You are offered a deal in which you are asked to flip a coin ten times. If any one of the flips comes up tails, you are swiftly and painlessly killed. If it comes up heads ten times in a row, you are given a banana. Do you take the deal?
For the purposes of this thought experiment, we may assume it is a perfectly fair coin, and that you like bananas, although not any more so than would generally be considered healthy. We may also assume for simplicity that your life or death is of absolutely no consequence to anyone but yourself: you live in secret on a deserted island, isolated from contact with the outside world, where you have everything you need other than bananas. We may finally assume that we know for certainty that there is no afterlife; upon death, you simply cease to exist in any form. So, there is an approximately 99.9% chance that you will be dead, which by hypothesis implies that you will feel no regrets or feelings of disappointment. And if you survive, you get a banana. What do you think?
Now change the experiment a little. Instead of flipping a coin, you measure the x-component of the spin of an electron that has been prepared in an eigenstate of the y-component of the spin; according to the rules of quantum mechanics, there is an even chance that you will measure the x-component of the spin to be up or down. You do this ten times, with ten different electrons, and are offered the same wager as before, with spin-up playing the role of “heads” for the coin. The only difference is that, instead of a classical probability, we are dealing with branching/collapsing wavefunctions. I.e., if you believe in something like the many-worlds interpretation of quantum mechanics, there will always be a branch of the wavefunction of the universe in which you continue to exist and now have a banana. Do you take the deal?
I suppose the question is moot in the second case since there will inevitably be a universe in which you take the deal and a universe in which you don’t. 🙂
And thus, there is a probability there-in, that the small portion of the wavefunction that has been “pinched” into another Universe, has to be parametrically Time-stamped?
You had better hope that the other Universe has the same number of Proton/Neutron ratio’s, and the ‘other’ Universe is in Expansion, expanding at the same rate?
If for instance you happen upon another Universe that is ‘out-of-phase’, then the total number of photons present, may fall WAY below the low-energy limit of our early Universe, and that of course will mean big trouble?
How can you fit a standard size banana from ‘this’ Universe, into a Universe that is probably no larger than a standard size current Proton?
The probability function is matter determined?..the branching off (many worldline collapse function?)surely is a stastistical function of ‘our’ unique Universe?
Not to mention that there is a more than likelyhood that the branched off Universe would contain no Electrons that are Orbiting stable Atoms?
I’d eat the banana before I travelled!..rather that take risky !chance”
Since in 999 universes out of 1000 branches of the multiverse, I’d be dead, it probably isn’t worth it.
In both cases, absolutely. Nothing to live or die for in the first, except maybe a banana, and in the second case a banana-in-hand is guaranteed.
Actually, sounds like one hell of a deal.
Anonymous is on to something.
I suppose I’d have to believe in the many-worlds interpretation really, really strongly.
I read a paper quite some time ago that proposed an experiment like this as a way to test the “many-worlds interpretation” of quantum mechanics. Does anyone remember this particular paper?
To make it a stronger test, of course, we should decrease the survival probability substantially — if you perform a quantum Russian Roulette experiment with a survival probability of 10^10 or so, and you survive, then you at least will have a pretty strong conviction of the truth of the MWI.
Of course, if you have a colleague of yours perform the experiment, it’s unlikely to prove anything to *you*, though you would would do well to get him to name you as a beneficiary on a life insurance policy…
We can have even more fun with this: suppose you perform this experiment without telling anyone that you are going to do so. After you survive, you inform the world that the MWI is correct, as your survival demonstrates with high probability. A skeptical world asks you to repeat the experiment, and when you do so, well, in most branches of the wavefunction, you are dead, and the skeptical world shakes its head and goes back to whatever else it was doing. But in *your* branch of the wavefunction, you survive again — so what can you now claim you have demonstrated to the skeptical world?
If you carry this logic just a little further, the MWI seems to imply that at least to the extent that the random vicissitudes of life are governed by quantum processes, each of us will eventually only experience a branch of the wavefunction in which we live as close to forever as is quantum-mechanically possible. If we think of long life as good, then the MWI says that we really *do* live in the best of all possible worlds…
By the way, the paper I probably had in mind is The Interpretation of Quantum Mechanics: Many Worlds or Many Words?, by Max Tegmark.
Here is Tegmark’s website with related articles…
How does the MWI explain that we fall asleep each night? Wouldn’t there be a universe branching off in which we never lose our consciousness, and this is the one we should be “trapped” in?
invcit —
If you go without sleep long enough, you die. If you are awake and observing now, then the only past histories possible are those in which you got enough sleep to remain alive, and the *typical* past histories are those in which you got a *typical* amount of sleep. It’s only the cases in which you go to sleep *and never wake up* that you can exclude from your calculations, in this notion of the MWI.
First case: No, I don’t take the chance. I still have some stuff I’d like to do, and though bananas are ok, I’m not bananas about them.
Second case: No, I don’t take the chance. For one, observing the spin will fundamentally change me. The notion of multiple states existing post-observation doesn’t make sense to me (but perhaps that reflects more on me than quantum mechanics). And regardless, I’m not even sure quantum mechanics explains such a momentous decision accurately! And I am SURE that quantum mechanics doesn’t explain some things. Say, gravity.
I take that back. I’m not sure quantum mechanics doesn’t explain gravity. But somebody might be.
But seriously, folks – let’s distinguish between the ‘You’ that exists in the Youniverse and the many alternate ‘yous'(youse guys?) that exist elsewhere in the multiverse. If all these multiverse yous are meaningfully associated with You why don’t You share the experiences of these yous? Why would the many-world yous share Your experience if You don’t share theirs? When You die you simply appropriate or override the continuity of an alternate you? Which particular alternate you’s experience would You appropriate or override?
The idea is that at every moment (every moment is an ‘event) You branch off into a zillion new versions of Yourself. Why would You follow one of an infinite selection of continuities of experience up to the point of your death then suddenly switch to an alternate continuity? Why do we assume that dying is, as an experience, different in essence from any other experience? If You are terminated in the Youniverse, the splitting-from-You process would end, although previously generated yous might carry on. Even if, at the instant of Your death there was a final splitting, the spilttee yous would be no more associated with You than any previous yous were.
In short, why would the existence of alternate yous be of any relevance in terms of Your own continuity given that they are independent of and inaccessible to You?
I wouldn’t take the deal.
Alex: I’m not sure I buy your explanation. It sounds more like consistent histories than many worlds. I can’t quite put my finger on it, but there is *something* fishy about discontinuity of consciousness combined with many worlds.
This thought experiment, which Max posed some time ago as noted above, was one that, more than anything, made me think the many-worlds interpretation is just nuts. You can make the experiment quite precise (i.e. by a nuclear bomb connected to a geiger counter, so it is painless and instantaneous). The notion that you would repeatedly ‘pull the trigger’ and surive struck me as completely absurd. Worse yet, suppose I just aim a gun at my head. In some universe, no matter how improbable, *something* will prevent me from dying (e.g., the bullet will just tunnel to the other side of my head, without harm.) Now, there are many more possibilities where I am horribly maimed but do not die, so this is inadvisable, but I think it is the logical conclusion of the ‘quantum suicide’ train of thought. I think we can all agree that this sort of twisted immortality is disturbing.
But by strange coincidence I was just thinking of it today (before I saw this blog), and realized that it may also be argued to apply an infinite universe: in an infinite universe there are infinitely many copies of exactly the same surroundings you see now. Suppose we take a finite region around us, and assume we are in some definite quantum state out of the possible set of states of that region. Then there are infinitely many other such regions in that same quantum state. Now suppose you take the bet, but in the copenhagen interpretation. The wave function in each of the copies in the ensemble collapses into either the ‘alive’ or ‘dead’ state. Only the alive ones will have you continue to exist, so you will experience one of those. Does anyone see any essential difference between this and the ‘many worlds’ version of quantum suicide? I don’t. I suppose I must then either reject an infinite universe (which I do otherwise believe in), or accept that the end of my life will be a sequence of horrendous but life-saving miracles, or accept that my previous dismissal of many-worlds is premature because something is wrong with the basic argument. I’m not fond of any of the three options. Can anyone help?
My version of the thought experiment (which I first heard from philosophers) was secretly a pro-MWI argument. Yes, most people would not take the bet in the quantum case, even though there is some amplitude that they would live forever, and this is supposed to demonstrate that nobody really believes in the many-worlds interpretation. But most people wouldn’t take the bet in the classical case, either, and I honestly don’t see the difference. In either case there are two possibilities: you don’t exist, or you have a banana. Whether those possibilities are classical alternatives or branches of the wavefunction doesn’t seem especially relevant to me. So I conclude that it’s just not a very probative thought experiment.
I think that the way we act right now includes a reluctance to be dead in the future, even if we are absolutely sure that once we’re dead we won’t be regretting anything. The fact that the only surviving versions of me, either in branches of the wavefunctions or far away in an infinite universe, will be doing fine just doesn’t change my feelings very much.
I don’t need a thought experiment to prove that there are multiple universes branching off a possible decision. I have driven in the streets of Boston. Every intersection is a demonstration of chaotic universe branching, where my car (the Electron) got through the intersection unharmed.
I think the crux of the question is whether you would be more likely to take the bet in the Everett vs. the Copenhagen interpretation. I would be. Imagine the experiment with a star-trek transporter instead of QM:
First, the transporter just teleports you across the room by disassembling your constituents and reassembling them across the room. Fine, you feel safe (Depending, perhaps, on your philosophical predilictions).
Next, set the transporter to make *two* copies on the left and right side of the room. I think there was an episode like this. Now you feel doubly safe getting in, but might be confused as to which side of the room ‘you’ will end up on. Of course both of you will claim to be ‘you’. But nevermind this.
Now, make it simple again by, at random, turning off transport to the left or right side. Now you are back to case 1, but you randomly reassemble on one side or the other. Again you feel no fear.
Penultimately, add a third option, so that half of the time the transporter will make both copies rather than one or the other. As per previous logic, you should feel even safer.
Finally, suppose 50% of the time the ‘reassemble’ sequence is never activated at all, and 50% of the time it is activated in the left side. Would you feel safe going through *this* transporter 10 times?
the last two seem to me to be just analogous to the Everett and Copenhagen interpretations.
My serious answer would be no because no matter how much I support MWI there’s always a significant possibility I’m completely wrong about it. 🙂
An interesting question for those people who believe this experiment would prove MW is probably correct (and I might well be one of them) would be whether they think it implies that it is impossible for a conscious entity to die. I think it’s _just_ about possible to have one without the other but I’d have to think about it some more.
Sean: Just in case you read my entry at #12 and give a hoot.. I’m not arguing against the multiverse – just against the common notion that the multiverse is an argument for immortality. I like the multiverse model; it’s elegant and no more anti-intuitive than the notion of an infinite classical universe or of a finite classical universe existing nowhere in the middle of nothingness. I’m neither a physicist nor a mathematician and so my understanding of these matters is much less sophisticated than that of most of the participants in this blog.. but, whatever it’s worth, I appreciate your ability to explian QM to the layman and am happy to know that there’s a name physicist out there who has the b#**s to get philosophical from time to time.
I think that Tegmark made a mistake when he claimed that according to the MWI you should always survive such ”quantum suicide experiments”. In principle, one has to deal with a static wavefunction. I.e. even though the wave function evolves according to the Schrödinger equation, the ”wave function of the entire multiverse” does not evolve in time. In fact, there is no meaningful notion of a time parameter across the entire multiverse.
So, in principle, you have to deal with an ”a-priori” probability distribution over all possible observer states. The correct way to calculate probabilities of experimental outcomes is to consider the a-priori probability of the observer finding some experimental outcome.
If the probability of dying during the experiment can be ignored, then the probabilities are conserved. I.e., the sum of probabilities of all possible outcomes equals the probability of doing the experiment. In this case one can define conditional probabilities in a meaningful way as ratios of the two a-priory probabilities after and before the experiment.
Tegmark’s mistake was to assume that the conditional probability is fundamental and that it can be used even in case the experimentor dies depending on the experimental outcome (according to him ”dead states” don’t count and the conditional probabilites had to be renormalized, so that you are alive after the suicide experiment with probability 1).
Instead, the experimentor should assume that at any particular moment of his life he is sampled from a (static) set of states. The probability distribution is fixed by the laws of physics plus structure of the multiverse. The reason why we experience a flow of time is simply because any generic observer state has a memory of being in states related to him by a time translation operations. So, all the observer states are equally real; there is no need to postulate a ”time pointer” making some states real and then moving on to time translated ”successor states”.
“Do you take the deal?”
No.
This idea is similar to one floated by computer scientists called “anthropic computing”. For instance, here’s how it would work for the problem 3SAT, which is NP-complete: given a formula φ, use a quantum procedure like the above to guess a random assignment x. If x does not satisfy φ, kill yourself. If you believe in the many worlds interpertation, then there’s guaranteed to be a universe in which you’re still alive and looking at the right solution, meaning you’ve solved this instance of φ in polynomial time.
Turns out this is idea has been put to some practical use in the theory of computing. More details are in an interesting survey by Scott Aaronson called “NP-complete Problems and Physical Reality”.
Hi Sean!
Does this imply that “making the decision to take the deal” suddenly splits the universe up into multiple possibilities? I’d rather think that if the multiverse exists, the universe is going to split whether or not I am going to take the deal or not. Thus in the deal you lay out, there will be versions of me that take the bet and versions that do not.
I thought this is funny though, since it seems like a way to fit a deteministic picture into a quantum mechanical setting.
If you believe in many worlds doesn’t that then mean that in some worlds you will have taken the chance and in others you didn’t? Therefore, you will have taken the chance.
“Turns out this is idea has been put to some practical use in the theory of computing.”
It’s also a practical method of population reduction.
Joking aside, the abstract to the paper the commenter mentions is at
http://arxiv.org/abs/quant-ph/0502072