Overall, we end up with four spots or locations for the electrons at the end with an equal intensity on the screen: 1/4 went up and left, 1/4 went up and right, 1/4 down and left, 1/4 down and right.OK, as expected. Measurements taken along perpendicular axes would register no particular correlation. I take it that the deflection is small enough that a single second device measures both outputs of the first device.
Now, what happens if you do the experiment slightly differently? Instead of having two pieces of apparatus, with one just in front of the other, we will use just one very long Stern-Gerlach apparatus and slowly rotate the apparatus while the electrons are travelling through it. Initially the apparatus would be aligned in z-axis direction when the electrons enter it, it would then be rotated so that the magnetic field was aligned in the y-axis direction by the time the electrons exit from it.Not sure. A quantum measurement is already taken (collapsed so to speak) by the initial z-alignment, so at no point is the new angle not yet measured. I think it will carry this collapsed state through the rotation, leaving again two dots. Before, you were measuring a previously unmeasured y component. Not the second time.
I take it that the deflection is small enough that a single second device measures both outputs of the first device.Yes, that is the situation I'm trying to go for. Historically, the up / down separation was sufficiently large that they needed two pieces of Stern-Gerlach apparatus for the the second y-axis alignment, one for each beam coming out of the first apparatus. We're going to keep the deflections small enough that we will be able to get all the output from the first apparatus into the central channel of the second apparatus (with some tolerance). As a thought experiment only, it won't make any difference whether you do need two pieces of apparatus for the second measurement. All we wanted to demonstrate was just that the y-axis component of spin, when measured, can be + or - with equal probability independantly of the first measurement.
That's my take anyway.Thank you. Also, this isn't anything I'm actually doing or desperately need an answer for. It's just something that was of interest, so you don't have to spend too long here. The thread will be here for a long time, if anything does come to mind.
More interestingly we can send the electrons through a z-axis aligned apparatus and then send them through a y-axis aligned apparatus.Ahem! SG1 device splits a single beam up/down relative to its incoming vector. You now have two beams U, D with different vectors, each of which is split left-right by SG2.
At the end of the experiment then, the electrons near the North pole of the last apparatus were not necessarily near the North pole of the first apparatus, they could have come from the South pole in the first apparatus.is potentially misleading.
so you really need two SG2s to do the second splitSeems like a splitting of hairs - but OK... as mentioned in post #3 or my second post, have two SG apparatus, one for each beam emerging from the first.
I can imagine a magnetic field that rotates with distance along the z axis,OK... but I'm having the electrons generally travel along the x-axis all the time. The SG apparatus can only be aligned with the magnetic field in the y-axis direction or z-axis direction, please.
the question is what do you mean by "slowly rotating" the device?I mean put the device in or on something which you can slowly rotate around the x-axis. Do that while the electron is travelling through it (along the x-axis).
or in practice a series of SGs each slightly rotated with respect to the previous oneThat is exactly how you might try to imagine the situation.
we'd get a circular distribution at the exit.Why do you think that? Do you mean two spots at any moment of time BUT, if the apparatus was rotating then these trace out a circle on the screen over time? I would still call that only two spots. Alternatively, did you mean that you get a circular distribution of electrons on the screen in every moment?
You might be interested in the umpteen ways we manipulate proton spins in an MRI system!Always willing to hear some interesting things and always grateful for any expertise.
how are the silver atoms entrained in a beam?Put silver in a furnace chamber, it will eventually start to vaporise. Put a small hole in the side of the chamber and a beam of essentially atomised silver streams out of it.
on Earth- which is rotating.It is, although not in the way we (possiby just I) want to rotate it. The centre of rotation and axis are in the wrong places.
However the question is what do you mean by "slowly rotating" the device? I can imagine a magnetic field that rotates with distance along the z axis, or in practice a series of SGs each slightly rotated with respect to the previous one, so if we ignore the essential divergence of the beams at each point, we'd get a circular distribution at the exit.IMO, it depends on how strong the magnetic field divergence is, and the rate of change of the SG apparatus axis along the path of the atoms.
If the divergence is strong enough, and the rate of change of the axis is slow enough, then the final result is two dots along the axis at the end of the SG apparatus.I'm not sure what you meant by "slow enough" change of the axis.
The results can be explained by assuming that the passing through SG apparatus changes the orientation of the atoms spin. Just like how polarizers change the polarization axis of the passing light.Sorry, no, it isn't simple to assume the SG actively changes the spin. Polarising filters and polarised light can also have similar problems.
I'm not sure what you meant by "slow enough" change of the axis.It can be measured by degree of axis change per cm.
Sorry, no, it isn't simple to assume the SG actively changes the spin. Polarising filters and polarised light can also have similar problems.We know pretty sure that polarizing filters change the polarization of light. Quarter wave plates can turn a linearly polarized light into a circularly polarized light.
If a SG device was a simple machine that just twisted the spin of a particle when it passes through, then it ought to do the same thing every time. It doesn't.It does in some cases, such as in the top diagram. If the second SG apparatus is inverted up and down, then all streaming atom will go down, and none goes up.
See your own diagram, last line and focus on the last or right-most SG apparatus. Send in electrons one at a time. They were all the same as far as you can make them (for example, if we assume the SG is a machine to change spins then they have just come out of the previous machine with spin +1/2 in the x-axis and we would reasonably accept that one electron is the same as another electron). The last SG apparatus spits out those electrons sometimes with spin +1/2 and sometimes -1/2 in the z-axis, that is utterly random. The SG isn't following any deterministic rules that a machine acting on the spin should have.It can be explained by assuming that there is some precession or non-zero residual random spin in the other axis. If the second SG apparatus is aligned in the same axis as the first one, then this residual random spin has no perceivable effect. On the other hand, if the second SG apparatus is aligned in the perpendicular axis to the first one, then this residual random spin brings the only perceivable effect. In between, the effect is a combination between the two factors, depending on which one is stronger.
I searched for electrogravity on Youtube, and this video shows up in the results.You can skip to the experiment part at around 5:30.
...
It does in some cases, such as in the top diagram.Yes, which is also consistent with taking a measurement. The component of spin in the z-axis was already known from the first apparatus. No wave function collapse was required in the second apparatus.
It can be explained by assuming that there is some .... random spin in the other axis.No, not quite. The phrasing needs to be very carefully constructed and precise here. This (un-measured) component of spin along a different axis isn't something that affects anything. I don't mean it doesn't affect the next SG apparatus and what happens in that, I mean it doesn't affect anything, not anything what-so-ever or at all. A property that the particle has really should be something that matters to the particle. It has got to affect something about its behaviour, future evolution... or be important to something involving the particle and what it does. If we bend the rules for declaring what is a property of the particle, then we can make up a new thing, let's say "the shoe size" of the particle and assume that is a property of the particle. Provided the value of this "shoe size" doesn't appear in any equation governing the behaviour or future evolution or anything about the particle, then it doesn't matter, we can assume it's a property of the particle. Similarly we can say that "the colour of my wall", "your weight in ounces", or "the Zippy-Zappy coefficent of Kryptonite" are all properties of the particle. Clearly, we don't want to bend the rules for declaring something to be a property of the particle: A property of the particle really should be something that matters to the particle somehow.
Worth being a bit pedantic and pointing out that it's more complicated with electrons, or any charged particle, in a magnetic field, because their path will also be be deflected by the Lorentz force.Their path can still be calculated.
That said, if we start with an electrically neutral atom we know that application of a homogeneous field results in alignment, and a divergent field produces separation,We've got the same conclusion here.
so sequential application of N divergent fields, each slightly rotated with respect to its predecessor, would be expected to produce a circular distribution consisting of 2N opposing arcs.But different here.
That video seems to be presenting an alternative view of what gravity might be. I only watched a minute, its relevance to the thread seemed limited.You can skip to the experiment part at around 5:30.
Homogeneous field only twist dipole objects in it without moving them from their existing position. Whereas diverging field can move them from their existing position.
This (un-measured) component of spin along a different axis isn't something that affects anything. I don't mean it doesn't affect the next SG apparatus and what happens in that, I mean it doesn't affect anything, not anything what-so-ever or at all. A property that the particle has really should be something that matters to the particle. It has got to affect something about its behaviour, future evolutionYou wrote contradicting statements in the same paragraph. Precession or wobbling is a widely observed phenomenon in macroscopic spinning objects. Assuming its complete absence in microscopic objects is an extraordinary assumption, IMO.
You wrote contradicting statements in the same paragraph.I don't see that anything was contradictory. However, some sentences did have a lot of negations in them: Don't, doesn't, not etc. and it may not be clear what they meant.
Precession or wobbling is a widely observed phenomenon in macroscopic spinning objects.By your own words, that is a macroscopic phenomenon.
Assuming its complete absence in microscopic objects is an extraordinary assumption, IMO.1. Something which happens in a macroscopic scale doesn't always happen at the microsocopic level.
I don't see that anything was contradictory.I do. You said it doesn't affect anything, right after saying it may affect the next SG apparatus.
I didn't suggest that precession can't happen. However, as it turns out, precession of spin in a magnetic field is handled slightly differently.Who handled what?
Whenever you measure the component, say the x-component of spin for an individual atom you won't get the value ~ Sin ωt, you will only ever get the value + or - 1/2.The SG apparatus can be turned to +/- 45 degree. How do you think the distribution will be, if the source is still unaligned?
In a single Stern-Gerlach apparatus, a beam of electrons is divided in two, you don't recombine the beams but you can show that sending either part of the split beam--each is spin polarized but oppositely--through a second doesn't conserve spin states.Afaik, Stern and Gerlach used silver atoms instead of electron.
If you have a spin up polarized half-beam, and it goes through a second apparatus which is rotated by some angle, maybe perpendicular, the spin up state doesn't distribute like in Boolean logic. If you build up a sequence and try to determine spin states for each beam you can't use the "previous state", you can't build what's known as a distributive lattice with the logic.What if it's not perpendicular? In the first configuration of the picture below, the spin from previous stage is maintained.
I do. You said it doesn't affect anything, right after saying it may affect the next SG apparatus.I think this is a language problem. The fault is mine and I should have tried to use clearer phrases. I don't think you really want me to go over it all again, it would take at least as much space as last time.
Afaik, Stern and Gerlach used silver atoms instead of electron.Yes but the Original Post didn't. It was talking about electrons.
The SG apparatus can be turned to +/- 45 degree. How do you think the distribution will be, if the source is still unaligned?For any individual electron, you can only ever get a value of +(1/2) ħ or - (1/2) ħ when you measure the component of spin along any direction.
Yes but the Original Post didn't. It was talking about electrons.The experiment using electron or ion add complexity to the resulting pattern caused by Lorentz force to the moving charged particle.
https://arxiv.org/pdf/1504.07963.pdf
Observing the spin of free electrons in action
(Stern-Gerlach experiment by free electrons)
Patent:139350140003006698 ,Tuesday, September16, 2014 1
Hosein Majlesi 2
Independent Researcher
Abstract
Stern-Gerlach experiment by free electron is very important experiment because it answered some questions that
remain unanswered for almost a century. Bohr and Pauli considered its objective observation
as impossible while some other scientists considered such observation as possible. The experiment on free
electrons has not been conducted so far because the high magnetic field gradient predicted there was thought
as impossible to generate. This paper proves that it is not only possible but also observable using a high
vacuum lamp which is deionized well. To obtain a high magnetic field gradient, it is not necessary to have
a very strong magnetic field and it is possible to observe the phenomenon using a very sharp pointed magnet
and adjusting the voltage in a certain distance from free electron beams. that objective observation
requires your consideration of some technical points simultaneously.In this experiment, no electric field and
no magnetic field does not change with time.
Figure 7: Figure 7-a represents the spiral path of
electrons caused by interaction. Figure b shows the
spiral path of electrons when confronted with inhomogeneous magnetic field
If we know nothing about the state of the electrons on entry, then we can say very little about how many would be deflected either way by the SG. Every electron is going up or down (well, diagonally up or diagonally down) none will go straight or only half of a unit diagonally etc. but we can say nothing about the intensity or numbers of electrons that pile up at each of the two possible exit points.In my question, it's unaligned, i.e. fresh from the oven.
Afaik, Stern and Gerlach used silver atoms instead of electron.Yes, sorry. I was generalising without thinking about it. It's a beam of fermionic states of silver atoms.
What if it's not perpendicular? In the first configuration of the picture below, the spin from previous stage is maintained.No it isn't. I think you misunderstand what the diagrams are about.
Any quantum physicist will tell you the spin state of fermionic bits of matter is only conserved until you measure it.Passing them through an SG apparatus is counted as a measurement.
Passing them through an SG apparatus is counted as a measurement.But you also say that the spin state is "maintained" from a previous stage. What does that mean?
Passing them through an SG apparatus is counted as a measurement.But you also say that the spin state is "maintained" from a previous stage. What does that mean?
What if it's not perpendicular? In the first configuration of the picture below, the spin from previous stage is maintained.It's my commentary on the first diagram, where z+ stream from first stage is maintained in second stage. Nothing changes into z-.
Apropos practicality, I guess that nowadays we could use a collimated stream of neutrons rather than silver atoms.I'm sure you could. Just try to use a particle of spin 1/2 so that the quantum number mz takes only two values. A Neutron would satisfy that and Silver atoms also did in the original experiment (as you may know, Silver has an electronic structure where most orbitals are full and contribute 0 net spin, only the unpaired electron in the 5s orbital contributes spin).
So any polarised stream S passing through a field at angle X to the plane of polarisation would be split into S(X) and S(-X)But if that angle, X, is 0 degrees then none at all are split and sent to your S(-X) collection point. We also know that when X = 90 degrees, S(X) and S(-X) have equal intensity.
Quote from: alancalverd on Today at 09:41:26
So any polarised stream S passing through a field at angle X to the plane of polarisation would be split into S(X) and S(-X)
But if that angle, X, is 0 degrees then none at all are split and sent to your S(-X) collection point. We also know that when X = 90 degrees, S(X) and S(-X) have equal intensity.
It's my commentary on the first diagram, where z+ stream from first stage is maintained in second stage. Nothing changes into z-.No that isn't what "happens".
Again, the diagram at the top doesn't say what you say.If you have a spin up polarized half-beam, and it goes through a second apparatus which is rotated by some angle, maybe perpendicular, the spin up state doesn't distribute like in Boolean logic. If you build up a sequence and try to determine spin states for each beam you can't use the "previous state", you can't build what's known as a distributive lattice with the logic.What if it's not perpendicular? In the first configuration of the picture below, the spin from previous stage is maintained.
(https://upload.wikimedia.org/wikipedia/commons/thumb/3/35/Sg-seq.svg/1280px-Sg-seq.svg.png)
I should have written Sx and S-xI don't think the notation is a serious problem, I knew what you meant and my reply just continued with that notation.
I can't imagine why anyone would want to blow neutrons through a magnetic trombone anyway.I don't expect I will ever do the experiment or have a practical application for it. However, you've got to ask "what if" questions at least some of the time when you're studying any science.
What constitutes a measurement and when does it happen?I think it is shorthand for the point at which a particle or photon interacts with something else.
Apropos practicality, I guess that nowadays we could use a collimated stream of neutrons rather than silver atoms.AFAIK, not all metal atoms produce the same effect. Gemini says that neutron can't be used in Stern Gerlach experiment to produce the same results as silver atoms.
Gemini says that neutron can't be used in Stern Gerlach experimentI don't know where Gemini was getting its information. It seems that neutrons have been put through a SG.