Another question inspired by John Gribbin’s “In Search of Schrodinger’s Cat” (books on quantum physics are dangerous!):
I was reading the chapter on the Many Worlds Interperetation, and decided to try to calculate just how many “Many” universes would be. For the sake of simplicity, let’s assume a universe where every particle makes a 50/50 quantum decision once every second (hey, it should at least get us in the ballpark).
So, every second from the first there will be a node where the universe splits into some number of daughter universes. The number of branches at each node should be 2[sup]n[/sup], where n is the number of particles involved (since each particle has a 50/50 choice). The total number of universes will increase (as the nodes beget further nodes) in the manner (2[sup]n[/sup])[sup]t[/sup], where t is the number of seconds from the beginning.
I believe I have heard estimates of about 10[sup]80[/sup] particles in the universe, and an age of around 10[sup]15[/sup] years, which is just about 310[sup]23[/sup] seconds. That would give us a total of about (2sup[/sup])[sup]310[sup]23[/sup][/sup] universes. “Many” is starting to sound quite the paltry epithet.
Finally the question(s): does this sound like a reasonable estimate for the number of universes in the metaverse predicted by the Many Worlds Interperetation? Does anyone care (or know how) to juggle those exponents around so that we can get a number which is easier to read, say one with more tens and less twos, threes, twenty-threes, and eighties? Can I name this number the “McCloskey” after myself? I used 50/50 choices as an assumption, but how does the Many Worlds Interperetation handle situations where a quantum decision has odds of, say, 70/30? How would the universe split then? And what of situations where there is more of a continuum of possible outcomes, like the angles a particle may be deflected at?
The age of the universe is about 1.5 times 10 to the 10th years, which would be 5 times 10 to the 17th seconds. But in any case, quantum particles make decisions much, much often than once a second.
Yeah, that’s my bad. I meant 15 billion years, I don’t know where 10[sup]15[/sup] came from. 5*10[sup]17[/sup] is indeed the correct value for t.
Yeah, but I was trying to find an average. I figured that, while particles within a star are reacting every nanosecond or more, a particle in the depth of space might go quite a while without reacting to cause a split of universes. Of course, this doesn’t take into account vacuum fluctuations. I admit I pretty much pulled that average out of my butt, for simplicity’s sake (although I still flubbed the math ;)). Anyone care to provide a better estimate of the average time between quantum decisions for a particle?
As it stands, the revised estimate for number of universes (taking into account the correct value for the age of the universe) is (2sup[/sup])[sup]5*10[sup]17[/sup][/sup].
Re the 70/30. Beats me. I thought about it once. Can’t remember.
Re the continuum of angles: Not sure what situation you are describing. If you mean the possible directions that a baseball will go after the batter hits it, then you have to realize that this has only one outcome, not a multitude. That one outcome is the result of the velocity of the ball, the velocity of the bat, and the relative positions of the ball and bat at the moment of impact.
Each of those factors, however, have multiple possibilities. The air turbulence that the ball encounters after being thrown will push it one way or another. Loose or tense muscles will influence the bat. Each of these will be determined by zillions of microscopic events, and gazillions of quantum events.
But in case, I think we can always establish that there is never a smooth continuum, but always an almost-infinite set of discrete possibilites.
Keeve, say a hydrogen atom is sitting by itself in the middle of nowhere, and that its electron is in an excited state. At some random time the electron will fall to the ground state, giving off a photon. Couldn’t this photon be emitted travelling in any possible direction? It seems as if it would have to spawn off an infinite number of universes, one for every conceivable direction the photon could take.
I used 50/50 choices as an assumption, but how does the Many Worlds Interperetation handle situations where a quantum decision has odds of, say, 70/30? How would the universe split then? And what of situations where there is more of a continuum of possible outcomes, like the angles a particle may be deflected at?