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dankomed says:

Dear Cathy Cramer, (and prof. J. G. Cramer)

I am surprised to have seen your setup today (24 March 2008), possibly a month after I have submitted my own article entitled "Quantum complementarity in a pseudo delayed choice double lens setup". Indeed the experiment proposed by me is possibly what I see on the figure above - I have theoretically invented EPR photon pair and 2 lenses - one measuring the signal photon at the focal plane always, while the second lens measuring the idler photon at the image plane. Then if a lens always provides which way information at the image plane, then one should expect the effect described by Kim et al. 1999 in their paper:
Kim YH, Yu R, Kulik SP, Shih YH, Scully MO (2000) A delayed choice quantum eraser. Physical Review Letters 84: 1-5. arxiv.org/abs/quant-ph/9903047

that is: one should expect if the image plane of the lens 2 records the which way information of the idler photon, then due to entanglement the interference at the focal plane of the signal photon will be destroyed .

However this is going to severely fail, because in coherent setup lens does not provide which way information. Therefore I have proposed this experimental proof as "direct evidence" that lens at image plane does not measure which way information. The latter claim is mathematically proved rigorously by me, prof. Tabish Qureshi and Daniel Reitzner, and my debate with W.G. Unruh is available at my web:
www.sciuni.com/physics.html

Well, I have seen Cathy Cramer to use the WRONG argument of linearity of QM, etc., which was used quite dully against me by Unruh. However Cathy as well as Unruh make overlook, which is explained in my last paper:
Georgiev DD. Quantum operator approach to Unruh's and Afshar's setups. The Icfai University Journal of Physics 2008; 1(1): 7-33.
www.sciuni.com/database/icfai_j.pdf

Briefly, in order to have bifurcation of paths you need normalization! This means you multiply by 0.7 (1/sqrt(2)), e.g. imagine a beamsplitter. Now if you want to overlap again already bifurcated paths, you need second double bifurcation so you get 4 pieces of 0.7x0.7 = 0.5 beams. Now if all these are orthogonal you cannot overlap them, so you cannot interfere them. In order to interfere them due to conservation of energy you can positively interfere 2 of the beams ONLY AND ONLY IF the rest 2 beams destructively interfere and annihilate each other.

SO -- bifurcations DESTROY the linearity logic. The argument by Cramer and Unruh raised in 2004 is BOGUS.

In case of overlaps there is always (!) destructive interference and so amplitudes disappear and always some paths get ZEROED amplitudes annihilate! (this is because there is also positive interference somewhere else, and need for conservation of energy)
and the other thing is that at the time of bifurcations an amplitude is "gained" because 0.7 + 0.7 = 1.4. All this is linked with the normalization requirement and the Born's rule

Therefore it is very tricky to decide which path is annihilated, and which path is contributing amplitude to be "squared" by Born's rule.

As a consequence the linearity argument is mathematically inconsistent. One cannot mathematically play with zeroes (in the way it is dangerous to play with infinities). In my reply to Unruh I have replied "if you multiply by zero, you cannot recover the lost path" [see the operator approach, it depends how you look the matrix, it may be zero operator, or operator acting on vector in its own kernel returning zero].

This is the simplest way to explain the severe overlook by prof. Cramer. This message is addressed to physicist prof. Cramer, and is NOT to any of the layman bloggers. I do not intend to argue with anyone of the readers, nor I intend to post spam.

Indeed I am highly excited because I thought that what I have proposed in article to be published soon in Optics journal, and also in my web, is going to be checked experimentally. I am 100% sure that prof. Cramer will fail, due to the mathematical proof that image plane of a lens does not provide which way information in coherent setups. This is also the explanation of Afshar's error - even if there is no wire grid, or any obstacle on photon path in Afshar's setup, there is NO which way information to start with.

Kind Regards,

Danko Georgiev,
Kanazawa University
Posted 21 months ago. ( permalink )