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FQXi BLOGS
CATEGORY: Blog
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TOPIC: Quantum Grantmaking
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At about 1 AM GMT on April 20, 2007, the Universe split into at least 32,768 nearly-identical copies. How? And did it really?
The event was precipitated by yours truly gathering a quantum-mechanically random number between 1 and 10,000. Generating this number required making at least 15 quantum measurements, each yielding one random bit. In the course of each measurement, a solid-state device effectively fired a single photon through a half-silvered mirror, as shown in the first figure.
The photon, being a quantum object, corresponded to a wave-function, and each firing then corresponded to a photon wavefunction that split into two superposed pieces, one of which hit the ‘0’ target and one of which hit the ‘1’ target in the figure.
However, thinking a bit more carefully, the ‘mirror’, the targets, and in fact the whole computer card, while big, should still be fundamentally quantum-mechanical. Thus what was really created was a superposition between one state describing a computer card that supplied a ‘0’ bit, and one that supplied a ‘1’ bit.
But then, carrying this thinking forward, by asking for this random number, I really created a superposition of internets, and computers, and Anthonys, in one of which a ‘1’ bit appeared, and one of which a ‘0’ bit appeared. And after 15 such measurements, a superposition of 32,768 Anthonys was formed. Further, on the basis of the number between 1 and 10,000 (which served as the ‘seed’ for generating further pseudo-random numbers), a piece of software run by Anthony determined the results of the FQXi minigrant lottery , and so – in the wavefunction -- there are at least 10,000 copies of each FQXi minigrant applicant, some of which correspond to applicants who get their minigrants, and some of which do not.
Now, some questions. First, can we observe more than one of these distinct outcome happening? No. The large number of degrees of freedom involved, including the ‘environment’, mean that – by a process called ‘decoherence’ - all interaction between the branches will be suppressed. Only one gets experienced at a time. Second: Are all of these ‘branches of the wavefunction’ equally real? Some interpretations of quantum mechanics say yes, some say no. Both are troubling.
If no, then we might ask: at what stage did one of them become real, and the other not? And what is this ‘realness’ that goes beyond the mathematics of the wavefunction? The unpleasantness of both questions leads some thinkers to say ‘yes’ and embrace various versions of the ‘Many Worlds’ interpretation of quantum mechanics.
But if yes, there are even more questions. In particular, what determines what actually gets experienced, and why do the quantum probabilities apply? The core of this problem can be seen as follows. Suppose a mad scientist came to you and told you that he had built a teleporter. But due to some intrinsic constraints, it would create two nearly-identical copies of you. One would be teleported far away, to whatever pleasant destination you wish, but the other would be forced to endure a prolonged and agonizing death. (There is a recent movie along these lines, but I will not mention it for fear of including spoilers). I, and I suspect you, would be very hesitant to enter the machine: isn’t there a good chance that the next thing ‘you’ will experience is painful execution? Now, however, the scientist tells you “don’t worry! I have a little dial I can set, and the probability of your ending up in the pleasant place can be set to 99.999999%; the chance of you being the one that dies can be made tiny!”
I don’t know about you, but I would still not set foot in the machine: how could he possibly “send” my personal experience one way versus the other with such confidence?
This, of course, is just what Many Worlds asks us to believe: that in a quantum measurement both outcomes occur, and are experienced by two otherwise equivalent observers. Yet you are supposed to believe that the probability of your becoming one versus the other of those observers is governed by the probabilities of quantum mechanics (the ‘Born rule’). For the life of me, I don’t see how this can make sense.
So while I’d like to believe that FQXi has funded all of its minigrant applicants, I don’t REALLY believe that it has. But hopefully the applicants do, and can take great comfort in this.
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Have you ever been under global anesthesia? If so, when you came to, how did you know you were still you? You probably asked yourself questions like "where am I?" and the answers came back to you, from memory, as an internal dialogue. This, our memory and internal dialogue, is how we perceive our "self." If we were to make perfect copies, classical or quantum, and these selves were to ask themselves, "am I me?" the answer would come back: "yes, of course!" to both copies. It doesn't matter that there was an interruption in the stream of consciousness, any more than it mattered that your stream of consciousness was interrupted by anesthesia -- you still came back as you, and you know it because of how your memories and internal dialogue proceeded from that point forward.
If the duplication was done, and one of the copies was killed without ever being returned to consciousness, the other copy would never be the wiser -- you'd just think you were put under then brought back.
We're just not used to our classical worldline branching, so it seems bloody weird to think about.
And, umm, at one point there was another possible me very happy to receive a minigrant for a new snowboard, but I'll never get to ride it since I never applied.
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Garrett,
I agree that it's perfectly clear that both 'Anthony's will think they are 'me'. The question is: imagine the machine is sitting there in front of you. Knowing that the next moment there will be exactly two 'Garret's, one of which is suffering an agonizing death, would you step in or not?
If yes, how do you explain your decision to the really angry (and horribly dying) Garrett?
If not, how could you believe in the Many Worlds Interpretation? (To make this more poignant, you could get up a quantum-gun that, when you pull the trigger, fires with P=0.00000000001, and aim it at your foot. Most people after seeing this gun go 'click' a many, many times would be willing to 'shoot' it at their foot for, say $50. But if you believe MWI, but would *not* step in the described machine, I think you'd be crazy to do this).
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I would have to make a decision on the desirability of the experiences of my future selves -- even though these experiences would not be shared amongst the different copies. If one of the copies is just to be snuffed out, or never revived, it's an easy decision -- since one never experiences being dead. My worldline would have a tiny dead-end stub, but otherwise continue with a happy life,
(:-D
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$
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(:-)
If one of the me's was to be painfully tortured, I would have to weigh the negative value of that experience against the reward and decide. I'm a pretty happy guy, so it would have to be a big reward... here you can see a future me with a double chin (and, of course, still bald),
(:-))
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$ (:-(
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(:-)
Even though the future copies do all exist, independently, the rational choice should still be based on a weighing of cost vs benefit -- effectively the same as when one uses likelihoods of possibilities to make a decision.
This same decision process would apply to being paid to maybe shoot myself in the foot.
There is a difference between the classical copying and quantum splitting though: In the classical copying, I'd have to take into account the guilt felt by the surviving me, who watched the other me suffer while telling him it was worth it (thus the double chin, brought on by guilt induced binges). In the quantum splitting, it's best not to worry about your other, effectively nonexistent selves -- since they can't effect you (unless you're very small) -- and just role the dice.
| | this post has been edited by the author since its original submission |
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Ah, I just thought of an amusing way to think about copying yourself:
Pretend you're an Amoeba.
Pity they're not talking... no, wait, that's probably a good thing.
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Garrett,
Ahh, but do the feelings of your 'tortured' version count as much as the non-tortured one? Probably you would say yes, and this is the whole point: in MWI, we are supposed to make decisions (such as whether to do a measurement that could, with tiny probability, cause our painful death) on the basis of the quantum probabilities. But tell that to the copy who is asphyxiating. :-o
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(btw, it was another me who made the amoeba comment)
Yes, the tortured version counts as much, but should be weighted by its probability. Drowning is a terrible thing to experience (I've come close) so the motive would have to be very strong -- a girl would need to be involved (otherwise it's hard to be that crazy).
In QM, and in classical Bayesian probability, our other versions don't effect us -- so, effectively, they don't exist and we shouldn't feel guilty about them.
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Garrett,
Sorry, the question was in the context of the teleporter machine, or MWI, in which both copies exist for certain.
I agree that in a Copenhagenesque view, the probabilities of one thing happen versus the other matter very much.
A
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Sure, we just have to think like amoeba's: our current self will be experiencing both outcomes, separately. There is a small difference though: In the teleporter case, we have to live with the fact that our other version died in our branch of reality; but in the MWI case our other version died in a reality separate from ours. This means our decision in the MWI case should be the same as for any classical gamble -- since the other selves effectively won't exist for each other. In the teleporter case, we'll be involved in a murder.
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(Heh, I had posted two replies. But one of them just vanished. I guess I feel OK with that.)
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"At about 1 AM GMT on April 20, 2007, the Universe split into at least 32,768 nearly-identical copies. How? And did it really?"
Well, if we are going to treat the observer not as external but internal to the multiverse and subject to the laws of quantum mechanics (leading to the copies of the same observer), then we must also describe the decisions the observer makes also using these laws.
So, it should be clear that the split into the "32,768 nearly-identical copies" was not really caused by a choice someone made that had it not been made would not have resulted in the universe splitting, because Anthony himself is part of the multiverse and there exists an Anthony who decides to have a lottery and there exists an Anthony who makes a different choice. These different Anthonies exist a priori with some amplitudes in the multiverse and nothing can "change" that fact.
So, the spittings are just artefacts of looking at special sectors of the multiverse and then comparing that sector with a another sector you obtain by applying the time evolution operator. If you apply the time evolution operator on the entire multiverse you would probably see no splittings at all because the entire multiverse could well be an exact eigenstate of the Hamiltonian.
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Garrett:
Yes, those superpositions collapsed. (or did they just decohere....)
Count Iblis:
I agree that if we assume that the universe is in a definite quantum state evolved by some fixed Hamiltonian, then there is no place for 'branching' of the cosmic wavefunction, but rather an evolution that describes one 'Anthony' and then, later, many. But as far as I (Anthony) am concerned, this certainly is a 'branching.' So whether the 'world splits' depends on how self-centered you are...
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I would not hesitate to enter the "transporter", even without prior knowledge of the favourable probability constraint.
I would rely on the fact and knowledge based on current "experience", I would know that I would STILL remember my/the past, wheras my copy would have a 50/50 chance of remembering the/it's future!
I would retain a "current" past history, I am,thefore I am?
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I would not hesitate to enter the "transporter", even without prior knowledge of the favourable probability constraint.
I would rely on the fact and knowledge based on current "experience", I would know that I would STILL remember my/the past, wheras my copy would have a 50/50 chance of remembering the/it's future!
I would retain a "current" past history, I am,thefore I am?
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WOW! either I hit the hidden variable "re-copy" button, or the transporter "me" is falsifying my previous post!
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There is another constraint, which may be intepreted thus, I have a proven history, before copies were made and placed into the transporter. The "copies" history are dependant upon the transporter, they have no history prior to their creation?
Each destination has to be contained within the copies "known" historical existence, there was no point of existence prior to their creation?..so each prefered path (destiny route), is pre-chosen, and both are in a virtual future.
I would not experience any of the "destiny" outcomes, the fact is that the Transporter acts as a cut-off point for both copies that enter?
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