Spooky action at a distance not allowed?

In summary, Sabine Hossenfelder discusses the concept of entanglement and how it is often misunderstood as allowing for immediate communication between particles. She explains that in reality, changes made to one entangled particle will only affect the other once it is measured. Sabine also suggests that there may be both local and non-local aspects to hidden variables in entangled systems. However, her argument may be flawed as she does not consider the potential for a hidden variable aspect that is both local and non-local. Overall, her comments bring attention to the complexities of entanglement and the need for precise language in discussing these phenomena.
  • #1
kurt101
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TL;DR Summary
I came across a video by Sabine Hossenfelder where she claims that doing something to one entangled particle does not immediately affect the other one.
Sabine Hossenfelder implies spooky action at a distance is wrong. She says “They seem to think if you do something to one particle in an entangled pair, then that will immediately affect the other one. But this isn’t so. It’s only when you measure one particle, then you have to update the wave function of both. So long as you don’t measure them, doing something to one particle won’t affect the other one. You could for example flip the spin of one of the particles in the entangled pair, so that one becomes minus one and other other way around. You can do that without measuring spin. Like, you can do this in reality, in the laboratory, not just with mathematics. If you flip the spin of one particle, without measuring it, this will not do anything to the particle it’s entangled with.”

She made these comments here in a video she made.

I understood her above example to mean that if before you measure either particle that if you flip the spin of one of the entangled particles and then you measure the two particles, instead of measuring them as having opposite spin you will measure them as having the same spin. And that she is saying this proves that you can change one of the entangled particles and it does not change the other. If you think I am misunderstanding her example please let me know.

In my discussion with @DrChinese in this thread it was made clear to me that once a particle is measured in its basis state it can’t be non-locally steered out of it.
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This seems to leave the possibility that an entangled particle can be steered non-locally within its basis state. For example a photon’s polarization can be measured as 0 or 1 for a given polarizer at some angle, but the actual pointer state, if it was possible to observe it, could be +/- 45 degrees from the polarizer's angle and still be measured as having the same 0 or 1 state. In Sabine's example of flipping, a rotation of 90 degrees on one photon would not affect the other photon's pointer within its basis state because you are rotating it by 90 degrees and so it will just end up in the same place as opposed to if you rotated it by something other than 90 degrees.

Is Sabine making a mistake in her reasoning that spooky action at a distance is not possible because she is not considering steering of a particle’s pointer state within its basis?

I understand that in either case no signaling is allowed.
 
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  • #2
In general, you have a single state for the two-particle system. Changing that state may leave the particles entangled. It's slightly ambiguous what you mean by changing the spin of one particle. If the state is entangled, then you must be changing the spin of the entangled system.

As always a precise experimental or mathematical specification of what's happening would be preferred.
 
  • #3
PS I didn't watch the video.
 
  • #4
kurt101 said:
Sabine Hossenfelder implies spooky action at a distance is wrong.
Depends on what you mean by "spooky action at a distance". That phrase is vague ordinary language and can be given multiple meanings.

kurt101 said:
I understood her above example to mean that if before you measure either particle that if you flip the spin of one of the entangled particles and then you measure the two particles, instead of measuring them as having opposite spin you will measure them as having the same spin.
Yes. Operations like this are common in quantum computing; you should look at the quantum computing literature for good discussion.

kurt101 said:
In my discussion with @DrChinese in this thread it was made clear to me that once a particle is measured in its basis state it can’t be non-locally steered out of it.
You can't non-locally "steer" a particle at all. The "spin flip" operation discussed above is a local operation: the particle whose spin you want to flip has to locally pass through the appropriate quantum "gate" (the quantum computing term for it).

kurt101 said:
she is saying this proves that you can change one of the entangled particles and it does not change the other.
Again, that depends on what you mean by "changing". As @PeroK has pointed out, for two entangled particles you do not have a definite state for either particle by itself; you only have a definite state for the two-particle entangled system. The "spin flip" operation applied to one particle changes the two-particle entangled state. So that operation can be viewed as changing both particles, since it changes the two-particle system. But the operation only operates locally on one particle, so it can also be viewed as just changing that one particle.

What all of this shows is that vague ordinary language is the wrong tool to use in trying to understand these phenomena.
 
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  • #5
PeterDonis said:
Depends on what you mean by "spooky action at a distance". That phrase is vague ordinary language and can be given multiple meanings.

Sabine says “if you do something to one particle in an entangled pair, then that will immediately affect the other one.”

I think Sabine is describing how someone might think of entanglement using a hidden variable theory where each particle has its own state variable and non-local action is used to synchronize their states. If this is an acceptable premise for discussion, I would like to continue using it.

I think the flaw in Sabine's argument is that she is not considering the possibility that there can be a hidden variable aspect that is local and a hidden variable aspect that is non-local.

The local hidden variable aspect being:
We know from experiments that once an entangled particle has been separated into its basis state, whatever you do to its entangled partner won’t change it out of its basis state.

The non-local hidden variable aspect being:
We know from Bell experiments that there needs to be some aspect of a hidden variable that is shared or non-local.

For example you can describe two entangled photons A and B as having these variables to describe their polarization:
basis state (local aspect)
shared state (non local aspect)

Initially the entangled photon A and photon B have the same values for both the basis state and the shared state

If photon A goes into a polarizer at orientation of angle X then its new basis state is X and its shared state is changed by this interaction. Meanwhile the shared state of photon B is instantly updated to match A, but its basis state is not changed. And so A and B no longer match in their basis states.

Now if photon B goes to polarizer with orientation of angle X then it will be the same as A again. If photon B instead goes to a polarizer at a different angle then then it will have a different basis and shared state.

And going back to Sabine’s example of flipping, this could be done by changing the basis state, but keeping the shared state the same.

And you might ask what is the purpose of the shared state variable in this example? The purpose is when a photon enters a polarizer and is transitioning between basis states, it uses the shared state to determine the new basis rather than the basis state. Think of the basis state as a reference point and boundary for the shared state.

My point of this thread, is that I don’t think Sabine is making a valid argument against someone who thinks “if you do something to one particle in an entangled pair, then that will immediately affect the other one.”
 
  • #6
kurt101 said:
I think Sabine is describing how someone might think of entanglement using a hidden variable theory where each particle has its own state variable and non-local action is used to synchronize their states.
I doubt that, since there is no such theory.

kurt101 said:
If this is an acceptable premise for discussion
It's not, since there is no such theory. The rest of your post is personal speculation and is off limits here.
 
  • #7
PeterDonis said:
I doubt that, since there is no such theory.
There is no specific theory, but of course the concept of hidden variable theories are discussed all the time in Quantum Mechanics and on this forum.

PeterDonis said:
It's not, since there is no such theory. The rest of your post is personal speculation and is off limits here.
Ok, but it still seems to me her argument is wrong and worthy of a discussion somehow on this forum or somewhere else.
 
  • #8
kurt101 said:
the concept of hidden variable theories
Is not the same as actually having a specific theory that you can use to make predictions about a scenario. The latter is what you would need for what you are trying to do in this thread.
 
  • #9
kurt101 said:
it still seems to me her argument is wrong
So far all you have shown is that your understanding of what she is actually saying is wrong.
 
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  • #10
PeterDonis said:
So far all you have shown is that your understanding of what she is actually saying is wrong.
Like what?
 
  • #11
kurt101 said:
Like what?
Your basic claim is:

kurt101 said:
I don’t think Sabine is making a valid argument against someone who thinks “if you do something to one particle in an entangled pair, then that will immediately affect the other one.”
But so far, your descriptions of her argument are based on something @DrChinese said in another thread, which it's not clear to me is even related to this one, and a nonexistent hidden variable theory. Have you got anything else?
 
  • #12
PeterDonis said:
Your basic claim is:But so far, your descriptions of her argument are based on something @DrChinese said in another thread, which it's not clear to me is even related to this one, and a nonexistent hidden variable theory. Have you got anything else?
I think I can frame my argument using what I was trying to get across with the principle @DrChinese pointed out to me about steering in that other thread.

Once you separate a photon into one of two states using a polarizer, if you measure that photon in either path using a second polarizer with the same orientation you will only see that photon in the same state as it came out through the first polarizer. This is what is taught in a basic quantum mechanics course.

My point of bringing this up is there is nothing you can do to an entangled photon partner to steer a photon so it is detected in both paths of the second polarizer, but that does not mean the photon can't be steered. Just because a photon can only come out of two paths for a polarizer does not mean the actual photon can only have two polarizations values. The actual photon could have say a polarization value up to +/- 45 degrees from the state it came out of the first polarizer and still go through the second polarizer and only be detected in one path.

In the example Sabine gives, you can apply the above principles, and assume flipping one entangled photon can't do anything to change how its partner is measured when both photons are measured the same way. Both photons will be measured as either the same or opposite based on whether you applied the flip or not. However again using the same principle above, that does not mean there is not steering going on, but you won't see it when you measure the photons the same way.

And why do I think there is steering going on? Because when you measure the two entangled photons at an angles different from each other, you see differences that follow cosine(theta)^2 where theta is the difference between the angles. If there no steering, you would see a straight line graph instead.
 
  • #13
kurt101 said:
Once you separate a photon into one of two states using a polarizer
This has nothing to do with two entangled photons, which is the subject of Sabine's video.

kurt101 said:
there is nothing you can do to an entangled photon partner to steer a photon so it is detected in both paths of the second polarizer
That's because there is no photon state, period, which gets detected in both arms of any polarizer. Again, it has nothing to do with entanglement.

kurt101 said:
that does not mean the photon can't be steered
Of course not. Sabine is not saying that photons can't be steered.

kurt101 said:
Just because a photon can only come out of two paths for a polarizer does not mean the actual photon can only have two polarizations values
Of course not. Sabine is not saying anything different.

kurt101 said:
In the example Sabine gives, you can apply the above principles, and assume flipping one entangled photon can't do anything to change how its partner is measured when both photons are measured the same way.
That's not what Sabine says. You even quoted her in your OP: "It’s only when you measure one particle, then you have to update the wave function of both." It doesn't matter what kind of measurement you make on one of the particles (as long as you're measuring the observable that is being entangled and which your "flip" operation manipulates, namely polarization). It's the mere fact of making a measurement at all on one particle that makes the difference. That's what Sabine is saying. But that's not what you're claiming she is saying.

kurt101 said:
why do I think there is steering going on? Because when you measure...
In other words, when you actually try to state your own position, it is the same as what Sabine said. You agree with her that it is measuring one of the particles that makes the difference. Obviously the specific results that you measure will depend on the specific entangled state you started with and the specific manipulation you did before the measurement. Sabine is not saying anything different from any of that.

In short, you think you are somehow refuting something Sabine said, when in fact everything you say is consistent with what she said.

So what, exactly, is the point of this thread?
 
  • #14
kurt101 said:
If there no steering, you would see a straight line graph instead.
What is your basis for this claim?
 
  • #15
PeterDonis said:
This has nothing to do with two entangled photons, which is the subject of Sabine's video.
It does. It says you can't make the photon A go into both paths of the second polarizer no matter what you do to its entangled partner. It says that whatever hidden variable model one uses, it has to have this property. It gives guidance to why Sabine's flip example works as it does in a hidden variable model.
PeterDonis said:
That's because there is no photon state, period, which gets detected in both arms of any polarizer. Again, it has nothing to do with entanglement.
Ok, maybe I said that using wrong terminology, but that does not take away from my point. I thought it was called "state" as what you measure when you detect what path the polarizer it went through. Maybe measurement value is the right term?

PeterDonis said:
Of course not. Sabine is not saying that photons can't be steered.
I agree that she is not saying photons can't be steered at all, but just when they are measured. So I would amend my comments slightly, but the entirety of my argument still stands and I still disagree when she says "So long as you don’t measure them, doing something to one particle won’t affect the other one."

The problem with measurement being when the photon's state is updated is that the non-local decision is made when the photon goes through the first polarizer and not when it is actually detected later on say using a second polarizer of the same orientation with some kind of detector / counter. So logic says it has to be at the time of separation into the two values and not the actual detection.

PeterDonis said:
Of course not. Sabine is not saying anything different.
Ok, but see above comment on how we still differ.

PeterDonis said:
That's not what Sabine says. You even quoted her in your OP: "It’s only when you measure one particle, then you have to update the wave function of both." It doesn't matter what kind of measurement you make on one of the particles (as long as you're measuring the observable that is being entangled and which your "flip" operation manipulates, namely polarization). It's the mere fact of making a measurement at all on one particle that makes the difference. That's what Sabine is saying. But that's not what you're claiming she is saying.
Ok, same thing you are right and I overstated what she was saying. My defense for this mistake is that I kept going back to her first statement that I do take issue with "“They seem to think if you do something to one particle in an entangled pair, then that will immediately affect the other one."

PeterDonis said:
In other words, when you actually try to state your own position, it is the same as what Sabine said. You agree with her that it is measuring one of the particles that makes the difference. Obviously the specific results that you measure will depend on the specific entangled state you started with and the specific manipulation you did before the measurement. Sabine is not saying anything different from any of that.
PeterDonis said:
In short, you think you are somehow refuting something Sabine said, when in fact everything you say is consistent with what she said.
PeterDonis said:
So what, exactly, is the point of this thread?
Again I disagree with her in that I think "if you do something to one particle in an entangled pair, then that will immediately affect the other one". and that is where we disagree.
PeterDonis said:
What is your basis for this claim?
If the polarization of a photon was not rotated when it goes through a polarizer and you put it through a polarizer at orientation X versus a polarizer at orientation Y then I would expect the difference to be linear as you increase the difference in the angle. It clearly is not and so I have to assume the polarization got rotated.
 
  • #16
kurt101 said:
It says you can't make the photon A go into both paths of the second polarizer no matter what you do to its entangled partner.
It says you can't run any experiment that will detect a single photon in both paths of the second polarizer. It says that whether or not the photon is entangled with another one. The entangled partner is irrelevant. It is of course true that this statement holds for an entangled photon--because it holds for any photon whatever. But it is irrelevant to any discussion of entanglement since it has nothing to do with entanglement.

kurt101 said:
I thought it was called "state" as what you measure when you detect what path the polarizer it went through. Maybe measurement value is the right term?
"State" as I was using the term means what can be prepared in an experiment. To rephrase what I said without that word: it is impossible to prepare a photon by any process whatever such that it will be detected in both output arms of a polarizer.

Again, this is true whether or not the photon is entangled, so it tells you nothing useful about entanglement.

kurt101 said:
I agree that she is not saying photons can't be steered at all, but just when they are measured.
No, that's not what she's saying. She's saying that unless and until you measure one of a pair of entangled photons, you cannot say that "steering" one of the photons has any effect on the other. Only the results of measurements will show any such effects. But you can of course "steer" one photon by some non-measurement operation (such as a quantum computing gate) either before making a measurement, or without making any measurement at all. Sabine is not saying anything different.

kurt101 said:
The problem with measurement being when the photon's state is updated is that the non-local decision is made when the photon goes through the first polarizer
What is your basis for this claim?

kurt101 said:
I disagree with her in that I think "if you do something to one particle in an entangled pair, then that will immediately affect the other one"
So far you have provided no basis whatever for such a claim.
 
  • #17
kurt101 said:
If the polarization of a photon was not rotated when it goes through a polarizer and you put it through a polarizer at orientation X versus a polarizer at orientation Y then I would expect the difference to be linear as you increase the difference in the angle.
Why? It looks to me like you are just making up another personal speculation model here.
 
  • #18
PeterDonis said:
It says you can't run any experiment that will detect a single photon in both paths of the second polarizer. It says that whether or not the photon is entangled with another one. The entangled partner is irrelevant. It is of course true that this statement holds for an entangled photon--because it holds for any photon whatever. But it is irrelevant to any discussion of entanglement since it has nothing to do with entanglement.
I should probably draw a picture to clarify as I think I can see where the confusion is coming from. Basically I would use beam splitting polarizers that split the photons into two paths. And I would use a cascade so after the first polarizer there would be two second stage polarizers and that would end up with a total of 3 polarizers and 4 detectors for a given arm of the experiment. And I would expect to only see photons show up on 2 of the 4 detectors no matter what I do to the entangled pair.
PeterDonis said:
No, that's not what she's saying. She's saying that unless and until you measure one of a pair of entangled photons, you cannot say that "steering" one of the photons has any effect on the other. Only the results of measurements will show any such effects.
But she said "So long as you don’t measure them, doing something to one particle won’t affect the other one." I agree that measuring is the only way you are going to be able realize what happened, but that is not the same as where the steering actually happened. In other words, I take the steering to happen where the polarizer splits the photons into the two paths and not at the photomultiplier where the photon is actually counted. The measurement is considered to be at the photomultiplier right?
PeterDonis said:
But you can of course "steer" one photon by some non-measurement operation (such as a quantum computing gate) either before making a measurement, or without making any measurement at all. Sabine is not saying anything different.
But she is saying that this steering is only local and that this shows that "doing something to one particle won’t affect the other one". I don't see how the flip proves "doing something to one particle won't affect the other one" in the general sense. One example is not proof.

PeterDonis said:
What is your basis for this claim?
So far you have provided no basis whatever for such a claim.
Because once the photon on one arm has entered the polarizer and has split off into one of the two different paths and the entangled photon on the other arm has done the same, there is spatial separation between the two paths. The photon can't go back and change its mind on what path it had already chosen. And keep in mind in theory you can do the actual photomultiplier detection many light years later on a given path. So you can be very sure the photon did not turn around and take the other path.
 
  • #19
kurt101 said:
I should probably draw a picture
Why not just give a reference to a valid source that describes the experiment you have in mind? If you don't have such a source, why are you even bringing the experiment up?

kurt101 said:
I agree that measuring is the only way you are going to be able realize what happened, but that is not the same as where the steering actually happened.
In the sense that the "steering" is whatever non-measurement operation you are doing (such as a quantum computing gate), yes, of course when the measurement happened is not the same as when the steering happened. But the steering only happens to one photon: that's obvious just from the way the steering operation is done: it is done on one photon. So if you are going to claim that the steering somehow affects the other photon, you need to say what your basis is for making such a claim. So far you have given no such basis; you just keep making the same assertion without any support.

kurt101 said:
she is saying that this steering is only local
Yes, because that's obvious from the way the steering is done: only one of the photons interacts with the steering apparatus.

kurt101 said:
I don't see how the flip proves "doing something to one particle won't affect the other one" in the general sense.
The math for any such operation will look the same, regardless of what kinds of particles you are operating on. Sabine is just giving that one example because it's a common example in actual experiments (since photons are much easier to work with than other quantum particles).

kurt101 said:
once the photon on one arm has entered the polarizer and has split off into one of the two different paths and the entangled photon on the other arm has done the same, there is spatial separation between the two paths.
Yes. But--

kurt101 said:
The photon can't go back and change its mind on what path it had already chosen.
The photon takes both paths. It doesn't "choose" one or the other. This is obvious if you set up an experiment which tests for interference between the paths.

The detectors will only detect a photon on one path or the other, but there is no way to control which path. But that is a property of the detectors, or more precisely of the entire experimental setup including photon, polarizer, and detectors, not a property of the photon or the polarizer by themselves. You can't say that the photon only took one path before detection. You can only say that a photon was detected in just one path.

I believe I have already commented that vague ordinary language is the wrong tool for jobs like this. We are illustrating that here again. You really need to look at the math to understand what is going on; you cannot reason correctly about these things with vague ordinary language.
 
  • #20
PeterDonis said:
Why not just give a reference to a valid source that describes the experiment you have in mind? If you don't have such a source, why are you even bringing the experiment up?
The one that comes to mind was on an online quantum mechanical course from Brilliant. So I will have to dig up a source, capture it, or draw a picture.
PeterDonis said:
You can only say that a photon was detected in just one path.
Ok
PeterDonis said:
I believe I have already commented that vague ordinary language is the wrong tool for jobs like this. We are illustrating that here again. You really need to look at the math to understand what is going on; you cannot reason correctly about these things with vague ordinary language.
I don't think there is any disagreement on the math, but just disagreement on where the non-local action takes place. I want to think my view that the non-local action takes place before the detection is as valid as the view Sabine is taking and her example is not enough to prove otherwise. I can't see how this difference in views can change the math.
 
  • #21
kurt101 said:
I don't think there is any disagreement on the math
I would hope not.

kurt101 said:
disagreement on where the non-local action takes place.
In general, this is a matter of QM interpretation. Not all interpretations will give the same answer. Experimentally, all we know is that there is no experiment that can support any claim of the form "it takes place before measurement happens", since any experimental procedure that produces data at all does so using measurements.
 
  • #22
kurt101 said:
I want to think my view that the non-local action takes place before the detection is as valid as the view Sabine is taking and her example is not enough to prove otherwise.
As far as I can tell, Sabine is simply pointing out that experimentally, we can only tell that "non-local action" takes place when we make measurements. I'm not sure she is taking sides for or against any particular QM interpretation: she is just pointing out that experimentally the only thing we know for sure is that whatever "non-local action" happens, it is only known to us when we make a measurement. In other words, she is taking the same position that I describe in the last sentence of post #21.
 
  • #23
The irony is that it is quantum (field) theory that's strictly local by construction, and indeed Hossenfelder is right when she says that there are no (there even cannot be) non-local spooky actions at a distance within any relativistic quantum-field theoretical description of any kind of experiments, including Bell experiments with photons, which are the paradigmatic example for an experiment describing long-ranged correlations between far-distant measurements on entangled photons within local QED.
 
  • #24
vanhees71 said:
The irony is that it is quantum (field) theory that's strictly local by construction, and indeed Hossenfelder is right when she says that there are no (there even cannot be) non-local spooky actions at a distance within any relativistic quantum-field theoretical description of any kind of experiments, including Bell experiments with photons, which are the paradigmatic example for an experiment describing long-ranged correlations between far-distant measurements on entangled photons within local QED.

I am very strongly with team local, but I think there are crossed wires here. Everyone hopefully agrees that quantum field theories are local in the sense you describe. The disagreement is whether this locality is an effective locality emerging from some deeper non-local character, responsible for classically forbidden things like entanglement.
 
  • #25
Which "deeper non-local character"? Standard local QFT does the job very well.
 
  • #26
vanhees71 said:
Which "deeper non-local character"? Standard local QFT does the job very well.
An opponent would say that even though spacelike separated observables commute, the long-ranged correlation between far-distant measurements on entangled particles are classically forbidden and therefore imply some non-local ontology.
 
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  • #27
That just tells us that Nature doesn't behave classically.
 
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  • #28
vanhees71 said:
That just tells us that Nature doesn't behave classically.
So it only remains to clarify what is meant by "behave classically".
 
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  • #29
To "behave classically" means that the system behaves as described by classical physics, i.e., by classical (Newtonian or relativistic) mechanics, classical electrodynamics, and classical thermodynamics. It's well understood, when these theories are applicable as an approximation of the full quantum description.
 
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  • #30
PeterDonis said:
As far as I can tell, Sabine is simply pointing out that experimentally, we can only tell that "non-local action" takes place when we make measurements. I'm not sure she is taking sides for or against any particular QM interpretation: she is just pointing out that experimentally the only thing we know for sure is that whatever "non-local action" happens, it is only known to us when we make a measurement. In other words, she is taking the same position that I describe in the last sentence of post #21.
If that is the case then my criticism is that she should have worded it better and not make it sound as if she was making a definitive statement. Again here are her words "They seem to think if you do something to one particle in an entangled pair, then that will immediately affect the other one. But this isn’t so."

Here is the picture of Stern Gerlach cascade that illustrates what I was trying to explain. It is just one arm of the entanglement experiment and uses particles with charge as opposed to photons and polarizers, but the same principle applies. Also imagine the 2nd arm with the entangled partner particle where you try to do something on it to steer its partner.

stern-cascade.png


Repeating my argument, but for this picture. Nothing you do to the entangled partner can give you anything other than 100 percent up state in the final Stern-Gerlach Bz. Meaning that any attempted steering when the particle is between the first Stern-Gerlach and the final Stern-Gerlach will not be noticed.

So if we take this as a matter of principle for entangled particles, flipping the spin of the entangled particle can't change the spin of its entangled partner otherwise you would violate this. So if steering is going to happen the steering has to remain in the up state of the z axis. I would think that being in the upstate of the z-axis doesn't mean it has to be a pointer perfectly aligned with the up vector, but could be at some angle from it, but never so much that it is closer to the down vector of the z-axis.

That said, I assume once it goes through a Stern-Gerlach that any vector state is going to be very much aligned with the magnetic field as we only find it in two spots on the detection screen.

So I don't think Sabine's example of flipping disproves instant non-local steering or what she describes as “if you do something to one particle in an entangled pair, then that will immediately affect the other one.”
 
  • #31
kurt101 said:
If that is the case then my criticism is that she should have worded it better
You're entitled to your opinion of course. However:

kurt101 said:
Here is the picture of Stern Gerlach cascade that illustrates what I was trying to explain.
You don't need to keep belaboring this. You're just repeating yourself, and responding would just mean others repeating themselves. Enough is enough.
 
  • #32
Thread closed for moderation.
 
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