Slide from this talk.
Survey questions:
1) Could you be Gork the robot? (Do you split into different branches after observing the outcome of, e.g., a Stern-Gerlach measurement?)
2) If not, why? e.g,
I have a soul and Gork doesn't
Decoherence solved all that! See previous post.
I don't believe that quantum computers will work as designed, e.g., sufficiently large algorithms or subsystems will lead to real (truly irreversible) collapse. Macroscopic superpositions larger than whatever was done in the lab last week are impossible.
QM is only an algorithm for computing probabilities -- there is no reality to the quantum state or wavefunction or description of what is happening inside a quantum computer.
Stop bothering me -- I only care about real stuff like the Higgs mass / SUSY-breaking scale / string Landscape / mechanism for high-Tc / LIBOR spread / how to generate alpha.
6 comments:
I'm pretty sure that even if Gork does collapse the wave equation (from his point of view), we still get the right answer.
Reminds me of an experiment where they used an electron to observe a photon, but we could decide after the fact whether it had been "observing" or part of a larger entangled system.
Somehow, everything works out in the end.
Yes, if Gork only causes *apparent* (to him) collapse, but actually splits into multiple branches (which are necessary for the quantum algorithm), then the computation proceeds as desired.
But, if Gork causes *fundamental* collapse (i.e., von Neumann projection, which is not unitary) then the QC does not exhibit unitary evolution and therefore does not execute the algortihm properly.
very crudely,
apparent collapse = many worlds
nonunitary collapse = Copenhagen
Hi Steve,
Well I definitely think I'm no different from Gork the robot.
I keep thinking that I must not be understanding something because I find that many worlds is the only theory that makes sense. To me, many worlds is no weirder than QM. Both are out of the sphere of our classical intuition.
I want to pin you down more on those pesky maverick worlds. Are you not happy with the claim that the probability of being in one is very low so you're hoping that there is a mechanism that makes them zero?
I guess I'm just a fatalist (or biologist) at heart because to me high probability is good enough.
cheers,
cc
Hi Carson,
The probability of being on a maverick branch is not low. There are many more maverick branches than non-maverick branches (overwhelmingly so). If you take a frequentist point of view, we should be on a maverick branch.
The only justification we can give for being on a non-M branch is that the M branches have small norm. But equating norm^2 = probability is simply the Born rule (which we were trying to *deduce* from many worlds), so this is circular reasoning. (But understandable, since when we first learn QM we are immediately told to equate norm^2 and probability.)
In many worlds there is no rule which says which branch *you* will end up in at a split. In particular, there is no rule that says that the branch with the largest amplitude is more likely than one with smaller amplitude. This result is to be *derived*. In the limit N -> infinity the maverick branches have exactly zero norm, so in the original Everett argument he just throws them out. But this is a technicality and furthermore N is probably not infinity.
I hope that helps! (You might have a look at the slides for more discussion...)
OK thanks. I finally get it. I've been conflating (L2 norm)^2 with probability but that is not a given a priori.
So in your slides, you argued that the small norm states are undetectable to the uncertainty in our measurements. Is that a self-consistent way for justifying the discreteness of space-time?
cc
Carson,
Yes, if you can eliminate small norm states you can derive the Born rule from MW.
Everett (and subsequent authors) emphasized N goes to infinity and tossing out exactly zero norm states.
If there is an inherent "fuzziness" in quantum state space (Hilbert space), we may be able to throw out the small norm states at finite N, which is what I proposed with Buniy and Zee. I wouldn't necessarily use this to argue for discreteness of spacetime, but the implication seems to go the other way. (Discrete spacetime means a limit to how well you can differentiate two different quantum states, which might indicate the fuzziness we want.)
BTW, this whole thing is tough to explain/understand because we are all so used to equating norm^2 = probability!
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