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## Question on the "probabilistic" nature of QM

 Quote by Ken G The reason it can't be probabilistic is that probabilistic theories are, almost by definition, not rock-bottom theories (probabilities reflect some process or information that is omitted on purpose, and probabilities are generated as placekeepers for what is omitted-- that's just what they are whenever we understand what we are actually doing).
I wish I could up-vote. This is precisely why I am disturbed by a probabilistic end. To me it means there is a black curtain. Some might say then "your assuming there is something going on behind the curtain, and that's hidden variables". I say "no", there doesn't even have to be something deterministic going on behind the curtain, but there is a curtain nonetheless, and when physics is revealed it is always random. To be told that all we will ever get to see is what the curtain reveals is disturbing.

 Quote by jfy4 To me it means there is a black curtain.
I must say I can't follow that one. To me probabilities are simply the result of stuff like Gleason's Theorem which shows determinism is not compatible with the definition of an observable. There are outs but to me they are ugly such as contextuality - of course what is ugly is in the eye of the beholder.

And observables to me are very intuitive since they are the most reasonable way to ensure basis invariance. Suppose there is a system and observational apparatus with n outcomes yi. Write them out as a vector sum yi |bi>. Problem is the yi are not invariant to a change in basis and since that is an entirely arbitrary man made thing it should be expressed in such a way as to be invariant. By changing the |bi> to |bi><bi| we have sum yi |bi><bi| which is a Hermitian operator whose eigenvalues are the possible outcomes of the measurement and basis invariant.

Thanks
Bill

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 Quote by Zmunkz You've outlined an interesting way of looking at this. Could you possibly elaborate on the above quotation? I'm trying to understand why by definition probabilistic theories cannot be foundational. I can see in the macro sense (something like flipping a coin for instance) probabilities are a stand-ins for actual non-probabilistic phenomenon... but I can't quite convince myself this analogy carries to everything.
It's not so much that I'm claiming it has to be true for everything, rather, I'm saying it is true every time we understand why our theory is probabilistic. So we can classify all our probabilistic theories into two bins-- one includes all the ones that we understand why a probabilistic theory works, and the other includes all the ones we don't understand. In that first bin, in every case the probabilistic theory works because it is a stand-in for all the processes the theory is not explicitly treating (flipping coins, shuffling cards, all of statistical mechanics and thermodynamics, etc.). In the second bin is just one thing: quantum mechanics.

So now we face two choices-- either there really are two such bins, and one of them holds "the rock bottom description", and all the rest hold every other type of probability description we've ever seen, or else there are not two such fundamentally different bins, there is just what we understand and what we do not. I can't say the latter interpretation is unequivocably superior, but when framed in these terms, I think it places that interpretation into a kind of proper perspective.
 This is the classic realist vs. instrumentalist debate. Looks like you fall on the instrumentalist side -- I am not sure if I can meet you there, although you make the case well.
Yes, I agree this is well-worn territory. In a sense I am siding with Einstein that "the Old One does not roll dice," but I am differing from him in concluding, therefore, that straightforward realism is the only alternative. In fact, what most people call realism, I call unrealism-- it requires a dose of denial to hold that reality uniformly conforms to our macroscopic impressions of it, when the microscopic evidence is quite clear that it does not. So if there are no dice to roll, and if there is also no precise reality where everything has a position and a momentum and the future is entirely determined by the past, then what is left? What is left is the actual nature of reality. That's realism, if you ask me.

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 Quote by jfy4 To me it means there is a black curtain. Some might say then "your assuming there is something going on behind the curtain, and that's hidden variables". I say "no", there doesn't even have to be something deterministic going on behind the curtain, but there is a curtain nonetheless, and when physics is revealed it is always random. To be told that all we will ever get to see is what the curtain reveals is disturbing.
I agree with you about the curtain, but I find the implications less disturbing. It reminds me of the way Hoyle found the Big Bang to be disturbing-- he could not fathom an origin to the universe, anything but a steady state was disturbing. But I always wondered, why wasn't a steady state disturbing too, because of how it invokes a concept of a "forever" of events? We invoke "forever" to avoid a "start", or we invoke a "start" to avoid a "forever", yet which is less disturbing? I ask, why are we disturbed by mystery?

Yes, the goal of science is to penetrate the shroud of mystery, but it's not to remove the shroud, because behind one shroud of mystery is always another. We are not trying to pull down that "curtain" you speak of, because there will always be a curtain, and there is supposed to be a curtain-- our goal is to get past as many curtains as we can. That may sound disturbing, but isn't it more disturbing to imagine an end to the curtains?

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 Quote by bhobba I must say I can't follow that one. To me probabilities are simply the result of stuff like Gleason's Theorem which shows determinism is not compatible with the definition of an observable.
Gleason's theorem is a theorem about the theories of physics that can match observations, yet the "curtain" is an image about the connection between theories and reality. I think that is what you are not following there-- you are not distinguishing our theories from the way things "really work." I realize this is because of your rationalistic bent, you imagine that things really work according to some theory, and our goal is to either find that theory, or at least get as close as we can. That's a fine choice to make, rationalists abound who make that choice, and some get Nobel prizes pursuing it. But it's why you won't understand non-rationalists who don't think the world actually follows theories, because theories are in our brains, and the world is not beholden to our brains, only our language about the world is. The world is doing something that closely resembles following theories, but every time we think we have the theory it follows, we discover not just that the theory has its domain of applicability, but much more: we discover that the ontological constructs of the theory are completely different in some better theory. Why would we imagine that will ever not be true?
 There are outs but to me they are ugly such as contextuality - of course what is ugly is in the eye of the beholder.
Contextuality is like determinism or probability, it is an aspect of a theory. We must never mistake the attributes of our theories for attributes of reality, or else we fall into the same trap that physicists have fallen for a half dozen times in the history of this science. When do we learn?
 And observables to me are very intuitive since they are the most reasonable way to ensure basis invariance. Suppose there is a system and observational apparatus with n outcomes yi. Write them out as a vector sum yi |bi>. Problem is the yi are not invariant to a change in basis and since that is an entirely arbitrary man made thing it should be expressed in such a way as to be invariant. By changing the |bi> to |bi>
I think that's a lovely way to explain why observables are associated with operators, which is probably the most important thing one needs to understand to "get" quantum mechanics (that and why the basis transformations need to allow complex inner products, and I know you have some nice insights into that issue as well). Also, we can agree that the job of a physics theory is to connect reality to the things we can observe about it. But none of this tells us why a description of reality that connects our observables with mathematical structures that predict those observables has to be what reality actually is. There is a weird kind of "sitting the fence" between objectivism and subjectivism that is required to hold that stance-- you invoke subjectivism when you build the theory from the need to give invariant observables (rather than from some more fundamental constraint on the quantum state itself), yet ally with objectivism when you promote the resulting quantum theory to the level of a description of reality. If you instead simply say it is a description of how we observe reality, hence how we interact with reality, hence how we give language to our interaction with reality, then you arrive finally at Bohr's insight that physics is what we can say about reality.

 the problem with the probability in quantum physics is that it actually is not "rock bottom". if it were it would not cause so many troubles. the problem is the equations of motion of any quantum theory provide a totally deterministic and even local theory. in a sense this part if very classic. but on top of that comes the probability (and non-local) part when one starts to measure. thus the probability arises somewhere in between of a deterministic theory sandwich at micro (QM equation of motion) and macro level (classical physics). because the theory lacks a well defined mechanism to provide when the collapse exactly happens it is very hard to tell the probability and the deterministic elements apart (you don't know when exactly the QM equations of motion become invalid and you have to apply the collapse instead).

 Quote by Ken G Gleason's theorem is a theorem about the theories of physics that can match observations, yet the "curtain" is an image about the connection between theories and reality. I think that is what you are not following there-- you are not distinguishing our theories from the way things "really work." I realize this is because of your rationalistic bent, you imagine that things really work according to some theory, and our goal is to either find that theory, or at least get as close as we can. That's a fine choice to make, rationalists abound who make that choice, and some get Nobel prizes pursuing it. But it's why you won't understand non-rationalists who don't think the world actually follows theories, because theories are in our brains, and the world is not beholden to our brains, only our language about the world is. The world is doing something that closely resembles following theories, but every time we think we have the theory it follows, we discover not just that the theory has its domain of applicability, but much more: we discover that the ontological constructs of the theory are completely different in some better theory. Why would we imagine that will ever not be true?
Hi Ken

I have said it before and I will say it again. You are a wonder. Thats exactly it and exactly why I don't get it.

Reading you is like reading Wittgenstein - at first you say no he can't be right but you think about it a bit more and you realize he has a point. You may still not agree with him (and I don't) but he has a point.

Thanks
Bill

 Recognitions: Gold Member Thanks bhobba, as you know my goal is not to change your mind, because your view is as valid as anyone else's, but merely to clarify the alternatives.

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 Quote by Ken G Yes, the goal of science is to penetrate the shroud of mystery, but it's not to remove the shroud, because behind one shroud of mystery is always another. We are not trying to pull down that "curtain" you speak of, because there will always be a curtain, and there is supposed to be a curtain-- our goal is to get past as many curtains as we can. That may sound disturbing, but isn't it more disturbing to imagine an end to the curtains?
I would love to pull down the curtain, only to find another, and if you got the opposite impression it wasn't my aim. But it's disturbing to me that this may be the last curtain.

 Recognitions: Gold Member Ah, I see, you are not worried that we will pull this curtain down to find none behind it, you are worried we'll never pull this one down. Who knows, maybe we will, but I think it might take a better theory about how our minds process sensory information. If there's a universal wave function, we won't understand it until we understand where our consciousness inhabits it, and if there's no universal wave function, then we still have to understand why our perceptions are as if there were invariant collapses in one.