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By: Albert van der Sel

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Fig. 1: Here, 7 approaches are shown in simple pictorial figures.

It's true that at least 7 or 8 "ideas"/"models" exists, from which it follows that the existence of parallel universes

might be possible. Here, a few originate from "

from theoretical physics and cosmological models.

Let's take a brief look what on they are about... Maybe you even like it!

However, most ideas are considered only by limited number of physicists.

Indeed, it is fair to say that a minority of physicists probably accept Parallel Universes.

Even if you are a "supporter": we simply have no truly conclusive "evidence" that one of them is on the right track.

Indeed: no real pointer at all. However, maybe some pointers will be found sometime from now, possibly through experiments.

However, the general idea among physicists is, that some ideas are a bit stronger compared to others.

But that still varies a bit over time. For example, I always thought that support for "Everett's MWI theory (1957)" (see below)

declined during the '80's/90's, but it still amazes me how many articles still keep appearing, in favour of Everett's idea's

or derivates of those idea's.

Also, as another model, "Poirier's MIW theory (2012)" seems rather tight, but at the same time I never could find

many supporters for this theory.

It's not impossible that experiments performed in the coming years will make a point for a certain theory.

For example, some Cosmological Brane-world scenario's also predict certain particles/fields (undetected up to now, e.g. "branons"),

that are in line with Brane-world scenario's. It's not impossible that future LHC experiments will provide

some clues for the existence of such particles/fields.

By the way: The LHC is currently the world's largest particle acclerator.

In a discussion about SpaceTime, a review of "Parallel World" theories, is absolutely justified.

So, let's see what we are dealing with...

I simply randomly picked a theory to start with, and I will gradually work (briefly) through all of them.

Let's start with the older "Everett's MWI" theory.

Certainly not. But, it should cover some mainstream lines of thought.

However, as to be expected from science, new- (or revived older-) "contours" come up all the time.

Some of those newer thoughts are not included yet in this simple note.

A rather remarkable theory is Zurek's "Many Minds" approach, which might be viewed as a "softer" model

of Everett's MWI theory, and specifically includes the "mind" of the observer.

This "somehow" also borders to psychology (or should border) and other Human sciences, and that's why

I was a bit reluctant to place it in this simple text either. But it also contains enough physics.

If unknown to you, I certainly encourage you to take a look at Zurek's (Saunders, Barrett) approach.

Also, as you will notice, a clean and rigorous mathematical treatment is absent in this simple note.

Yes really.., I absolutely insist on the fact that this note

Personally, I am not especially "pro" for any of such theories covering "Parallel Worlds".

However, some theories seem to be quite waterproof, and kept physicists busy for decades.

And the subject is facinating...

I am not sure if I am doing a good job here. Just let me try.

1. Everett's "Many Worlds Interpretation MWI" (1957).

2. Hubble Volumes.

3. Poirier's theory of interfering "classical" universes (MIW).

4. Inflation with bubbles / eternal inflation / chaotic Inflation.

5. The Universe as an emulation, or "physical reality=virtual reality".

6. Brane - World Cosmology.

7. Proposed tests, using Quantum Mechanics and Quantum Computing.

Ofcourse we might be able to apply the rules of a certain mathematical framework, but that does not mean

we truly understand what is really behind it. So, many wonder on how we must

Even today, there is still no absolute answer. At least, the following important interpretations exists:

Table 1:

-The Copenhagen interpretation.

-QM with Hidden variables

-Decoherence as a successor to the Copenhagen "collapse"

-Everett's Many Worlds Interpretation (MWI) -

-The Many Minds Interpretation -

-Poirier's "Waveless" Classical Interpretation (MIW) -

-The transactional interpretation

-de Broglie - Bohm "Pilot Wave" Interpretation (PWI)

-possibly also the "Two State Vector Formalism"

As you can see from the listing above, Everett's "Many Worlds Interpretation MWI" is a well-known interpretation of QM.

It's a remarkable long listing indeed. If you would like a brief and very simple overview on most of those interpretations first,

you might like to see this note.

That's one of my notes, so it certainly is not "great" or something, but at least it's short (and hopefully not too boring).

In this section, we will briefly focus on Everett's (and Wheeler's) "Many Worlds Interpretation" (MWI).

It stems from around 1957, and it is indeed a

the article, it needed a couple of years "to sink in" in the community of physicists.

The way I see it, from around 1965 to about 1985, it was a very serious competitive theory amongst all other

interpretations. I would say, that in it's "best years", probably over 30% of physicists gave it serious thought

and a relevant fraction of those physicists even believed it was the best we had.

A mechanism called Quantum Decoherence, was first formulated by Zeh, around 1970. This was a good alternative

for the "strange" collapse of the Copenhagen interpretation. Initially, it seemed that it did not land in the community.

However, from (about) 1990, Zurek gave new momentum to Decoherence, and Copenhagen and also MWI, lost popularity. Even without

considering Zeh/Zurek's "decohrence" paradigm, many scientists gradually discovered more and more, that MWI lacked

a true "oncology", and that it actually focussed too much on an objective "wave function" (or statevector) itself.

I would say, that from around 1995 (or so), more and more studies appeared which all made it quite likely that

it's really difficult to sustain MWI as one of the best candidates anymore, and that it even might be flawed,

but the latter was (probably) never really proven.

I must however hastely add that MWI still has a certain base of supporting scientists.

To make that a bit stronger: regularly (even today) new articles are published which makes a case for the MWI theory,

so, if I made the suggestion that MWI is "nearly dead", this is by no means true.

However, the supporting base of physicists supporting MWI, seems to be decreasing, since, say, 1980 or so.

to look at QM, like the Copenhagen Interpretation, or Hidden variables,

in the context of parallel universes. Therefore, theories which explicitly uses parallel universes or "many worlds",

I would call "non-orthodox" interpretations in QM.

Ofcourse, it's quite hard to sustain that a theory like the "pilot-wave" (of de Broglie-Bohm) is really "orthodox", since

it's certainly not. However, it does not refer to "Many worlds". So, I hope you get my idea here.

So, let's first take a quick look at a typical

Let's suppose we have a fictitious Quantum System that we can represent by a "vector" (or State vector).

|BOX1>, |BOX2> and |BOX3>, meaning..., yeah... Meaning what?

In the Copenhagen interpretation it is said that there is a chance that when a measurement takes place, we may

find the particle either in BOX1, or BOX2, or BOX3, with probabilities for which hold |a|

The latter equation is not strange, since all probabilities must add to 1 (or 100%).

But equation 1

is in BOX1, and BOX2, and BOX3

Yes, indeed. This is very strange, since we have no classical equivalent for something like this.

However, for example the QM solutions for the position of an electron in a Hydrogen atom, is quite similar to what we have above.

But here we have a measurement problem. The moment you open the boxes, and say, you find the particle in BOX3, what

happened to the superpostion (expressed in equation 1) ?

The Copenhagen interpretation now postulates that the Statevector (like equation 1) "collapses" into one

of it's

Here we have a real problem in QM, and facts like this one, triggered lots of people to ponder on how to interpret QM.

Most notably, in the twenties, thirties of the former century, there was quite some opposition to the Copenhagen view.

However, some of the people who favoured it, quite often saw it as just a "working" methodology, since

But, many were not happy at all, and for instance Einstein proposed that QM is "not complete".

It also lead somewhat later to the postulate of "Hidden Variables", that is, variables we do not know yet, but if we would known them,

it would remove all "vaque-ness" and made QM deterministic again.

By the way, in table 1, you can see quite some alternatives for the Copenhagen interpretation, like for example the "Pilot Wave"

interpretation of de Broglie, which was leter picked up by Bohm again.

Or explaining Quantum phenomena using the idea of "hidden variables", in such a way, that if those variables were know,

we would have a deterministic theory again.

By the way, equation 1 shows a statevector which is expanded in 3 basisstates. In general, when dealing with "n" dimensions

with respect to the number of basisstates, we have:

the Grandmother of parallel universe Theories in QM. Slightly later, folks started to call it "The Many World Interpretation".

In short: The Many-Worlds Interpretation of QM holds that there are many worlds which exist in parallel in the same SpaceTime

where you are part of. In many cases, where Copenhagen would talk of the (strange) collapse at a measurement, in MWI

the current Universe "forks" into new chains of events. In a sense, the Theory is "deterministic" if the mechanics of how

the "forks" work, would be well explained.

Please note that Everett's original arcticle was called

Everett, an absolute state does not exist, and we are always dealing with "relative states".

He, more or less, reasoned along the following lines. Taking pure wave mechanics as the basis, he seems to fundamentally rejects

the "collapse" of the statevector to an eigenstate when a measurement takes place, since the mechanisme behind it,

is not explained at all. Further, for Everett the Wave function (or State vector) itself, is a physical reality.

Also, superposition of sub-states exists as well. Next, Everett then makes a remarkable observation that no subsystem

exist "just by it's own" but the collection of subsystems are not independent, but correlated.

Using a view of

is relative upon the mode of decomposition of the total wave function into the superposition, which actually means that any found

result state is "simply relative". He further shows that such a process is continuous, and thus will not stop.

In other words, the substates in the wavefunction can independently interact with the environment (like doing a measurement),

and they "fork off" and evolve independently.

This would explain why Albert finds a certain quantum result in an experiment, while Mary finds another.

There is ofcourse a mathematical framework in his original article. I do not repeat that here, ofcourse.

It is further extremely interesting that there really exists a "pre-seed" for "decoherence" in Everett's theory.

This is more for historians to investigate further.

Secondly, at some point Everett's also refers to the memory imprints related to observers. He literally writes in his article

that (quote) "....the machine has perceived A" or "the machine is aware of A" if the occurrence of A is represented in the memory,

since the future behavior of the machine will be based upon the occurrence of A...." (end quote).

In the article, Everett sees as likely that a measuring device might experiences outcomes A, B, C etc..

while based on his relative states formalism, depending on the mode of decomposition of the superposition, any legal sequence

of other outcomes could be possible too, and actually instantiates, or branches off, independently.

In effect, at any event (like a measurement) we have a definite observer state and a corresponding system state, but that's no more than

a branch from the potential in the superposition.

Everett further never refers to parallel universes or something similar. For him, the key words are "splitting in branches",

and this formalism was somewhat later called "Many Worlds" theory, and that "label" sort of kept stuck.

The original article is a "classic" in QM.

In a simple pictorial representation: Suppose we have a particle, and let's represent it by a "coin".

Ofcourse, this coint can be expanded in sub-coins (or basis coins), just like equation 2 above shows us.

So, our coin is a "superposition" (just like, for example, 1 euro is 10 x 10 cents, or 5 x 20 cents).

MWI acts like having that coin (the superposition), which is a large set of (sub-) coins (the subwaves),

and when you throw them away, they all roll into different directions, all acting differently with their own parts

of the environment.

Every such sub-coin, is now branched off into it's own "world".

Ofcourse, we need a bit imagination here, and just think that all those "private" parts of the environment,

which interacted with the n

I wonder in how much you will appreciate this section as a "Theory of parallel universes", but a fact is,

that some folks indeed do so.

Although I will refer sometimes to "Inflation" in this section,

discuss it in another chapter more thoroughly.

Even in the early years of the former century, it was theoretically made plausible (Friedmann), that the Universe

was expanding. Ofcourse, that was already implied by the GTR equations of Einstein, however, Einstein rewrote

his equations in order to have a steady state Universe, which was the dominant view in the twenties.

Somewhat later, Observational proof of the epansion was became really solid, when Hubble presented his "redshift" findings,

which made a real case for an expanding Universe: it seems to get larger all the time.

Well, you may wonder if that last sentence is a "good phrase" anyway. Reality maybe somewhat more complex.

The "history of science" is so much fun to study, but I have to stick to the real point of this section.

It is quite certain that from around 1950 (or so), it was mostly accepted that we have to deal with an

expanding Universe. That is, starsystems like remote galaxies seem to recede from us, and a peculiar thing is that they

For the larger part of the second half of the former century, questions remained like, for eaxmple, will the expansion

slowly decellerate at some point. Or, is it possible that the expansion comes to a halt, and that the Universe will undergo a Big Crunch again?

Or will it simply expand forever...?

Many of such questions were alive among cosmologists, and important pointers were under study like the "mass-energy"

distribution, and if SpaceTime was curved on a large scale etc...

At some point, folks started to realize that the "seemingly" enormous velocity of very remote systems, may have

a completely different origin. The velocities were based on the large "redshift" of the light of those remote systems,

just like the doppler effect for moving objects. However, the same effect occurs if

any direction. You probably know that famous example of a baloon, with dots on the surface (representing galaxies),

and when you inflate the balloon, all dots recede from each other, due to the fact that the balloon's surface expands.

Even at this "point", using the theory sofar, it makes sense to investigate the "horizon", or "Hubble volume".

Around 1998, a rather comprehensive study started to measure luminosities of several

which are "exploding" stars, but which have proven to be very accurate "candles" with a very definite luminosity.

They can be very useful to determine "distance/redshift" relations.

After sufficient data was accumulated, interpretations seem to suggest that the luminosity of more remote supernova

were actually (and this is the crux)

Ofcourse, the actual techniques are much more involved, but typically, the results are often shown in graphs which show

the observed magnitudes plotted against the (socalled) redshift parameter z.

The plots thus aquired, seem to suggest an

So, at this moment, most cosmologists believe that the Universe undergoes an accelerated expansion.

The source which drives that expansion still puzzles many physicists and cosmologists.

Several candidates were forwarded, as for example an

called "quintessence", or possibly some other source.

In general, the still unknown agent behind it, is collectively labeled as "Dark Energy".

While SpaceTime expands everywhere, for our local part of the Galaxy, there thus exists an

which is

There simply is too much expanding Space between us and this "event horizon".

In effect, this 'event horizon' defines a "region" (similar to a sphere), which is called a "Hubble Volume".

Some people also say that we actually dealing with

Also, some rephrase that as that we are living in our own

But, what is the connection with "parallel universes" or the "multiverse"?

Above it was made likely, that we are in our own "patch" of the Universe, or Hubble volume, which is bounded by

an event horizon. Beyond the horizon, given the data and observations we have today, similar conditions would apply.

Hence, far beyound our Horizon, it would be likely that at those places we have similar SpaceTime with the usual

"content" as we have "here" (Galaxies, clusters etc..). However, those far places are fully out of reach (even for light,

or any other forms of information exchange), and thus some folks talk about a "multiverse" or "parallel universes".

The fact that each Hubble volume has it's own "cutoff" for all possible other Hubble volumes, make that some folks

place this in the "Parallel Universe" (or multiverse) category.

called the

The "Many Interacting Worlds (MIW)" theory, is fully different from Everett's "Many Worlds Interpretation (MWI)".

The QM model devised by Poirier, originated somewhere around 2010 and went through further elaboration,

especially in cooperation with Schiff, and ended in about 2012 in something what's now called MIW.

I must say, that at this time (and it might seem a bit strange), it's not fully clear to me who first re-introduced

almost classical Physics into the dicussion of "interpretations of QM", and who actually introduced MIW.

Ofcourse, I have to say quickly that the Broglie-Bohm (pilot wave) interpretation uses many classical features as well.

However, in MIW, it truly goes one step further since each independend "world" in MIW, is fully ruled by classical physics.

It seems that Holland, Hall, and several others, do or did rather similar work as Poirier.

But, someone like Sebens also recently launced similar ideas as MIW.

But they all operate closely in the same "arena", and since most scientists seem to attribute MIW

to Poirier, from now on I will take that as a fact.

Considering the basics of the "Many Interacting Worlds" theory, You might see a parallel (no pun indended) to Everett's

"Many Worlds Interpretation" (MWI), but that would not be correct.

There are fundamental differences. Most notably:

- In Everett's MWI, the wave function is real and plays a central role. In MIW, the wave function does not exist,

and in fact MIW is a sort of QM "without the wavefunction". - In Everett's MWI, universes branches off due to the fact that superimposed waves each interact with the environment.

In Poirier's MIW, there is no branching, no wavefunctions, but the many worlds may "interact".

- Everett's MWI uses standard Quantum Mechanics (wavefunctions, probabilities etc..), however Poirier uses established

rules from many parts of physics, whereas many are simply familiar classical, like trajectories, position/impuls, Lagrangian etc..,

where paths over different trajectories relate to the Many Interacting Worlds.

It's more an illusion, due to the fact that in Poirier's "Many Worlds", an observable might have

well-defined values in different "Worlds", that is, each "World" it has it's own "private" values for that observable,

but since there exists variation between "Worlds", we percieve the illusion of a composed State vector where the same

experiment might show different values all the time.

So, if you like, you might say that there is no fuzziness in Poirier's theory: for example, particles

positions in any given world. However, these positions vary from world to world, and thus explaining why they appear

to be in several places at once. That we observe that, is due to the fact that (according to MIW), nearby "Worlds" interact.

It's that same interaction which makes us believe in the spreading of wavepackets and for example tunneling through a potential barrier.

In MIW, each world evolves according to classical Newtonian physics. All (illusionary) quantum e?ects arise from, and only from,

the interaction between worlds.

interact differently with the waves of the environment. Although quantum probabilities still hold, another key element of which

we must bee aware of, is that if Substate

each can "branch off" at interaction, and start a "life" by their own. Think of them as initially as orthogonal, and start their own

different projected life in the environment (where that microscopic environment is affected too ofcourse).

It's like having a coin (the superposition), which is a large set of (smaller) coins (the subwaves), and when you throw them away,

they all roll into different directions, acting differently with the environment.

In MIW it's a tiny bit more delicate.

A rather simple way is to take an aspect of the

If you would have "n" particles, then you might define one "configuration space" for that set of particles, which space

can be described by the vector:

It's important to keep in mind here, that we here use

When physicists work out such a model, then positions, and momentum, and other characteristics of the particles can be described

in such a framework.

The rather "bold" assumption in MIW is, that not only one "configuration space" might be possible, but say "J" seperate spaces,

where J might even go to infinity. That's rather new, to say the least. Now we have "J" spaces, where each "j" in J, defines

a configuration space, where each one "j" describes all the positions and momenta of those "n" particles.

Thus we might have:

{q

..

..

{y

the full configuration space (e.g. positions, momenta etc..) of "n" particles (or all particles).

-So, suppose we have just one particular j=j

and momenta of "n" particles, like for example {p

-And, suppose we have j=j

and momenta of the same "n" particles, like for example {q

with different positions and momenta compared to j=j

Did you noticed for example the different positions for j=j

When physicists further work out such a model, then positions, and momentum, and other characteristics of the particles

described by one "j", like j=j

like j=j

It can be further made likely, (using some math) that "close" "j" from the space of J "configuration spaces", tend to work

repulsive, so that the illusion is created that, for example, we are dealing with a spreaded wavepacket as a particle.

I hope this conveys at least a "glimse" of the heart of MIW. Actually, you might say that MIW turned QM around to be classical again.

uncertainty relations, which is a remarkable fact in QM.

The particular relation I am talking about, describes an uncertainty in "Energy" and "Time".

The relation say that in the microscopic domain, energy can be obtained from the vacuum as long

as the following holds: ΔE.Δt ≥ ħ/2 (where E is Energy, and T is time).

So, you can borrow energy for a certain timeslot, as long as it is returned later on, according to the relation.

The socalled microscopic "quantum fluctuations" are believed to exist literally everywhere in our present SpaceTime.

One such manifestation are the "virtual particles", which popup from the Vacuum, and destroy each other again, only

existing for a very brief moment.

The section above, has the advantage that we now are introduced to the concept of "quantum fluctuation",

in case you was not aware of it.

As of around January 1980, Alan Guth started talking openly on his new ideas of the origin of the Univere.

Then, in January 1981, a (nowadays) famous article was published (Physical review D), which beared the title:

This theory explained the birth of the universe in a unique and completely new way, and at the same time avoiding the

problems as mentioned in the title of the article. His theory of "inflation" was pretty good in describing the most

extremely early phases (like as from 10

but it did not correctly handled some later phases, as Guth admitted.

However, it was already a major step from the earlier "Big Bang" proposal, which presumed a strange superdense,

superheated

However, as people see it often today, is that when the Inflationary period ends, the next phase then fits the traditional

"Big bang" well, so it is nowadays often interpreted that the Big bang follows afer Inflation.

It was only a few years later (1983) that Andrei Linde proposed a revamped approach, and actually cured

the major problems in the original theory. However, Linde's approach, actually made

or a bubbled

So, for my purpose, that's a very interesting item to discuss.

since, time does not exist. So, the notion of "before" is non-existent. If you like, you may visualize it as if space and time

are both spatialized, but "0".

Modern theories try to unify the known forces in our present day Universe, and also try to unify fundamental

theories (like QM and gravity). It is expected that at extremely small scales, all the fundamental theories "converge"

to each other, and thus unify. In that sense, it may well be so, that that QM effects and Gravity are then very "close".

Now, the absolute "bootstrap" of the start of Inflation is still not solved, but it is often argued that in a period

around a period of 10

Once gravity exists, in whatever form, a certain format of Vacuum exists then too.

This extremely short period is sometimes referred to as the "Planck epoch".

Guth's theory states that this 'pre-space" is equivalent to an extremely small patch of

is the same as "negative pressure", or "positve gravity", which is a

Note: Maybe "positive" and "negative" pressure are confusing, but pressure behaves very much like gravity.

A positive pressure namely, equates to an attractive gravitational field. A negative pressure is repulsive.

The "negative pressure" or

exponentially since nothing holds it back. Secondly, since the false vacuum does not have anything to interact with,

the energy density stays the same, while the total energy increases. Inflation in that respect works like a magnifying glass.

Now, energy conservation says, that if the total energy in the patch increases, that must be equal to the "work" done

by the repulsive gravitational field, that is, the expansion itself. It seems as if "

Such a scenario looks, as if Inflation will never stop. There are some intracies indeed, and by the way, the number

of Inflational theories (since 1981) is quite large, each dealing with several subphases.

Guth further assumes on good grounds, that the Inflationary period itself is somewhere from 10

For now, we assume (as Guth) that the false vacuum went instable, and the false vacuum energy is released by "snowing" (condensate)

elementary particles (quark-gluon soup) from the vacuum.

Generally it is understood that the change of the false vacuum to "true vacuum" (or steps in false to less false), have lead

to particle production.

This phase is sometimes referred to as the "quark epoch". We are now still only about 10

That phase is ofcourse much more involved than my few line of text. For example, it's assumed that several forms of "symmetry breaking"

occurred, as the tempurature lowered, resulting in the basic forces as we know them today.

When the universe was about 10

into hadrons (hardron epoch).

Several other phases followed, like the lepton epoch.

How complex the various phases can be, is also illustrated by the fact that once matter and anti-matter existed, but Nature

seemed to have had a slight preference (bias) for matter (instead of anti-matter).

Noteworthy is then the fact, that, a long time later, about 380000 years after the birth of the Universe, the temperature has

dropped sufficiently for leptons and protons to form (mainly) hydrogen, and at that point, the Universe became transparant for light,

or electromagnatic radiation in general. This is the source for the "relic" "Big Bang" background radiation.

It might be interesting to spend a few words on those problems, which were probably solved by Inflationary Cosmology.

The fact that our observable Universe is so large, places us for some problems, using a traditional Big Bang scenario.

Very distant regions,

One problem (among other problems), is that the "relic" "Big Bang" background radiation (also called the 3K cosmic background),

is very accurately the same in all directions. In the traditional "Big Bang", this would not be the case. There would have been

considerable fluctuations.

In the Inflationary model, the initial false vacuum patch prior to the inflation, can be seen as very small

but causally connected region. In other words: uniform.

The inflationary epoch, evolved so extremely fast, that the homogenity was completely

we can still observe today in that famous uniform cosmic background radiation.

Thus, an original problem in the "full" Big Bang scenario, is often regarded as a "pro" for Inflation.

The "full or original" Big Bang scenario poses another famous problem: the flatness problem.

This is usually expressed by, and related to, the "critical density" Ω, for which hold

that Ω can be "< 1", or exactly "1", or "> 1".

Suppose the actual density is denoted by ρ

then the ratio Ω = ρ

and "dark energy" would influence it, is a very important question. However, I stick for now to the (say) traditional view,

because I like to demonstrate how Inflation solves the flatness problem, which would otherwise arise in the traditional

Big Bang theory.

The total density of matter and energy in the Universe, determines the curvature of SpaceTime.

In most conjectures, the General Relativity Theory (GRT) of Einstein, is the basis to start from.

Friedmann found a solution for the field equations of GRT. This solution shows a relation between

the gravitational constant, the speed of light, and some other parameters, and most importantly, the

(which is a measure for the rate of curvature of SpaceTime), and the

Three models come up from the equations of GRT and Friedmann: a (spherically) closed Universe, an open Universe, or a flat Universe.

Please note that here we are talking about the "geometry of the universe", that is, the sort of curvature of SpaceTime.

The "flat universe" means that we do not have a curved SpaceTime (globally), and that would only happen when we have

"curvature parameter" (k) to be 0. In that case, the critical mass-energy density Ω would be exactly "1".

Or, formulated more accurately: the ratio of the actual density to this critical value is defined as Ω.

Sometimes, for clarity in equations, Ω is rearranged to be the factor (Ω

So, flatness then means (Ω

If we go back to " Ω" again, thus the ratio of the actual density to the critical value,

If Ω > 1, then we obviously would have a large mass-energy density and the curvature is positive,

meaning a (spherically) closed Universe. Probably, after a certain time, the Universe might collapse.

If Ω < 1, then we would have a too small mass-energy density and the curvature is negative, meaning

hyperbolic open universe (with respect to curvature).

Now, most atronomers/cosmologists think we have a "fine-tunings" problem, since large-scale observations very strongly

points toward a flat universe. So, Ω seems to be "1", which is rather special, probably too special....

Why would it be exactly 1? Why would the Big Bang ultimately end up with this very special density, expressed

by Ω=1 ? This question is the "flatness problem".

If Inflation would solve this, then the next question is: why would Inflation "make" Ω=1?

This could be answered, if the Friedmann equation would still hold at the inflationary epoch. If so, then

mathematically it can be written as (Ω

Without considering the "cosmological constant" Λ, the equation actually is:

since it only contains factors like "c" (speed of light), "G" (gravitational constant) and some others.

To let the product in the leftside of the "=", be constant, while ρ increases, then the term (Ω

must

If this reasoning is correct, then Inflation makes Ω nearing the value "1", thus a flat universe follows.

I must say that this line of reasoning is not without critism, but anyway it's an agrument that's often heard to explain

the observed flatness of the Universe.

Above we have seen the first Inflation version from Guth. Next we will see Linde's interpretation, where the Multiverse plays

a key role.

By now, quite a few additional versions have appeared, by various authors, often focussing

on subphases (cooling and re-heating several times), and/or symmetry breaking.

Or, some later articles, also try to reconcile string theories with inflation.

Some newer inflational theory variants, expect a "multiverse", or multiple universes, to be a reality.

That's ofcourse very interesting for my note.

However, those newer theories themselves, and who was, or is, working on them, and when original ideas were expressed,

and how much "overlap" exists, is by no means very transparant.

Key terms anyway, are

pretty much similar. Well, at least for me that impression arose by now.

But

Also in those newer inflation theories, Guth himself is active. In a few rather recent articles, he proposes an "eternal inflation"

variant as a more complete theory, compared to the old (original) one. The multiverse is a collary of his central theme.

However, Guth was not the first who explored "eternal inflation", and it seems that Steinhardt and Vilekin were proposing

such idea's around 1983.

Linde seems more involved in something he called "chaotic inflation", and here too, the multiverse is a collary

of the central theme.

World cosmology", might not be so "incompatibel" with those newer inflation theories afterall, according to some authors.

I like to touch that subject (that is, Brane World cosmology) in the next chapter.

Let's stick with inflation for now. Andrei Linde seems to be very connected to the idea of chaotic Inflation and a bubbled multiverse.

In 29 october 1981, an article appeared called :

A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy

and primordial monopole problems.

True, later articles, as of 1983, referred explicitly to chaotic inflation. and it seems that most people refer to those articles.

More players than only Linde are active in chaotic inflation, especially from 1983 up to 1990 (or so).

Here are a few words on Linde's initial interpretation:

Chaotic Inflation (Linde):

After a "quantum fluctuation", a scalar field exists, with a certain initial potential ϕ energy.

You can indeed make educated guesses about that initial value, expressed in Planck Energy units, but Linde primarily

keeps his theory generic.

The value of the potential energy, behaves like a harmonic oscillator. Depending on the initial potential ϕ,

Linde shows that the value of the potential can "roll-down" rather slowly, or possibly"roll-down" rather quickly.

This is actually the "chaotic" in the name of his theory, since using various forms of equations for the initial potential ϕ,

(like polynomials, or others) does not really affect the main theme of his theory. Inflation will inevitably follow.

Here, the term "inflation" simply means "exponential expansion", like as you can write the expansion as an "e function".

In effect, Linde wrote down a relatively simple second order differential equation for the potential ϕ,

where as a term the Hubble parameter (H=a'/a) is present too (here, a' means velocity, and a is distance.)

Amazingly, it simply follows that:

Whatever you say, the startling thing is that, using almost highschool physics, leads to an exponential expansion,

and further he shows that the theory is quite immune to the form of the potential ϕ.

Next, Linde argues that if we take a good guess of the initial energy, then in about 10

the Universe inflates with an order of magnitude of 10

way way larger than what we today say is "the size of the observable Universe".

It indeed would explain why the Universe 'looks' flat, since, even if it was curved on a large scale, we would never

notice that in our small patch of the Universe.

At a certain "moment" ϕ is very small, and starts to oscillate around a "minimum". This is a particle

creation phase, where particles "snows" from the Vacuum.

Alright, now we understand what the "chaotic" means! This actually is Linde's main theme.

But next, he makes Inflation "eternal"....

Bubbled Multiverse, and Eternal Inflation (e.g.: Linde, Guth, Vilekin and others) :

During the inflationary period, small quantum fluctuations in ϕ were actually very likely, and when, nearing the ending

of inflation, ϕ got smaller, and those quantum fluctuations were the cause of smaller "density perbutations" which

many folks see as the cause for later galaxy formation.

This idea holds for virtually any inflational theory.

Chaotic inflation, at least according to Linde, implies a

are "large" quantum fluctuations during inflation, which increased the value of the energy density in ϕ, leading

to larger perturbations, and substantial "faster" inflation of such region.

Some interesting scenario's are possible:

Some authors (but a minority) see here the cause for "topological defects" or "domain walls", which ultimately

will seperate those pre-universes. This is not a mainstream view anymore, but I like to mention it anyway.

Linde argues that those subregions expands faster than the original domain, whereas in those subregions, the same

type of "large" quantum fluctuations may occur, which

This ultimately leads to a "bubbled" Multiverse.

Some authors even do not rule out that in fact we have "eternal inflation", since in the scenario above, it's not

simple to say that

But even in the scenario of a "true bootstrap", the "bubbled" Multiverse is a theoretically defendable proposition.

Although also matematical conjectures exists, to illuminate the above (although they are likely not "perfect"),

do not forget, that in an inflationary epoch, according to GUT theories, gravity and QM are very close.

Thus, the assumption of larger "quantum fluctuations" is quite reasonable.

Are they Testable theories?:

Recently, "gravitational waves" were detected. It was a very large event, and you can't have missed it.

It was on the news everywhere.

It's quite likely (or better: quite possible) that "ripples" in SpaceTime are going to be detected,

which, after analysis and interpretation, might be an indicator of an endphase of inflation.

When the LHC is fully operational again, and those folks at Cern are able to let protons collide with 14 TeV (or so),

then

into conditions of an earlier Universe (than we had before).

As an end remark, I must say that not all Cosmologists/Physicists, see the Inflationary scenario

as one that covers the whole package.

This sort of hypotheses are certainly not my favourites. It's sounds very weird, to view our Universe

similar to a "computer emulation", or as some strange form of "virtual reality".

Also, there are almost no physicists which give credit to any of these sort of ideas.

Still, it is an "option". Indeed, there exists some motivation for these lines of thought.

For example, Quantum Gravity theories propose SpaceTime quanta. This can be thought as dicrete units, which

form loops, or spin networks. Either way: they seem to be fundamental blocks, which seem to operate

on a scale of the length of Planck.

It is indeed tempting to view such a quantum as the most fundamental piece of information, like a "bit".

A bit in itself is no "information", but strings, or volumes, or surfaces (or whatever "construct")

To project constructs of SpaceTime quanta, as something that can be compared to memory units, is fully speculative.

However, there exists a low number of 'believers', or also, scientists with a sufficiently open mind, that they

are willing to consider such ideas.

However, there is nothing very

From

essentially says that the physical reality can be simulated by information processing.

-But then it is probably not like a very sophisticated 'weather model', who's prediction seems to be right the next day.

-It then has to be deeper than the example above. It has to be something like

is physical reality'.

It is certainly not so, that hypotheses like the "calculable Universe", float on determinism.

There seems to room for stochastic processes as well, in these theories.

However, full "determinism" in our Universe would be strange indeed, but then it might also form a case

pro "emulated reality" or "computed reality".

In QM, we have for example the famous EPR paradox. One possible solution is the assumption of "hidden variables",

which are undetected (as of yet) parameters, which can account for events we cannot understand so well,

like entanglement.

The debate is not settled yet, I believe. If ultimately it is found that "determinism" on a deep level is simply

a feature of our Universe, it might be a "pro" for some sort of "calculated Universe" model.

Something which is a remarkable mix of physics, engineering, and information sciences, is Quantum Computing.

It's something completely different from the "traditional" way of computing.

Indeed, remarks and notes have appeared related to "The Universe as a Quantum Computer".

Each time, solid pointers are not available, but the slogans are intruiging indeed.

It's fair to say that QC is still in it's infancy. As time goes on, we simply need to evaluate new

results and articles emerging from this field.

Physics and information sciences, cannot be fully covering for such hypotheses as presented in this section, I think.

It seems to me that psychology, and philosophy must come into play too..., somewhere.

I don't know "where". But if "physical reality=virtual reality", then this also must be related to how we percieve the World,

and it thus seems evident that such sciences have something to say too.

If such supercomputer would exist, it surely must be able to run a lot of models (realities) in parallel.

That's the connection.

However, I feel that the statement above, contradicts the hypotheses as touched upon above.

As a last subject for this section, I think the following qualifies too, to be mentioned.

An interesting idea is that of the "Block Universe". In essence, it seems to say that all events, in the past

the "now", and the future, is already fully encoded in the "Block Universe".

In effect: All of the space, and all time of the Universe, are there in the block.

It has primarily a certain (small) supporting base in community of philosophers.

However, some physicists do not reject this idea too, since it also provides a certain solution

to unsolved problems, like the "strange case of Quantum probabilities".

But you might argue contrary: Quantum probabilities disproves the "Block Universe", unless it also

provides for "branches" (or "splits" or "forks").

It's difficult to see a direct relation of the Block Universe" to "Parallel Universes".

Or, in how much this also connects to "determinism", or "hidden variables".

I only mention the idea, since you might argue that such "Block Universe", is the final computation

(

In this sense, it fits into this section too, since it resembles a computed reality.

Fig. 2: A "Jip-Janneke" image, showing two manifolds (Universes) called "branes".

Gradually, during the development of String / M-Theory, hypotheses emerged, stating that isolated

branes (manifolds in "superspace") might represent full Universes.

This is completely based on theoretical considerations, but indeed also with some "speculative sauce".

As such,

In the figure above (rather exaggerated, indeed), you can see such strings (with their endpoints) bound on their "world".

Sometimes these hypothetical worlds are referred to as "Coulomb" worlds, since the ElectroMagnetic interaction

is one of the primary forces between open strings.

In principle, more than one such manifold could exist, thus resulting in multiple "branes".

The "stuff" between branes (if we may say so), is called "the Bulk".

Closed strings are not bound on manifolds. Here, one candidate boson could indeed be such "particle",

the "graviton", responsible for Gravity.

Since it is not bound, it may even escape into the Bulk.

Some folks see a clue for this, in the fact that gravity in small environments is such a very weak force,

while on a large scale, gravity is the paramount force.

This model is still "alive" among certain groups of theoretical physicists.

Numerous physicists work on String theory, and M theory, and Cosmological models based on both themes.

of the Universe, Dark Matter, Dark Energy, and Unification of Quantum theories and Gravity), many physicists

are quite enthousiast for these theories. But at the same time, a lot are not.

The various models do not seem to be easily "testable". Ofcourse, science is Theory, in conjunction with Experiments.

However, there are some hypotheses which propose possible test scenario's, like the search to a "fifth" uncompactified dimension.

There are quite a few "Brane World" models actually.

Many modern ones are based on the Randal & Sundrum model, which is a (3+1) Brane in a 5 dimensional Bulk.

Please note that

in that (4+1) space. Here, one additional "extra" dimension is used, which is not compactified, and is only "accessible"

for gravity.

Further details on such a model can be found in a classical article (1999):

"An Alternative to Compactification (1999)", which can be found here.

Essentially, the authors describe a single 3+1-brane with positive tension, embedded in a (4+1) (fivedimensional) Bulk SpaceTime.

Using "gravity" as the vehicle to explore the scene, and using wavefunctions, they argue that a graviton in the Bulk neccesarily

will be in a confined bound state. Initially, they make no assumptions on the additional spatial dimension r

it could be compactified. Using rather involved math and letting r

the "four-dimensional effective Planck scale", to go to a "well-defined value" as well.

This means that a consistent 4 dimensional theory of gravity could be derived from the used model.

Such a 5 dimensional model, using no compactification, is a remarkable deviation from M-Theory based models.

Secondly, the bound state of the graviton as described in this article, actually means that they are close to (or near "at") the Brane,

and do not travel "freely" around.

Note that, in simple words, we can now speak of "distances" along that fourth spatial dimension. If you would insist, you can still use

more compactified dimensions. However, the one that (probably) only gravity is aware of, is that fourth spatial dimension.

It could represent a "testable" scenario. Indeed, several searches have been performed. No luck yet, for those theories.

Note that the original Brane World scenario's, might imply "Parallel Universes".

The Randal & Sundrum model, is not really involved into "Parallel Universes", since there might only exist

one Brane and the Bulk. However, extensions hereto are possible, and the number articles in this field is quite large.

and computing with a Quantum Computer. In other words: a Quantum Computer needs one Universe only, I believe.

But, it does not mean anything, that I have strong reservations.

Sure, many folks think differently, or have at least an open mind for such hypotheses.

Anyway, I like to spend a few words on various thoughts here.

However, I have extreme difficulties in finding "proper" models for "test scenario's".

A common "element" in Quantum Computing (QC), is the "qubit", which indeed is the basic "bit" in QC.

The basic expression for a standard Qubit is as follows:

is an observable of some suitable particle (like the electron).

When measured, it is either found as "up" (|1>), or "down" (|0>). However, unmeasured, this observable

is believed to be in a

So, indeed a sum of both basis vectors at the same time.

There was, and still is, quite some debate if superposition is

corresponds to a

Ofcourse, there is nothing special about "superpositions", and we can find it at many places in physics.

But as properties (observables) of (say) elementary particles, which seem to exist in a superpostion of

basis states, there were many, almost philosophical, related questions.

According to what we have seen in Chapter 3 (Poirier's theory of interfering "classical" universes (MIW)),

the classical and fixed values can be readily obtained in each "classical" Parallel Universes.

But those universes interact, and it sort of naturally follows, the "fuzziness" of Quantum Mechanics.

One might also consider Everett's Theory (Chapter 1, MWI), and see how it holds from the perspective of QC.

How can QC be used, to obtain evidence (or just a pointer) to the existence of Parallel Universes?

As already said above, I believe that it will not.

But many say that

Indeed QC is very complex. Apart from that, as I see it, on the one hand, we have the (more or less)

true scientific QC implementations using qubits and "gates" (in the form of lasers or EM radiation etc..),

So, am I saying that there are two "streams" in QC?

You can at least identfy three (sort of) streams in QC:

(1), In what I call "the first QC approach" of QC, and let's call that "the gate quantum computing".

(2). The "Quantum annealing" implementation by D-Wave (so I believe).

(3). Topological QC.

Some other lines of QC research takes place too, like those based on Majorana entities.

Some folks name (1) also "universal QC", since it seems that it can be applied to more algolrithms.

In order to say anything useful in the terrain of "

there is no other choice than to say some fundamentals those approaches first.

of the most simple ones as "Grover's algolrithm", it is really statistical.

So: as I see it, finding solutions using QC, is statistical in nature.

Let's first take a look at a classical case. Suppose you have a set of "N" values (or "N" records), and

you only want to search for one specific value, then on average "N/2" searches have to be performed,

assuming that we just have a "stack" or "heap" of values, and no "index" is present.

This is rather similar to a classical query on a database of N values.

Please understand that this specific value,

"select * from 'stack' where id=5.

And suppose your heap of values counts 8 members, then on average, 4 searches need to be executed.

If the same would be applied in a QC, one might use the following approach:

Using the Algolrithm in a QC implementation, one tries to apply the "diffusion" operator in "iterations",

and steadily lowering the amplitude of non-solutions, so that the real solution starts to "stick out".

The algolritm is "statistical", meaning that after "m" iterations, there is a very good chance of finding

the correct answer. The larger "m" is, the better that chance on finding the solution will become.

Suppose one starts with a three qubit state in the form:

An example from just 2 qubits might help. If they are really close, but not entangled, the

is the tensor product from the individual states. It's actually also a postulate in QM, but the model works.

So, suppose we have:

|φ

|φ

Then the tensor product is:

|φ

A similar product can be done with three qubits.

You might view equation 8 in this way, that |Ψ> is expanded into 8 basis states, each with a probability of 1/8

to be found when a measurement on that system is made.

Now, choose a certain substate of these component states. Then

by the quantum algolrithm. So, we could choose |010> or other of these 8 components.

In this sense, |Ψ> looks like our "database".

So, let's take for example |010>

(1). Marking the Solution:

Now, one

Note that this is not to be taken lightly. This is parallel processing.

It is possible, that the "solution" gets marked, for example by inverting it.

Just as in the classical case, there is nothing wrong that the solutions is known beforehand.

The same was true in the classical situation too.

Often, in QC as it is now, one goal is to compare the speed and efficiency of certain protocols,

using Quantum- and classical algolrithms.

Ofcourse, for some Quantum Algolrithms, there does not even exist a classical equivalent.

The term "Inspecting" does not mean "making a measurement". It might mean that we apply an operator (by some gate),

like implementing a "phase shift" or "inversion", or anything else suitable, on the components.

Ofcourse, just like the classical case (where id=4), the mode which we want to search for (|010>),

(2). Applying the diffusion operator:

The algolrithm furher starts to "stick out" the amplitude of |010>, and tries to diminish the amplitudes

of the other modes.

In this particular case, the process works in iterations. The more you apply, the better the statistical

change to select |010>, because now it sticks out "more and more" from all the others.

In classical terms, it "looks" like a query to find the one good answer from N values.

In the classical case, the answer returned is 100% correct, but on average the system must query N/2 values.

In turns out, that in general, the QC algolrithm performs better, using more qubits, and (hoping)

that "m" (number of iterations), can be kept rather limited. But: it's statistical.

A garantee on a 100% correct answer cannot be given, unless m gets higher and higher.

In this example, the diffusion operater is logically symbolized by "logical gates", which are

are the Quantum equivalents of Boolean gates (in traditional computing).

The physical implementation of such "gate", depends also on how your "qubit looks".

The quantum gate could be a laser pulse, an ElectroMagnetic pulse etc..

I think that such description seems rather typical for QC, at least for the algolritms I have "touched upon".

However, I must say that I have only followed (theoretically studied), just a few algolritms.

In the upper case,

between qubits is essential for certain other Quantum Computations.

However, no matter how important entanglement might be, the pure parallelism on a superposition

is a key concept of QC too. If you have a Gate "H", and apply it to input which is in a superposition,

then it is applied to all component vectors in that superposition simultaneously.

Now, here is my crux. Personally, I do not see any relation to Parallel Universes, for now, unless

the very idea of "quantum superposition" implies it (as theories of Pourier and Everett uses it).

But I must repeat:

are really quite serious in relating QC with Parallel Worlds.

If you like an intro on "universal QC", you might like the following article:

An Introduction to Quantum Computing for Non-Physicists

Rather interesting projects have been started, like further investigating AI using D-Wave systems.

D-Wave has, over a few years time, delivered systems using 128, 512, and over 1000 qubits. These are astounding

numbers for physicists working in the field of QC.

There were times that I seriously thought that D-Wave did NOT produced the "real thing".

The whole reason I bring up the D-Wave story at all, is that some important folks working at that place

on several occasions have stated that their systems, in operation, "are tapping into Many Universes...".

Wow..... Then we must also take a look at these methodologies.

There seems to be something "strange" about those D-Wave systems. First, so many qubits on a single chip

is indeed quite unheard of. Is the whole thing really a Quantum Computer?

I have to say that I also listen to the people who are really active in the field, and indeed many

were initially extremely skeptical, but slowly, many views have turned to the opinion that the systems

The principle D-wave uses is called "Quantum annealing". One feature this methodology uses is

That is the principle that a "wavefunction" has a non-zero probability to penetrate a barrier, which

classically spoken would not be possible.

A famous example is a particle (or wave) in a Potential Well, for example in 2 dimensions (x- and y axes).

For example, the potential at the "vertical" barriers "x=0" and "x=1", is very high, or maybe even infinite.

Classically, the particle is confined between the two barriers. However, from a QM perspective, the particle/wave

has a certain probability to "tunnel through" such barrier.

I am not a D-Wave expert. But one sort of theme can be found, by studying their articles.

One of their tracks even has some similarities with database technologies.

Suppose you have a very large "fact table". This one has a certain number of columns, and probably an

enormous number of rows. To "track" relevant information from that 2 dimensional object, can be a huge task.

If you connect that table, with just one dimension of information (another table) you are interrested in,

(which might e.g. only list regions, or products, or total sales etc..), then you have have constructed

a 3 dimensional "cube" of n-tuples.

If you are interested in such model, in maxima and/or minima, the "tunneling protocol" might

enable you to find such information faster than compared to traditional analysis.

In Jip-Janneke language: the tunnels go through barriers to find such minima (of "cost functions") only.

This does not explain the used algolrithms ofcourse, but it might help in visualizing in

what D-Wave systems might do, when extreme points must be found in large bulks of data, like for example

strong pressure points on a complex geometrical object, in some force field or fluid field.

Now, at least we have a simple representation of QC, both using "Quantum Gate" computing, and "Quantum Annealing".

By the way, the following article is how Nasa is using, and think to use, D-Wave systems. It tells a lot on the principles:

A NASA Perspective on Quantum Computing: Opportunities and Challenges

Suppose you have a flat conductor, and an elecric current is flowing in that conductor. If you introduce a Magnetic field

perpendicular to the conductor, the electrons will be pushed to one side of that material

due to the well-known (classical) Lorentz force on the electrons.

The "classical electric current", was always supposed "to flow" in the opposite direction.

In the upper case, you might view that classical current as "quasi-particles" flowing into

the opposite direction as the electrons do.

-Quantized Hall effect:

If a sheet of very thin suitable material is cooled down, to near 0K, and a strong Magnetic field

is applied, the electrons in that material form particular structures, with particular densities

and the "Hall conductivity" takes on very precise quantized values.

At the time that this was discovered (around 1980), it was soon realized that this might represent

a

In fact, ingredients as

"Quantized Hall effect".

-Loops:

One remarkable sitution may appear, where electrons form partners, and such subsystems move in loops

in the plane perpendicular to the magnetic field. These loops are quantized too.

It is often said that they behave as "quasi-particles" (called anyons).

These loops form the basis for qubits and gates.

Much research is going on today. A further remarkable benefit is that such "loops" are almost

not at all effected by decoherence, which always plagues the (gate based) "universal QC".

The robustness follows directly from topology: if you have a coffeecup, and some pieces fall off, you still

have a coffeecup, unless the typical handle falls off too, which changes the topology fundamentally.

This makes Topological QC possibly the best candidate for QC.

If you would like a good overview on Topological QC, you might like:

A Short Introduction to Topological Quantum Computation.