Universes by the quintillions

kw: book reviews, nonfiction, cosmology, multiverse, history

There is a corner of science in which I have much interest, cosmology. I usually avoid peeking into one corner of that corner. The various attempts to go onward from "What happened?" to "How did it happen?" and even "Why?" have been getting more and more strange for most of my adult life (50+ years). But I could not pass up the new book by Tom Siegfried, The Number of the Universe: A History of the Multiverse and the Quest to Understand the Cosmos.

I was quite entertained, and my history itch was well scratched by the author's thorough coverage of how the meanings of "world" and "universe" have morphed through the ages, at least since Aristotle. The early atomists were at odds with Aristotle, who embraced the Continuum. The atomists pointed to things like the hand of a bronze statue that had gradually become quite worn because people always touched or rubbed the fingers on their way by it.

Considering that this could equally be taken as evidence that the statue's material was continuous and thus could be removed in quantities as minute as one liked, their contentions held little water. They didn't convince Aristotle, who also declared that there could be no more than one world. The world as he understood it was equivalent to the universe, and consisted of a series of nested spheres; the outermost held the "fixed stars", the innermost consisted of the Earth, and those between carried the Sun, Moon and five planets in their pathways around the sky.

For reasons that escape me, the atomists also considered that there could be, and should be, something "outside" the outermost sphere. Perhaps other worlds like ours. Camille Flammarion in 1888 published a wood engraving that illustrated one such idea, but it is based on a flat earth, not the sphere that the Greeks understood for the earth's shape. It isn't known whether the original illustrator was displaying a true belief, or lampooning it.

Sixteen centuries were to pass until a clerical edict in 1277 threatened "natural philosophers" with excommunication if they continued to take Aristotle's anti-atomist and anti-multi-world pronouncements as truth. It is odd that, 350 years still later, Galileo was placed under house arrest for writings that contradicted Aristotle.

Mr. Siegfried takes us through the various twists and turns of the various meanings "world" and "universe" have taken on, from Aristotle onward. The "universe/world" of Ptolemy, complete with epicycles, was not far removed from the Aristotelian model. The "revolution" by Copernicus mainly caused the Sun and Earth to switch places, allowing only the Moon to keep orbiting Earth. We call it the solar system, but Copernicus called it the World.

After the telescope was invented, and rather large ones were produced, the Milky Way, or the Galaxy (from γάλα, or gala, for "milk"), was thought to be the whole universe, and the solar system including Earth was just a tiny part of that; the Earth was now "the world" and the rest was "the universe". Still later other galaxies, some found to be larger than the Milky Way, were called "island universes", but now "universe" means "everything". Now there are those who say the universe is "everything we can observe," and posit multiple universes, the multiverse.

The author points out several times that the arguments being put forth now against modern hypotheses of a multiverse are the same as those advanced time and again over the millennia. While reading the book I came to understand these comparisons as political framing. The point of the book is to defend the concept of Multiverse, even though there are between six and nine versions thereof being bandied about.

I will discuss only two of these. Firstly, what we can observe with our instruments reaches to 13.8 billion years ago, and a naïve concept of its radius is 13.8 billion light-years (Gly). However, back-calculating relativistic effects allows us to estimate that the "edge" of what we observe is actually now at a distance of about 75 Gly. That's how far cosmological expansion has carried things. But how big is the "rest of the universe"? We still have no way to know. Ignoring accelerated expansion (the dissension against this idea continues to increase, so I discount it), let's first guess that Alan Guth's inflation popped things open to such an extent that we can observe at most a percent of the whole. Even "inflation" didn't produce an infinite bubble of spacetime. One hundred times the volume is a little over 4.5 times the radius. Let's round that up to a radius of 350 Gly. That's the size of "our bubble universe".

The number of baryons (protons, neutrons and their kin) in the observable universe is thought to be about 10¹⁰⁰ (one Googol), and their number in "our everything", this bubble, may be 10¹⁰² (100 Googol).

One version of the multiverse hypothesizes that there are multiple bubbles, perhaps with differing values of the "natural constants" such as the ratio of mass of the proton/electron. In our universe, or at least on our lab benches, that ratio is 1,836 and change. If the ensuing multiverse is truly infinite, containing an infinite number of such bubbles (200-400 Gly across on average), it is thought that any particular configuration of particles and their motions will be repeated exactly an infinite number of times. Well, that's a lot of infinity. And all of it quite beyond the reach of any possible instrument.

I don't know how big the number of permutations and combinations each bubble consists of, but we can tinker with a few numbers:

• The coordinates of each particle and its velocity consist of six numbers. The position must be known with a precision of about the Planck length (1.6x10^-35 m), and similar precision for the velocity, to obtain a functional match.
• A complete specification for the state of a bubble at any point in time consists then of 6x10¹⁰²  numbers. Call this Nu, the "state number of a universe".
• The permutations of Nu are roughly its factorial: (Nu)!, a number with about 600 times as many zeroes as there are particles in "our" bubble. That's a very rough estimate based on Stirling's Approximation.

If there are at least that many universe-bubbles out there, then at least one pair of them will match exactly, at least at some point in time. Quantum effects may result in immediate divergence. It's a bit like the statement that the formulas for Earth's atmospheric interactions require that, at any one point in time, there are two antipodal points at which the temperature and barometric pressure and wind velocity and direction are exactly matched. But where those points may be, nobody can determine, and where they are a few milliseconds later, is anyone's guess. However, this hypothesis of a multiverse is one I can consider is at least possible. Highly unlikely—perhaps one chance in some number with a Googleplex of zeroes—but possible.

The other multiverse worth considering, if only as a straw man, is the one formulated by Hugh Everett III. Rather than accept quantum randomness, his model states that for every quantum "choice", both or all possible paths are taken, just in different universes. If I understand Dr. Everett correctly, every quantum event causes the splitting of the universe into two or more universes, each one holding one of those outcomes. He is quoted as stating that a "stupendous number" of parallel universes are thus produced every second, separated from one another by unknown mechanisms or materials. "Stupendous" is the understatement of the century.

Let's consider a very simple quantum event, the interaction of a photon with the surface of a sheet of glass. If the refractive index of window glass is taken as 1.5 at some wavelength of choice, then, for normal or near-normal incidence, the photon has a 4% chance of reflecting. Otherwise it passes into the glass. The Everett Multiverse works this way. Each such photon-glass interaction splits the universe into two. In one, the photon reflects, and in the other, it passes through. Or maybe there has to be a split into 25 universes; one of them gets the reflected photon and the rest get the transmitted photon. Let's go with the simple version.

I have a laser pointer with a beam that is nominally "less than 5mW", so I'll call it 4mW. I'll point it straight at my window. What happens? Here are the numbers:

• 0.004 W beam power
• 670 nm beam wavelength
• 6.242x10¹⁸ eV (electron Volts) per Joule (J); 1 W = 1 J/sec
• photon energy at 670 nm = 1.85 eV (proportionality constant 1240 eV-nm)
• 1.35x10¹⁶ photons/sec in the beam

The number of photons striking the near surface of the glass is 13.5 quadrillion per second. (In American units, a quadrillion is a million times a billion.) A slightly smaller number, 96% of 13.5 quadrillion, strike the far surface of the glass. Most of those that reflect inside the glass (about 54 trillion) pass through back upward, but a few are reflected downward again, and so forth. We can say that 27 quadrillion quantum interactions are happening, every second. That is not counting the quantum events that go into creating the laser beam photons in the first place.

I don't know how many universes were being created each second beforehand, but during the time I shined my 4mW beam at the glass, 27 quadrillion new universes were created, that would not have been had I kept the beam off. About every 37 seconds, I "create" a quintillion universes.

And some people think it incredible that God created one universe! Is it any surprise that I consider the Everett hypothesis of the multiverse as the sheerest nonsense? It violates Occam's Razor by the hugest, most incredible amount I have ever encountered.

Do I have an alternative? Indeed I do (and not the theological one)! Keeping my physicist hat on, I'll point out that I find superstring theory less incredible than the Everett hypothesis. These curious entities, if they exist, are something like a Planck length in size (see above) and vibrate at furious rates, at least as great as the frequency of the most powerful gamma rays. The "fundamental particles" that we call quanta, including protons and photons, would then be vibrational modes of one or more superstrings.

If the above is true, quanta have "fuzzy boundaries" with a lot of "buzzing" going on inside, and quantum randomness is then something related to Brownian motion caused by molecules striking tiny items such as pollen grains, in random clusters that don't quite balance out.

Consider the interaction of a photon with a piece of glass. The glass, volume-wise, consists mainly of oxygen atoms held together by covalent bonding with much smaller atoms of silicon, sodium, and a few other elements. The oxygen atoms are slightly ill-defined spheres or spheroids with a diameter of about 0.3 nm. A photon from my laser has a wavelength about 2,000 times as large. I don't know how "wide" a photon is, but the "wavicle" model indicates its "physical" length is probably 2-3 wavelengths. Suffice it to say that the photon interacts with a large number of oxygen atoms, or at least the electrons in their outer orbitals, while taking some fraction of a nanosecond "deciding" whether to turn tail (reflect) or slip past the surface (refract). During that interaction the vibrations of the superstrings involved cause a few trillion (or trillion trillion) jitters of this or that "part" of the photon against various numbers of electrons. Predicting which way a casino die will roll would be infinitely easier than determining beforehand what the photon will do (just bet the odds: 24 out of 25 times, it'll go through).

That is my superstring-Brownian-motion hypothesis for quantum randomness. I ought to copyright it (and I did, just by publishing it in this blog post).

P.S. This shows one concept of a wavicle that I found on zazzle.com. To this scale, the oxygen atoms in window glass would appear about 0.012 mm across, about three times the size of E. coli cells.