Revisiting The Concept Of 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:

y  = y(1) + y(2) + y(3) + .................y (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) are 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 Worlds" 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^-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 below 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 reiterate that this is an idealized model which assumes that N-cosmi were incepted at equal intervals of time - as manifested by the equal spacing in the longitude angle 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 proposed 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).

The Limits Of Scientific Inquiry & Research (1)

An unnerving item that appeared not long ago referenced that only a handful of people read nearly half of all scientific papers.  One estimate is that  1.8 million articles  are published each year, in about 28,000 journals. This elicits the question: who actually reads those papers?

According to one 2007 study, half of academic papers are read only by their authors and journal editors. This is nothing short of astounding but makes sense if one gets inside what research scientists actually do, which is to narrow their focus almost exclusively to their specific specialty areas  In addition, specialty areas themselves can be reduced to sub specialties, for example solar physics has a sub-discipline of solar flare magneto-hydrodynamics, another of solar flare predictions. Perhaps the former comprises 5 percent of solar physics and the latter 2 percent. Take the overlap between them and you may only find 50 solar physicists. Will they read beyond the 250 papers published annually in those two areas? Doubtful!  There simply isn't the time to do so, in addition to lecturing, attending conferences to present papers, etc.

Even more sobering, the authors found that 90 percent of papers published are never even cited by other researchers. Again, this isn't surprising. and let's also bear in mind that papers are of unequal quality - much of the lesser quality due to the "publish or perish" pressure. This mandate means professors will churn out papers merely to meet the quota mandates of their institutions, and may not have anything genuinely novel to report. Hence, the low quality.

This brings us to the other aspect: what methods are used by the researchers? Not only in astrophysics but physics as a whole, biology and chemistry.  If then academics are not clear on their methods, or what justifies them, then we are bound to see a wide array of quality. This is often because of the peer review process itself, see e.g.

https://newrepublic.com/article/135921/science-suffering-peer-reviews-big-problems

And the fact not all journals and peer-review processes are created equally. All of this evokes questions of how rigorous scientific methods are applied to any scientific discipline and whether a specific reliable method exists in the first place.

According to biologist Lewis Wolpert, writing in his book 'The Unnatural Nature Of Science' (1992):

"It is doubtful there is a scientific method except in very broad and general terms".

Some of the advice referenced by Wolpert distilled from practicing scientists includes: "never try to solve a problem unless you can guess the answer, seek simplicity, seek beauty".

All of which are fine aspirations, but let's face it, rarely achieved in doing real science - say in stochastic realms like climate science and solar flare physics.

He follows these examples by reinforcing his original claim (ibid.):

"No one method, no paradigm, will capture the process of science. There is no such thing as the scientific method".

Which is a statement very likely to shock most high school science students, who will swear their teachers have shown them exactly what the scientific method entails, viz.

- Define the problem in respect to the specific phenomenon being investigated

- Gather information, data related to the problem

- Observe the phenomenon related to the problem

- Formulate a hypothesis related to the phenomenon and problem

- From the hypothesis make predictions that can be tested

-  Observe and/or experiment to test the hypothesis

Of course, in real life there is no such set formulaic pattern. Indeed, one can point to discoveries in the history of science (e.g. black holes such as Cygnus X-1) and show that scientists are led by theory almost as often as they are led by the observations.  There are also many permutations which led Wolpert to make the claim that "there is no such thing as the scientific method."

The single template presentation  - such as presented in high school science teaching- is a myth, an artificial scheme, rarely followed. It is only used for pedagogic purposes and convenience.. The fact is, when one reads most scientific papers - including in physics and astrophysics - there are large assumptions made and no particular method has been followed other than perhaps to gather the data as methodically as one can, usually by painstaking observations or experiments, and subject it to critical statistical or mathematical analysis. The latter usually entails the development of a consistent mathematical model.

However, and here is the kicker - depending on one's overarching choice of underlying philosophy, there may be no connection of the model to physical reality. Among the philosophies of science most powerful right now are positivism and reductionism. In the first case, one does not expect coincidence with physical reality but rather that the model "works" mathematically. To quote Stephen Hawking from his hypothesis for quantum coherence ('The Nature of Space and Time', p.3-4):

"I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All one can ask is that its predictions should be in agreement with observation."

The original positivist emphasis in physics perhaps appeared in the quantum theory first, with its Copenhagen Interpretation. In this interpretation, the wave function Y  is purely statistical in nature, following the original proposal of Max Born. We cannot use it to effect specific computation concerning individual particles of a quantum system but are constrained to work only with collective properties.

In Born's view, the presence of i (the imaginary number i = Ö(-1)) in the quantum wave function divested it of any real, physical significance. A wave with an imaginary number is an abstraction - nothing more. In Born's statistical interpretation, it was useful for describing the changing probability of finding a micro-system in a particular quantum state. However, one was sensible enough not to take it literally, as a physically real entity.  Thus, the positivist interpretation or CI which still holds sway for most physicists.

Quantum theory accurately predicts the wavelengths of spectral lines, e.g. for hydrogen and other  spectra:









so whether it "really"  embodies physical reality is less important than that its observational predictions can be verified.

Reductionism is also a recurring and mesmerizing motif in most physics approaches, though it has also now diffused to other scientific disciplines. The pinnacle of reductionism, not surprisingly, was achieved in classical physics, based on Newton’s laws of motion. Its quintessential form, Mechanics, ultimately became the model for all of science by virtue of its sophisticated and elegant mathematics. Its power, particularly to make predictions, was so beguiling that it led to an entire mechanical paradigm for the universe. 

An illustration can help to clarify why mechanical reductionism became so beguiling to later scientific minds. One of the more interesting systems is the Attwood machine in which we have two masses suspended at opposite ends of a string on a single pulley, but with one mass exceeding the other, e.g.  m2 > m1. Then, when set up, the masses will accelerate in the direction of the greater mass, since an unbalanced force is now acting, e.g.

 A typical  problem for this simple pulley system is to find the acceleration resulting. Since m2 > m1 the acceleration is in the direction of  m2, and using two free body force diagrams (right side of graphic)  we may write (since T1 = T2 = T) 2 separate equations of motion:

m2 a = m2g – T

m1a = – m1 g + T

Adding the two equations:    a(m1 + m2) = (m2 – m1)g

Hence:  a =    (m2 – m1)g / ( m1 + m2)

Thus, if we take m1 = 0.5 kg, m1 = 1.0 kg and g = 10 N/kg  then:

a = (1.0 - 0.5)kg (10 N/kg)/  (1.0 kg + 0.5 kg) =  5 N/kg / (1.5) = 3.33 N/kg

Perhaps the single comment that embodies both positivism and ardent reductionism comes via Victor Stenger’s  attempt  to dash the validity of real quantum nonlocality (cf. God and the Folly of Faith, 155) :

It does not matter whether you are trying to measure a particle property or a wave property. You always measure particles. Here is the point that most people fail to understand: Quantum mechanics is just a statistical theory like statistical mechanics, fundamentally reducible to particle behavior

The biggest contradiction to Stenger’s interpretation comes by way of.  J.S Bell ( Foundations of Physics, (12, 989 ):

Although Y is a real field it does not show up immediately in the results of a ‘single measurement’, but only in the statistics of many such results. It is the de Broglie –Bohm variable X that shows up immediately each time.

These examples are meant to show why there is so much disagreement among physicists to account for differing observed phenomena.  For example, this is manifested to an extreme degree in the recent controversy over quantum "qbism", e.g.

http://brane-space.blogspot.com/2014/05/qbism-remains-quantum-stepchild.html

This underscores a point made by Julian Baggini in his book, The Edge of Reason ('Chapter Two, 'Science for Humans',):

"The quirks and deviations from the official version of pure experiment and deduction are deeply embedded in the way science works".

Something that can be easily gleaned just by referring to the link above. Or, one can get hold of any number of different scientific papers, say from different journals. Is there one method of approach? No there is not.   If I had one major gripe about discussing scientific methods, approaches it is in ignoring that ultimately scientific advance is predicated on successive approximations. If high school (or even university) students learn anything, it is to master this subtle principle.

You have data, and accessory information which leads to some initial result (observation, experimental outcome)  which tests a particular hypothesis- call it 'x'. You then acquire better data (perhaps because of refined instruments, techniques ) and are led to a modified (improved) result such that:

x (n+1) = x + P(x) where x(n +1)

denotes an improvement via iteration, with P(x) the process (acting on x) that allows it.

Later, more refined data become available, such that:

x(n + 2) = x(n + 1) + P'(x + 1) and so on, and so on and so forth.

Each x, x(n+1), x(n+2) etc. being a successive approximation to what the objective, genuine value should be.

Beyond this, one must grasp different approaches are dictated depending on the discipline or sub-discipline and their respective empirical limits. Take the cases of the solar physicist and the lab plasma physicist. The solar physicist - with few exceptions, e.g.

http://brane-space.blogspot.com/2016/12/coronal-mass-ejections-successfully.html

 

is perforce afforded a more passive role than his lab plasma physicists counterpart. And while the solar physicist can apply plasma physics principles to his object of inquiry, say solar flare plasma of differing polarity deduced from  vector magnetograms.

he cannot extract that flare plasma and subject it to experimental or diagnostic tests - say to check the Debye length of the plasma.  In effect, solar physics differs from lab plasma physics in the respective degrees of control which can be exerted on the lab and solar plasma. This then must be understood from the outset in order to fully appreciate the methodology applied in each discipline.

Even so, there are huge assumptions often made before the investigator in either discipline can proceed. That also often means skating over "outliers" in data, and ignoring minor discrepancies in order to arrive at a larger, overarching picture more amenable to publication. We will get into some of these in the next part.

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.

The EPR Paradox and Quantum Nonlocality (Part 1)

In 1935, Einstein along with two colleagues, Boris Podolsky and Nathan Rosen, devised a thought experiment.[1]  This has since been called the EPR experiment based on the first initials of their names.  Einstein, Podolsky and Rosen (E-P-R) imagined a quantum system (atom) which could be ruptured such that two electrons were dispatched to two differing measurement devices. Each electron would carry a property called 'spin'. Since the atom had zero spin, this meant one would have spin (+ 1/2), the other (-1/2). The diagram below illustrates this, the atom being disrupted inside the box, with its opposing spin electrons sent to the left and right.
 
A1 (+ ½ ) <----------->(- ½ )A2


Orthodox quantum mechanics forbade the simultaneous measurement of a property (say different spin states) for the same system. If you got one, you could not obtain the other. This was a direct outcome of the Heisenberg Indeterminacy Principle which stated that simultaneous quantum measurements could not be made to the same precision.

 E-P-R argued that this showed the incompleteness of quantum mechanics. It was not the 'paragon' of physical theories its apologists claimed, if such indeterminacy was fundamentally embedded within it. At the same time they conceived an 'experiment' in which both spins could be identified - with the sole assumption that both were in definite states from the instant of their parent atom's disruption.

 Then, we need only know one spin to obtain the other. Say we know or can measure one spin to be (+1/2).[2] Since the total atomic spin is zero, the other electron must have spin (-1/2) since:   (-1/2) + (+1/2) = 0

 Thus, we manage to skirt the Indeterminacy Principle, and obtain both spins simultaneously without one measurement disturbing the other. We gain completeness, but at a staggering cost. Because this simultaneous knowledge of the spins implied  that information would have had to propagate from one spin measuring device (on the left side) to the other (on the right side) instantaneously! This was interpreted to mean faster-than-light communication, which violates special relativity. In effect, a 'paradox' ensues: quantum theory attains completeness only at the expense of another fundamental physical theory - relativity.

 By this point, Einstein believed he finally had Bohr by the throat. Figuring Bohr might come up with some trick or sly explanation, Einstein went one better at the 6th Solvay Conference held in 1930, actually designing a device (see image on next page) that he was convinced would have Bohr in tears trying to find a solution. (According to reports, it very nearly did, and a number of participants insisted Neils was in a state of "shock" believing there was no real solution.)

Using his hypothetical (purely on paper) thought device, Einstein wanted to put to rest once and for all the notion that quantum mechanics was complete, or was in any way a proper science. The mechanical device contrived by Einstein was designed as a counter-example to the Heisenberg Uncertainty principle for energy and time which states:

ΔE Δ t ³  h/2π

Fig. 1: Einstein’s Thought Experiment Device

In the device, a weight scale is located and one can see it when a door (front of box) opens, with the door controlled by a clock timer. Whenever the door flaps open, even for a split second, one photon escapes and the weight difference (between original box and after) can be computed using Einstein's mass-energy equation, e.g.: m = E/ c². Thus, the difference is taken as follows:

Weight(before door opens) - weight (after - with 1 photon of mass m = E/ c²   gone)

     Thus, since the time for brief opening is known (Δ t) and the photon's mass can be deduced from the above weight difference, Einstein argued that one can in principle  find both the photon's energy and time of passage to any level of accuracy without any need for the energy-time uncertainty principle.

     In other words, the result could be found on a totally deterministic basis!

     Bohr nearly went crazy when he studied the device, and for hours worried there was no solution and maybe the wily determinist was correct after all. When Bohr did finally come upon the solution, he realized he'd hoisted the master on his own petard.

     The thing Einstein overlooked was that his very act of weighing the box translated to observing its displacement (say, dr = r2 - r1) within the Earth's gravitational field. But in Einstein's general theory of relativity, he'd found that clocks actually do run slower in gravitational fields (a phenomenon called 'gravitational time dilation') In this case, for the Earth, one would have the fractional difference in proper time, as a fraction of time passage t:

dt/ t » GM(1/r1 - 1/r2) » g(dr)/ c²

where G is the Newtonian gravitational constant, M is the Earth's mass, and g is the acceleration of gravity (g = 980 cm/ sec² in cgs) and c = 3 x 10¹⁰ cm/sec.

Let us say the box deflection (r2 - r1)was 0.001 mm = 0.0001cm, then:

dt/t ~ (980 cm/s²)(10^-4 cm)/ (3 x 10¹⁰ cm/sec )²

dt/t »  10^-22

and for an interval say t = 0.01 sec,  and:

 

dt =   (10^-22 )(0.01 sec) = 10^-24 sec

In other words, the observation would actually generate a time uncertainty of 10^-24  sec- and hence an uncertainty dE in the energy of the photon. In other words, after the displacement (r2 - r1) arising from the measurement, the clock is in a gravitational field different from the original one. (The Energy uncertainty can meanwhile be computed from the Heisenberg energy -time relation to be dE  » 10^-10 J)

Quantum theory prevails again!

 Einstein's challenges to Bohr in the aftermath were all kind of half-hearted and had nowhere near the intensity of his clock-door device work of art. Rather than join happily with other QM theorists at the last Solvay Conference in 1933 Einstein - the perpetual determinist- remained on the sidelines "feeling the same uneasiness as he had before".

He went to work separately, on a "unified field theory" while the quantum theory edifice was formulated to its present maturity without him.

 Aside:   Most people outside physics are unaware there were seven Solvay Conferences in all, in the course of which the essential underpinnings and core interpretation of quantum mechanics was thrashed out – leading to the Copenhagen Interpretation.

 In the orthodox Copenhagen (and most conservative) interpretation of quantum theory, there can be no separation of observed (e.g. spin) state until an observation or measurement is made. Until that instant (of detection) the states are in a superposition, as described above.   More importantly, the fact of superposition imposes on all quantum phenomena an inescapable ‘black box’. In other words, no information other than statistical can be extracted before observation.

2. Bell's Theorem and the Aspect Experiment

 Years later, mathematician John S. Bell asked the question: 'What if the E-P-R experiment could actually be carried out? What sort of mathematical results would be achieved?' In a work referred to as "the most profound discovery in the history of science", Bell then proceeded to place the E-P-R experiment in a rigorous and quantifiable context, which could be checked by actual measurements.

 In a landmark theoretical achievement in 1964, Bell formulated a thought experiment based on a design similar to that shown at the opening of the chapter. He made the basic assumption of locality (i.e. that no communication could occur between A1 and A2 at any rate faster than light speed). In what is now widely recognized as a seminal work of mathematical physics, he set out to show that a theory which upheld locality could reproduce the predictions of quantum mechanics. His result predicted that the above sum, S, had to be less than or equal to 2 (S £ 2). This is known as the Bell Inequality.

 To test quantum conformity to Bell's Theorem, Alain Aspect and his colleagues at the University of Paris, set up an arrangement as sketched below.[3]  In these experiments, the detection of the polarizations[4] of photons was the key. These were observed with the photons emanating from a Krypton-Dye laser and arriving at two different analyzers, e.g.

 

(P1) A1 ¯| <------------> |­ A2 (P2)

                                              

Here, the laser device is D, and the analyzers (polarization detectors) are A1 and A2 along with two representative polarizations given at each, for two photons P1 and P2. The results of these remarkable experiments disclosed apparent and instantaneous connections between the photons at A1 and A2. In the case shown, a photon (P1) in the minimum (0) intensity polarization mode, is anti-correlated with one in the maximum intensity (1) mode.

 Say, twenty successive detections are made and we obtain, at the respective analyzers (where a ‘1’ denotes spin  +1/2 detection and ‘0’ spin  (-1/ 2):

A1:   1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0

A2:   0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

 

On inspection, there is a 100% anti-correlation (i.e. 100% negative correlation) between the two and an apparent nonlocal connection. In practice, the experiment was set out so that four (not two - as shown) different orientation 'sets' were obtained for the analyzers. These might be denoted: (A1,A2)I, (A1,A2)II, (A1,A2,)III, and (A1,A2)IV.

 Each result is expressed as a mathematical (statistical) quantity known as a 'correlation coefficient'.[5] The results from each orientation were then added to yield a sum S:

S = (A1,A2)I + (A1,A2)II + (A1,A2,)III + (A1,A2)IV

 In his (1982) experiments, Aspect determined the sum with its attendant indeterminacy to be:[6]   S = 2.70 ±  0.05 and in so doing experimentally validated Bell’s Inequality.

 The crucial significance of the Aspect experiment (1982) and earlier the Clauser experiment in 1969, had not been lost on physicist David Bohm.  Both experiments reinforced for him that a novel concept had to be introduced to account for these nonlocal results. The old answer of the Copenhagen theorists: 'Leave it alone!', wouldn't do any more. In essence, Bohm had become convinced that the entrenched vagueness and philosophical abdication of the standard Copenhagen Interpretation could no longer be supported.

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    [1] Einstein, Podolsky, and Rosen.: Physical  Review, 777.

[2] More technically, this is what is referred to as ‘the z-component of electron spin’, since the electron is visualized as a spinning top, with z-axis (i.e. component) in the axial or z-direction.

    [3] Aspect, Grangier, and Roger: Physical Review Letters, 91.

    [4] Polarization is the orientation in space of the electric field E, associated with light. This can be altered, subject  to the imposition of different filters and devices.

    [5] For example, if a set of data: 1, 1, 1, 1 is correlated with another set: 0.5, 0.5, 0.5, 0.5, the correlation coefficient is 1.0. The range is between 0 (no correlation) and 1.0 (perfect correlation).

    [6] Aspect, A. et al, op. cit.