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The visualisations of spin half described in this thread all involve tethered objects. One end rotates, the other is fixed.
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This not only explains spin half, but is also a mechanism for nonlicality ( contextuality).
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On 6 May 2022, at 02:38, Jay R. Yablon <yab...@alum.mit.edu> wrote:
Actually, it is only two pages. :-)
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Using to separate photon beams that are not physically connected, to do a Bell type experiment."Bell-type Polarization Experiment With Pairs Of Uncorrelated Optical Photons""Bell-type Polarization Experiment With Pairs Of Uncorrelated Optical Photon.We present a Bell-type polarization experiment using two independent sources of polarized optical photons, and detecting the temporal coincidence of pairs of uncorrelated photons which have never been entangled in the apparatus. Very simply, our measurements have tested the quantum-mechanical equivalent of the classical Malus’ law on an incoherent beam of polarized photons obtained from two separate and independent laser sources greatly reduced in intensities.The outcome of the experiment gives evidence of violation of the Bell-like inequalities."
On May 6, 2022, at 1:35 AM, Richard Gill <gill...@gmail.com> wrote:
I must say that I don’t like your notation. Why is there a script B as a non-argument to function script A? Maths notation has evolved to be very expressive and at the same time very compact; not wasting the reader’s brain-power by distracting it with the task of decoding superfluous symbols.
https://arxiv.org/abs/1312.6403
The triangle wave versus the cosine: How classical systems can optimally approximate EPR-B correlations
The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind consists of striking certainty relations: perfect correlation and perfect anti-correlation in certain settings. The second kind consists of a number of symmetries, in particular, invariance under rotation, as well as invariance under exchange of components, parity, or chirality. In this note, I investigate the class of correlation functions that can be generated by classical composite physical systems when we restrict attention to systems which reproduce the certainty relations exactly, and for which the rotational invariance of the correlation function is the manifestation of rotational invariance of the underlying classical physics. I call such correlation functions classical EPR-B correlations. It turns out that the other three (binary) symmetries can then be obtained "for free": they are exhibited by the correlation function, and can be imposed on the underlying physics by adding an underlying randomisation level. We end up with a simple probabilistic description of all possible classical EPR-B correlations in terms of a "spinning coloured disk" model, and a research programme: describe these functions in a concise analytic way. We survey open problems, and we show that the widespread idea that "quantum correlations are more extreme than classical physics allows" is at best highly inaccurate, through giving a concrete example of a classical correlation which satisfies all the symmetries and all the certainty relations and which exceeds the quantum correlations over a whole range of settings
On 6 May 2022, at 13:29, Chantal Roth <cr...@nobilitas.com> wrote:
Chantal,
In your email note on June 1, there are references on experiments using photons and a few comments about the possibility of losing photons (a detection loophole).
Yes, working with photons and trying to correlate measurements in two separate detection systems, needs some caution. One of them is your detection geometry – things like if your collecting lens is collecting all photons necessary for a good correlation with the twin photons and so on. There are probabilities that “good” photons (pair member) are lost as well as “bad” photons (uncorrelated photons) are detected … Of course, these can be statistically checked.
This can be even more stringent in the case of photons with a total angular momentum that includes orbital angular momentum (helicity, in a broad sense). The electromagnetic field associated with these photons can be used to define the creation operators for photons carrying this orbital angular momentum. The detection system must be able to collect (twin) photons with all the wave vectors associated with that orbital angular momentum mode. Failing to do that, a poor result is achieved.
Orbital angular momentum is NOT associated a single photon but with the MODE in which that photon is excited.
There are systems to detect orbital angular values for each detected photon, eg. l1 and l2, given that the total orbital angular momentum for the two photons start with L=l1+l2. I wrote a short note about this some time ago [September 15, 2008 / Vol. 33, No. 18 / OPTICS LETTERS 2119] entitled “On the distinguishability of downconverted modes with orbital angular momentum”.
To better understand the arguments in this note, it may be useful to read “Wave function for spontaneous parametric down-conversion with orbital angular momentum” [PHYSICAL REVIEW A 80, 063833 (2009)].
Geraldo
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On 4 Jun 2022, at 18:56, James Tankersley Jr <jim.t...@gmail.com> wrote: