Stern Gerlach Experiment and Spin

[cooev769]

I'm trying to get my head around this spin idea, the idea that particles behave like tiny dipole magnets when passing through a magnet field, either spin up or spin down. Because unlike magnets they don't produce a spread on at the end, they are either top or bottom.

So the problem I have with this is that this would suggest that the particles have some property, like charge, that is it is either + or -, spin up or spin down, some property that exist in one dimension forward or back. But now dealing with spin our teach is talking about spin in 3 components as if it is a property in 3 dimensional space which makes no sense because if it was, it wouldn't produce the discrete pattern seen in the Stern Gerlach experiment, you could put a particle through of spin z h bar/4 and get it somewhere in between. Can somebody please explain what the tap-dancing christ is going on!

Thanks.

 

[Orodruin]

You can measure the spin of a particle in any direction you would like. However, if it is a spin-1/2 particle, you will always get a result which is either +1/2 or -1/2. Now here is the thing: If you measure a particle to have spin +1/2 in the z-direction, you will know nothing about its spin in the x-direction. If you have several such particles and do repeated measurements on them, you will see that such particles have a 50% probability of having spin 1/2 in the x-direction and 50% probability of having spin -1/2 in the x-direction. This is due to the quantum mechanical state with spin 1/2 in the z-direction being a superposition of the different x-direction states.

In the end, it turns out that there is a statement which is based on an extended version of the uncertainty principle which tells you that you cannot know the intrinsic angular momentum of a particle to arbitrarily good precision in all directions at once - you have to decide which direction you want to know. This is analogous to not being able to determine a particle's position and momentum at the same time.

 

[cooev769]

So can the spin of a particle be h/2 or -h/2 in every single direction in 3 dimensional vector space.

 

[Nugatory]

So can the spin of a particle be h/2 or -h/2 in every single direction in 3 dimensional vector space.

Yes, but not all at once. We can only measure the spin in one direction at a time.

 

[cooev769]

What the heck, and then it will turn out to be in that direction either up or down when you do measure it.

 

[Nugatory]

What the heck, and then it will turn out to be in that direction either up or down when you do measure it.

Yes. Confirmed by experiment so often and in so many different ways that we're stuck with it. The world really does work that way.

This is one of the experiments where the idea of "wave function collapse" can help us form a usable mental model of what's going on: we have this blurry fuzzy wave function with no definite spin in any direction, and when we make a measurement by applying a magnetic field, the measurement causes the wave function to collapse into some definite state, either aligned with or against the magnetic field. (but be careful - that's just a usable mental model, a way of visualizing what the math of QM is telling us).

 

[cooev769]

Thanks so much for the answers I think I understand it now. So When you collapse the wave function for example into the eigenfunction of the Sx operator in the Sz basis by passing it through a stern gerlach aligned with the x-axis and then Th rough one aligned with the z axis, the spin can no longer be anything it is in the x direction, which if you were to measure the z component, because x spin it isn't an eigenfunction of the Sz operator you would only get spin up and spin down in the z direction with probabilities equal to the square of the coefficients of the eigenfunction of the Sx operator in the Sz basis?

Sorry if that's confusing but hopefully you understand what I'm asking.

 

[phyzguy]

If it's any help, you are not the only one that struggles to "get your head around" the ideas of quantum mechanics. There comes a point where you just need to accept that this is how the universe works and move forward. I like this quote from "The Feynman Lectures on Physics",

"One might still like to ask, "How does it work? What is the machinery behind the law?" No one has found any machinery behind the law. No one can "explain" any more that we have just "explained". No one will give you any deeper representation of the situation. We have no ideas about a more basic mechanism from which these results can be deduced."

 

[cooev769]

Yeah well it helps that I personally think Bells inequality is fallacious and that quantum mechanics is most likely missing something, so I don't really feel the need to understand something I don't believe is the true nature of the universe.

 

[Nugatory]

Thanks so much for the answers I think I understand it now. So When you collapse the wave function for example into the eigenfunction of the Sx operator in the Sz basis by passing it through a stern gerlach aligned with the x-axis and then Th rough one aligned with the z axis, the spin can no longer be anything it is in the x direction, which if you were to measure the z component, because x spin it isn't an eigenfunction of the Sz operator you would only get spin up and spin down in the z direction with probabilities equal to the square of the coefficients of the eigenfunction of the Sx operator in the Sz basis?

Sorry if that's confusing but hopefully you understand what I'm asking.

Yes, that's pretty much it.

 

[cooev769]

Thanks nugatory, that's a conceptual barricade that has been annoying me for a long time and I believe I finally understand it, as well as it can be understood anyway.

 

[phyzguy]

Yeah well it helps that I personally think Bells inequality is fallacious and that quantum mechanics is most likely missing something, so I don't really feel the need to understand something I don't believe is the true nature of the universe.

I'm sorry to hear that, because unless you discard that attitude, you will cease to make progress. The universe is what it is, not what you wish it might be. Bell's inequality is telling us important information about how the universe works, and has been experimentally verified many times. I advise you to accept it and move forward.

 

[cooev769]

I disagree. Just because something is hasn't proven to be wrong doesn't make it true. If Einstein had accepted the classical model as the nature of the universe because it had been proved correct many times over then relativity may not even exist. I can't like Einstein just accept the fact that God plays dice with the world. Who knows maybe some day somebody will finally provide a deterministic model with no uncertainty.

 

[phyzguy]

I disagree. Just because something is hasn't proven to be wrong doesn't make it true. If Einstein had accepted the classical model as the nature of the universe because it had been proved correct many times over then relativity may not even exist. I can't like Einstein just accept the fact that God plays dice with the world. Who knows maybe some day somebody will finally provide a deterministic model with no uncertainty.

Oh,well. I tried.

 

[Orodruin]

Just because something is hasn't proven to be wrong doesn't make it true.

This is true. However, something that has been proven wrong typically is wrong as is the case with a hidden variable interpretation of QM.

What Bell's theorem (along with measurements) states is that local realism (essentially your determinism) is false, not that QM is true. QM and its generalizations are very likely not to tell the entire story, but the entire story is not local realism.

 

[DrChinese]

Yeah well it helps that I personally think Bells inequality is fallacious...

And you believe that for a scientific reason, or because you don't like the implications of Bell?

quantum mechanics is most likely missing something, so I don't really feel the need to understand something I don't believe is the true nature of the universe.

QM is a useful model. It is not reality itself. There is plenty more to be learned, I am quite confident. New discoveries have been arriving at breakneck speed over the past 50 years and we are still trying to understand the full meaning of many of these.

As mentioned above, Bell's Theorem provides some constraints which are quite useful in the search for greater understanding.

 

[Nugatory]

At 8:37 AM US east coast:

Thanks so much for the answers I think I understand it now.

At 8:42 US east coast:

Yeah well it helps that I personally think Bells inequality is fallacious and that quantum mechanics is most likely missing something, so I don't really feel the need to understand something I don't believe is the true nature of the universe.

It is possible that five minutes isn't long enough to fully process the epiphany.
Just sayin'...

 

[Nugatory]

If Einstein had accepted the classical model as the nature of the universe because it had been proved correct many times over then relativity may not even exist.

Although there is a powerful myth about Einstein challenging classical physics, that's not what actually happened.

It became clear during the second half of the nineteenth century that classical mechanics (Galileo/Newton) and classical electromagnetism (Maxwell) could not be reconciled in any way that matched experimental results. This was the great unsolved problem of nineteenth century physics, and it engaged some of the greatest minds of the era. Many people found pieces of the solution (there's a reason why we call the transformations of special relativity "Lorentz transforms" instead of "Einstein transforms", for example). When Einstein published his SR paper in 1905, it wasn't seen as a challenge to classical physics, it was seen as the answer to a known and vexing unsolved problem in classical physics, the answer that people had been looking for for decades.

It is worth noting that the title of Einstein's 1905 paper was "On the electrodynamics of moving bodies". It's hard to imagine more convincing evidence that he was after the problem of reconciling classical mechanics and classical electromagnetism.

It's also worth noting that Einstein was able to come up with his solution only because he was already deeply familiar with classical physics. If he hadn't studied and understood classical physics in great depth, he wouldn't even have been able to understand the problem, let alone propose a solution.

 

[phyzguy]

Although there is a powerful myth about Einstein challenging classical physics, that's not what actually happened.

It became clear during the second half of the nineteenth century that classical mechanics (Galileo/Newton) and classical electromagnetism (Maxwell) could not be reconciled in any way that matched experimental results. This was the great unsolved problem of nineteenth century physics, and it engaged some of the greatest minds of the era. Many people found pieces of the solution (there's a reason why we call the transformations of special relativity "Lorentz transforms" instead of "Einstein transforms", for example). When Einstein published his SR paper in 1905, it wasn't seen as a challenge to classical physics, it was seen as the answer to a known and vexing unsolved problem in classical physics, the answer that people had been looking for for decades.

It is worth noting that the title of Einstein's 1905 paper was "On the electrodynamics of moving bodies". It's hard to imagine more convincing evidence that he was after the problem of reconciling classical mechanics and classical electromagnetism.

It's also worth noting that Einstein was able to come up with his solution only because he was already deeply familiar with classical physics. If he hadn't studied and understood classical physics in great depth, he wouldn't even have been able to understand the problem, let alone propose a solution.

Very well stated. If Einstein had said, "I don't accept electromagnetism - it must be wrong," he would not have made the contributions that he did. Instead he asked, "How can I make sense of what the experimental data is telling me?"

 

[harrylin]

Yeah well it helps that I personally think Bells inequality is fallacious and that quantum mechanics is most likely missing something, so I don't really feel the need to understand something I don't believe is the true nature of the universe.

I suspect that you are right, but the issue is rather subtle. Even before I (maybe) reach a conclusion for myself, I'll have to plow much further through Jayne's statistics book (or cite a convincing counter example; but so far no-one came up with one!). He and several others of less fame pretended that Bell's proof was insufficient, as it appears to include at least one unwarranted mathematical assumption. Note also that all too often, people suppose "local reality" to imply that (unwarranted?) assumption by definition - and with such a re-definition Bell's theorem is practically unbeatable but possibly irrelevant. If you search this group for such terms as "Jaynes" and "Bell's theorem" you will find a great number of past discussions on that topic.

 

[DrChinese]

[Jaynes] and several others of less fame pretended that Bell's proof was insufficient, as it appears to include at least one unwarranted mathematical assumption. Note also that all too often, people suppose "local reality" to imply that (unwarranted?) assumption by definition - and with such a re-definition Bell's theorem is practically unbeatable but possibly irrelevant.

None of these statements are a fair representation. There is no unwarranted assumption, mathematical or otherwise. Generally, Jaynes' objections are rejected by the scientific community. Bell continues to stand strong as ever.

Further, discussion of Jaynes does not belong in this thread.

 

[Jilang]

I'm not quite sure what all the fuss is about. The results of QM are incompatible with hidden variables, but the results of QM are what you obtain when you take measurements. We don't have to assume that what we measure represents the state of affairs prior to measurement necessarily. A system will be disturbed by any measurement by a minimum amount of action, h. You cannot disturb a system by an arbitrarily small amount.

 

[harrylin]

None of these statements are a fair representation. There is no unwarranted assumption, mathematical or otherwise. Generally, Jaynes' objections are rejected by the scientific community. Bell continues to stand strong as ever.

Further, discussion of Jaynes does not belong in this thread.

While you are of course free to disagree with Jaynes and others, indeed this thread isn't the place to discuss that. BTW, I fullly agree with your earlier post in this thread.

 

[harrylin]

I'm not quite sure what all the fuss is about. The results of QM are incompatible with hidden variables, but the results of QM are what you obtain when you take measurements. We don't have to assume that what we measure represents the state of affairs prior to measurement necessarily. A system will be disturbed by any measurement by a minimum amount of action, h. You cannot disturb a system by an arbitrarily small amount.

The fuss is about giving a plausible and reasonable explanation for the measurement results. Already it is hard to come up with a simple explanation why the magnets split the ion beam up in two distinct beams, and since Bell it is widely held that the results corresponding to the "collapse of the wave function" of distant particles imply an instantaneous (and rather magical) "action at a distance".

 

[kith]

I'm not quite sure what all the fuss is about. The results of QM are incompatible with hidden variables, but the results of QM are what you obtain when you take measurements. We don't have to assume that what we measure represents the state of affairs prior to measurement necessarily. A system will be disturbed by any measurement by a minimum amount of action, h. You cannot disturb a system by an arbitrarily small amount.

That's not correct. A system in an eigenstate of the observable in question remains undisturbed.

 

[Jilang]

That's not correct. A system in an eigenstate of the observable in question remains undisturbed.

I am thinking that if you perform the same measurement on the system, then the action would be zero as the system already is a solution of the SE with the same end boundary condition?