How many Universes Are There?

 

The "Many Worlds" interpretation (MWI) of quantum mechanics was developed 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. 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 wave function, instead of collapsing at the moment of observation, carries on evolving in a deterministic fashion, embracing all possibilities 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 having 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, 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 brings to mind the remark by the Captain in charge of the Christian crusade against the heretical Cathars in Beziers, in the 13^th century. When asked how to distinguish the heretics from Catholics, he replied: "Kill them all, God will know his own." In one of the MWI’s, perhaps 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, that’s about 1 ten-octillionth the diameter of an atom.

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 that’s the size of one instantaneous potential universal reality. Every Plank volume in the universe-sphere has a particular state, 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, that’s 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 10²⁹⁶⁴⁶⁰ universes. That’s 1 followed by 296460 zeroes. Another way of looking at it is that this is the number of all possible "shuffles" of every Planck card in the universe-wide deck.  The size of the deck includes all the Planck cards that have existed throughout the entirety of Planck-time history.  (But see the note below.)

At 250 characters per page, to write the number 10²⁹⁶⁴⁶⁰ would require about 1200 pages of printed numbers – a book that wouldn't be too heavy to carry around with you.  Of course, that master index book merely refers to the number of other, much larger books in the library of some immense virtual monastery, each one describing the 10²⁴³ quantum states of the universe it represents.  At 250 characters per page -- figuring simplistically that each quantum Planck state could be represented by a single character -- each of those books would be about 10²⁴¹ pages long.   Let's describe the size of each book in terms of tons of paper required to print it.  A ton of paper consists of about 200,000 sheets, or 2 X 10⁵.  One of the Planck universe "plan" books would thus weigh about 10²³⁶ tons.  The scale is still incomprehensible.  OK, let's try again.  One estimate I found for the weight of the planet Earth is 10²³ tons.  The book would weigh as much as 10²¹³ Earths.  No, no help at all.  Try this: I saw an estimate for the mass of the entire universe, which was about 10⁵⁰ tons.  So each book in that monastery weighs as much as 10¹⁸⁶ universes.  That's 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000 universes at 10⁵⁰ tons each.  And there are 10²⁹⁶⁴⁶⁰ - 1 other books of equal size in the library.

 

Aw hell, it's just a really, really big 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 -- about 10²⁶³³⁵⁰ of them. That seems plenty enough to include at least one that embodies peace and happiness for all Mankind. Or maybe I’m just a unredeemable optimist…

   Back to Lost Articles...  

 

Image at top Copyright Terra Zone

---

It's easy to technically criticize the derivation of this 10²⁹⁶⁴⁶⁰ 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 10²⁹⁶⁴⁶⁰ 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