Undergrad Is there a way to translate a particle's spin into regular motion?

[vanhees71]

And polarization can be affected by the principles behind quantum entanglement, yes? Also, just for confirmation, this Mach-Zehnder interferometer would be able to convert momentum into polarization?

In addition, unrelated question, but I'm curious if all particles are waves as well, does that mean all particles have polarizations?

And separately, reversing the mechanism that could differentiate between two values of given spin, say up or down, and subsequently, "translate," that either value of spin into a corresponding direction in motion?

It's very confusing to say "convert momentum into polarization". What happens in a Stern-Gerlach experiment for spin and with polarizing beam splitters is that you entangle the polarization with the momentum of the particle. Take, e.g., some birefringent crystal as a polarizing beam splitter. It can be described with classical physics: Due to the anisotropic dielectric tensor the refraction index is different for horizontal and vertical polarized field modes and thus the refraction angle for these two polarization modes is different, which means that an arbitrarily polarized beam gets split into one beam horizontally and the other vertically polarized, i.e., the momentum (direction) is entangled with the polarization. Using single photons in arbitrary polarization it gets randomly refracted in the one or the other direction with probabilities weighted as the intensity of the corresponding classical em. waves, i.e., the single photon behind the beam splitter is in a state where the polarization is entangled with its momentum. The entire description of a lossless (idealized) polarizing beam splitter is given by some unitary operator.

 

[vanhees71]

The experiment is discussed by Ballentine in his notorious Quantum Mechanics book. In the 1998 edition, it is referenced in Chapter 9, p243. Unfortunately, Balletine's book is especially flawed and tainted by his eccentric personal views in that chapter, so reader beware!

To the contrary, Ballentine's book is one of the few that is not spoiled by the notorious collapse doctrine, but that's interpretation and belongs to the corresponding subforum!

 

[Vanilla Gorilla]

Can particles like electrons have polarization, since they are also waves?

 

[PeterDonis]

Can particles like electrons have polarization, since they are also waves?

In quantum mechanics, "polarization" is just another term for spin, applied to massless particles like photons. It has nothing to do with waves.

 

[vanhees71]

Yes, but also massive particles (or rather ensembles of massive particles) can be polarized. E.g., at the Relativistic Heavy Ion Collider there are experiments with polarized protons to investigate their spin properties (generalized parton-distribution functions etc.).

 

[Vanilla Gorilla]

Ok, thank you!

 

[Vanilla Gorilla]

Separate question:
Were the time crystals developed in the 2010s looping in their quantum spin, or their linear momentum?
In 2016, https://en.wikipedia.org/w/index.php?title=Norman_Yao&action=edit&redlink=1 et al. proposed a different way to create discrete time crystals in spin systems. From there, Christopher Monroe and Mikhail Lukin independently confirmed this in their labs. Both experiments were published in Nature in 2017. In 2019 it was theoretically proven that a quantum time crystal can be realized in isolated systems with long-range multi-particle interactions (Wikipedia)

In these experiments, was it the quantum spin that underwent the looping time crystal phenomenon, or was it the actual linear motion which underwent this mechanism where it would repeat in time? If not, could we engineer a time crystal which loops over time not in linear motion, but with regards to its spin?

 

[PeterDonis]

Separate question:

You already asked this in a separate thread (which is the proper way to ask a new question):

https://www.physicsforums.com/threads/time-crystals-and-spin.994042/

Further discussion of this question should be in that thread.

 

[Vanilla Gorilla]

ok