The Multiverse
    By Amir D. Aczel | November 4th 2012 01:01 PM | 9 comments | Print | E-mail | Track Comments
    About Amir D.

    Amir D. Aczel, Ph.D., studied mathematics and physics at the University of California at Berkeley and also holds a doctorate in mathematical statistics...

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    Alan Guth, the discoverer of cosmic inflation, gave a talk at MIT on November 1, which convinced me, a natural skeptic about these issues, that the multiverse may very well exist. Two routes to the multiverse were never to my liking.

    One is "Many Worlds," Hugh Everett IIIs idea that quantum events whose wave functions seem to "collapse" in our world to yield specific measurements actually never collapse but realize all other characteristics implicit in their wave functions in "other universes." Every time something happens here--of all the very large number of possibilities--all the rest of them happen in other universes.

    The second such approach comes from string theory, where the equations make mathematical "sense" in more than 4--possible 10 or 11--dimensions, so along these "curled-up" dimensions that string theorists talk about, other universes flourish.

    Photo Credit: NASA

    One could question both theories on many grounds. It's true that when Paul Dirac solved his famous equation for the electron in 1928 and noticed positive and negative energy levels, he boldly interpreted the negative ones as belonging to an anti-electron, or positron--thus predicting the existence of particles nobody could even imagine before. But does this mean that mathematical solutions always result in new and real discoveries? 

    According to Brian Greene, a string theorist, the order of infinity of the multiverse is that of the points on the real line (he said this during my interview with him on C-Span). I find such a statement very hard to accept. The points on the real line are infinitely "dense," in the sense that between any two points on the line, no matter how close, there is always another point. If universes were so infinitely tightly packed, we should be experiencing these other universes with every step we make!

    So to paraphrase Enrico Fermi (who said this about the question of aliens): "Where is everybody?" An infinitely dense multiverse seems very hard to believe--given that we have no evidence at all for it. And "many worlds" is equally maligned: its size is immense, and where would all these other universes that we must use as "dumps" for all our non-occurring quantum events in our own world be?

    But the multiverse from cosmic inflation tells a completely different story. Guth's talk was titled "Inflationary Cosmology, The Origin of Density Perturbations, and the Door to the Multiverse," and he showed directly how the process of inflation believed to have followed the Big Bang most likely leads to other universes. The way in which this happens is fascinating. Inflation is a field with certain characteristics--for example, it is a scalar field, just like the Higgs field, and some physicists believe that the Higgs boson therefore may have played a key role in inflation.

    The field intensity starts at an unstable point, and then "rolls off" that point, triggering the exponential growth of our universe--which "irons out" all the kinks in the early universe, producing the very nearly "flat," or mathematically Euclidean, space we see around us today. The quantum imperfections in this process are what caused the formations of the seeds for all the galaxies in the universe--and we see these "flaws" on maps of the microwave background radiation measured in space (through the WMAP and other satellites). Both the uniformity of the satellite picture of the microwave data emanating from the very early universe (to a lever of 1/100,000), and the "flaws" in it--leading to the formation of galaxies--agree to a stunningly high degree with the predictions of Guth's inflationary universe cosmology.

    So here is where the other universes come in. The inflationary field is a quantum field, and therefore it is given to quantum fluctuation. It inflates our universe, and then stops. But it can't really stop, because of these quantum fluctuations in the field intensity--so the field, where its intensity is still high--goes elsewhere. Quantum uncertainty, quantum fluctuations, make it impossible for the inflationary field to die. It moves to another part of the universe, and inflates another universe, and so on forever.

    I asked Guth what is the cardinality of the multiverse created by inflation, and he answered: "Aleph-zero." This was a far better answer than the one given me by Brian Greene. Aleph-zero is the order of infinity of the integers and the rational numbers. It is a far more "pedestrian" kind of infinity than that of the real line. You can think of these universes as the integers: 1, 2, 3, 4,... Every time inflation finishes doing its trick on one universe, it moves on to the next in line. And since there is no stopping it, inflation continues this way, so that as time goes to infinity, the number of universes gets the infinite cardinality of the integers. From this kind of very reasonable infinity to the immensely complicated, infinitely-dense real line of universes there is a long, long way to go. 

    Amir D. Aczel's book on the Higgs discovery, Present at the Creation: Discovering the Higgs Boson, is reissued in paperback this month by Broadway Books.


    Welcome to the dark side...;-p

    And by the way I just finished watching the C-Span interview with Brian Greene you mention (and link to) above, and I have to say I thoroughly enjoyed every minute!! Highly recommended to anyone looking for non-technical discussion of physics' foundational issues! (Especially those for whom a standard television popularization would be unbearably slow and tedious.)

    And on the topic of that interview, you mention your dissatisfaction with Mr. Greene's choice to equate (a universe's) infinite spatial extension with the "infinity of reals" (due of the latter's unphysical density, I think?), versus Guth's suggestion of "Aleph-zero." I'm not sure if you talked with him (Greene, that is) about the issue off camera, but in the video it seemed (from the way he answered) like it's possible he was just putting forth an example to satisfy the request at hand. It'd be interesting to know his thoughts in retrospect.

    Amir D. Aczel
    Thanks, Eloheim!! Honestly, I hesitated about including that link to the video. It was an unfortunate interview. I liked Greene a lot before this happened and had met him and had good rapport. At the interview, he had some weird demands: He insisted to the Museum of Science that we both appear from behind a screen, for dramatic effect, (rather than walk on stage as is always done), and he wanted to dictate to me what questions to ask! This offended me and pre-set a bad atmosphere already, which is unusual for me (all my other interviews have been very friendly, conversation-like). And I felt that my important questions, such as what is the basis we have to assume a multiverse, were being ignored. Still, he managed to make me look bad. At any rate, the Guth talk, a year and a half later, answered all these questions, and now I believe that a multiverse is very likely (of the kind Inflation implies). The simplest way to look at it is the following: In physics, anything that can happen (given the right conditions; and it not violating some law) eventually will happen. So as time goes on, it will happen infinitely often. Cheers, Amir  
    Amir D. Aczel
    Amir D. Aczel
    I forgot to mention a funny, and apparently even true, anecdote about the multiverse. At a recent conference, famous cosmologists were asked what they would bet that there is a multiverse. Martin Rees, the UK's Astronomer Royal, said he would bet his dog's life that there is a multiverse. Andrei Linde, the Russian-American cosmologist from Stanford, said he would bet his own life that there is a multiverse. And Steven Weinberg, the American Nobel Prize winning physicist, said that he would bet both Andrei Linde's life and Martin Rees's dog's life that there is a multiverse.
    Amir D. Aczel
    I am reasonably sure I am farther from Paul Erdos and Kevin Bacon than Brian Greene is.  
    Amir D. Aczel
    Ah well, Brian got his Erdos=2 from his advisor Yau (of Calabi-Yau manifold fame) at Harvard, who'd worked directly with Erdos; and the Bacon number through his documentary and TV work. But he is wrong about the genesis: Erdos numbers come long before the Bacon number idea.
    Amir D. Aczel
    I don't get your point about Aleph-zero. As you mention yourself, it's the cardinal of the rationals. In every neighbourhood of a rational, no matter how small, there's an infinity of other rationals. The situation is perhaps not as bad as with the reals, but it's not much better, is it?

    Amir D. Aczel
    Great question, Anonymous! You can map the rationals onto the integers, as Cantor had done, which stunned everyone 100 years ago, using the famous "diagonal argument." Make an array: to the right you run the integer that is the numerator; and downwards its the denominator integer; the array is infinite. But you create a one-to-one map from this array to the natural numbers by assigning 1 to 1/1, 2 to 2/1, 3 to 1/2, 4 to 3/1, 5 to 3/2, 6 to 3/3 (I may be mixing up the details, but you can look it up). The point is that the rationals (and all algebraic numbers, such as sqrt(2) as well!) can be associated with the (discrete and separated) integers! But for hardcore irrationals (unlike algebraics), e.g., pi or e, this doesn't work! Cantor's proof of that fact is even more amazing: Assume you COULD make such a list of all the reals (as you did with the rationals using the diagonal-weaving argument) what would that list look like? Let's start small: Make a list of all the numbers between 0 and 1, in no particular order. E.g:
    I can ALWAYS exhibit a number NOT on your list. Here goes:
    How did I do it?
    Amir D. Aczel
    Amir D. Aczel
    A few more points to the last comment: So while you are right and you can find rationals between two rationals, the rationals CAN be made "discrete" and "pedestrian" as I call it--just by applying the diagonal argument: they are cardinally the same as the integers, or just the natural numbers 1, 2, 3,... For the algebraics the proof is trickier (they are irrational!) and has to do with the fact that they can be "mapped" by the equations that spawn them! An algebraic number is one that is the solution to an equation with rational coefficients--so we get a handle on their size by "counting" these equations, which can be indexed by their rational (hence aleph-zero) coefficients! One last point: Cantor even showed that there are as many points (cardinally) on a 1x1 square as there are on the 0-1 interval. When he proved it, he wrote to a friend: "I see it, but I don't believe it!" It stunned even him. This is how he did it: Let a point along the east-west direction of the square be: 0.a1a2a3a4... and one along the north-south direction of the 1 by 1 square be: 0.b1b2b3b4... Now consider the number: 0.a1b1a2b2a3b3a4b4  It's a one-to-one mapping from the sides to the inside of the square.
    Amir D. Aczel
    I read what Vongehr writes but I can't understand it.

    "If you count unobservable like virtual particles (like in my fundamental description of totality), you must take into account continuous phases (QM unitarity) and transformations between pure states that are never mixtures, and that means the state space is similar to that of the reals (no, you would not feel it, also because it includes unobservable, but not anyway)"

    A language problem? Perhaps it would be O.K. in German.