The probability of two divergent universes converging (except maybe a picosecond or less after diverging) is so small as to be impossible. Kind of a drunkards walk with two drunkards.
Lawrance Watt-Evans, in “Why I Left Harry’s All-Night Hamburgers”, explicitly states that the multiple universes exist even before they diverge from each other, implying that before divergence, they must have been identical. And I’m pretty sure that Niven addressed this, too, in one of his “The Theory and Practice of…” essays, if not in “All the Myriad Ways”.
What exactly is it that has shifted universes?
Assuming (as we must) an identical “you” that shifted from that universe, nothing has changed in either universe. Unless you posit some mysterious non-physical property that defines “you” (a soul, I suppose), what you describe is meaningless.
It’s like the old Stephen Wright joke about someone stealing everything in his apartment and replacing it with identical copies. If it happens in an instant, and the copies really are identical, in what sense was there a shift?
I have been assuming that in this thread, we are talking about the different “universes” that get talked about in string theory and brane theory and so on. In those theories, the different “universes” are located spatially with regard to each other, so that in the scenario described in the post you are responding to, what has changed is the location of two distinct (though structurally identical) objects.
In the “many worlds” interpretation of quantum mechanics, there can’t be two identical universes because by definition two universes with exactly the same quantum state (probably not the right terminology) are in fact not two universes at all, but one. If it’s “many worlds” quantum stuff the OP has in mind, then the answer to his question is, no, there could not be two identical universes.
There could, however, be two exactly similar earths in different non-identical universes. And if I and my counterpart on such a world perform the described experiment, then certainly something would have changed. I would have started out in a world where, say, particle Z in the Andromeda galaxy is located at point P, and I would have ended up in a world where that particle is located two inches to the left of P relative to myself.
-FrL-
It’s worth mentioning, BTW, that the best exploration of this I’ve encountered in SF was in the otherwise mostly forgettable last entry in Douglas Adams’ Hitchhiker’s series, Mostly Harmless.
Adams describes the universe-hopping Arthur Dent’s discomfiture at the realization that although he seems to have managed to return to his own universe, he cannot be certain that somewhere on the other side of the world, there is not a tiny clover (perhaps long-since withered and gone) that has a slightly different number of leaves than it does in “his” universe.
Adams describes the universes not as separate, but as occupying different points in a five-dimensional space. Most objects in Arthur’s “four-leafed clover” universe would occupy the same coordinates in space and time as objects in the “three-leafed clover” universe, but would be separated along the axis of the fifth dimension, probability.
I always thought this was a uniquely perceptive and parsimonious explanation, and I don’t think I’ve ever seen it clearly expressed elsewhere.
Are you sure?
It seems to me that from your perspective, particle Z in the Andromeda galaxy would have quantum-tunneled two inches to the left, while to an outside observer in either world, the particles in your brain forming the physical representation of your memories would have simultaneously quantum-tunneled to states which correspond to new memories in which particle Z was recently in a different place than it was. (Unless you were never aware of the position of Z, in which case no one would notice a difference.)
According to any of the models you mentioned, how would my explanation not be preferred to one in which all of your quantum furniture was stolen and replaced with identical copies? Or does something other than quantum state and relative location distinguish structurally identical particles? (In other words, what makes the structurally identical objects you describe in your post “distinct” other than their spatial relation to each other, which does not observably change in the course of the experiment?)
DISCLAIMER: My qualifications for participating in thread consist in the following: I am reasonably bright and once owned (but did not read) copies of both Six Easy Pieces and A Brief History of Time. Go easy on me! 
My qualification’s are a curiousity on a subject that’s been done to death in books and shows, and having extrapulated a variation of that, which I thought must hold true, if the first was excepted as true. This could led the person into thinking his machine was a time machine, but he was only popping into worlds that were the same as his however many years ago. This takes us into time travel theories though. Some are based on you visiting a universe that is currently at the point you wished to visit in you universe. You don’t achieve true time travel, you achieve travel to an exact copy of your universe matching it at the period you wish to travel to. You go to a universe that is the same as yours was 100 hundred years ago, to see what happened one hundred years ago in your universe. This nicely allows you to muck things up and not affect your history either. You should however feel bad about destroying the world you visit, because when you go back the other people are still dead and you can’t change their being dead by returning to an earlier point.
The input has been great here.
This is an old, old idea in science fiction. In fact, I’m re-reading one version of it now – Freedric Brown’s wonderful 1950s comment on sf and sf fandom, what Mad Universe.
It’s a fun idea, and takes many forms – as Exapno indicates, there’s a difference between the infinite number of all possibilities and just an infinitely large number of possibilities. You could have universes “split” every time there’s a choice, human or quantum, between two alternatives, but that wouldn’t be the same as “all possibilities”. (Brown’s system, in WMU, clearly encompasses all possibilities, since a character remarks that “There is a universe in which this exact same scene is being played out, only you’re wearing brown shoes.”)
If the univerrse splits at every choice, you have an interesting philosophical and moral situation – you can always wonder “what would have happened if I’d done x?”, but, in reality, you’ve done x, since both universes exist from that choice point. Can you be held responsible for your actions if both choices physically exist (albeit in different universes)?
It wouldn’t surprise me if a huge number of identical universes existed. Heck, if multiple universes existed, and the differences were trivial, or far from your bubble of experience and never directly influenced you, you might be switching universes all the time and never know it. (“I was born in a universe where Ulan Patay was born in Indonesia in 1948, but I now live in one in which he was never born. But I never meet him, and he never influences anyone outside his village, so it makes no difference.”)
Personaly, I’m a fuddy duddy, and think that this is the only universe we’vve got. I don’t know where these parallel universes that spliot off from one another even exist. I’ll entyertain the idea of other universes elsewhere somehow, but the notion that they have to look like ours strikes me as absurd as those Star Trek episodes with planets that look exactly like Earth.
Yeah, I know – other universes exist in other “dimensions”. The term gets used a lot by people who latch onto it as a vague idea, but don’t usually know what it really means. These people need to read Abbott’s Flatland and its many sequels and imitators.
I assume it is a response to your question about my post. The “joke” of my comment about my infinity being bigger than yours is that while you could have infinite possibilities you could still have repetitions in infinite universes.
<mathematicians, please cover your eyes>
Think of the odd natural numbers and all the natural numbers. They are both infinite but you could argue that there are double the amount of natural numbers than there are odd numbers. A bigger infinity.
<mathematicians can uncover their eyes from here>
You are discounting the butterfly effect. Sure you never met Ulan but when he kicked Ugun’s chicken, Ugun’s wife made a bitchy comment to Butan’s wife so she nagged to him and they decided to move to Japan where he took the job that Shutiko would have taken which made him kill himself so he never met Konishi who then moved to Los Angeles and married John who then never started his internet startup which meant Peter never got that job and then stayed in Boston where he ran you over in a drunken night.
Nothing of small probability is impossible. Impossible is probability of exactly 0. In the real world we have to make judgements about probability and possibility, like DNA testing matches. Probability of a DNA match is never exactly 100% but the courts say 99.99999% is good enough for a conviction. Philosophy regarding the universe, however, is not about practical matters. In fact, many say that our own universe is incredibly improbable, so much so that it would be impossible except at the will of a deity. But incredibly improbable does not mean impossible.
This gets into a truly philosophical area of free will. Is there really such thing as a human choice? Decisions are the result of a physical and chemical process in the brain. If a person were to re-experience the same situation, down to the quantum states, wouldn’t the same choice be repeated, no matter how many repetitions? Further discussion on that point gets redirected to GD. 
:dubious: Why would they do that? The scenario described is just one where I switch with my doppelganger from another world. It is stipulated that I and my doppelganger are identical down to the quantum level.
Well, that’s fine. Not noticing a diference doesn’t mean there isn’t a difference. My point was that in the many-worlds type of multiverse scenario, every universe is at least slightly different. If I have a doppelganger in one, and I switch places with him, then I am now in a universe that is in theory quantifiably distinct from the one I inhabited before.
If by “explanation” you mean to refer to something in your present post, then I would say you’ve offered no explanation but simply a scenario alternative to the one that was given. A scenario was being discussed in which I and a doppelganger switch with each other, while remaining the same as we were before. You gave a different scenario in which I and my doppelganger switch places, and simultaneously, our quantum states are changed to give us nwe memories matching those we would have had had we been in our new universe all along.
Their spatial relation to other things changes. Right now, I am in front of desk X, while desk Y, in front of which my doppelganger is sitting, is seventy thousand jillion gazillion thrillion light years away from me. After the switch, desk Y is right in front of me, while desk X is seventy thousand jillion gazillion thrillion miles away from me.
I’ll grant from the outset that as the scenario has been described, there’d be no way in practice to know that any switch had occured. But thereis a clear distinction that can be made by giving the following counterfactual: Before the switch, had I had the opportunity to investigate particle Z, I would have found it at location L, while after the switch, had I had the opportunity to investigage particle Z, I would have found it at a location two inches to the right of L relative to my location at the time of the switch.
My qualifications? A fucking philosophy degree. In other words, I’m making shit up as I go along. But it’s the right shit to make up.
-FrL-
Maybe that was what h was responding to. I hope he didn’t think I needed to be educated about the existence of distinct infinities. (For example, countable infinities as opposed to uncountable ones.) Because… I don’t.
You probably know this, but just to nitpick: Since the even numbers and the natural numbers can be put into a one to one correspondence with each other, they are the same size. But the natural numbers and the real numbers can’t be put in such a correspondence, because, in a real sense, there are more real numbers than natural numbers.
Anyway, my original point was this: It is not true that if there are an infinite number of universes than some of them must be identical, unless there are only a finite number of possible internal configurations of universes.
-FrL-
This has been a very amusing thread. It’s been very worthwhile for me, and I thank the participants. Anybody having anything to add, feel free to continue posting. I can get a foothold on an idea, I just can’t bring it to a conclusion by myself.
Impossible in the sense that I don’t buy it. Actually, though, it is impossible to determine if two universe are identical, since to do so we would have to know the location and velocity of all particles in each at some point in time - which is impossible.
As for the improability of the universe as related to card - it is the difference between the improbability of getting a single hand, and that of getting the same hand a million times in a row.
Anything in particular that is troubling you?
I took a lot of philosophy in college, but I felt like it was too practical, so I switched to theology!
I think it might help you in understanding my position to know that I am a pure physicalist: I believe that a complete list of the quantum states and probability fields (and whatever else a physicist would add) of the fundamental particles in the universe tells us everything there is to know.
So the question is, in your two scenarios, one in which you switched places with your doppleganger and one in which you didn’t, what would be different on those lists? If you and your doppleganger have identical quantum states, then nothing would be different. You can claim that it would be a different set of quarks and electrons (ones that used to exist somewhere else) sitting at your computer typing to me, but if they have the same quantum states and locations as the other set would have had, I think they are the same and that nothing has changed.
Now, given my physicalist biases, I get a little twitchy talking about things like consciousness and perceptions, but I suppose you may want to say that from your perspective, you would (or could) notice the difference in the position of particle Z. But position and velocity are all relative, of course, and I suspect that motion along whatever axis separates multiple universes is too. Did you move, or did the universes? Without a specific mathematical model to explain just what these parallel universes are, we can’t answer that question (and I couldn’t understand such a model anyway). But based on what you said, I suspect that it would make just as much sense to say that particle Z moved relative to your position as to say that you switched universes.
I can agree that a complete list of the quantum states of all the particles in the universes (plural because we are supposing that there are multiple universes) tells me everything there is to know. But involved in knowing the quantum states of every particle is knowing which particles have which states. I and my doppelganger are different because we are composed of different particles. When we switch, something has changed because particles have gone from being in one location to being in another location. Location is (to my recollection) part of a quantum state, so another way of putting this is, something has changed because some particles have changed their quantum state by virtue of having changed their locations.
As you know, we are supposing it to be possible to travel from one universe to another. Suppose I’ve got this machine that does so. It works reliably. It trades my particles for whatever particles occupy some particular identically shaped area of space in another universe. So every time I use it, I pop out of the universe I’m in, and pop into a different universe. Clearly something has changed in these cases–namely, my location with respect to the field of universes. Now, sometimes, I use the machine, and find myself in a situation where, as far as I can determine, nothing has changed. (My doppelganger, of course, has an experience quite identical to my own.) I would argue that it is very strange, implausible even, to say that the machine does something in all other cases, yet in this case, despite the fact that it goes through exactly the same motions as in the other cases, somehow, it has failed to do anything.
If the machine effected a change of location in the usual cases, I see no reason to say it hasn’t effected a change of location in the twin-switching case. And this is reflected in a complete description of the quantum states of the particles involved, because previous to the switch, Particle X inside me had quantum state Y entailing it has location Z, while subsequent to the switch, Particle X had quantum state Y’ entailing it has location Z’.
You can’t describe the universe by simply listing all the properties which attach to the objects in it, unless you have named all the specific objects in order to explain which ones get which properties. My name is Kris. I name my doppelganger Kris-Prime. When we switch, Kris is occupying the space formerly occupied by Kris-Prime, and vice versa.
-FrL-
This is where we disagree. As I understand it, a particle is a collection of quantum states. If particle X has quantum state A, and is “replaced” by particle Z with quantum state A, all that has happened is you’ve changed the name. There is no particle, just a quantum state.