Free floating electron quantum spin axis locked to space?

[Leef]

This is my attempt at understanding any real world physical effects from quantum spin.

I will start with the short version first.

A ... When we have a free floating electron in space is the physical orientation of the quantum spin axis locked into a fixed 3D orientation and from there can only be flipped? Locked to empty space??

Long version

So if we have a simple free single electron with random 3D physical orientation flying through space at a well defined speed and direction. Electron is known to have only 2 states of quantum spin Up or Down. For this electron we will assume it has no physical spin, it is not tumbling. This electron is not in an atom thus NOT in an orbit / shell. Now this random electron passes through a Stern–Gerlach like devise with vertical magnetic field north up and horizontal electric field both of proper proportions to remove the electron charge effect (Lorentz Force).

B ... What are the possible observations about the spin? Only deflects up or down indicating its quantum spin or does it land anywhere on the lip shaped profile giving an ordination value of the spin axis?

C ...Is there a 50% chance a discreet photon is emitted indicating a spin flip or some random energy as the electron oscillates into alignment?

D ... Or in this context quantum spin is not applicable, it can only be applied in conjunction with other quantum values and or other quantum particles?

 

[Nugatory]

A ... When we have a free floating electron in space is the physical orientation of the quantum spin axis locked into a fixed 3D orientation and from there can only be flipped? Locked to empty space??

No matter what direction you set you Stern-Gerlach machine to, you will find the electron spin up half the time and down half the time, and you will either get a full-flip photon or no photon at all. So it's not locked in any orientation until you measure, yet when you go to measure, it behaves as if was already locked up or down on whatever orientation you chose.

Once it's been through the S-G machine, it is definitely in whatever state the S-G machine left it in. If it encounters another S-G machine set to another angle, it will come out either up or down with probabilities $\sin^2\frac{\theta}{2}$ and $1-\sin^2\frac{\theta}{2}$ where $\theta$ is the angle between the two settings.

 

[Leef]

OK thank you very much, now we are getting somewhere!

So after passing through S-G spin is known and set and stays that way for days if not disturbed and with perfect alignment of a second S-G the spin will measure the same correct?

So is it reasonable to say before measurement it was locked to space but with unknown spin of course do to lack of reference frame.

In reference to the image below I have done some searching and failed to find any experiments that do an S-G type of experiment with a rotating magnetic field. Seems like an obvious interesting direction to validate QM theories.

By using this device passing a single spin particle through looking for photon emission locations what does QM expect? An evenly distributed dot dot dot or dash dot dash dot or no emission?

My point being REALLY REALLY? In QM we can’t just slowly reorient a free floating electron in 3D Euler Space without a quantum jump?

 

[Nugatory]

So after passing through S-G spin is known and set and stays that way for days if not disturbed and with perfect alignment of a second S-G the spin will measure the same correct?

In principle, yes. In practice it's very hard to keep a charged particle like an electron from interacting promiscuously with its environment, so you'd be lucky to get more than a few milliseconds before it interacted with a stray air molecule or something, changing its state again.

So is it reasonable to say before measurement it was locked to space but with unknown spin of course do to lack of reference frame.

You'd think so, wouldn't you? Einstein did, so you'd be in good company. However...
It was only in the 1960s, well after Einstein's death, that John Bell was able to show (and eventually scored a Nobel prize for it) that "locked in space but with unknown spin" will produce different results in some experimental setups than the quantum mechanical model that the direction of spin doesn't even exist in any direction until it's measured. These experiments were done (and the many of the experimenters shared that Nobel) and they have pretty convincingly supported the quantum mechanical view and rejected the more commnsense view that there is a definite spin and we just don't what it is until we measure.

For a good non-technical overview of this entire history, I recommend Louisa Gilder's "The Age of Entanglement".
For slightly more technical overview, including links to the most crucial papers (Einstein in 1935, Bell in 1964) try our own DrChinese's website http://www.drchinese.com/Bells_Theorem.htm. There are also countless threads here (and please read them before posting if you think you've found a flaw in the logic!).

In reference to the image below I have done some searching and failed to find any experiments that do an S-G type of experiment with a rotating magnetic field. Seems like an obvious interesting direction to validate QM theories.

You might have more luck searching for charged particle interactions with circularly polarized electromagnetic fields, because that's really what you're talking about here. (You may not find much that makes sense if you're not at least a grad student in physics though - this is somewhat esoteric stuff). However, these interactions are well-studied, and they validate QM.

My point being REALLY REALLY? In QM we can’t just slowly reorient a free floating electron in 3D Euler Space without a quantum jump?

As I said above, you're in good company wanting to reject that notion, but... Yes, really.

But do note that you're making an assumption, probably without even realizing it, when you use the words "reorient" and "jump". You jump when you start in one place and suddenly move to another and you reorient when you start in one place and slowly move to another; so both models assume that we start in a definite spin state that can be changed to a another definite spin state by applying the inhomogeneous magnetic field in the S-G machine. That assumption is inconsistent with quantum mechanics and experiments.

 

[Heinera]

It was only in the 1960s, well after Einstein's death, that John Bell was able to show (and eventually scored a Nobel prize for it) that "locked in space but with unknown spin" will produce different results in some experimental setups than the quantum mechanical model that the direction of spin doesn't even exist in any direction until it's measured. These experiments were done (and the many of the experimenters shared that Nobel) [...]

Nobel prize to John Bell? Well, he was nominated for one, but that was as far as it got.

 

[Nugatory]

Nobel prize to John Bell? Well, he was nominated for one, but that was as far as it got.

Huh - I was posting without fact-checking - silly indeed because I did double-check his publication date instead of relying on memory. Sorry about that, you're right.

 

[Heinera]

The Royal Swedish Academy of Sciences (which picks the laureates) has avoided Bell's theorem and the associated experiments like the plague. Maybe that will change after the Delft experiment, but I have my doubts.

 

[Leef]

Thank you very much for replies I totally understand it takes time and that is valuable.
Feel free to correct my forum etiquette if needed.

Wow interesting because I didn’t talk Entanglement, Bell, or Delft experiment yet those are the very reasons I am on this forum. Delft BTW from what I can tell (the magic box) all sequences are initiated with a set of entangled photons so BS on the “no loop holes”

A Little about me skip if you like @@@@@@@@@@@@@@@@@@

I was a small town farm boy that at age 12 in the 70’s read my first book on particle physics and got hooked. Started college as AG major ended with BS Industrial Engineering.
Jobs: Electronic Engineer, Product Design Engineer, Chief Mechanical Engineer, Engineering Manager
Oh and computer programming on the side always

Particle Physics / QM all my life wandering in the back of my mind.

This is not my first rodeo for example my first day working as a Mechanical Engineer I had zero knowledge of that field. I was hired because I produced great prints. 3 months of late night study I had it down. 2 years later had moved from drafting to the Chief Engineer in a department of 30 engineers.

End of about me @@@@@@@@@@@@@@@@@

I am an OCD thinker so if I don’t understand something a mad search is underway.

I am here to learn the QM language kind of like a musician that can’t read music, time to find out if I have any QM insight or not. Bucket list thing I am over 50 now.

Clarification on my inadequate term "space" … I meant like outer space, vacuum nothing to interact with other than S-G mag and elec fields required to cause a straight fly through path of an electron. I am sure to do this in a lab would be challenging.
Yes all those tiny charged things are very Promiscuous, love that line.

I said "My point being REALLY REALLY? In QM we can’t just slowly reorient a free floating electron in 3D Euler Space without a quantum jump?"
Your reply

As I said above, you're in good company wanting to reject that notion, but... Yes, really.

By no means do I want to reject that idea but I do want to very clearly understand that in the current state of QM art this is factual observations.

But do note that you're making an assumption, probably without even realizing it, when you use the words "reorient" and "jump". You jump when you start in one place and suddenly move to another and you reorient when you start in one place and slowly move to another; so both models assume that we start in a definite spin state that can be changed to a another definite spin state by applying the inhomogeneous magnetic field in the S-G machine.

Did you miss the “can’t reorient”?? Either way very nice clarification. Yes I did and do realize the assumptions (kind of mostly). I am pleased that my careful inelegant way of wording it got the point across.

That assumption is inconsistent with quantum mechanics and experiments.

Here's my best guess at your meaning here …. It is unprofessional and or not precise or just can’t be a truly correct statement without laying the ground work to define all the other parameters …. This I understand (I’m under construction here)

Thanks again, all replies are greatly appreciated.

 

[Nugatory]

Clarification on my inadequate term "space" … I meant like outer space, vacuum nothing to interact with other than S-G mag and elec fields required to cause a straight fly through path of an electron. I am sure to do this in a lab would be challenging.

When we do experiments with electrons in a lab we put the source, the detector, and everything in between inside a single container and then use a vacuum pump to evacuate it and then sometimes chill the whole thing with liquid nitrogen to condense the vapors that the vacuum pump left behind - "cryopumping". The resulting vacuum is not as good as far outer space, but it's good enough to get reasonable experimental results.
However, all of this leads to experimental setups that are complicated, expensive, fragile (one little vacuum leak and you start all over), and have to fit into a volume that we can evacuate in a reasonable time. Thus, when it's possible to do an equivalent experiment with photons that's usually the preference - they move through many meters of air without any difficulty and can be moved for many thousands of meters through fiber-optic cables that cost less per meter than high-quality pasta.

Here's my best guess at your meaning here …. It is unprofessional and or not precise or just can’t be a truly correct statement without laying the ground work to define all the other parameters …. This I understand (I’m under construction here)

I mean that statement cannot be right, no matter how carefully and thoroughly the other parameters (which are called "hidden variables" in the context of Bell's theorem) are defined. Quantum mechanics says it's not right because the original state going into the S-G machine is not the same as a state of spin of definite and unknown spin and experiments based on bell's theorem have confirmed that claim. There really truly is not an "initial spin" to jump from or reorient from. Until we did the measurement there was no spin, in any direction.

 

[Leef]

The ol cryopump … Sorry a memory flash 1988, my First job out of college was Capital Records manufacturing plant making Compact Discs in a clean room. This included a Vacuum Metallizer with Oil diffusion and a cryopump.

OK I think I’m about to have a break through moment and learn something new.

Before this posting I thought Bell's theorem, No-go theorem ect only applied to a few odd things like entanglement and such. After a revisit on those I see they are far more reaching than that so I am getting there thank you.

I do understand the uncertainty principle (I think). I also get that measurements will always have an unavoidable statistical (probability) range do to the very nature of QM study.

I have designed and built analog to digital converter circuits many times, understand aliasing, heterodyning ect.

As a teen I understood that quantizing in QM is a built in requirement by more than one factor:
1. The very nature of Elementary Particles.
2. We are measuring the smallest things that exist with equipment that can only be made out of the very same E-Ps.
3. The signals (information) to and from any E-P will alls change some or all of the properties of the E-P under examination.

But this? “The Electron can have no spin”

I mean that statement cannot be right, no matter how carefully and thoroughly the other parameters (which are called "hidden variables" in the context of Bell's theorem) are defined. Quantum mechanics says it's not right because the original state going into the S-G machine is not the same as a state of spin of definite and unknown spin and experiments based on bell's theorem have confirmed that claim. There really truly is not an "initial spin" to jump from or reorient from. Until we did the measurement there was no spin, in any direction.

No spin?? Do you mean spin state would be considered in superposition? Not sure in this situation if up down spin can or are complementary variables.

Repeat here: In a vacuum we have a tight stream of incoming free floating electrons with an appropriate speed range but we know nothing else about these electrons. So before entering the S-G they would or should have a randomly oriented spin axis in 3D space” In the S-G machine we are looking for photon emission from the electron spin flip, we should see a ~50% hit rate.

So if the Statement in red is not consistent with QM’s because QM would say there was no spin before measurement then WOW I am about to get educated.

Here's a few guesses at it ...
1. Maybe this is a pure logic thing "Electrons can only be said to have spin at the moment some outside influence caused a reaction we can measure, at all other times it is considered to have no spin, not to be confused with 0 spin?
2. Electrons are known to only have spin when in an influencing magnetic field is present? This would be a big surprise to me.EDIT hours after posting ….. referring to #2. In QM world or any world would this be nearly impossible to know (prove) because of the electron charge there would be a conflict? You have to move a dipole to produce charge to measure dipole and you have to move dipole to produce charge to measure a dipole. That does not mean it is not so but it is impossible to verify?

 

[Nugatory]

No spin?? Do you mean spin state would be considered in superposition? Not sure in this situation if up down spin can or are complementary variables.

Superposition or not isn't an interesting distinction because it changes according to the basis you use to write the state. For example, the state in which a measurement will produce spin up along the z-axis 100% of the time (which we might write as $|+\rangle$ and is the state of those particles that have been deflected upwards by an S-G device aligned along the z-axis) is also the superposed state $\frac{\sqrt{2}}{2}(|L\rangle+|R\rangle)$ where $|L\rangle$ and $|R\rangle$ are the two states (deflected left and deflected right) that come out of a horizontally oriented S-G device. All I've done is write the same state using a different basis.

Up and down (along any axis) are not complementary variables, they're the two possible values of the same variable, namely spin along that axis. However, any measurements on any two different axes (180 degrees apart doesn't count, that's just relabeling up and down) are complementary variables.

Repeat here: In a vacuum we have a tight stream of incoming free floating electrons with an appropriate speed range but we know nothing else about these electrons. So before entering the S-G they would or should have a randomly oriented spin axis in 3D space” In the S-G machine we are looking for photon emission from the electron spin flip, we should see a ~50% hit rate.

So if the Statement in red is not consistent with QM’s because QM would say there was no spin before measurement then WOW I am about to get educated.

How did you prepare the incoming electron? If you prepared it in such a way that nothing except its speed range was controlled, then its state must be described by a density matrix... and yes, the formalism of QM refuses to assign a definite orientation in space to it. If you prepared it by passing it through a horizontally oriented S-G machine and picking out one of the left-deflected ones, then you've prepared it in the state $|L\rangle$ and we can say with confidence that it is in that state until the next interaction that disturbs it. Prepare it some other way, you'll get some other state.
(It remains in that state because $S_i$, the operator corresponding to a measurement of the spin along a given axis, commutes with the Hamiltonian. If we prepared a state of something that didn't commute with the Hamiltonian, such as position, it would tend to spread out over time).

Here's a few guesses at it .
1. Maybe this is a pure logic thing "Electrons can only be said to have spin at the moment some outside influence caused a reaction we can measure, at all other times it is considered to have no spin, not to be confused with 0 spin?
2. Electrons are known to only have spin when in an influencing magnetic field is present? This would be a big surprise to me.

It's a stronger than #1, "considered to have no spin". If we take the position that it might have a definite spin direction but we don't know what it is so we'll consider it to have no spin direction, we'll run up against Bell's theorem. Instead, we have to say that the electron has spin (definitely not zero!) but the spin has no direction until it interacts appropriately.
However, it's not as dire as #2: Once we've prepared them in a particular state by passing them through the magnetic field they stay that way even after we remove the magnetic field.

What's really going on here is that QM is a theory about the results of measurements and is completely silent about what might perhaps be happening behind the scenes. Given a system prepared in a particular state, QM will tell us the probabilities of getting various results out of whatever measurement we choose to make, no more and no less... And whatever measurement we make is also the state preparation procedure for the next measurement.

 

[vanhees71]

Nobel prize to John Bell? Well, he was nominated for one, but that was as far as it got.

I'm pretty sure that John Bell would have gotten a Nobel, if he lived longer. In my opinion, his work on the foundations of quantum theory is the most important work on the foundations of quantum theory since its discovery in 1925! Nowadays, that the violation of his famous inequality is proven (even claimed to be "loophole free" very recently), I'm pretty sure that he'd get the Nobel prize for this. Imho he'd also deserved a Nobel prize (together with Stephen Adler, and Roman Jackiw) for his discovery of anomalies (particularly the axial U(1) anomaly, which is widely known under the name of the three) in quantum field theory.

 

[Heinera]

I'm pretty sure that John Bell would have gotten a Nobel, if he lived longer. In my opinion, his work on the foundations of quantum theory is the most important work on the foundations of quantum theory since its discovery in 1925! Nowadays, that the violation of his famous inequality is proven (even claimed to be "loophole free" very recently), I'm pretty sure that he'd get the Nobel prize for this. Imho he'd also deserved a Nobel prize (together with Stephen Adler, and Roman Jackiw) for his discovery of anomalies (particularly the axial U(1) anomaly, which is widely known under the name of the three) in quantum field theory.

Well, they had nearly 30 years to award him the Nobel until he died at the young age of 62. The committee has always favoured experimental breakthroughs, and theory prizes has usually been awarded only when it has been connected to experimental results (either before or after). And, they have a criterion that prizes should go to "new physics". As fascinating as Bell's theorem is, it did not advance physics. It is interesting in a philosophical way, but its main achievement is to rule out old conceptions that no one believed in anyway.

 

[Leef]

Nugatory Thank you so much I have gotten more from this then you could possibly know.

I am getting a perception that in the physics community the entire Einstein Bell Hidden Variables thing is a highly opinionated debat pickings side issue like “republican OR democrat”?

I ask one more thing of you and quote me on this. In this forum where do I give warm fuzzies I need to send you an A+. The detail of the replies short sweet to the point yet lengthy in just the right places. You’re dealings with me a “stranger of unknown knowledge” was spot on. Much thanks.

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I am not asking to end (close) the thread here but for some personal closure I am going to ramble randomly a bit on some loosely related subject matter. Replies are welcome but not necessary. For the good of the forum we want to avoid subject divergent and dribbling on forever.

From a very early age I have been Hypothesizing physics, by sheer luck I found an older brother’s college physics book, 101 I would guess. I was fascinated by that Einstein guy in there. I am the youngest of 7, I would have been about 6th grade. I read the book cover to cover many many time because if I didn’t understand I had to read it again. From there on book reports were on particle physics.

Through the years I would check in on the state of quantum theory and I like most have my own hypothesis on the inner working of it all. About 10-15 years ago I had an epiphany while reading up on ultra low momentum neutrons. From there a revisit to double slip and entanglement and of course BAM Einstein Bell and Hidden Variables. Well if you can guess why ULMNs set me that path leave a comment. Life went on job family ect. Well I am back to plow this field. If you want to know the Earth isn’t flat you have to test the edge.

I have my own hypothesis on the Einstein Bell Hidden Variables stuff. So far my own personal understanding and hypothesis is holding up well. I dare not attempt explaining it yet, lots of due diligence needed and searching for facts that smack me down. Follow me if you dare I will be dipping my toe slowly hoping to avoid being perceived like vomit in print.