God’s Many Dices (I) – The Science of Parallel Universes

Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is
(Douglas Adams, “The Hitchhiker’s Guide to the Galaxy”)

By considering the implications of contemporary Science and in particular of the Cosmology of Parallel Universes, it is now possible to build an all-encompassing Model of Reality

From solid scientific bases, such a Model may be able to move Science itself beyond the “Realm of the Whats” and into the “Region of the Whys”: providing clues not only for what is out there, but also for the reasons why things are the way they are

Not only can we say that All-There-Is (let’s call it the Cosmos) is far larger and more diverse than we have ever fathomed. We can even work out elegant explanations on scientific conundrums like:

1. Why our Universe is so very well “tuned” for life, and especially for intelligent life to exist
2. Why is Mathematics such a powerful tool in our scientific investigations
3. And why against a microscopic world driven by probabilistic quantum mechanics, there is the macroscopic deterministic-like tangible reality of our day-to-day experience

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“Parallel Universes” is the title of a thought-provoking Scientific American article (now a Special Report) written by Max Tegmark, currently working at the Dept. of Physics at the MIT in Cambridge, MATegmark’s Parallel Universes are not meant to be fifth-dimensional ghosts lying next to us, metaphysical threats that can be visited by opening the wrong door as in overdone horror sci-fi movies

In fact, Tegmark writes that the most logical deduction from all known cosmological observations is that Parallel Universes are just “out there”, albeit exceptionally far

In this respect, the Cosmos becomes the set of all Parallel Universes, plus the empty space in-between

Some of those “Parallel Universes” are identical copies of ours. Some are more or less similar to what we experience. Others are barely alike our Universe, others still less and less so

Present-day theories and observations “predict” 3 or 4 types of mutually compatible “Multiverses” (i.e., collections of “Parallel Universes”):

• Level I – Universes with different initial conditions
• Level II – Universes with different physical constants and particles
• Level III – The Many-Worlds interpretation of quantum physics
• Level IV – Universes with different physical laws

In some Universe, a copy of me has never completed writing this article (for great joy of the readers, no doubt). In other Parallel Universes, neither I nor you exist, and there are completely different subatomic particles, physical laws, even mathematical structures

Tegmark defines “Level I Multiverse” as the collection of “Hubble Volumes” similar to the one we inhabit, composed of the same stuff and following the same laws of physics

Only, as the initial conditions were different, the history of each Universe differs. Still, the “simplest and most popular cosmological model predicts that you have a twin in a galaxy about (10 to the power of 28, or 10^28) meters away”

Such a number, the result of a straightforward computation based on the size and composition of the known Universe, means that there is a massive 10 billions of billions of billions of meters between each of us and a doppelganger sharing the same history (at least so far)

On the other hand, that’s “just” 25 times as far as the radius of our own Universe (the so-called “Hubble Volume”)

Much farther away: another solar system and, say, a 100-light-year radius of space completely identical to ours (10^92 meters); and an entire Universe practically indistinguishable from ours, with all the galaxies and stars and planets and people, all in the same position (10^118 meters)

Remarkably, the “currently popular theory of chaotic eternal inflation” predicts also the existence of a “Level II Multiverse”, a collection of Level I’s (like “gas pockets in a rising loaf of bread”) each with its own set of “nature fundamentals”

Within Level II, some Level I Multiverses will have extra spacetime dimensions, some will be made of different elementary particles, some will be built around different physics constants

Perhaps somewhere out there, there really is the Liquid Space of Species 8472, from the TV series Star Trek Voyager. But that’s still not all in this fascinatingly game towards increasingly weirder levels of Multiverses

Tegmark describes as out there, on the edge of anybody’s wildest imagination, “all mathematical structures exist as well”

This is the “Level IV Multiverse“: and its existence may help us clarify the so-called Miracle of Mathematics

In the 1960’s paper “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” Nobel Prize E. P. Wigner has extensively written about such a “miracle”, describing the unease of the scientist when realizing how “the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena”

A clear example is in the theory of gravitation, extremely simple in its formulae and yet capable to account for the behavior of an enormous number and variety of planets, stars and galaxies

In a large Level IV Multiverse, if there are enough Level II Multiverses each with its own mathematics, then one or more of them will be bound to possess a coincidence between mathematics and physics as strong as the one we experience

At the same time, in some place far, far away, there is a completely different mathematics at play. And so if our Earth’s orbit is an graceful, regular ellipse, the path followed by another Earth in another Universe will resemble the work of a madman

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The Level III Multiverse deserves particular attention

Prof. Tegmark describes Level III as the standard “Many-Worlds” interpretation of Quantum Physics

“Many-Worlds” is an attempt at reconciling the probabilistic behavior predicted by Quantum Physics for microscopic particles with the deterministic working of the day-to-day macroscopic environment

In the famous example of Schroedinger’s Cat, a (macroscopic) feline is locked in an opaque box next to a weapon triggered by the nuclear decay of a (microscopic) atom

(Disclaimer: No animal has been harmed during the writing of this article)

In the box, the cat is somehow alive and dead. The atom’s decay is described statistically as a quantum phenomenon. The so-called “wave function” of the cat-weapon-atom system, provides a measure of the probability for either event (“cat alive” and “cat dead”), will have to “collapse” to a single outcome when the box is opened, and the cat can be seen alive or dead, not a collection of probabilities

In the Many-Worlds interpretation, that is explained by postulating that our Universe is “branching” into a Universe (A) where the cat is alive, and another (B) where the cat is dead. By hearing the meowing, we observe that we have somehow landed in A (an identical copy of us will of course mourn the unfortunate mammal in B)

Now, this is ridicule even more than most Models of the Cosmos. With a “branching” for anything happening to each atom and subatomic particle, the number of copies will have to increase exponentially trillions of trillions times a second (perhaps made by some Humongous Celestial Photocopier forever replicating Universes?)

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Thankfully, we can get out of that physical cul-de-sac by considering that all possible Universes already exist at Levels I and II Level, rather than having them perpetually xeroxed at Level III

Tegmark reports indeed equivalence between the Level III Multiverse (the probabilistic cosmos of quantum physics) and the Level I/II Multiverse (Parallel Universes with different initial conditions, physical constants and particles)

Tegmark goes on to say that Level III “adds nothing new”

That is not strictly true: it adds a lot:. It means that the number of Parallel Universes is gargantuan: because for the Level I/II-Level III equivalence to work, all the possible “wave function collapses” of every particle of our Universe have to be happening somewhere, sometime in the Level I/II Multiverse

And so the Multiverse is extraordinarily big and contains a huge number and a very large variety of Universes. And the Cosmos is not deterministic: it only appears as such to our limited experience, lacking the ability to “see” what happens in other Universes.

Paraphrasing Albert Einstein (once scorning Quantum Mechanics by saying that “God does not play dice with the Universe”): God (if one exists) does indeed play with the Universe(s), but with a very large lot of dices, making sure that all possible results do happen

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In this respect my only negative comment about Prof. Tegmark’s text’s is the cavalier usage of the term “infinite”The number of Level I/II Parallel Universe is giant, enormous, hard-to-describe, colossal, etc. etc. But needs not be “infinite”

Tegmark himself acknowledges as much, when he writes “The estimate [that we have twins in galaxies on average 10^28) meters away] merely [assumes] that space is infinite (or at least sufficiently large)” (my emphasis)

For example, to us puny human beings, measuring in the region of 2 meters / 6 feet a finite space with a radius of, say, 10^(one million) meters would behave as infinite for all intents and purposes without possessing any of the logical impossibilities of the “infinite”

“Infinite” carries a baggage of apparent impossibilities: for example, “infinite” is as large as “two infinites” and “half a infinite”. An infinite space cannot expand as it always occupies by definition its own maximum volume. Etc etc

French authors Luminet and Lachieze-Rey appear to make a big fuss about precisely the same point in “L’Univers Chiffonné” (Fayard, 2001)

As “infinite” has historically been a dangerous word for discussions, and arguments about its nature risk overshadowing the actual gist of an article or book, we should refrain from using that word at all cost apart from the exceptional circumstances when it is strictly necessary

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The existence of a very large number of Parallel Universe has several interesting upshots

As Tegmark writes, when seen through the Quantum Physics’s lenses of “Many-Worlds” the Levels I Multiverse may explain Time, as “a never ending slide from one already-existing state to another”: like an unending jumping from one Universe to another, and so on and so forth

In other words, if there are enough Universes out there, there will be a Universe “T+1” with a copy of you, one second in your future: so instead of imagining yourself traveling forward in time one second per second, “the passage of Time” could just mean yourself “in Universe T+1”

Tegmark explains also how a very large number of Parallel Universes can help us confine the (in)famous Anthropic Principle to the annals of irrelevant philosophy

Our Universe is “fine tuned”: even tiny changes to one physical constant or another would make our very existence next to impossible

This is called the “Goldilocks Enigma”, after the fairy tale about a girl entering the house of the three bears. Why are the Universe’s characteristics not too warm, not too cold, and just about right?

Past answers included the self-referential “Anthropic Principle”, stating more or less that the Universe is like it is because otherwise we wouldn’t have been here to talk about it: a bit like analyzing a defeat by stating “you’re a loser”

Tegmark elegantly prefers taking a different route

Within a Level II Multiverse, inside our particular Level I Multiverse our particular Hubble Volume does harbour life because there’s lots (really lots) of other Hubble Volumes out there, in many Level I Multiverses: and one (or more) of them is bound to be just about right for life as we know it

This is a bit like analyzing a defeat by stating that “not all participants to a competition can be winners”

Goldilocks may have just had to taste three soups before finding one not too warm, and not too cold. In our case, the Cosmos may need to have 3 trillion Universes, or many more, before getting it “right” for humans to exist: but the underlying principle is the same

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What is there to prevent all that from happening? Is all of the above just too large, too complex, too un-necessary, or even not elegant enough?(a) Are all those Parallel Universes an ugly waste of space and time?Years ago people argued against there being a galaxy of stars, as the absolutely vast majority of them do not provide heat or illumination to any human whatsoever

Tegmark also asks, “What precisely would nature be wasting?”

In fact, if there are huge quantities of Hubble Volumes (“Universes”) at Level I and II, there is no reason why there would not be huge quantities of universes at Level IV

Furthermore, the Level IV Multiverse is truly an esthetically pleasing Cosmos, even from a strictly philosophical point of view

We have learned that our planet is not the Center of the Universe. Apart from being able to harbor life, Earth is a run-of-the-mill planet in an average star in a not-so-special galaxy, belonging to an ordinary Local Group gravitationally linked to a Supergroup like many others, in a corner of the Universe that is not extraordinary at all

Let’s call that the “Banality Principle”, with us since at least since the times of Copernicus (banality “with life”, obviously)

And in the Cosmos of the Levels I, II and IV, isn’t our own very Universe just one of many, sporting one of many possible sets of initial conditions, elementary particles, physical laws, mathematical structures, in a virtually unbound escalation of the very same “Banality (with life) Principle”?

(Is there anything then beyond Level IV? I bet there is. But our imagination is silent about it, at least for now)

(b) Would a Cosmos made of all those Parallel Universes be just too complex to comprehend?

Tegmark replies that more often than not there is far less complexity in defining a set with a general overarching rule, rather than a particular item of that set with a precise description: “complexity increases when we restrict our attention to one particular element in an ensemble”

Consider in fact a description of the Cosmos, “All-There-Is” as the Level IV Multiverse: there are many sets of physical laws and mathematics, each at work in its own Level II Multiverse, all expressed following a large variety of different initial conditions in a large number of Hubble Volumes (Level I Multiverse)

That’s 38 words

A description of our own Hubble Volume, with all its physical constants having particular values, and all the galaxies and stars and human beings placed in a particular position, etc etc would be definitely much, much longer than 38 words

And a Cosmos made up of a single Hubble Volume is complicated indeed

“The simplest and arguably the most elegant theory involves Parallel Universes by default” – writes Tegmark. “To deny the existence of those universes, one needs to complicate the theory by adding experimentally unsupported processes and ad hoc postulates” (like finite space)

And finally, “Our judgement therefore comes down to which we find more wasteful and inelegant: many worlds or many words” (my emphasis)

(c) Is all the above just too weird?

Illuminatingly, Tegmark responds “[…] what did we expect? When we ask a profound question about the nature of reality, do we not expect an answer that sounds strange?”

(d) Are all those Universes just too far away to care?

I am not sure that remains a relevant question against a Model that provides new insights into the nature of Mathematics and Time, the Goldilocks Enigma, the Many-Worlds interpretation of Quantum Physics and Einstein’s dice-playing Divinity

Anyway, it is true that spatial distances even to the nearest Parallel Universe are too large to comprehend, let alone traverse or even use to communicate anything.

Or are they? There is a phenomenon called “Quantum Entanglement” or (by Einstein) “action at a distance”. If you get two particles A and B to share the same quantum state, by observing A it is possible to know the state of B: actually, the state of B is “instantaneously” determined by the observation of the state of A, no matter how far separated they are

Now, if we only could demonstrate entanglement between two or more Parallel Universes…

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Anyway, we need now not limit ourselves to pure science…what are the philosophical consequences of a Cosmos made of a humongous number of Parallel Universes?