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

[Vanilla Gorilla]

TL;DR

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

Is there a way to translate a quantum particle's spin into regular motion in any of the directions?

 

[Dale]

Sort of. You can annihilate a particle with its anti particle. The resulting particles can have a large KE. But it isn’t exactly just converting its spin into KE, it is converting everything into other stuff including additional KE

 

[Vanilla Gorilla]

Are there any other known mechanisms?

 

[Dale]

No. You cannot separate a particle’s spin from the particle itself. It is part of what makes the particle what it is. All you can do is change it into a different particle by annihilation or other decay.

 

[Vanilla Gorilla]

Ok, thank you for the help :)

 

[vanhees71]

Maybe I misunderstand the orginal question, but isn't this precisely what the Stern-Gerlach experiment is about? Running through an inhomogeneous magnetic field the particle is deflected depending on the spin projection (magnetic moment) in direction of this magnetic field, i.e., you get an entanglement between this spin component and the particle's momentum and/or position.

 

[Dale]

The spin is the same before and after so spin is not converted into linear motion.

 

[vanhees71]

In an SG the spin is not necessarily the same, it's precessing around the magnetic field, and that's the dynamical reason, why the SGE sorts particles according to the values $\pm \hbar/2$ of the spin component in direction of the magnetic field.

Of course it's not "converted" into linear motion. As I said, maybe I haven't understood the question right.

 

[Dale]

My understanding is that he wants to take a spin 1 particle at rest and make it into a spin 1/2 or a spin 0 particle with linear momentum. Like dropping a spinning tire onto a road and letting it convert angular momentum into linear momentum. The difference is that the tire is still the same tire if you change its spin, but if you change a particle's spin it is no longer the same particle.

 

[Vanilla Gorilla]

I think I phrased the question somewhat poorly. My bad. What I meant to ask was whether or not there is a known 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.

 

[Dale]

Please try to be more courteous in the future. I wasted my time responding to you because you failed to write a clear question in the beginning. Please ignore all of my comments here since I misunderstood what you asked and nothing that I have said is relevant to your actual question. If you had written a three line question instead of a one line question then I could have answered it immediately.

The answer to your clarified question is yes. The Stern-Gerlatch experiment mentioned by Vanhees is an example.

Edit: looking back, I see that it was not purely a miscommunication on your side, but also a misreading on my side. I read "convert" instead of "translate". In any case, a more clear question would have been appreciated.

 

[Dale]

Maybe I misunderstand the orginal question

Nope, it was me who misunderstood.

 

[Vanilla Gorilla]

My bad, I'm sorry. Not an excuse, but I'm new, so that's probably why I'm not good at writing these yet.

 

[PeroK]

I think I phrased the question somewhat poorly. My bad. What I meant to ask was whether or not there is a known 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.

That would be the famous Stern-Gerlach experiment, as described in post #6.

 

[Vanilla Gorilla]

Ok, thank you all for your aid! In addition, I am deeply apologetic for any distress I may have caused.

 

[Vanilla Gorilla]

Is there a way to do the reverse?

 

[PeterDonis]

Is there a way to do the reverse?

Meaning, reverse a Stern-Gerlach experiment? In principle, yes, it would be possible, but the practical difficulties would be very great. You would have to redirect both output beams from one Stern-Gerlach device back into a second device in such a way that they recombined.

Doing the equivalent operations with photon polarizations is much easier; that's basically what a simple Mach-Zehnder interferometer does (it splits a photon at one beam splitter and recombines it at a second beam splitter after reflecting off a mirror in each arm).

 

[vanhees71]

The question about reversing the SGE has been treated by Schwinger, Englert, Scully, et al in a very informative series of papers on "Is spin coherence like humpty dumpty?":

https://link.springer.com/article/10.1007/BF01909939
https://www.osti.gov/etdeweb/biblio/6857431
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.40.1775

 

[Vanilla Gorilla]

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?

 

[PeterDonis]

this Mach-Zehnder interferometer would be able to convert momentum into polarization?

The term "convert" is not a good term to use to describe what devices like beam splitters and polarizers (for photons) and Stern Gerlach magnets (for electrons) do. They don't "convert" linear momentum into polarization/spin, or vice versa; the magnitude of both the linear momentum and the spin of the particle is the same after going through the device as before.

What they do is (possibly) redirect the momentum of the particle based on its polarization/spin. For example, a Stern-Gerlach magnet, when used normally, bends the path of an electron one way for spin up and the other way for spin down. (In a "reverse" usage, the magnet would have to be taking in two beams, one for spin up and one for spin down, and bending each one so that they come out in just one beam.)

A Mach-Zehnder interferometer actually doesn't care about the polarization of the photons (since it uses simple beam splitters that are insensitive to polarization). It just splits (or recombines) photon beams. But there are more complicated quantum optics devices that are sensitive to polarization.

 

[Vanilla Gorilla]

By bends the electron, I'm assuming you mean that it would just accelerate the electron one way for one spin value, and a correspondingly opposite way for the opposite spin value?

 

[PeterDonis]

By bends the electron, I'm assuming you mean that it would just accelerate the electron one way for one spin value, and a correspondingly opposite way for the opposite spin value?

That's what a Stern-Gerlach device does, yes: it has an inhomogeneous magnetic field that splits the input beam into two output beams, one for spin up and one for spin down.

 

[Vanilla Gorilla]

Alright, thank you!

 

[Vanilla Gorilla]

And the reverse process "translates" (Sorry, can't think of a better term) direction of momentum into spin?

 

[PeterDonis]

And the reverse process "translates" (Sorry, can't think of a better term) direction of momentum into spin?

No. I already explained what it does do: it recombines two input beams into one output beam, assuming the two input beams have opposite spin values (one is spin up and one is spin down) because they were produced by a previous Stern-Gerlach device operating in the "forward" direction.

 

[PeterDonis]

@Vanilla Gorilla,

Please re-read this from one of my previous posts:

the magnitude of both the linear momentum and the spin of the particle is the same after going through the device as before

It is very important to keep this in mind as you think about what these devices do.

 

[Vanilla Gorilla]

So the reverse process not have anything to do w/ momentum? I'm really sorry if I'm missing something

 

[PeterDonis]

So the reverse process not have anything to do w/ momentum?

It combines two beams into one, which means it affects the direction of the momentum of the beams. It does not affect the magnitude of the momentum of the beams. It also does not affect the spins themselves, although it does affect the correlation between the momentum and the spins.

 

[romsofia]

Just to clarify before I write something up, @Vanilla Gorilla it seems to me that your questions are basically the following:

Your first one is: By ONLY knowing the particle's spin, can I map out its' equation of motion?
Your second one is: Since I measured the particles spin, is it possible to know its' equation of motions before the measurement took place?

 

[atyy]

Is there a way to do the reverse?

Yes, the experiment was reported on by:
Explicit experimental verification of quantum spin-state superposition
J. Summhammer, G. Badurek, H. Rauch, U. Kischko
Physics Letters A Volume 90, Issue 3, 28 June 1982, Pages 110-112
https://doi.org/10.1016/0375-9601(82)90709-5
"... In 1963 Wigner [1] proposed a Gedankenexperiment where he imagined a double Stern—Gerlach arrangement to separate and subsequently recombine coherently the z-spin components of an x-spin particle. Zeilinger [2] suggested the realization of such an experiment by means of neutron interferometry. The detailed theoretical framework by means of which the measured results can be interpreted conveniently is treated by Eder and Zeilinger [3]. In this letter we report on an experiment with polarized neutrons that was performed at the perfect crystal neutron interferometer setup (Dl8) at Grenoble [4]. ..."

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!