I recently watched a documentary featuring michio kaku ( please excuse as I doubt my spelling is correct) and the subject was parallel universes. I've also seen him speak on the possibility of time travel. Aside from being a taboo subject aren't the two theories in direct contradiction with one another? The parallel universe theory says that there are infinite realities in which every possible circumstance is played out. And that each is seperate and has its own timeline in which its realities take place. If this is true and if it is also true that the same matter cannot exist twice in the same space at the same time it would thereby be reasonable to assume that time travel would be a fundamental impossibility and that if it where to happen it would result in the universal destruction of reality. If subject a from reality a were to travel to a time in their past to change his pants because the ones they wore to work that day were too long and caused them to trip and break their ankle that timeline would immediately merge with the one in which that decision had already been made thus causing the two realities to converge and thereby destroy the universe. My question is whether my train of thought has been completely derailed or if it has some merit. This is just the type of thing that I enjoy thinking about and I would greatly appreciate any thoughts to help me better understand. Thank you
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? (Which is what you referred to when you referred to "infinite realities in which every circumstance is played out".
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 superficial 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" (again not to be confused or conflated with the parallel universes spawned via cosmic inflation), 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 model shown in the graphic (done with my Mathcad program) I depict a possible parallel universe model. Here 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
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].
If such condition is met, there could be "interphasing" of two such universes, and at least one author (David Deutsch) has proposed an experiment (See: The Fabric of Reality) to detect the interphasing of a parallel universe and how it can be carried out.
In terms of "time travel" - still totally speculative, it might be feasible only between the present of one parallel universe and the past of another, but never between the present and pasts of the selfsame cosmos. (According to Hawking's Temporal Censorship postulate). Obviously, in such a far fetched case there's no problem of altering the future (or past) in one's own cosmos since timelines are distinct as the model graphic discloses. Personally, it likely would be a waste of time to even try since histories would be different as well. So why even bother.
Anyway, hopefully this answer provides you some fodder for thought!