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I want to understand a subtle difference between cascaded Stern Gerlach and polarization experiments.

Both affect spin 1/2 phenomena.

In Stern Gerlach the standard textbook description is like this:

  1. Atoms are split into |↑⟩ and |↓⟩. The |↑⟩-atoms are kept while the |↓⟩ are absorbed. This absorption is what turns this first to a measurement device and distinguishes it from a mere splitter, producing an entanglement between position (exit paths) and spin.
  2. Atoms then are split into |←⟩ and |→⟩, but only the |←⟩ atoms are kept. Thus, one would expect that the spin of the atoms points |↑⟩ and |←⟩.
  3. If these atoms are again brought into a B-field which separates the atoms into |↑⟩ and |↓⟩, one would expect that we obtain only |↑⟩ atoms, because we kept only those atoms in step 1. However, we find that the atoms are again split into |↑⟩ and |↓⟩. Thus, we conclude that the second measurement superposes the |↑↓⟩ spin direction.

Now: In Stern-Gerlach experiments I believe that we can replicate these thoughts by experiments.

With polarization experiments, however, I see a subtle difference. In all polarization experiments I know I cannot observe the "surviving" photons between the first and the second polarizer. All I can do is detect the photons which passed through all three polarizers at the very end of the cascade. Counting a photon destroys it in the detector (whereas counting a silver atom in a Stern Gerlach device, does not destroy it).

Thus my questions:

  1. How do we know that the experiments are similar.

  2. How do I know that the photon I finally detect after the third polarizer is indeed the one which passed through polarizers one and two? (In my naive phantasy in the Stern Gerlach experiments I somehow can track the silver atoms, at least "virtually" through the three SG magnets).

  3. How do we know that the polarizers may be viewed as wave-function collapsing measurement devices (as opposed to a beam-splitting type of device).

The reason for my question is: I want to get a better understanding for what we know from experiment and for what we know from textbook theory.

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I will answer your second question.

How do I know that the photon I finally detect after the third polarizer is indeed the one which passed through polarizers one and two?

In a polariser, photons are not absorbed and re-emitted in the transmission direction. And photons are indivisible units from their emission to their absorption. So it is clear that the photons in front of the polarisers are the same as on the detector screen. The polarizers influence the direction of the electric (and magnetic) field only from a random distribution to a polarization.

With a polariser tuned to a certain wavelength, approx. 50 % of the photons pass through the polariser. This is the case if the radiation was not polarised before.

Since half of the photons pass through the first polariser and are aligned with their fields after passing through (that is what we mean by polarization), we can conclude that the photons with a field direction +/-90° to the slits undergo a rotation and get aligned. The other half of the photons are absorbed or reflected. Of course, the photons passing through are blocked at the next polariser, where the slits are 90° to the first polariser. All photons get absorbed or reflected.

So what a placed in between polarizer with an orientation of 45° degrees do? He rotates the incoming photons nearly without any losses to to the 45°. And the third polarizer do the same. That is why the structure of three polarizers is transparent.

Can you now try to apply this view to your first question.

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  • $\begingroup$ You reply is helpful because I now better understand how I should have asked. Stern-Gerlach looks very much different to me particularly after having found arxiv.org/abs/1112.4522 . Stern-Gerlach produces an entanglement of spin and position. Polarization filters seem to do a measurement. So could I convert a polarizing beam splitter into a polarization filter by adding an absorber to one branch of the splitter? Probably? $\endgroup$ Mar 14, 2021 at 12:26
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  1. The experiments are similar because both deal with particles, both divide into two groups, and most importantly both devices rotate the particles to align with the slit or the magnetic field. In other words they don’t just divide they also influence. (2) The photons or the electrons reaching the detector are the same ones all the way through the experiment because you can eliminate all other sources and leave only one path from source to detector through the experiment. (3) Particles are sent through either device and they make it through or they don’t. It has nothing to do with wave-functions collapsing. As a particle travels through it is also rotated to align with the slits or magnetic fields. It’s important to remember these devices are not just dividing into groups they are also rotating the spins and polarization’s each time.
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  • $\begingroup$ I am not sure. The source of my problem is arxiv.org/abs/1112.4522 where the author describes a subtle difference. It looks like the polarizer collapses and measures whereas Stern-Gerlach and beamsplitters do not. That is how I read that paper. Actually the polarizer does NOT divide into two groups. I only can collect the particles which passed through, the others are destroyed. I am trying to get a more in depth answer on this aspect. $\endgroup$ Mar 14, 2021 at 12:20
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    $\begingroup$ @Nobody-Knows-I-am-a-Dog The Paper relies too much on eigenstates, wave functions, collapsing, superpositions, erasers, retro causality, entanglement and particles somehow being in two places at one time. In fact the bullet point in the introduction Talks about a remedy for separation fallacy but I believe it has it backwards. On the contrary, the real problem is that particles (real physical objects) are not taking serious enough. Everyone talks about duality but they seem to only comprehend waves. Two correlated (Not Entangled) Particles can answer any of these questions. $\endgroup$ Mar 15, 2021 at 20:40
  • $\begingroup$ You are touching upon an aspect I would like very much to learn more of. Do you have some pointers to papers or books on this aspect? This would be very much appreciated. I share the view that the particle concept has much of the classical, macroscopic thinking and tend to favor the wave concept myself. Therefore I am searching for more documents which might falsify this view and correct my mistake. $\endgroup$ Mar 16, 2021 at 11:54
  • $\begingroup$ @Nobody-Knows-I-am-a-Dog there is a paper “Single Edge Certainty” posted at billalsept.com that gives you a particle derivation of the double slit. The link to my website is at the top of this page. $\endgroup$ Mar 18, 2021 at 5:25

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