Do physically rotating particles affect Stern Gerlach results?

[CountingKeys]

TL;DR Summary

If a spin 1/2 particle rotated 360 degrees flips the quantum spin of a particle, wouldn't rotating particles smear the 2 beams in the Stern Gerlach experiment?

If a spin 1/2 particle we're to be rotating as it was passing through a Stern Gerlach experiment wouldn't this create particle paths which may switch from spin up to spin down or vice versa, or even oscillate in mid flight?

If the experiment were done with a rapidly rotating silver atom source, as the atoms are evaporated would the rotating atom's path through the experiment be relatively flat as the particle's spin rapidly oscillated between up and down?

Thanks

 

[PeterDonis]

If a spin 1/2 particle we're to be rotating

What do you mean by "rotating"? How would you prepare a spin-1/2 particle in a "rotating" state? Bear in mind that we are talking about QM here; "particles" in QM are not little billiard balls.

 

[CountingKeys]

I'm envisioning the sample of silver is attached to a motor so that the sample can be spun. If the motor rotates the sample 360 degrees in physical space within the Stern Gerlach apparatus the quantum spin of each rotated spin 1/2 particle would flip. Varying degrees of physical rotation would produce varying probabilities of quantum spin flips for each particle in the sample. If the rotating sample has atoms evaporating off while spinning, each of these atoms should remain rotating as it is spun off the sample. If this spinning atom passes through a magnetic field and during this passage rotates 360 degrees then its quantum spin will flip and a particle entering with up spin would change to down spin while passing through the magnetic field. One quantum spin flip in the middle of the apparatus would mean the particle spends half the time curving in one direction then the other half curving in the opposite direction resulting in hitting the detector in the center. A rapidly rotating atom's spin could oscillate many times again hitting the detector in the center.

If it is the case that a rotating atom can change quantum spin and thus reverse its path curvature within the Stern Gerlach apparatus, then the experiment could be refined so that a single isolated atom is sent through with a rotation speed that results in one quantum spin flip. Then based on the point of detection, one could extrapolate possible paths the atom took, with the goal of narrowing it down to one possible path and identifying the point at which the quantum spin flip occurred. Knowing when the spin flip occurred would allow a deterministic history of the atom to be known.

 

[PeterDonis]

I'm envisioning the sample of silver is attached to a motor so that the sample can be spun.

I'm not sure how you would do that inside a Stern Gerlach apparatus since the source of the silver atoms is not inside that apparatus. The silver atoms inside the S-G magnet are traveling freely in space; they aren't attached to anything.

 

[CountingKeys]

I'm proposing to spin the silver before and while it is evaporated. I'm aware the atoms are not attached to anything after they are evaporated.

 

[PeterDonis]

I'm proposing to spin the silver before and while it is evaporated.

Why do you think that will make the silver atoms "rotate" once they exit the source? All it will do is make it harder to aim them at the S-G magnet.

 

[PeterDonis]

A rapidly rotating atom

Is what, exactly? I'm looking for an answer in terms of the math of QM: what wave function do you think describes such "a rapidly rotating atom" when it exits the source, and how is it different from the wave function that describes the silver atoms when they exit the source in a normal S-G experiment?

I strongly suspect that (a) you do not have an answer to this question, and (b) there isn't an answer to this question, because the concept you think you have of "a rapidly rotating atom" actually doesn't make sense.

 

[CountingKeys]

If you are suggesting that the atoms do not rotate, then where does all the angular momentum of the rotating silver sample go? And at what size do you suggest this rotation disappear? Can two silver atoms rotate?

 

[PeterDonis]

If you are suggesting that the atoms do not rotate

That's not what I'm suggesting. I'm suggesting that the concept you are using of "atoms rotating" does not make sense.

The way to change my mind is not to keep throwing words at me. it is to show me the math, as I have already asked. What wave function describes these "rotating atoms" of yours, and how is it different from the wave function of silver atoms emitted from the source in a normal S-G experiment?

where does all the angular momentum of the rotating silver sample go?

This is orbital angular momentum relative to the center of mass of the source of silver that is being spun. It shows up in the fact that, as I said, it gets a lot harder to aim the atoms at the S-G magnet; extra forces would need to be applied to make the silver source wobble as well as spin so that the atoms coming out would point towards the S-G magnet as the source spins around. Those extra forces would be associated with their own angular momentum which would compensate for any changes as the silver atoms were emitted.

In any case, none of this supports your claim that the atoms themselves are "rotating" after they exit the source.

Can two silver atoms rotate?

I don't know, because you still haven't shown me any math that explains what you mean by "rotating".

 

[PeterDonis]

I'm envisioning the sample of silver is attached to a motor so that the sample can be spun.

Although this thread is in the QM forum, It's worth noting that even classically, your reasoning here is not valid.

Consider, for example, an ordinary garden sprinkler with a rotating head. The rotating head means the source of the water being sprayed is rotating. If you like, you can even attach the sprinkler head to a tank of water under pressure that rotates with the head. Does that mean the sprayed water itself is rotating? Or does it just mean that the trajectory of the spray changes with time as the head goes around?

 

[CountingKeys]

This can be cleared up rather simply. Imagine there is a nonrotating space ship in outer space that contains a stationary mass of silver connected to a motor. We then start rotating the motor and silver. When the silver spins the spaceship begins to counter rotate. Angular momentum is conserved. We then evaporate the silver and shoot it along the axis of rotation, the evaporated silver collects and condenses on the other end of the spaceship. Once all the silver has been evaporated and condensed, is the spaceship rotating or not rotating? The only valid reasoning I can see is the spaceship is no longer rotating, all angular momentum is conserved and the evaporated atoms are rotating as the spaceship counter rotates until the atoms condense and transfer momentum back to the spaceship and both silver and spaceship stop rotating.

Are you absolutely sure the evaporated atoms do not rotate? If they didn't that would very hard to believe.

Perhaps someone else who knows about the original question can respond instead.

 

[PeterDonis]

This can be cleared up rather simply.

It could be if you would show the math I have asked for. Why aren't you?

We then evaporate the silver and shoot it along the axis of rotation

How? You can't just magically do this and also say the silver is "rotating". If the silver has angular momentum relative to the ship's center of mass, it cannot be moving in a straight line along the axis of rotation.

At least, that's what would be the case in classical physics. Which is why, as I have already pointed out, your analysis is not valid even in classical physics.

But this discussion is about quantum physics, so the atoms are described by a wave function. I have asked you more than once now to say what wave function you think describes the "rotating" atoms and how it is different from the wave function that would describe the atoms--presumably "non-rotating"--in the normal S-G experiment. If you cannot do that, then we have no valid basis for discussion and this thread will be closed.

Are you absolutely sure the evaporated atoms do not rotate?

Once more, that is not what I said. Go back and read my posts again, carefully.

 

[CountingKeys]

I read it again. You're position is the spaceship would magically still be rotating since the evaporated atom are not rotating once they leave the silver sample.

In any case, none of this supports your claim that the atoms themselves are "rotating" after they exit the source.

You're input is received and has received the consideration is deserves. I would like a diversity of opinions on the original question. You're opinion is already noted.

 

[PeterDonis]

You're position is the spaceship would magically still be rotating since the evaporated atom are not rotating once they leave the silver sample.

No, I did not say that.

I would like a diversity of opinions on the original question.

Unless you can show some actual math, nobody will have any better basis for an opinion than I do. And I have not given any opinion. All I have done is point out reasons why your analysis is not valid. I have not given any analysis of my own, because there is no valid basis for one: you haven't shown me a wave function.

 

[PeterDonis]

Thread closed for review by other moderators.

 

[Nugatory]

If the motor rotates the sample 360 degrees in physical space within the Stern Gerlach apparatus the quantum spin of each rotated spin 1/2 particle would flip

This is where you are misunderstanding how quantum mechanics is so different from what we expect from a lifetime’s experience with non-quantum systems.
What’s actually going on here is that quantum spin has no direction until after it has interacted with the inhomogeneous magnetic field in the SG device so there is nothing to flip or rotate. And here when I say “no direction” I really mean exactly that: the spin has no direction. It’s not that it has some direction but we don’t know what it is until we’ve measured it, it has no direction the way that I don’t have a lap when I’m standing or a fist when my hands are open.

This idea that a particle can have spin yet there is no axis around which it is spinning until it interacts with the magnetic field and then the magnetic field provides the axis is completely alien to our intuition about the how the world works. Because we can’t trust our intuition we have to rely on the math, and that’s why @PeterDonis is asking you for the math. But if we cut some (actually a lot) of corners, I can jump ahead and say that the wave function of the silver atoms emitted from your hypothetical rotating source will be the same as the wave function of the silver atoms emitted by the non-rotating source.

Although there is no substitute for starting with a real textbook, you could try Giancarlo Ghirardi’s book “Sneaking a look at God’s cards”. It is reasonably layman-friendly and avoids many of the oversimplifications and misdirections found in most math-free explanations of QM.

 

[PeterDonis]

The OP question has been answered. Thread will remain closed.