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bio website aquantumoftheory.wordpress.co…
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visits member for 2 years, 3 months
seen Dec 14 '12 at 13:26

I'm a theoretical physicist, working on the foundations of quantum theory, non commutative geometry and information theory.


Sep
24
awarded  Autobiographer
Sep
18
awarded  Yearling
Feb
2
awarded  Nice Answer
Sep
18
awarded  Yearling
Dec
4
comment Conjugate Variables, Noether's Theorem and QM
I never claimed anything else? You must have misunderstood my argument. I never relate conservation to commutativity, instead I relate non-commutativity to unitary representations of translations. The part about conservation is solely about translations being generated by their conjugate momenta. Two different things.
Dec
4
comment Conjugate Variables, Noether's Theorem and QM
What do you mean, "were they ever commutative?"?. The observable algebra on the classical phase space IS commutative. My point is merely that you point to another question, namely why quantization works like that, which is in no way obvious.
Dec
4
comment Conjugate Variables, Noether's Theorem and QM
This leaves the question why quantization has to make conjugate pairs non-commutative. If you just look at the geometric meaning of conjugate pairs you can avoid that question.
Dec
4
answered Conjugate Variables, Noether's Theorem and QM
Nov
26
awarded  Caucus
Nov
26
comment Born rule and unitary evolution
So you know an application of the Born rule outside of the context of quantum measurement?
Nov
26
comment Born rule and unitary evolution
That's not what you wrote in your answer however
Nov
26
comment Born rule and unitary evolution
Quantum meausrements are the building blocks for more complex meauserements. Nobody would call a derived result like the halflife of an atom a quantum measurement. Also, this does not even fit a POVM scheme, so you're disagreeing with yourself. The OP clearly talked about quantum measurements in a way that is really hard to misunderstand. Why you're trying to take that to somewhere entirely unrelated is beyond me.
Nov
26
comment Born rule and unitary evolution
We're talking about quantum measurement here, which both of your example are not. So of course you cannot express them in terms of the Born rule. And that's totally missing the point.
Nov
26
comment Born rule and unitary evolution
That statement would require an exact definition of what a measurement is and how it is applied to a subsystem. Also, it makes no practical difference. If you know how a Born style measurement works you understand how a POVM works.
Nov
26
comment Born rule and unitary evolution
You are arguing that the same input state gives different output states, which is not unitary. That argument is false because you don't know that the input state is different for different outcomes, simply because you don't know the state of the unknown environment, by definition, that leads to the different outcomes. I'm not saying that your conclusion is wrong, but your argument certainly is.
Nov
25
comment Born rule and unitary evolution
Also, in order to see if your plate has been affected by light you have to look at it. So at the very latest then you will subject it to massive interaction with an unknown environment
Nov
25
comment Born rule and unitary evolution
The environment always plays a role in quantum theory. You cannot remove the quantum fields from space, no matter how perfect your vacuum is. There will always be interaction on some level, and ignoring that is surely not helpful for understanding the properties of quantum systems. You seem to be thinking is more or less classical terms with your photographic plate example.
Nov
25
comment Born rule and unitary evolution
Even in your perfect vacuum you always have an interacting environment. And of course the environment may not be needed for the resolution of the measurement problem, but it might possibly be necessary, and so you cannot simply exclude it. It is at least a plausible source for randomness due to our lack of information about its state.
Nov
25
answered Born rule and unitary evolution
Nov
24
comment Born rule and unitary evolution
POVMs can be regarded as Born type measurements in a larger space, so you're back where you started.