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How many Universes Are There?

 

I'm going to discuss a really big number here. Bigger than the national debt. Bigger than the distance to the farthest star in the universe. Bigger than anything you've ever contemplated before.

It is an estimate of how many universes exist.

I believe it to be the largest number that has ever been derived from a real-world, physical speculation. Stay close while I wring it out. Take the math for granted. I won't dwell too awfully much on it. You only need to recall that scientific notation, for example 106, is the easy way of writing big numbers. In this case, it's equal to 1 followed by 6 zeroes (1,000,000).

The "Many Worlds" interpretation (MWI) of quantum mechanics was developed way back in 1957 by Wheeler & Everett. It says that every physically permissible outcome that could happen in a subatomic transaction does happen. But because the results of each potential transaction are all mutually exclusive, they spin off their own separate, adjacent universes, therein to fully manifest themselves.

So in consequence, there are untold new universes spinning off every instant, in every conceivable direction, in response to every single possibility. In some of these, Hitler won the Second World War. In others, the digital computer was never conceived. There are many where dinosaurs still rule the Earth, and we small mammals scuttle from one rock to another, avoiding them.

In slightly more technical terms, in MWI all the possible outcomes of a quantum interaction are realized. The Schrodinger wave function, instead of collapsing at the moment of observation, carries on evolving in a deterministic fashion, embracing all solutions that are embedded within it. All outcomes exist simultaneously--as orthogonal vectors in Hilbert state space--but do not interfere further with each other. Each single prior world is split into mutually unobservable but equally real worlds.

From a recent poll taken of the leading cosmologists and quantum physics theorists, about 60% of them believe the Many Worlds interpretation to be the true one.

The MWI is, to date, the only logically consistent explanation of quantum mechanics. Thinking about it more, the idea does give one some psychological comfort. For example, it takes the edge off to think that all the unfortunate people around you who get caught up in a bad Karmic trip in your world have a much more benevolent universe out there in which their "true" selves are thriving and happy.

For some utterly perverse reason, this also brings to mind the remark by the Captain in charge of the Christian crusade against the heretical Cathars in Beziers, in the 13th century. When asked how to distinguish the heretics from Catholics, he replied: "Kill them all, God will know his own." In many of the MWIs, all those poor Cathars and their Catholic neighbors survived this merciless slaughter.

If alternate universes do actually ensue from every quantum-level interaction, there would be a truly huge number of outcomes. I've often wondered just how big a number that would be.

According to modern physical theory, quantum events occur on an extraordinarily small scale. The smallest physical space possible is defined by something called a "Planck length". This is the scale at which the universe ceases to be a continuum and becomes "grainy". Indeed, the whole idea behind quantum physics is that events at this level can only be described as step-changes (quanta) of energy or mass, and not by a smooth, continuous (analogic) function. The Plank length is the area within which quantum events emanate--for example, "vacuum fluctuations", wherein virtual particle pairs are spontaneously created and (normally) rejoin and self-destruct an instant later.

The Planck length is 1.6 X 10-35 (undecillionth) meter. For a sense of scale, thatís about 1 ten-octillionth the diameter of an atom. Tiny, indeed!

The universe--as we know it today--is about 1026 (octillion) km wide. The volume of a sphere this large is about 1081 (sexvigintillion) cubic meters. You can pack 10186 (unsexagintillion) Planck-sided cubes into this volume. So I figure thatís the size of one instantaneous potential universal reality. Every Plank volume in the universe-sphere has a particular state--here, I assume for simplicity a digital state, 0 or 1--and the single unique combination of all those states represents one "Wheeler-Everett World". (At this point, I can't resist coining an acronym for this: WHEW!)

Of course, thatís just in one instant. The timescale of quantum events is described by a unit called the Planck time. This is the time it would take a photon traveling at the speed of light to cross a distance equal to the Planck length. This is the "quantum of time," the smallest measurement of time that has any meaning. No smaller division of time can be contemplated. This defines what an "instant" is.

The Planck time has a duration of 10-43 (ten-tredecillionth) seconds.

The cosmologists tell us that our "mother" universe started in a "Big Bang" from a Planck-length-sized point, about 14 billion years ago--4 X 1018 (40 quintillion) seconds in the past. Since then, it has evolved through a Minkowsi space-time volume that is calculated as the volume of a hypercone. Described in this fashion, the space-time volume of our universe is on the order of 6.2 X 10243 (octogintillion) Plank space-time "globs" big. This describes the total number of Plank-volume potentialities existing in the universe in every instant since the beginning of time.

If you assume that a particular overall Planck-volume state arrangement establishes a unique universe, then an upper bound for the total number of MWI universes that could have spun off from our Mother Universe since the beginning of time is the factorial of the number of Planck space-time globs, or 10243! (A factorial of a number, whose symbol is an exclamation point, is the multiplicand of all the counting numbers up to and including it, e.g., 10!=10 X 9 X 8 X 7...) The total of 10243! comes out to (roughly) 10243^(10243) universes. Reduced, that equals 101,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 . . . oh heck, my finger is getting tired typing zeroes. Just imagine this exponent carried out to 245 digits.

This number defines the total of all possible combinatory "shuffles" of every Planck card in the universe-wide deck. For a normal deck of cards, this would be given as 52!. But the size of the deck I'm talking about includes all the Planck cards that have existed throughout the entirety of Planck-time history.

The number is way too large to write out in its entirety; we can only represent it in exponential format. There are not nearly enough trees in the universe to make paper enough to print it out in its expanded form. Consider that scientists estimate the total number of primary atomic particles in the universe to be about 1080. If you assigned them each a digit, they couldn't even come close to representing this number.

But think about this: There are 1043 Plank-time units in every second. If there are 10186 Plank-unit volumes within the (present) universe-volume, that comes out to 10229! (factorial of one hundred quinseptuagintillion) universes spinning off every second. That seems plenty enough to include at least one that embodies peace and happiness for all Mankind.

Or maybe you can just mark me down as one of those naively unredeemable optimists!

 

 

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It's easy to technically criticize the derivation of this number.  For example, even though the vacuum at the Planck length viewpoint is a frothing sea of instantaneously generated and self-extinguishing "virtual" quantum events, you could suppose that most of the Planck volumes at any given instant of time are in a "zero" or "true vacuum" base state.  One base state is probably the same as another, so there really wouldn't be any difference in the universal arrangements when you shuffle just the zero-state cards.  These "null" situations might actually make up most of the overall combinatory population.  Also, it's likely that most of the "non-null" shuffles aren't valid to begin with, because many would be a product of quantum state outcomes that have zero-probability of occurring.  And to be a valid outcome, a quantum transaction must emanate from a true and good probability wave function.  Lastly, being neither mathematically nor physically literate, my whole methodology and calculation might just be dead wrong!  Anyway, this whole thing is just for mental kicks, right?

If there is nothing smaller than the Planck length, and nothing quicker than a unit of Planck time, I wonder if there are no valid counting numbers beyond the number of MWI universes resulting from these givens?  Notwithstanding the fact that you can write a larger number, or even manipulate it mathematically (just as I can write a length shorter than the Planck length here:  1 X 10-36 meter -- and do calculations based upon it), the reality of those numbers is invalid and meaningless in any physical sense. They simply don't have any enumerative meaning.  It would certainly be helpful to have a way of eliminate terms of infinity from popping up in the results of complicated physics calculations.  I say, let infinity be equal to my number and be done with it!

By the laws of thermodynamics and conservation of energy as I understand them, the total mass-energy in any given MWI universe must remain constant and equivalent to its "mother" universe.  I suppose you could envision a valid (though highly unlikely) quantum history whereby all but one of the Planck-length volumes in the universe evolves to a "base state" of zero energy and zero mass (i.e., a true vacuum condition), leaving all the potential mass-energy of that universe to pop up in the single leftover Planck volume.  It would be as if that universe contracted to a single Planck-length volume in size.  And the next vacuum fluctuation would have to happen at that one remaining Plank volume, since quantum mechanics obeys relativity and is governed by local, linear wave equations.  (While it may be the epitome of heresy -- undoubtedly mixed with a lot of ignorance of physics -- it seems to me that the Minkowski light-history cone must contract as the outer Plank volumes go to their zero mass-energy states.  Remember, if those remote states go to zero, not even a photon survives.  And the universe's history cone can't expand in the absence of light and/or other kinetic energy.  No events can happen, except within that Minkowski cone.)  The kinetic expression of all the potential mass-energy contained in the original universe within one Planck volume would surely end up as a Big Bang, wouldn't it?  Perhaps you can get smaller, more localized Big Bangs inside any given universe if not all, but just many of the Planck volumes in a particular region evolve to a base vacuum state.  That is, the overall Minkowski light cone in that universe might develop a pucker.  It could happen right in your living room!  (That might explain why you keep finding the corner of your oriental carpet there turned up.)  However, it's much, much more physically likely that all the molecules of oxygen in the room would decide to congregate in one corner of the room, resulting in your asphyxiation...

Following are links to a few reference sites of interest.  Since you will undoubtedly get fascinated whilst reading them, and then end up surfing deeper and farther away from here, I may as well just say goodbye now.  Thanks for coming;  I'll keep the light on for you...

http://plato.stanford.edu/entries/qm-manyworlds/

http://kuoi.asui.uidaho.edu/~kamikaze/doc/many-worlds-faq.html

http://home.earthlink.net/%7Emrob/pub/math/numbers-13.html#l_p0_62e243

http://space.mit.edu/home/tegmark/multiverse.html

http://g42.org/tiki/tiki-index.php?page=BigNumbers

http://www.ie.lspace.org/books/dawcn/dawcn-english.html

 

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