Quantum P and GR

[sjastro]

Originally Posted by CraigS

Yep .. Steven;

I was waiting for your advice on this .. just below equation (1) there is some dialogue about how it is supposed to come about. Unfortunately, it kind of just states that the 'expectation value' can be complex number and because of this, the weak value 'could be used to indicate both real and imaginary parts of the wavefunction'. (No further explanation seems to be given).

I wasn't too sure about my interpretations of it all, but it seems that you may see it as being a bit deficient, also.

Not to worry … I'll bet there's a whole textbook on all this somewhere and I'll bet the unintuitive part is explained in the derivations of equations (1) and (2).

Thanks for reading up on it though.

Just the measurement apparatus is hard to understand …let alone how it relates to the wavefunction !

Thanks for access to the paper too, Carl.

Cheers

Equations (1) and (2) is textbook quantum mechanics.

The problem lies in this statement.

Consider the measurement of an arbitrary variable A.....

Followed a few lines later by

......Unlike the standard expectation value <A>, the weak value <A>w can be a complex number.

This implies that the expectation value of <A> is real.
For this condition to be true A needs to be a Hermitian operator not an arbitrary variable A as stated in the first quote.
While this may seem trivial if you made this error in a maths exam on quantum mechanics, would result in certain failure.

Regards

Steven

[CraigS]

This 'Lundeen' guy has written several papers (6 since 2005) on weak measurement and double slits. He's also specialised on sorting out this 'Hardy's Paradox'.

I think the explanation for all this must be somewhere in the other papers ..
(if one has the energy to wade thru 'em all).

Cheers

[renormalised (Carl)]

Just checked....plenty of articles but none of them are too specifically related to this article (direct quantum wavefunction measurement). At least, those I saw listed there and not using the methods from this article.

Lundeen has 27 papers listed at arXiv.org.

[renormalised (Carl)]

Originally Posted by CraigS

This 'Lundeen' guy has written several papers (6 since 2005) on weak measurement and double slits. He's also specialised on sorting out this 'Hardy's Paradox'.

I think the explanation for all this must be somewhere in the other papers ..
(if one has the energy to wade thru 'em all).

Cheers

It probably is, seeing that these earlier papers probably lead upto this one. At least some of the theory would've been covered in the earlier articles.