Friday, April 29, 2016

Max Tegmark's Multiverse Types - And "Alternate" Universes (Tegmark's Type 3)

One idealized model of a Type II Multiverse with two localization angles defined.

Much of the discussion concerning the Multiverse has been muddied because of lack of clarity about what it means. Let us concede that for many years humans conceived of only one manifestation of the whole or 'universe' (the Milky Way galaxy itself was at one time conflated with 'universe' ) and it has taken the push of modern physics to acknowledge this grand assembly may not be the final statement of physical reality. Thus, by way of several theories - which we will get into. - one comes into the conceptual purview of the Multiverse - composed of perhaps an infinity of universes with differing properties, cosmological constants etc.

One person who has tried to provide categories and clarity is Max Tegmark of M.I.T. He has suggested a fourfold classification scheme, but only three of them are relatively comprehensible to most ordinary folk without advanced physics backgrounds. (It is those I will deal with in this post.)

Type 1:

The simplest or Type 1 Multiverse is essentially an infinite extension of the acknowledged universe. Our most advanced telescopes like the Hubble can only see to a certain limit given the finite speed of light (c = 300,000 km/ sec)  which means our vision is confined to a limited radius. This is called the "Hubble radius" and is generally equal to the age of the cosmos translated into distance or 13.8 billion light years.

Thus, if light takes 13.8 billion years to travel to the maximum distance we can actually see (assuming space is static) that turns out to be 13,8 billion LIGHT YEARS. (One light year being the distance light travels in one year.)

In fact, this is a simplification because space or rather space-time isn't static.  Because of its expansion immediately following the Big Bang the actual radius of the cosmos is 42 billion light years or some 28.2 billion LY greater than the telescopic limit.   Assuming physical reality, i.e. the universe, exists beyond the actual Hubble radius then all permitted arrangements may exist - and in infinite numbers.

In effect one finds separate "cosmi", cut off from each other by their own individual Hubble radii. These would be like separate compartments or "bubbles" cut off from each other.  The key point is that the laws of physics in one "bubble" are the same in those in all the others because in the end the universe - despite the disparate "bubbles- is one entity.

Type 2:

While the Type 1 version is based on the cosmological principle, so the laws of physics are the same in all the separate "bubbles" with their own Hubble radii, in this Type 2 case they can vary from one universe to another. The value of G, the Newtonian gravitational constant may be G as we know it (6.7 x 10-11 Nm2/kg2) in our universe, but 1.1G in another in the Type 2 Multiverse, and 0.98G in another. The result would be separate universes remarkably different from each other.

As I noted in previous blog posts, the genesis of the Type 2 Multiverse is distinct from the Type 3 which is really Hugh Everett's "Many worlds" quantum-based theory (which we will get to.) In the Type 2 all the universes in the Multiverse were spawned as a result of cosmic inflation immediately following 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 dominated. 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. If such an "inflationary field" could spawn our universe it could spawn many others (up to an infinite number).  Further, there is no reason why these offshoot universes from inflation should have the same laws of physics as any of the others.

This is a delightful conclusion since it disposes at once of the "specialness" of the cosmos that too many invoke as a cosmological argument to demand a deity or "Creator".  However, if universes are commonplace, and the physical laws that govern each vary, then the need for a "human-friendly" creator vanishes. It is no longer a fluke that one universe has just the right conditions for life if gazillions of them don't.

Type 2 universes, then, aptly deal with the annoying fine tuning problem that religionists endlessly invoke.

Type 3

The Type 3 "Multiverse" is in reality a product of Hugh Everett's Many worlds quantum interpretation, which was devised to counter the Copenhagen Interpretation's strange ramifications. In the Copenhagen Interpretation, any observer's consciousness is theoretically capable of "collapsing" the wave function, yielding one and only one eigenstate or final observation, i.e. observed state. Everett, to his credit, argued that rather than dealing with one wave function for whatever observed entity (particle, universe, cat in a box - subject to release of cyanide if a cesium atom decays triggering the release device) one might let ALL possible outcomes occur.

In this case, the universe is constantly undergoing a kind of multiple "fission" of reality into umpteen daughter universes where different events unfold from the one we're in. To fix ideas, in one of them Lee Oswald is a published Professor of History at Tulane, not an accused assassin. In the same or other universe, LBJ's plan to have JFK killed is exposed before the executive action and the SOB is tried for treason. In another the Challenger disaster never occurs, it goes off perfectly because NASA took the time to solve the O-ring problem. In yet another, there is no Indonesian tsunami that killed 200,000 in December, 2004 - but there is a massive ocean asteroid strike that kills just as many in SE Asia. You see what I mean?

Here's the catch: All those other universes are inaccessible to those of us in this universe. Hence, for THAT particular universe any given observer picked at random will see only ONE outcome - his own, i.e. from his history- events record. If he observes the outcome of LBJ being hung or shot for treason, he will not observe the outcome in ours where Lee Oswald was framed and LBJ got away with the crime of the century. To put it in the context of Everett's Many Worlds interpretation, the wave function will appear to have collapsed, say  for LBJ's treason and punishment- but that sole wave function collapse (to the exclusion of all other possibilities) is not really what happened. In other ("alternate")  universes other outcomes would have occurred - such as in ours where Oswald is found guilty in absentia and Johnson's Warren Commission fiction and fraud is promoted by a feckless political and media community.

Let's go back to why 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 or collapse 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) leads inexorably to wave function collapse. 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.

Again, in Copenhagen, the key to getting from [x,p] = - i h/ 2π to [x,p] = 0 is the presence of an observer capable of collapsing the relevant wave function for the system observed. But the problem  is that peculiar considerations enter. For example, a major irritation is the incessant Copenhagenites' debate over the level of consciousness required for a given observer to collapse a wave function. Perhaps this was best epitomized in Richard Schlegel's  Superposition and Interaction:Coherence in Physics (1980, University of Chicago Press, p. 178,) referring 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 from metaphysical conjectures.

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. Then,  on observation, 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 thought of all quantum states (prior to observation) as co-existing in one phase space representation . Then 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, as per the examples given above.

In a way, then, Everett's "Many worlds" interpretation  is actually a theory of alternate universes, at least at the level of potential quantum states. It is more compellingly described this way than as a third type  Multiverse, in my opinion. Especially the Type 2 comprising actual physical universes 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 set of universes. Thus, all putative parallel universes plausibly emerged from the primordial vacuum the way ours did, e.g. from the Big Bang.

In the graphic, I show an "idealized Type 2 multiverse" with an infinite set of members, each specified under a coordinate φ, and separated by uniform angular measure Θ from two 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

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" (e.g. in complex time)  another 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 an exact parallel time displacement we might be able to show how one 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 adjacent 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.

This isn't necessarily poppycock.  Stephen Freeney of Imperial College, London has surmised that two adjacent universes in a Type 2 Multiverse could conceivably 'butt up' against each other and leave "imprints" in each other's space. He reasons that these imprints would likely show up in the cosmic microwave background radiation, generating 'splotches' in the radiation field or differing energy density signatures. As yet no such signal has been found, but in truth we may not yet possess the instruments needed to identify such signatures.

Another experiment proposed to test one's conviction in Everett type worlds is best called "quantum Russian roulette" and is only to be undertaken by the most cocksure quantum physicists. (Say like that lot that makes pronouncements on the JFK assassination simply because they have a QM background.)  The experiment is analogous to the one for Schrodinger's cat - with the experimenter inside a sealed off room connected to a cyanide injector with release of a gas capsule  governed by the decay of a radioactive isotope.

 In some futures the guy will be killed, in others he will remain alive. But since  -from his point of view - he is only aware of being alive he will only perceive that he survives. Hence, he does survive.

So far there have been no takers to carry this one out.

1 comment:

Hayat Faqeer said...

Interesting read. Thank you for posting it.