hyper-sphere.  If say, one somehow for some reason briefly overlapped another, one would expect an interphase condition. This then would permit a time slip to occur but it would not be between times in the same universe (say for the Brit pair between the 1901 and 1789 Earth as we know it) but between TWO distinct parallel universes. That is, they'd have slipped from 1901 in this universe with the Earth as it exists therin, to another (parallel) universe with the Earth as it existed in 1789.

Let's now explore the dynamics more closely, using the diagram shown at the very top, for two spaces in  algebraic homology:

T = S1 X S1

The first (space) is the circle all the way around the middle of the 'donut's body. The second (time) is the circle around a section of the donut itself. Here (diagram), the respective spaces (circles S1) define two dimensions for what we will call the global state space GL. Thus, we have:

GL = S1 X S1 = (SPACE) X (TIME)

The line marked 'Axis' defines the center of the toroidal space we are looking at. The important point is that the time cycle is mapped all along the (single) S1 cycle of space. The space cycle therefore defines all hyperdimensional cosmic time cycles that ever have, or will, exist. Evidently, there are an infinite number of such cycles, since an infinite number of points can be mapped onto the space cycle as well.

All cycles are identical in the infinite series (Σi Θi) but also different. Identical, since each cycle goes from 0 through 360 degrees, folding back on itself so that a particular beginning (Big Bang = 0) and ending (Big Crunch = 360°) for each universe occurs at one and the same point (0° = 360°). Hence the same initial and final coordinates apply to all cosmic cycles. Θ is thus a fixed dimension of the Young-model ‑hypertorus, much like time in the Minkowski universe. Indeed, in the hypertorus overview, any position can be fixed by two coordinates (φ, Θ) where the φ is used for space and Θ for time. In fact, since both are circles, it makes sense to assign them angles: one (φ) for space, the other (Θ) for time.


Consider now, the mapping for the phase space volume we called the global state space. It is the (topological) space of all possible times and all possible spaces, for all possible universes. Thus, it is an imaginary (in the mathematical sense!) space. Two possible events in this global state space might be designated:


Ξ = (φ, Θ) AND Ξ' = (φ',Θ')


By way of example, Ξ could be the assassination of Hitler, and Ξ' the event wherein Hitler escapes assassination. Either one is possible but not both simultaneously in the same cosmic cycle or universe! We already know we inhabit the cycle for which Ξ' holds, so the other (Ξ) cannot. The "pasts" are thus mutually exclusive, which further reinforces Hawking's "temporal censorship" postulate that one cannot go back and change the past.. The topological space of the hypertorus 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, the set of specific times t_i C Θ_i, and the set of specific 4-dimensional spaces R_i C φ_i, so the space of all local states, L is the product space of four dimensional spaces and specific times:


L = R X t


We now need to look at is how L and GL are related, and the space and time sets within them:  L Ì GL That is, the local state space L is contained within the global state space GL, but can never be equal to it The same applies to the subsidiary spaces: R in relation to φ, and the specific times: t in relation to Θ.


For example, for Θ, there is some spatio-temporal matrix M with generalized dimensional indices {x0, x1, x2, x3}. No one of these is 'time' specifically and uniquely. Rather, "time" arises when the three space indices have been assigned (i.e. if φ= {x1, x2, x3}, then Θ = {x0}. In effect, as S. Auyang observes: "the structure M is too primitive to confer special meaning on the time dimension. M is not in time, it is all times." (How is Quantum Field Theory Possible?, Oxford University Press, 1995, p. 169). By contrast, 't carries the load of temporal significance'. (Note here that when the 4 dimensional indices for each parallel universe are defined, then it becomes possible to more rigorously separate the parallel universes, i.e. in terms of their respective physical constants, specific times of origin, and duration.)


"Time" then is by no means as straightforward as often assumed, especially if one can plausibly have both time and space uncertainty - i.e. the Heisenberg Indeterminacy principle applicable to each. If this be so, then one can conjecture unusual conditions in which both space and time indeterminacy for two adjacent parallel universes allow for brief interphasing. If a sentient person, human, happens to be at such a location when this indeterminacy of space and time occurs, he can experience a "time slip".


Again, we cannot say the person or persons are really "going back in time". Instead, only that they have transitioned from a current coordinate Θ1 in one universe to Θ2 in other. While Θ2 appears to be "backward" in time by the reckoning of the person at Θ1 it is not really in relation to their own universe.


Part 3: Can I do a time slip to take me to the Kennedy assassination in any universe?

Time Slips(1) : Flights of Fancy or Temporal Displacements Based on Real Physics?

Diagram of the multiverse with two localization angles which may be used to pinpoint parallel universes within it. Is it possible for two longitude lines (each designating a parallel universe) to be so close together that an interphasing is possible? Might this account for the phenomenon of "time slips"? 

In L. Sprague de Camp's classic scifi novel  'Lest Darkness Fall', (1939), a 20th century professor - Martin Padway -  finds himself suddenly hurled back to the Roman Empire in the sixth century by encountering a "time slip" in Rome. While doing the tourist thing in Rome near the Coliseum, he's suddenly transported back in time. He is forced to live by his wits, eventually using his knowledge of Latin and how to make paper (from vellum), to produce a newspaper.

The idea of time slips received more fact-based currency with the publication of Oxford physicist Michael Shallis' book, 'On Time'. Therein, (pp. 161-62) Shallis documents actually reported incidents of factual people who - somehow or some way- found themselves cast back into the past. Among the more famous is the incident involving two women from 1901, Charlotte Moberly and Eleanor Jourdain, who found themselves in the Versailles of 1789 while visiting a park in that location in 1901. As Shallis describes it (p. 161):

"To the ladies of 1901 the experience was one they lived through, but if they stepped into another time, they either did so as a sort of ghost or else as real live people".

Meanwhile, the Wikipedia account of  Moberly's reported experience reads as follows:

"We walked briskly forward, talking as before, but from the moment we left the lane an extraordinary depression had come over me, which, in spite of every effort to shake off, steadily deepened. There seemed to be absolutely no reason for it; I was not at all tired, and was becoming more interested in my surroundings. I was anxious that my companion should not discover the sudden gloom upon my spirits, which became quite overpowering on reaching the point where the path ended, being crossed by another, right and left…Everything suddenly looked unnatural, therefore unpleasant; even the trees behind the building seemed to have become flat and lifeless, like a wood worked in tapestry. There were no effects of light and shade, and no wind stirred the trees. It was all intensely still."


What does this mean? Is this the domain of the supernatural, or is real physics involved? The Wiki article goes on to add:

" In the Versailles case, the two ladies were apparently seen, and spoken to, by people they saw"

In other words, there were real physical interactions, which implies a genuine physics basis. At the same time, Moberly's description reads as if the pair were in some sort of simulacrum world and not an actual past Earth ("the trees behind the building seemed to have become flat and lifeless", "no effects of light and shade").

This suggests perhaps a parallel universes "interphasing" effect. Something I had described in an earlier blog:

http://www.brane-space.blogspot.com/2012/08/is-it-possible-to-detect-parallel.html

Therein, I referenced the (David) Deutsch experiment (See: 'The Fabric of Reality') to detect  how 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...

Is it feasible then, that the two 1901 Brit women time-slipped into 1789 by virtue of  stepping into an interphased domain where two parallel universes merged: one from a 1789 Earth and the other from a 1901 version? Is it possible that the reason their time-slipped Versailles of 1789 appeared "gray and lifeless" is because they were seeing it via shadow photons - the only ones available?

What would the ladies have found had they conducted an interference experiment along the lines suggested by Deutsch? Would the shadows have been more intense to the point of overriding the rest of the pattern?

We consider this in the next part!

Is It Possible to Detect a Parallel Universe?

Diagram of the multiverse with two localization angles which may be used to pinpoint parallel universes within it. Might it be possible to conduct an experiment to demonstrate the influence of one such parallel universe?


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 10¹²  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!

Are There Parallel Universes?

The issue of whether there exist parallel universes has been around for some time, and become more or less a stock theme for a lot of science fiction, some good, most bad. But what do we mean by the term "parallel universe" and is it possible one might ever detect one? Is a parallel universe the same as a "universe" based on the "Many worlds" quantum mechanical interpretation of Hugh Everett III?

Let's take the first last, because it's the easiest to deal with. It also eliminates one potential source of confusion (and unfortunate conflation) right off the bat. In fact, Everett's "Many Worlds" interpretation was devised specifically as an alternative to the Copenhagen Interpretation of QM - in order to physically make sense of the principle of superposition in QM. According to this principle, before an observation is actually made to establish a determinate state, the object or particle exists in a multitude of different (quantal) states simultaneously.

As to the more exact definition of a "state" this was first given by Paul Dirac in his monograph Quantum Mechanics ('The Principle of Superposition', p. 11):

"A state of a system may be defined as a state of undisturbed motion that is restricted by as many conditions or data as are theoretically possible without mutual interference or contradiction"

This definition itself needs some clarification. By "undisturbed motion" Dirac meant the state is pure and hence no observations are being made upon it such that the state experiences interference effects to displace it. In the Copenhagen Interpretation, "disturbance" of mutually defined variables (say x, p or position and momentum) occurs when: [x, p] = -i h/ 2π, where h is the Planck constant. Thus, an undisturbed state must yield: [x, p] = 0. Another way of putting this is that in the latter case the 2 variables commute, and in the former they do not. Hence, Dirac's setting of upper limits in the last part of his definition, specifying as many conditions that "are theoretically possible without mutual interference".

Now, we need to fix ideas further to grasp what the Copenhagen Interpretation (which Dirac held to) was all about. Let's say I fire electrons from a special "electron gun" at a screen some distance away. At first glance one might conclude, reasonably and intuitively, that the electron motion behaves like an apple's if tossed at a wall. That is, there is always one electron which is on a single predictable path, following stages 1, 2, 3 and so on over time, toward the screen. This is a reasonable, common-sense sort of expectation but alas, all wrong!

According to the Copenhagen Interpretation of quantum theory the instant the electron leaves the "gun" it takes a large number of differing paths to reach the screen. Each path differs only in phase (but the differing phases determine the states), and has the same amplitude as each of its counterparts, so there is no preference. How does the electron differ from the apple? It takes all paths to the screen, the apple takes only one (at a time) to the wall. And the electron exhibits phases (as a wave) while the apple doesn't. The electron's wave function can be expressed:

U = U(1) + U(2) + U(3) + .................U(N)

Here the total wavefunction for the electron is on the left hand side of the equation, while its resolved wave amplitude states (superposition of states) is on the right-hand side. If they are energy states, they would correspond to all possible electron energies from the lowest (1) to the highest or Nth state (N). There is absolutely no way of knowing which single state the electron has until it reaches the screen and an observation is made, say with a special detector (D).

What bothered Everett and others was the Copenhagenites' claim that all such differing states existed simultaneously in the same observational domain for a given observer. And then, all but one of the states magically disappeared (referred to as "wave function collapse") when the actual observation was recorded.

To Everett it all seemed too contrived and artificial. What if...he asked himself...instead of explaining the superposition of states this way, one instead used the basis of "many worlds"? Not literal worlds, but rather "worlds" separated from each other denoting specific quantum states, in this case, for the electron?

Thus, instead of thinking of all quantum states (prior to observation) as co-existing in one phase space representation (by which I mean differing phase coordinates could be assigned to each electron) one could think of each phase attached to another "world", a quantum world. For the total duration T of time before the observation was made, all these "worlds" existed at the same time, and then ....on observation....the "choice" for one became reality .....however, in other quantum worlds those other choices might materialize.

Personally, I suspect Everett had a much more significant reason than superificial aesthetics to devise the "Many World" interpretation. That is, it eliminated the troublesome issue of observer disturbance of observations so peculiar to the Copenhagen Interpretation. The core problem or basis is best summarized in Dirac's own words (op. cit,. p. 4):

"If a system is small, we cannot observe it without producing a serious disturbance and hence we cannot expect to find any causal connections between the results of our observations"

In other words, the observation itself disrupts causation. For if the state is "interfered" with such that the observables don't commute (e.g. don't yield [x, p]= 0) then one can't logically connect states in a causal sequence. To quote Dirac (ibid.): "Causality applies only to a system which is left undisturbed".

The other issue that likely bugged Everett, propelling him towards "Many worlds", was the incessant Copenhagenites' debate over what level of consciousness was required for a given observer to collapse a wave function. Perhaps this was best epitomized by Richard Schlegel in his Superposition and Interaction:Coherence in Physics (1980, University of Chicago Press, p. 178,) who refers to the opinion expressed once by Prof. Eugene Wigner (at a conference) that "the consciousness of a dog would effect the projection into a single state whereas that of an amoeba would not."

So, in this sense, "Many worlds" provided welcome relief.

However, it must not be confused with the "parallel universes" to which I will now turn, which I regard as actual PHYSICAL cosmi likely incepted from the selfsame primordial vacuum state (via inflation) as our own universe. Thus, an actual primordial vacuum - not a human observer or consciousness making observational choices- 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 the agency of inflation 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^-15m, 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 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.

Now, 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. If the topological condition above has not been met, then we expect the Deutsch experiment will render a negative result, but this doesn't mean the parallel universe theory is necessarily invalid- only that the specific topological condition hasn't been met! (Absence of evidence here is not evidence of absence).