Superposition Revisited

[Alan Grayson]

I find the accepted interpretation of superposition in error, namely the conclusion that a system in such a state, is simultaneously in all states in its sum. For example, in the SG experiment, the UP / DOWN final states are defined by the orientation of the magnets. But here's the rub; we can do a transformation to any other basis set. So if the measured system is in some superposition, and is interpreted as being in those particular UP / DOWN states simulataneously, can't we say the system is ALSO in any other basis states obtained through a transformation from the measured states? Since these basis states are different, the standard interpretation of superposition implies the system is simultaneously in all basis states at the same time. AG

[Brent Meeker]

It's a vector.  I can be a a superposition just like a vector from Atlanta to New York is a superposition of a North vector and a East vector.

Brent

On 7/10/2025 3:49 PM, Alan Grayson wrote:

I find the accepted interpretation of superposition in error, namely the conclusion that a system in such a state, is simultaneously in all states in its sum. For example, in the SG experiment, the UP / DOWN final states are defined by the orientation of the magnets. But here's the rub; we can do a transformation to any other basis set. So if the measured system is in some superposition, and is interpreted as being in those particular UP / DOWN states simulataneously, can't we say the system is ALSO in any other basis states obtained through a transformation from the measured states? Since these basis states are different, the standard interpretation of superposition implies the system is simultaneously in all basis states at the same time. AG --
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[Alan Grayson]

On Thursday, July 10, 2025 at 6:47:37 PM UTC-6 Brent Meeker wrote:

It's a vector.  I can be a a superposition just like a vector from Atlanta to New York is a superposition of a North vector and a East vector.

Brent

That's exactly my point; any vector can be decomposed using any other basis states, which is another superposition. So, do you claim that the system is in all basis states simultaneously? AG

[Brent Meeker]

On 7/10/2025 7:39 PM, Alan Grayson wrote:

On Thursday, July 10, 2025 at 6:47:37 PM UTC-6 Brent Meeker wrote:

It's a vector.  I can be a a superposition just like a vector from Atlanta to New York is a superposition of a North vector and a East vector.

Brent

That's exactly my point; any vector can be decomposed using any other basis states, which is another superposition. So, do you claim that the system is in all basis states simultaneously? AG

First, it can be in a superposition of two basis vectors which are orthogonal to all the other basis vectors of the Hilbert space.  So it can't necessarily be decompose using any other basis stated  Think of a vector, v, in the x-y plane.  Choosing any pair of orthogonal vectors in the x-y plane you can write v=ax + by  You can choose some other basis vectors in the x-y plane, X and Y, and write the same state v=cX + dY  but you can't include a z component.  It's not in all x-y basis ever.  It's just in v, but v can be written in terms of different bases.  This is nothing unique to quantum mechanics.  It's just true of vector spaces.  Where QM differs is that in some cases we only have instruments to measure in a certain basis, or we could measure in any basis but we don't know v so we don't know the adpated basis in which to measure.

Brent

On 7/10/2025 3:49 PM, Alan Grayson wrote:

I find the accepted interpretation of superposition in error, namely the conclusion that a system in such a state, is simultaneously in all states in its sum. For example, in the SG experiment, the UP / DOWN final states are defined by the orientation of the magnets. But here's the rub; we can do a transformation to any other basis set. So if the measured system is in some superposition, and is interpreted as being in those particular UP / DOWN states simulataneously, can't we say the system is ALSO in any other basis states obtained through a transformation from the measured states? Since these basis states are different, the standard interpretation of superposition implies the system is simultaneously in all basis states at the same time. AG 

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[Alan Grayson]

On Thursday, July 10, 2025 at 11:04:21 PM UTC-6 Brent Meeker wrote:

On 7/10/2025 7:39 PM, Alan Grayson wrote:

On Thursday, July 10, 2025 at 6:47:37 PM UTC-6 Brent Meeker wrote:

It's a vector.  I can be a a superposition just like a vector from Atlanta to New York is a superposition of a North vector and a East vector.

Brent

That's exactly my point; any vector can be decomposed using any other basis states, which is another superposition. So, do you claim that the system is in all basis states simultaneously? AG

First, it can be in a superposition of two basis vectors which are orthogonal to all the other basis vectors of the Hilbert space.  So it can't necessarily be decompose using any other basis stated  Think of a vector, v, in the x-y plane.  Choosing any pair of orthogonal vectors in the x-y plane you can write v=ax + by  You can choose some other basis vectors in the x-y plane, X and Y, and write the same state v=cX + dY  but you can't include a z component.  It's not in all x-y basis ever.  It's just in v, but v can be written in terms of different bases.  This is nothing unique to quantum mechanics.  It's just true of vector spaces.  Where QM differs is that in some cases we only have instruments to measure in a certain basis, or we could measure in any basis but we don't know v so we don't know the adpated basis in which to measure.

Brent

In the SG experiment, we have two basis vectors, UP and DN which are determined by the orientation of the magnets. Based on linear algebra, the wf before measurement is a linear sum of these basis vectors. Are you claiming that this wf cannot be written as a sum of two other basis vectors, which could be measured by changing the orientation of the magnets? I think this is wrong. The same wf can be written as a superposition of any other basis vectors, whether we reorient the magnets or not. So, applying the standard interpretation of superposition in QM, the electron can be in all basis states before measurement -- a conclusion I find preposterous. AG

[Brent Meeker]

On 7/10/2025 10:52 PM, Alan Grayson wrote:

On Thursday, July 10, 2025 at 11:04:21 PM UTC-6 Brent Meeker wrote:

On 7/10/2025 7:39 PM, Alan Grayson wrote:

On Thursday, July 10, 2025 at 6:47:37 PM UTC-6 Brent Meeker wrote:

It's a vector.  I can be a a superposition just like a vector from Atlanta to New York is a superposition of a North vector and a East vector.

Brent

That's exactly my point; any vector can be decomposed using any other basis states, which is another superposition. So, do you claim that the system is in all basis states simultaneously? AG

First, it can be in a superposition of two basis vectors which are orthogonal to all the other basis vectors of the Hilbert space.  So it can't necessarily be decompose using any other basis stated  Think of a vector, v, in the x-y plane.  Choosing any pair of orthogonal vectors in the x-y plane you can write v=ax + by  You can choose some other basis vectors in the x-y plane, X and Y, and write the same state v=cX + dY  but you can't include a z component.  It's not in all x-y basis ever.  It's just in v, but v can be written in terms of different bases.  This is nothing unique to quantum mechanics.  It's just true of vector spaces.  Where QM differs is that in some cases we only have instruments to measure in a certain basis, or we could measure in any basis but we don't know v so we don't know the adpated basis in which to measure.

Brent

In the SG experiment, we have two basis vectors, UP and DN which are determined by the orientation of the magnets. Based on linear algebra, the wf before measurement is a linear sum of these basis vectors. Are you claiming that this wf cannot be written as a sum of two other basis vectors, 

No.

which could be measured by changing the orientation of the magnets? I think this is wrong. The same wf can be written as a superposition of any other basis vectors, whether we reorient the magnets or not. So, applying the standard interpretation of superposition in QM, the electron can be in all basis states before measurement -- a conclusion I find preposterous. AG

Do you find it preposterous that the vector from Atlanta to NYC can be written as a superposition of two other vectors in infinitely many different ways?

Brent

[Alan Grayson]

Of course not, because there are infinitely many paths in space between any two points. What you're ignoring is the third entity, the system being represented by the UP / DN superposition. In this case, according to the standard superposition interpretation in QM, the system will be in all basis states UP / DN simultaneously, including SG orientations not being measured. Why is this interpretation preferred compared to the Ignorance Interpretation? AG

[Brent Meeker]

There's no aUP+bDN superposition because UP and DN are the same up to a phase.  

How am I ignoring UP or DN.  Are you ignoring the Atlanta to NYC vector because you can write it as a sum of an east vector and a north vector?

In this case, according to the standard superposition interpretation in QM, the system will be in all basis states UP / DN simultaneously, including SG orientations not being measured. Why is this interpretation preferred compared to the Ignorance Interpretation? AG

Explain how your ignorance interpretation would work and I might be able to answer that.

Brent

[Alan Grayson]

On Friday, July 11, 2025 at 6:32:53 PM UTC-6 Brent Meeker wrote:

On 7/11/2025 4:27 PM, Alan Grayson wrote:

On Friday, July 11, 2025 at 1:19:10 PM UTC-6 Brent Meeker wrote:

On 7/10/2025 10:52 PM, Alan Grayson wrote:

On Thursday, July 10, 2025 at 11:04:21 PM UTC-6 Brent Meeker wrote:

On 7/10/2025 7:39 PM, Alan Grayson wrote:

On Thursday, July 10, 2025 at 6:47:37 PM UTC-6 Brent Meeker wrote:

It's a vector.  I can be a a superposition just like a vector from Atlanta to New York is a superposition of a North vector and a East vector.

Brent

That's exactly my point; any vector can be decomposed using any other basis states, which is another superposition. So, do you claim that the system is in all basis states simultaneously? AG

First, it can be in a superposition of two basis vectors which are orthogonal to all the other basis vectors of the Hilbert space.  So it can't necessarily be decompose using any other basis stated  Think of a vector, v, in the x-y plane.  Choosing any pair of orthogonal vectors in the x-y plane you can write v=ax + by  You can choose some other basis vectors in the x-y plane, X and Y, and write the same state v=cX + dY  but you can't include a z component.  It's not in all x-y basis ever.  It's just in v, but v can be written in terms of different bases.  This is nothing unique to quantum mechanics.  It's just true of vector spaces.  Where QM differs is that in some cases we only have instruments to measure in a certain basis, or we could measure in any basis but we don't know v so we don't know the adpated basis in which to measure.

Brent

In the SG experiment, we have two basis vectors, UP and DN which are determined by the orientation of the magnets. Based on linear algebra, the wf before measurement is a linear sum of these basis vectors. Are you claiming that this wf cannot be written as a sum of two other basis vectors, 

No.

which could be measured by changing the orientation of the magnets? I think this is wrong. The same wf can be written as a superposition of any other basis vectors, whether we reorient the magnets or not. So, applying the standard interpretation of superposition in QM, the electron can be in all basis states before measurement -- a conclusion I find preposterous. AG

Do you find it preposterous that the vector from Atlanta to NYC can be written as a superposition of two other vectors in infinitely many different ways?

Brent

Of course not, because there are infinitely many paths in space between any two points. What you're ignoring is the third entity, the system being represented by the UP / DN superposition. 

There's no aUP+bDN superposition because UP and DN are the same up to a phase.  

I've seen articles about SG and the wf is written as a superposition of UP and DN. AG 

How am I ignoring UP or DN.  Are you ignoring the Atlanta to NYC vector because you can write it as a sum of an east vector and a north vector?

In this case, according to the standard superposition interpretation in QM, the system will be in all basis states UP / DN simultaneously, including SG orientations not being measured. Why is this interpretation preferred compared to the Ignorance Interpretation? AG

Explain how your ignorance interpretation would work and I might be able to answer that.

Brent

The igorance interpretation says the electron before measurement is either UP or DN with some probability for each (which sums to unity). IOW, it has a value before measurement, but we don't know which one. What is the argument that it is both UP and DN before measurement? AG 

[Brent Meeker]

On 7/11/2025 7:04 PM, Alan Grayson wrote:

On Friday, July 11, 2025 at 6:32:53 PM UTC-6 Brent Meeker wrote:

On 7/11/2025 4:27 PM, Alan Grayson wrote:

On Friday, July 11, 2025 at 1:19:10 PM UTC-6 Brent Meeker wrote:

On 7/10/2025 10:52 PM, Alan Grayson wrote:

On Thursday, July 10, 2025 at 11:04:21 PM UTC-6 Brent Meeker wrote:

On 7/10/2025 7:39 PM, Alan Grayson wrote:

On Thursday, July 10, 2025 at 6:47:37 PM UTC-6 Brent Meeker wrote:

It's a vector.  I can be a a superposition just like a vector from Atlanta to New York is a superposition of a North vector and a East vector.

Brent

That's exactly my point; any vector can be decomposed using any other basis states, which is another superposition. So, do you claim that the system is in all basis states simultaneously? AG

First, it can be in a superposition of two basis vectors which are orthogonal to all the other basis vectors of the Hilbert space.  So it can't necessarily be decompose using any other basis stated  Think of a vector, v, in the x-y plane.  Choosing any pair of orthogonal vectors in the x-y plane you can write v=ax + by  You can choose some other basis vectors in the x-y plane, X and Y, and write the same state v=cX + dY  but you can't include a z component.  It's not in all x-y basis ever.  It's just in v, but v can be written in terms of different bases.  This is nothing unique to quantum mechanics.  It's just true of vector spaces.  Where QM differs is that in some cases we only have instruments to measure in a certain basis, or we could measure in any basis but we don't know v so we don't know the adpated basis in which to measure.

Brent

In the SG experiment, we have two basis vectors, UP and DN which are determined by the orientation of the magnets. Based on linear algebra, the wf before measurement is a linear sum of these basis vectors. Are you claiming that this wf cannot be written as a sum of two other basis vectors, 

No.

which could be measured by changing the orientation of the magnets? I think this is wrong. The same wf can be written as a superposition of any other basis vectors, whether we reorient the magnets or not. So, applying the standard interpretation of superposition in QM, the electron can be in all basis states before measurement -- a conclusion I find preposterous. AG

Do you find it preposterous that the vector from Atlanta to NYC can be written as a superposition of two other vectors in infinitely many different ways?

Brent

Of course not, because there are infinitely many paths in space between any two points. What you're ignoring is the third entity, the system being represented by the UP / DN superposition. 

There's no aUP+bDN superposition because UP and DN are the same up to a phase.  

I've seen articles about SG and the wf is written as a superposition of UP and DN. AG 

My mistake.

How am I ignoring UP or DN.  Are you ignoring the Atlanta to NYC vector because you can write it as a sum of an east vector and a north vector?

In this case, according to the standard superposition interpretation in QM, the system will be in all basis states UP / DN simultaneously, including SG orientations not being measured. Why is this interpretation preferred compared to the Ignorance Interpretation? AG

Explain how your ignorance interpretation would work and I might be able to answer that.

Brent

The igorance interpretation says the electron before measurement is either UP or DN with some probability for each (which sums to unity). IOW, it has a value before measurement, but we don't know which one. What is the argument that it is both UP and DN before measurement? AG m.

From my lecture:  Particles can be prepared with their spin in a particular direction by use of a Stern-Gerlach instrument. This is two magnets with their North and Sout poles facing each other and shaped so that one is a ridge and the opposite one is a valley.   The resulting field causes particles to align their spin along the axis from one pole to the other.  They may align either UP or DOWN and they are deflected in opposite directions depending on which way they align.  So whatever particles go into the S-G they come out in two beams, one with the spins aligned UP and the other with them aligned DOWN.  



One of the interesting things you can show with an S-G is that although the particles are deflected into different beams that actually each particle travels down both beams and it is only at a measuring instrument point that the measurement projects out a choice between one and the other. In the upper diagram particles are first put into spin +Z states and then the -Z ones are absorbed.  Then a second Stern-Gerlach which is turned on it's side relative to the first one, puts the particles into +X spin states, e.g. Pointing either right or left.  Now you might suppose that the Z spin component has been filtered out, but when you put the +X particles through a third S-G to measure their Z spin you find they are half up and half down.  But that's not hard to understand, the S-G mechanism is acting on the particles so it turns half the +X up and half of them down.  And you can block the +X side and let the -X particles go through the third S-G and find the same result: half +Z and half -Z.  So what happens if you let both the +X and the -X go through the third S-G?  You might think you'd get half +Z and half -Z, but NO!   They two recombine to produce the +Z only.  Which means that each particle took both paths so that it's two parts could recombine in phase to reproduce the +Z state.

Brent

[John Clark]

On Fri, Jul 11, 2025 at 10:04 PM Alan Grayson <agrays...@gmail.com> wrote:

> What is the argument that it is both UP and DN before measurement? AG 

Experiments have shown that Bell's Inequality is violated. You've asked this question several times before and I've answered it several times before, and in considerable detail, showing why the only logical conclusion we can make from that violation is that reality must be fundamentally different from what we might naïvely expect. 

John K Clark    See what's on my new list at  Extropolis 

vci

[Alan Grayson]

When I started this thread, I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. As I now recall, you discussed in detail three conditions, not all of which you claimed, can be true. But these were just assertions on your part, not in any respect proof of what you allege above.  Also, I didn't fully understand your assertions, assuming they were valid. AG

[Alan Grayson]

IIUC, you seem to have proven the Ignorance Interpretation of Superposition is false, without any reference to Bell experiments, but that's what I thought Bell experiments established for the first time starting around 1964. Since the SG experiment was first done in 1922, and Einstein passed away in 1955, how could Einstein presumably believe in the Ignorance Interpretation, given these results many years before his passing? Or am I mistaken that Einstein continued to believe in the Ignorance Interpretation despite the SG evidence to the contrary? TY, AG

[John Clark]

On Sun, Jul 13, 2025 at 1:31 AM Alan Grayson <agrays...@gmail.com> wrote:

> I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. 

I am now going to repeat a post I've sent to this list at least twice at your request, it's about what the Bell Inequality is and what the experimental fact that it is violated tells us about the nature of reality:

=== 

 

This is going to be a long post, you asked for it. First I'm gonna have to show that any theory (except for superdeterminism which is idiotic) that is deterministic, local and realistic cannot possibly explain the violation of Bell's Inequality that we see in our experiments, and then show why a theory like Many Worlds witch is deterministic and local but NOT realistic can.

The hidden variable concept was Einstein's idea, he thought there was a local reason all events happened, even quantum mechanical events, but we just can't see what they are. It was a reasonable guess at the time but today experiments have shown that Einstein was wrong, to do that I'm gonna illustrate some of the details of Bell's inequality with an example.

When a photon of undetermined polarization hits a polarizing filter there is a 50% chance it will make it through. For many years physicists like Einstein who disliked the idea that God played dice with the universe figured there must be a hidden variable inside the photon that told it what to do. By "hidden variable" they meant something different about that particular photon that we just don't know about. They meant something equivalent to a look-up table inside the photon that for one reason or another we are unable to access but the photon can when it wants to know if it should go through a filter or be stopped by one. We now understand that is impossible. In 1964 (but not published until 1967) John Bell showed that correlations that work by hidden variables must be less than or equal to a certain value, this is called Bell's inequality. In experiment it was found that some correlations are actually greater than that value. Quantum Mechanics can explain this, classical physics or even classical logic can not.

Even if Quantum Mechanics is someday proven to be untrue Bell's argument is still valid, in fact his original paper had no Quantum Mechanics in it and can be derived with high school algebra; his point was that any successful theory about how the world works must explain why his inequality is violated, and today we know for a fact from experiments that it is indeed violated. Nature just refuses to be sensible and doesn't work the way you'd think it should.            

I have a black box, it has a red light and a blue light on it, it also has a rotary switch with 6 connections at the 12,2,4,6,8 and 10 o'clock positions. The red and blue light blink in a manner that passes all known tests for being completely random, this is true regardless of what position the rotary switch is in. Such a box could be made and still be completely deterministic by just pre-computing 6 different random sequences and recording them as a look-up table in the box. Now the box would know which light to flash.

I have another black box. When both boxes have the same setting on their rotary switch they both produce the same random sequence of light flashes. This would also be easy to reproduce in a classical physics world, just record the same 6 random sequences in both boxes. 

The set of boxes has another property, if the switches on the 2 boxes are set to opposite positions, 12 and 6 o'clock for example, there is a total negative correlation; when one flashes red the other box flashes blue and when one box flashes blue the other flashes red. This just makes it all the easier to make the boxes because now you only need to pre-calculate 3 random sequences, then just change every 1 to 0 and every 0 to 1 to get the other 3 sequences and record all 6 in both boxes.

The boxes have one more feature that makes things very interesting, if the rotary switch on a box is one notch different from the setting on the other box then the sequence of light flashes will on average be different 1 time in 4. How on Earth could I make the boxes behave like that? Well, I could change on average one entry in 4 of the 12 o'clock look-up table (hidden variable) sequence and make that the 2 o'clock table. Then change 1 in 4 of the 2 o'clock and make that the 4 o'clock, and change 1 in 4 of the 4 o'clock and make that the 6 o'clock. So now the light flashes on the box set at 2 o'clock is different from the box set at 12 o'clock on average by 1 flash in 4. The box set at 4 o'clock differs from the one set at 12 by 2 flashes in 4, and the one set at 6 differs from the one set at 12 by 3 flashes in 4.

BUT I said before that boxes with opposite settings should have a 100% anti-correlation, the flashes on the box set at 12 o'clock should differ from the box set at 6 o'clock by 4 flashes in 4 NOT 3 flashes in 4. Thus if the boxes work by hidden variables then when one is set to 12 o'clock and the other to 2 there MUST be a 2/3 correlation, at 4 a 1/3 correlation, and of course at 6 no correlation at all.  A correlation greater than 2/3, such as 3/4, for adjacent settings produces paradoxes, at least it would if you expected everything to work mechanistically because of some local hidden variable involved.

Does this mean it's impossible to make two boxes that have those specifications? Nope, but it does mean hidden variables can not be involved and that means something very weird is going on. Actually it would be quite easy to make a couple of boxes that behave like that, it's just not easy to understand how that could be. 

Photons behave in just this spooky manner, so to make the boxes all you need it 4 things:

1) A glorified light bulb, something that will make two photons of unspecified but identical polarizations moving in opposite directions so you can send one to each box. An excited calcium atom would do the trick, or you could turn a green photon into two identical lower energy red photons with a crystal of potassium dihydrogen phosphate.

2) A light detector sensitive enough to observe just one photon. Incidentally the human eye is not quite good enough to do that but frogs can, for frogs when light gets very weak it must stop getting dimmer and appear to flash instead. 

3) A polarizing filter, we've had these for well over a century.

4) Some gears and pulleys so that each time the rotary switch is advanced one position the filter is advanced by 30 degrees. This is because it's been known for many years that the amount of light polarized at 0 degrees that will make it through a polarizing filter set at X is [COS (x)]^2; and if X = 30 DEGREES (π/6 radians) then the value is .75; if the light is so dim that only one photon is sent at a time then that translates to the probability that any individual photon will make it through the filter is 75%.

The bottom line of all this is that there can not be something special about a specific photon, some internal difference, some hidden local variable that determines if it makes it through a filter or not. Thus if we ignore a superdeterministic conspiracy, as we should, then one of two things MUST be true:

1) The universe is not realistic, that is, things do NOT exist in one and only one state both before and after they are observed. In the case of Many Worlds it means the very look up table as described in the above cannot be printed in indelible ink but, because Many Worlds assumes that Schrodinger's Equation means what it says, the look up table itself not only can but must exist in many different versions both before and after a measurement is made.

2) The universe is non-local, that is, everything influences everything else and does so without regard for the distances involved or amount of time involved or even if the events happen in the past or the future; the future could influence the past. But because Many Worlds is non-realistic, and thus doesn't have a static lookup table, it has no need to resort to any of these non-local influences to explain experimental results.

Einstein liked non-locality even less than nondeterminism, I'm not sure how he'd feel about non-realistic theories like Many Worlds, the idea wasn't discovered until about 10 years after his death.

  John K Clark    See what's on my new list at  Extropolis 

da7

[John Clark]

I should add that experimentalists have found that not just Bell but Leggett's Inequality is also violated, and that tells us that even if we assume that things are non-local they STILL can NOT be realistic, that is to say unmeasured things can NOT exist in one and only one definite state. You may not like that fact but the universe doesn't care if you like it or not.

 John K Clark    See what's on my new list at  Extropolis

e22

[Brent Meeker]

Barandes Minimal Modal Interpretation is non-local but realist (unmeasured things exist in a specific state) and is consistent with all standard QM results.

Brent

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[Alan Grayson]

On Sunday, July 13, 2025 at 4:49:46 AM UTC-6 John Clark wrote:

On Sun, Jul 13, 2025 at 1:31 AM Alan Grayson <agrays...@gmail.com> wrote:

> I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. 

I am now going to repeat a post I've sent to this list at least twice at your request, it's about what the Bell Inequality is and what the experimental fact that it is violated tells us about the nature of reality:

=== 

 

This is going to be a long post, you asked for it. First I'm gonna have to show that any theory (except for superdeterminism which is idiotic) that is deterministic, local and realistic cannot possibly explain the violation of Bell's Inequality that we see in our experiments, and then show why a theory like Many Worlds witch is deterministic and local but NOT realistic can.

Thanks for this post. Before going further into this issue, please define your three terms: deterministic, local and realistic. I think realistic means a system has a unique value of an observable to be measured, before the measurement occurs, which IMO implies the Ignorance Interpretation of any superposition. AG

The hidden variable concept was Einstein's idea, he thought there was a local reason all events happened, even quantum mechanical events, but we just can't see what they are. It was a reasonable guess at the time but today experiments have shown that Einstein was wrong, to do that I'm gonna illustrate some of the details of Bell's inequality with an example.

Do you understand how to derive Bell's Inequality, and exactly what, and why, its violation means? Wouldn't this be a better place to start your argument? AG 

[John Clark]

On Mon, Jul 14, 2025 at 5:41 AM Alan Grayson <agrays...@gmail.com> wrote:

> Thanks for this post. Before going further into this issue, please define your three terms: deterministic, 

True randomness is impossible because every event has a cause, although information about that cause may not always be available to every observer.  

> local 

The speed at which information can be transmitted, and the speed of cause-and-effect in general, is finite; and X cannot produce a change in Y without producing a change in something between X and Y.

> and realistic.

Every observable about an unmeasured particle exists in one definite state.  

No quantum interpretation that is consistent with experiments can be all three, Many Worlds is deterministic and local but it is not realistic, Pilot Wave theory is deterministic and realistic but not local, Objective Collapse is local and realistic but not deterministic. As for Copenhagen, its followers can't agree even among themselves what it is.

John K Clark    See what's on my new list at  Extropolis 

xr3

[Alan Grayson]

On Monday, July 14, 2025 at 5:44:37 AM UTC-6 John Clark wrote:

On Mon, Jul 14, 2025 at 5:41 AM Alan Grayson <agrays...@gmail.com> wrote:

> Thanks for this post. Before going further into this issue, please define your three terms: deterministic, 

True randomness is impossible because every event has a cause, although information about that cause may not always be available to every observer.  

This seems to be your interpretation of determinism. I thought it means there are non probabilistic laws that cause all events. AG 

> local 

The speed at which information can be transmitted, and the speed of cause-and-effect in general, is finite; and X cannot produce a change in Y without producing a change in something between X and Y.

Or, I suppose you could say, there is no instanteous action at a distance. AG 

> and realistic.

Every observable about an unmeasured particle exists in one definite state.  

No quantum interpretation that is consistent with experiments can be all three,

What is the origin or justification for this claim? TY, AG 

[Alan Grayson]

On Sunday, July 13, 2025 at 2:27:00 PM UTC-6 Brent Meeker wrote:

Barandes Minimal Modal Interpretation is non-local but realist (unmeasured things exist in a specific state) and is consistent with all standard QM results.

Brent

By non local, do you mean instantaneous action at a distance, and if so, how is this consistent with standard QM results? AG 

Here's one of his lectures,  https://www.youtube.com/watch?v=YbmDwww-65o , The Major Problem No One Solved in Quantum Theory

AG

[John Clark]

On Mon, Jul 14, 2025 at 10:42 PM Alan Grayson <agrays...@gmail.com> wrote:

>> No quantum interpretation that is consistent with experiments can be all three,

 

> What is the origin or justification for this claim? TY, AG 

The justification, as I have said before, is that experimenters have found that Bell's Inequality is violated and, as I have also said before, if you want to get an intuitive understanding of what this is all about then read my long post about that which I have sent at least three times.

John K Clark    See what's on my new list at  Extropolis 

ob1

[Alan Grayson]

On Tuesday, July 15, 2025 at 4:11:56 AM UTC-6 John Clark wrote:

On Mon, Jul 14, 2025 at 10:42 PM Alan Grayson <agrays...@gmail.com> wrote:

>> No quantum interpretation that is consistent with experiments can be all three,

 

> What is the origin or justification for this claim? TY, AG 

The justification, as I have said before, is that experimenters have found that Bell's Inequality is violated and, as I have also said before, if you want to get an intuitive understanding of what this is all about then read my long post about that which I have sent at least three times.

I AM reading it, but parsing it as you always do to my comments. AG 

[Brent Meeker]

On 7/14/2025 2:41 AM, Alan Grayson wrote:

On Sunday, July 13, 2025 at 4:49:46 AM UTC-6 John Clark wrote:

On Sun, Jul 13, 2025 at 1:31 AM Alan Grayson <agrays...@gmail.com> wrote:

> I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. 

I am now going to repeat a post I've sent to this list at least twice at your request, it's about what the Bell Inequality is and what the experimental fact that it is violated tells us about the nature of reality:

=== 

 

This is going to be a long post, you asked for it. First I'm gonna have to show that any theory (except for superdeterminism which is idiotic) that is deterministic, local and realistic cannot possibly explain the violation of Bell's Inequality that we see in our experiments, and then show why a theory like Many Worlds witch is deterministic and local but NOT realistic can.

Thanks for this post. Before going further into this issue, please define your three terms: deterministic, local and realistic. I think realistic means a system has a unique value of an observable to be measured, before the measurement occurs, which IMO implies the Ignorance Interpretation of any superposition. AG

No.  A superposition is a definite state, it's just expressed as the sum of two different basis states.  For example a spin state of UP is also a superposition of LEFT and RIGHT states.  The LEFT and RIGHT states have coherent probability amplitudes such that they add to an UP state.  The ignorance interpretation applies to mixed states.

Brent

The hidden variable concept was Einstein's idea, he thought there was a local reason all events happened, even quantum mechanical events, but we just can't see what they are. It was a reasonable guess at the time but today experiments have shown that Einstein was wrong, to do that I'm gonna illustrate some of the details of Bell's inequality with an example.

Do you understand how to derive Bell's Inequality, and exactly what, and why, its violation means? Wouldn't this be a better place to start your argument? AG 

When a photon of undetermined polarization hits a polarizing filter there is a 50% chance it will make it through. For many years physicists like Einstein who disliked the idea that God played dice with the universe figured there must be a hidden variable inside the photon that told it what to do. By "hidden variable" they meant something different about that particular photon that we just don't know about. They meant something equivalent to a look-up table inside the photon that for one reason or another we are unable to access but the photon can when it wants to know if it should go through a filter or be stopped by one. We now understand that is impossible. In 1964 (but not published until 1967) John Bell showed that correlations that work by hidden variables must be less than or equal to a certain value, this is called Bell's inequality. In experiment it was found that some correlations are actually greater than that value. Quantum Mechanics can explain this, classical physics or even classical logic can not.

Even if Quantum Mechanics is someday proven to be untrue Bell's argument is still valid, in fact his original paper had no Quantum Mechanics in it and can be derived with high school algebra; his point was that any successful theory about how the world works must explain why his inequality is violated, and today we know for a fact from experiments that it is indeed violated. Nature just refuses to be sensible and doesn't work the way you'd think it should.            

I have a black box, it has a red light and a blue light on it, it also has a rotary switch with 6 connections at the 12,2,4,6,8 and 10 o'clock positions. The red and blue light blink in a manner that passes all known tests for being completely random, this is true regardless of what position the rotary switch is in. Such a box could be made and still be completely deterministic by just pre-computing 6 different random sequences and recording them as a look-up table in the box. Now the box would know which light to flash.

I have another black box. When both boxes have the same setting on their rotary switch they both produce the same random sequence of light flashes. This would also be easy to reproduce in a classical physics world, just record the same 6 random sequences in both boxes. 

The set of boxes has another property, if the switches on the 2 boxes are set to opposite positions, 12 and 6 o'clock for example, there is a total negative correlation; when one flashes red the other box flashes blue and when one box flashes blue the other flashes red. This just makes it all the easier to make the boxes because now you only need to pre-calculate 3 random sequences, then just change every 1 to 0 and every 0 to 1 to get the other 3 sequences and record all 6 in both boxes.

The boxes have one more feature that makes things very interesting, if the rotary switch on a box is one notch different from the setting on the other box then the sequence of light flashes will on average be different 1 time in 4. How on Earth could I make the boxes behave like that? Well, I could change on average one entry in 4 of the 12 o'clock look-up table (hidden variable) sequence and make that the 2 o'clock table. Then change 1 in 4 of the 2 o'clock and make that the 4 o'clock, and change 1 in 4 of the 4 o'clock and make that the 6 o'clock. So now the light flashes on the box set at 2 o'clock is different from the box set at 12 o'clock on average by 1 flash in 4. The box set at 4 o'clock differs from the one set at 12 by 2 flashes in 4, and the one set at 6 differs from the one set at 12 by 3 flashes in 4.

BUT I said before that boxes with opposite settings should have a 100% anti-correlation, the flashes on the box set at 12 o'clock should differ from the box set at 6 o'clock by 4 flashes in 4 NOT 3 flashes in 4. Thus if the boxes work by hidden variables then when one is set to 12 o'clock and the other to 2 there MUST be a 2/3 correlation, at 4 a 1/3 correlation, and of course at 6 no correlation at all.  A correlation greater than 2/3, such as 3/4, for adjacent settings produces paradoxes, at least it would if you expected everything to work mechanistically because of some local hidden variable involved.

Does this mean it's impossible to make two boxes that have those specifications? Nope, but it does mean hidden variables can not be involved and that means something very weird is going on. Actually it would be quite easy to make a couple of boxes that behave like that, it's just not easy to understand how that could be. 

Photons behave in just this spooky manner, so to make the boxes all you need it 4 things:

1) A glorified light bulb, something that will make two photons of unspecified but identical polarizations moving in opposite directions so you can send one to each box. An excited calcium atom would do the trick, or you could turn a green photon into two identical lower energy red photons with a crystal of potassium dihydrogen phosphate.

2) A light detector sensitive enough to observe just one photon. Incidentally the human eye is not quite good enough to do that but frogs can, for frogs when light gets very weak it must stop getting dimmer and appear to flash instead. 

3) A polarizing filter, we've had these for well over a century.

4) Some gears and pulleys so that each time the rotary switch is advanced one position the filter is advanced by 30 degrees. This is because it's been known for many years that the amount of light polarized at 0 degrees that will make it through a polarizing filter set at X is [COS (x)]^2; and if X = 30 DEGREES (π/6 radians) then the value is .75; if the light is so dim that only one photon is sent at a time then that translates to the probability that any individual photon will make it through the filter is 75%.

The bottom line of all this is that there can not be something special about a specific photon, some internal difference, some hidden local variable that determines if it makes it through a filter or not. Thus if we ignore a superdeterministic conspiracy, as we should, then one of two things MUST be true:

1) The universe is not realistic, that is, things do NOT exist in one and only one state both before and after they are observed. In the case of Many Worlds it means the very look up table as described in the above cannot be printed in indelible ink but, because Many Worlds assumes that Schrodinger's Equation means what it says, the look up table itself not only can but must exist in many different versions both before and after a measurement is made.

2) The universe is non-local, that is, everything influences everything else and does so without regard for the distances involved or amount of time involved or even if the events happen in the past or the future; the future could influence the past. But because Many Worlds is non-realistic, and thus doesn't have a static lookup table, it has no need to resort to any of these non-local influences to explain experimental results.

Einstein liked non-locality even less than nondeterminism, I'm not sure how he'd feel about non-realistic theories like Many Worlds, the idea wasn't discovered until about 10 years after his death.

  John K Clark    See what's on my new list at  Extropolis 

da7

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[Brent Meeker]

On 7/14/2025 11:42 PM, Alan Grayson wrote:

On Sunday, July 13, 2025 at 2:27:00 PM UTC-6 Brent Meeker wrote:

Barandes Minimal Modal Interpretation is non-local but realist (unmeasured things exist in a specific state) and is consistent with all standard QM results.

Brent

By non local, do you mean instantaneous action at a distance, and if so, how is this consistent with standard QM results? AG 

No.  There are two kinds of "local" in play here.  Bell's inequality is based on the wave-function factoring into one for particle A and one for particle B.  So it excludes correlations between the two.  Barande's theory excludes faster-than-light signaling but allows correlations due to quantum entanglement.

Brent

Here's one of his lectures,  https://www.youtube.com/watch?v=YbmDwww-65o , The Major Problem No One Solved in Quantum Theory

AG

On 7/13/2025 4:28 AM, John Clark wrote:

I should add that experimentalists have found that not just Bell but Leggett's Inequality is also violated, and that tells us that even if we assume that things are non-local they STILL can NOT be realistic, that is to say unmeasured things can NOT exist in one and only one definite state. You may not like that fact but the universe doesn't care if you like it or not.

 John K Clark    See what's on my new list at  Extropolis

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[Alan Grayson]

On Tuesday, July 15, 2025 at 1:45:07 PM UTC-6 Brent Meeker wrote:

On 7/14/2025 2:41 AM, Alan Grayson wrote:

On Sunday, July 13, 2025 at 4:49:46 AM UTC-6 John Clark wrote:

On Sun, Jul 13, 2025 at 1:31 AM Alan Grayson <agrays...@gmail.com> wrote:

> I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. 

I am now going to repeat a post I've sent to this list at least twice at your request, it's about what the Bell Inequality is and what the experimental fact that it is violated tells us about the nature of reality:

=== 

 

This is going to be a long post, you asked for it. First I'm gonna have to show that any theory (except for superdeterminism which is idiotic) that is deterministic, local and realistic cannot possibly explain the violation of Bell's Inequality that we see in our experiments, and then show why a theory like Many Worlds witch is deterministic and local but NOT realistic can.

Thanks for this post. Before going further into this issue, please define your three terms: deterministic, local and realistic. I think realistic means a system has a unique value of an observable to be measured, before the measurement occurs, which IMO implies the Ignorance Interpretation of any superposition. AG

No.  A superposition is a definite state, it's just expressed as the sum of two different basis states.  For example a spin state of UP is also a superposition of LEFT and RIGHT states.  The LEFT and RIGHT states have coherent probability amplitudes such that they add to an UP state.  The ignorance interpretation applies to mixed states.

Brent

Interesting point. TY. So in the case of mixed states, the Ignorance interpretation is not controversial. I suppose we can refer to those who think it is, as Ignorant? Succinctly, what are coherent probability amplitudes? AG 

[Alan Grayson]

On Sunday, July 20, 2025 at 5:54:09 PM UTC-6 Alan Grayson wrote:

On Tuesday, July 15, 2025 at 1:45:07 PM UTC-6 Brent Meeker wrote:

On 7/14/2025 2:41 AM, Alan Grayson wrote:

On Sunday, July 13, 2025 at 4:49:46 AM UTC-6 John Clark wrote:

On Sun, Jul 13, 2025 at 1:31 AM Alan Grayson <agrays...@gmail.com> wrote:

> I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. 

I am now going to repeat a post I've sent to this list at least twice at your request, it's about what the Bell Inequality is and what the experimental fact that it is violated tells us about the nature of reality:

=== 

 

This is going to be a long post, you asked for it. First I'm gonna have to show that any theory (except for superdeterminism which is idiotic) that is deterministic, local and realistic cannot possibly explain the violation of Bell's Inequality that we see in our experiments, and then show why a theory like Many Worlds witch is deterministic and local but NOT realistic can.

Thanks for this post. Before going further into this issue, please define your three terms: deterministic, local and realistic. I think realistic means a system has a unique value of an observable to be measured, before the measurement occurs, which IMO implies the Ignorance Interpretation of any superposition. AG

No.  A superposition is a definite state, it's just expressed as the sum of two different basis states.  For example a spin state of UP is also a superposition of LEFT and RIGHT states.  The LEFT and RIGHT states have coherent probability amplitudes such that they add to an UP state.  The ignorance interpretation applies to mixed states.

Brent

Interesting point. TY. So in the case of mixed states, the Ignorance interpretation is not controversial. I suppose we can refer to those who think it is, as Ignorant? Succinctly, what are coherent probability amplitudes? AG 

 

Does this mean that when a superposition represents the state of a system before measurement, the system is in all component states of the superposition simultaneously before measurement? AG 

[Alan Grayson]

On Sunday, July 20, 2025 at 10:21:14 PM UTC-6 Alan Grayson wrote:

On Sunday, July 20, 2025 at 5:54:09 PM UTC-6 Alan Grayson wrote:

On Tuesday, July 15, 2025 at 1:45:07 PM UTC-6 Brent Meeker wrote:

On 7/14/2025 2:41 AM, Alan Grayson wrote:

On Sunday, July 13, 2025 at 4:49:46 AM UTC-6 John Clark wrote:

On Sun, Jul 13, 2025 at 1:31 AM Alan Grayson <agrays...@gmail.com> wrote:

> I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. 

I am now going to repeat a post I've sent to this list at least twice at your request, it's about what the Bell Inequality is and what the experimental fact that it is violated tells us about the nature of reality:

=== 

 

This is going to be a long post, you asked for it. First I'm gonna have to show that any theory (except for superdeterminism which is idiotic) that is deterministic, local and realistic cannot possibly explain the violation of Bell's Inequality that we see in our experiments, and then show why a theory like Many Worlds witch is deterministic and local but NOT realistic can.

Thanks for this post. Before going further into this issue, please define your three terms: deterministic, local and realistic. I think realistic means a system has a unique value of an observable to be measured, before the measurement occurs, which IMO implies the Ignorance Interpretation of any superposition. AG

No.  A superposition is a definite state, it's just expressed as the sum of two different basis states.  For example a spin state of UP is also a superposition of LEFT and RIGHT states.  The LEFT and RIGHT states have coherent probability amplitudes such that they add to an UP state.  The ignorance interpretation applies to mixed states.

Brent

Interesting point. TY. So in the case of mixed states, the Ignorance interpretation is not controversial. I suppose we can refer to those who think it is, as Ignorant? Succinctly, what are coherent probability amplitudes? AG 

 

Does this mean that when a superposition represents the state of a system before measurement, the system is in all component states of the superposition simultaneously before measurement? AG 

IIUC, a superposition is written as a sum of basis states, each of which will be the result of a measurement. Since vectors in vector spaces written in this form can be legitimately interpreted as being in all basis states simultaneously, is this what QM affirms? TY, AG 

[John Clark]

On Wed, Jul 23, 2025 at 3:02 PM Alan Grayson <agrays...@gmail.com> wrote:

> IIUC, a superposition is written as a sum of basis states,

Yes.

 > each of which will be the result of a measurement. 

I think that's probably true but I'm surprised that you do too. Any individual experimenter will only see one basis state as a result of his measurement, but according to Hugh Everett's idea about Many Worlds some observer somewhere will see every possible basis state; and I think Everett was probably correct. 

John K Clark    See what's on my new list at  Extropolis 

w3n

[Alan Grayson]

What I mean is that one of the basis states will be the result of a measurement, not all. But the question I am asking is the state of the system before measurement. Is the system in all basis states before measurement, like the person traveling from Dallas to NY city can be described as being in all basis sets simultaneously, even those not orthogonal? AG 

w3n

[Brent Meeker]

On 7/23/2025 12:02 PM, Alan Grayson wrote:

On Sunday, July 20, 2025 at 10:21:14 PM UTC-6 Alan Grayson wrote:

On Sunday, July 20, 2025 at 5:54:09 PM UTC-6 Alan Grayson wrote:

On Tuesday, July 15, 2025 at 1:45:07 PM UTC-6 Brent Meeker wrote:

On 7/14/2025 2:41 AM, Alan Grayson wrote:

On Sunday, July 13, 2025 at 4:49:46 AM UTC-6 John Clark wrote:

On Sun, Jul 13, 2025 at 1:31 AM Alan Grayson <agrays...@gmail.com> wrote:

> I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. 

I am now going to repeat a post I've sent to this list at least twice at your request, it's about what the Bell Inequality is and what the experimental fact that it is violated tells us about the nature of reality:

=== 

 

This is going to be a long post, you asked for it. First I'm gonna have to show that any theory (except for superdeterminism which is idiotic) that is deterministic, local and realistic cannot possibly explain the violation of Bell's Inequality that we see in our experiments, and then show why a theory like Many Worlds witch is deterministic and local but NOT realistic can.

Thanks for this post. Before going further into this issue, please define your three terms: deterministic, local and realistic. I think realistic means a system has a unique value of an observable to be measured, before the measurement occurs, which IMO implies the Ignorance Interpretation of any superposition. AG

No.  A superposition is a definite state, it's just expressed as the sum of two different basis states.  For example a spin state of UP is also a superposition of LEFT and RIGHT states.  The LEFT and RIGHT states have coherent probability amplitudes such that they add to an UP state.  The ignorance interpretation applies to mixed states.

Brent

Interesting point. TY. So in the case of mixed states, the Ignorance interpretation is not controversial. I suppose we can refer to those who think it is, as Ignorant? Succinctly, what are coherent probability amplitudes? AG 

Coherent means having fixed relative phase (remember they are complex numbers with a phase term exp(-iHt) )

 

Does this mean that when a superposition represents the state of a system before measurement, the system is in all component states of the superposition simultaneously before measurement? AG 

IIUC, a superposition is written as a sum of basis states, each of which will be the result of a measurement. Since vectors in vector spaces written in this form can be legitimately interpreted as being in all basis states simultaneously, is this what QM affirms? TY, AG 

That's essentially correct.  One sometimes tricky point is that the basis states (just basis vectors) are not necessarily the same as the states you can measure.  Usually the two are chosen to align, but they don't have to; just like your compass measures magnetic north but your map is in terms of true north.   

Brent

The hidden variable concept was Einstein's idea, he thought there was a local reason all events happened, even quantum mechanical events, but we just can't see what they are. It was a reasonable guess at the time but today experiments have shown that Einstein was wrong, to do that I'm gonna illustrate some of the details of Bell's inequality with an example.

Do you understand how to derive Bell's Inequality, and exactly what, and why, its violation means? Wouldn't this be a better place to start your argument? AG 

When a photon of undetermined polarization hits a polarizing filter there is a 50% chance it will make it through. For many years physicists like Einstein who disliked the idea that God played dice with the universe figured there must be a hidden variable inside the photon that told it what to do. By "hidden variable" they meant something different about that particular photon that we just don't know about. They meant something equivalent to a look-up table inside the photon that for one reason or another we are unable to access but the photon can when it wants to know if it should go through a filter or be stopped by one. We now understand that is impossible. In 1964 (but not published until 1967) John Bell showed that correlations that work by hidden variables must be less than or equal to a certain value, this is called Bell's inequality. In experiment it was found that some correlations are actually greater than that value. Quantum Mechanics can explain this, classical physics or even classical logic can not.

Even if Quantum Mechanics is someday proven to be untrue Bell's argument is still valid, in fact his original paper had no Quantum Mechanics in it and can be derived with high school algebra; his point was that any successful theory about how the world works must explain why his inequality is violated, and today we know for a fact from experiments that it is indeed violated. Nature just refuses to be sensible and doesn't work the way you'd think it should.            

I have a black box, it has a red light and a blue light on it, it also has a rotary switch with 6 connections at the 12,2,4,6,8 and 10 o'clock positions. The red and blue light blink in a manner that passes all known tests for being completely random, this is true regardless of what position the rotary switch is in. Such a box could be made and still be completely deterministic by just pre-computing 6 different random sequences and recording them as a look-up table in the box. Now the box would know which light to flash.

I have another black box. When both boxes have the same setting on their rotary switch they both produce the same random sequence of light flashes. This would also be easy to reproduce in a classical physics world, just record the same 6 random sequences in both boxes. 

The set of boxes has another property, if the switches on the 2 boxes are set to opposite positions, 12 and 6 o'clock for example, there is a total negative correlation; when one flashes red the other box flashes blue and when one box flashes blue the other flashes red. This just makes it all the easier to make the boxes because now you only need to pre-calculate 3 random sequences, then just change every 1 to 0 and every 0 to 1 to get the other 3 sequences and record all 6 in both boxes.

The boxes have one more feature that makes things very interesting, if the rotary switch on a box is one notch different from the setting on the other box then the sequence of light flashes will on average be different 1 time in 4. How on Earth could I make the boxes behave like that? Well, I could change on average one entry in 4 of the 12 o'clock look-up table (hidden variable) sequence and make that the 2 o'clock table. Then change 1 in 4 of the 2 o'clock and make that the 4 o'clock, and change 1 in 4 of the 4 o'clock and make that the 6 o'clock. So now the light flashes on the box set at 2 o'clock is different from the box set at 12 o'clock on average by 1 flash in 4. The box set at 4 o'clock differs from the one set at 12 by 2 flashes in 4, and the one set at 6 differs from the one set at 12 by 3 flashes in 4.

BUT I said before that boxes with opposite settings should have a 100% anti-correlation, the flashes on the box set at 12 o'clock should differ from the box set at 6 o'clock by 4 flashes in 4 NOT 3 flashes in 4. Thus if the boxes work by hidden variables then when one is set to 12 o'clock and the other to 2 there MUST be a 2/3 correlation, at 4 a 1/3 correlation, and of course at 6 no correlation at all.  A correlation greater than 2/3, such as 3/4, for adjacent settings produces paradoxes, at least it would if you expected everything to work mechanistically because of some local hidden variable involved.

Does this mean it's impossible to make two boxes that have those specifications? Nope, but it does mean hidden variables can not be involved and that means something very weird is going on. Actually it would be quite easy to make a couple of boxes that behave like that, it's just not easy to understand how that could be. 

Photons behave in just this spooky manner, so to make the boxes all you need it 4 things:

1) A glorified light bulb, something that will make two photons of unspecified but identical polarizations moving in opposite directions so you can send one to each box. An excited calcium atom would do the trick, or you could turn a green photon into two identical lower energy red photons with a crystal of potassium dihydrogen phosphate.

2) A light detector sensitive enough to observe just one photon. Incidentally the human eye is not quite good enough to do that but frogs can, for frogs when light gets very weak it must stop getting dimmer and appear to flash instead. 

3) A polarizing filter, we've had these for well over a century.

4) Some gears and pulleys so that each time the rotary switch is advanced one position the filter is advanced by 30 degrees. This is because it's been known for many years that the amount of light polarized at 0 degrees that will make it through a polarizing filter set at X is [COS (x)]^2; and if X = 30 DEGREES (π/6 radians) then the value is .75; if the light is so dim that only one photon is sent at a time then that translates to the probability that any individual photon will make it through the filter is 75%.

The bottom line of all this is that there can not be something special about a specific photon, some internal difference, some hidden local variable that determines if it makes it through a filter or not. Thus if we ignore a superdeterministic conspiracy, as we should, then one of two things MUST be true:

1) The universe is not realistic, that is, things do NOT exist in one and only one state both before and after they are observed. In the case of Many Worlds it means the very look up table as described in the above cannot be printed in indelible ink but, because Many Worlds assumes that Schrodinger's Equation means what it says, the look up table itself not only can but must exist in many different versions both before and after a measurement is made.

2) The universe is non-local, that is, everything influences everything else and does so without regard for the distances involved or amount of time involved or even if the events happen in the past or the future; the future could influence the past. But because Many Worlds is non-realistic, and thus doesn't have a static lookup table, it has no need to resort to any of these non-local influences to explain experimental results.

Einstein liked non-locality even less than nondeterminism, I'm not sure how he'd feel about non-realistic theories like Many Worlds, the idea wasn't discovered until about 10 years after his death.

  John K Clark    See what's on my new list at  Extropolis 

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[Brent Meeker]

And you can measure a variable whose eigenvector is not a basis vector.  The basis for measurement is usually chosen to match that of the object state.  But if you don't know the object state you can't be sure it's in your basis, you just have choose what to measure.

Brent

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[John Clark]

On Thu, Jul 24, 2025 at 5:00 PM Brent Meeker <meeke...@gmail.com> wrote:

> you just have choose what to measure.

Yes, and there was a reason Brent Meeker made the measurement choice that Brent Meeker did OR there was not and it was random. If Many Worlds is correct then there was a reason; Brent Meeker made every choice that did not violate Schrodinger's Wave Equation because Brent Meeker is part of the Universal Wave Function. 

 John K Clark    See what's on my new list at  Extropolis 

ebq

[Alan Grayson]

On Tuesday, July 15, 2025 at 1:45:07 PM UTC-6 Brent Meeker wrote:

On 7/14/2025 2:41 AM, Alan Grayson wrote:

On Sunday, July 13, 2025 at 4:49:46 AM UTC-6 John Clark wrote:

On Sun, Jul 13, 2025 at 1:31 AM Alan Grayson <agrays...@gmail.com> wrote:

> I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. 

I am now going to repeat a post I've sent to this list at least twice at your request, it's about what the Bell Inequality is and what the experimental fact that it is violated tells us about the nature of reality:

=== 

 

This is going to be a long post, you asked for it. First I'm gonna have to show that any theory (except for superdeterminism which is idiotic) that is deterministic, local and realistic cannot possibly explain the violation of Bell's Inequality that we see in our experiments, and then show why a theory like Many Worlds witch is deterministic and local but NOT realistic can.

Thanks for this post. Before going further into this issue, please define your three terms: deterministic, local and realistic. I think realistic means a system has a unique value of an observable to be measured, before the measurement occurs, which IMO implies the Ignorance Interpretation of any superposition. AG

No.  A superposition is a definite state, it's just expressed as the sum of two different basis states.  For example a spin state of UP is also a superposition of LEFT and RIGHT states.  The LEFT and RIGHT states have coherent probability amplitudes such that they add to an UP state.  The ignorance interpretation applies to mixed states.

Brent

Can you write the spin state UP as a superposition of LEFT and RIGHT states, and explain the physical reason that is possible? It would explain a lot. TY, AG 

[John Clark]

On Fri, Jul 25, 2025 at 6:23 AM Alan Grayson <agrays...@gmail.com> wrote:

> Can you write the spin state UP as a superposition of LEFT and RIGHT states, 

Yes.

> and explain the physical reason that is possible?

 

If we're working with spin-1/2 particles like an electron then the UP and DOWN states form one complete basis, while LEFT and RIGHT states form another complete basis. Since both are bases for the same two-dimensional Hilbert space, any state in one basis can be expressed as a linear combination of states in the other basis. But if you've not actually made a UP vs Down measurement then the particle is still in a superposition of UP and DOWN, and if you then make a measurement of Left vs Right then there's no way to ever know if the particle was ever originally UP or DOWN. That is very weird but that's the way nature behaves. 

[Alan Grayson]

John K Clark    See what's on my new list at  Extropolis BtW

My problem is I can't imagine the geometry.  AG

[John Clark]

On Fri, Jul 25, 2025 at 7:00 AM Alan Grayson <agrays...@gmail.com> wrote:

> Can you write the spin state UP as a superposition of LEFT and RIGHT states, 

Yes.

> and explain the physical reason that is possible?

 

>>If we're working with spin-1/2 particles like an electron then the UP and DOWN states form one complete basis, while LEFT and RIGHT states form another complete basis. Since both are bases for the same two-dimensional Hilbert space, any state in one basis can be expressed as a linear combination of states in the other basis. But if you've not actually made a UP vs Down measurement then the particle is still in a superposition of UP and DOWN, and if you then make a measurement of Left vs Right then there's no way to ever know if the particle was ever originally UP or DOWN. That is very weird but that's the way nature behaves. 

> My problem is I can't imagine the geometry.  AG

Think of up-down as being the x-axis and right-left being the orthogonal Y-axis. An unmeasured electron is in a superposition, not necessarily 50-50, of up-down and left-right. If you knew exactly where that unmeasured electron should be on those two axes then you would know it's exact position and momentum, but that is impossible because if you measure the exact up-down then you have no idea of the left-right, and if you measure the left-right exactly then you have no idea of the up-down, although you can make approximate measurements of both. 

 John K Clark    See what's on my new list at  Extropolis 

0o7

 

[Alan Grayson]

But before the measurement in the SG experiment, the electron is entirely in the Y-axis? What's the logic for inferring a superposition in this situation? AG 

[John Clark]

On Fri, Jul 25, 2025 at 10:56 AM Alan Grayson <agrays...@gmail.com> wrote:

>>>>If we're working with spin-1/2 particles like an electron then the UP and DOWN states form one complete basis, while LEFT and RIGHT states form another complete basis. Since both are bases for the same two-dimensional Hilbert space, any state in one basis can be expressed as a linear combination of states in the other basis. But if you've not actually made a UP vs Down measurement then the particle is still in a superposition of UP and DOWN, and if you then make a measurement of Left vs Right then there's no way to ever know if the particle was ever originally UP or DOWN. That is very weird but that's the way nature behaves. 

>>> My problem is I can't imagine the geometry.  AG

>> Think of up-down as being the x-axis and right-left being the orthogonal Y-axis. An unmeasured electron is in a superposition, not necessarily 50-50, of up-down and left-right. If you knew exactly where that unmeasured electron should be on those two axes then you would know it's exact position and momentum, but that is impossible because if you measure the exact up-down then you have no idea of the left-right, and if you measure the left-right exactly then you have no idea of the up-down, although you can make approximate measurements of both. 

> But before the measurement in the SG experiment, the electron is entirely in the Y-axis?

Before the experiment the right-left orientation was unknown and so was its position on the Y-axis, and the same thing could be said about up-down and the X-axis. 

 

> What's the logic for inferring a superposition in this situation? AG 

If you randomly rotate a Stern–Gerlach magnet and arbitrarily give that direction the name "the up-down axis" then if you measure a number of previously unmeasured electrons with that device you will always find that it will detect 50% of them as being spin up and 50% as spin down. So before it was measured physicists say the electron was in a superposition of spin-up and spin-down. 

After that measurement we now know that every electron is definitely spin-up or spin-down, but the electrons are still in a superposition of spin-right and spin-left. We could rotate the SG magnet 90° and measure the electrons again and if we did we would definitely know that every electron was either spin right or spin left, but if we did that we would no longer know anything about spin-up or spin-down.

 

  John K Clark    See what's on my new list at  Extropolis 

dsu

[Brent Meeker]

On 7/25/2025 3:15 AM, John Clark wrote:

On Thu, Jul 24, 2025 at 5:00 PM Brent Meeker <meeke...@gmail.com> wrote:

> you just have choose what to measure.

Yes, and there was a reason Brent Meeker made the measurement choice that Brent Meeker did OR there was not and it was random. If Many Worlds is correct 

If Many Worlds is correct then there are no probabilities and everything happens.  It's possible, but it's not the way bet.

Brent

then there was a reason; Brent Meeker made every choice that did not violate Schrodinger's Wave Equation because Brent Meeker is part of the Universal Wave Function. 

 John K Clark    See what's on my new list at  Extropolis 

ebq

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[Brent Meeker]

Look up Bloch sphere.

Brent

[Brent Meeker]

IT'S A VECTOR SPACE.  Every vector can be written as a sum (superposition) of other vectors.

Brent

[Brent Meeker]

I don't think you "know" that in the past tense "was".  If you measure left/right then you know that after the measurement the electrons are either left or right.  It's misleading to say that because you measured them to be left or right, that they were in those states before measurement.  This is illustrated if you simply use the SG to split the paths into left and right and then merge the paths again they will again be in up or down.

Brent

 

  John K Clark    See what's on my new list at  Extropolis 

dsu

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[Alan Grayson]

On Tuesday, July 15, 2025 at 1:45:07 PM UTC-6 Brent Meeker wrote:

On 7/14/2025 2:41 AM, Alan Grayson wrote:

On Sunday, July 13, 2025 at 4:49:46 AM UTC-6 John Clark wrote:

On Sun, Jul 13, 2025 at 1:31 AM Alan Grayson <agrays...@gmail.com> wrote:

> I had completely forgotten the Bell experiments which allegedly show that the Ignorance Interpretation of Superposition is wrong, and I've never seen a clear demonstation of that result. 

I am now going to repeat a post I've sent to this list at least twice at your request, it's about what the Bell Inequality is and what the experimental fact that it is violated tells us about the nature of reality:

=== 

 

This is going to be a long post, you asked for it. First I'm gonna have to show that any theory (except for superdeterminism which is idiotic) that is deterministic, local and realistic cannot possibly explain the violation of Bell's Inequality that we see in our experiments, and then show why a theory like Many Worlds witch is deterministic and local but NOT realistic can.

Thanks for this post. Before going further into this issue, please define your three terms: deterministic, local and realistic. I think realistic means a system has a unique value of an observable to be measured, before the measurement occurs, which IMO implies the Ignorance Interpretation of any superposition. AG

No.  A superposition is a definite state, it's just expressed as the sum of two different basis states.  For example a spin state of UP is also a superposition of LEFT and RIGHT states. 

If, say, in the SG experiment, the right-left axis, is along the path of an electron before reaching the magnets -- the spin state up, which is along the up-down axis where the magnets are located and orthogonal to right-left axis -- cannot be written as a superposition of the right-left axis. In a subsequent post, you claim this is possible because of a property of "VECTOR SPACES", but not in this case. AG

The LEFT and RIGHT states have coherent probability amplitudes such that they add to an UP state.  The ignorance interpretation appl\ies to mixed states.

Brent

[John Clark]

On Fri, Jul 25, 2025 at 8:41 PM Brent Meeker <meeke...@gmail.com> wrote:

> I don't think you "know" that in the past tense "was". If you measure left/right then you know that after the measurement the electrons are either left or right.  It's misleading to say that because you measured them to be left or right, that they were in those states before measurement. 

I think what you say is probably true.  I too think it is very unlikely the electron was in one and only one definite state before it was measured, that's basically why I think the Many Worlds idea is probably correct. But you think Many Worlds is complete bologna, so I was surprised to see you write the above.   

  John K Clark    See what's on my new list at  Extropolis 

iws

[John Clark]

On Fri, Jul 25, 2025 at 11:54 PM Alan Grayson <agrays...@gmail.com> wrote:

> If, say, in the SG experiment, the right-left axis, is along the path of an electron before reaching the magnets -- the spin state up, which is along the up-down axis where the magnets are located and orthogonal to right-left axis -- cannot be written as a superposition of the right-left axis. 

If you make a measurement with a Stern–Gerlach magnet and determine that an electron is spin up, that is equivalent to saying the electron is in a superposition of spin left PLUS spin right along the orthogonal axis. And it would be the same for spin down except that then, instead of being a superposition of spin left PLUS spin right, it would be a superposition of spin left MINUS spin right.

  John K Clark    See what's on my new list at  Extropolis 

v[3

[Alan Grayson]

What orientation of the axes are you using to get that result? Please be explicit. AG 

v[3

[John Clark]

On Sat, Jul 26, 2025 at 11:34 AM Alan Grayson <agrays...@gmail.com> wrote:

>> If you make a measurement with a Stern–Gerlach magnet and determine that an electron is spin up, that is equivalent to saying the electron is in a superposition of spin left PLUS spin right along the orthogonal axis. And it would be the same for spin down except that then, instead of being a superposition of spin left PLUS spin right, it would be a superposition of spin left MINUS spin right.

> What orientation of the axes are you using to get that result? Please be explicit. AG 

I'm not sure what you mean by that. Place a point at the center of a Stern–Gerlach magnet and place another point randomly at any point on the outside circumference, draw a line between those two points in extended in both directions to infinity, that is one axis, arbitrarily call one direction along that axis "up" and the other direction "down". Now draw another line 90° from the first one, that is your other axis, pick one direction along that axis at random and call it "left", and the other direction "right"    

 John K Clark    See what's on my new list at  Extropolis 

a]6

[Alan Grayson]

I don't follow. Isn't UP / DN along the path taken by the electrons when they exit the apparatus? How is  RT / LT defined? AG 

a]6

[Alan Grayson]

If UP/DN is along the path taken by the electrons as they exit the apparatus, and RT/LT is oriented 90 deg wrt to that axis, then UP or DN cannot be written as linear sum of RT/LT. It's like claiming the unit vector along the x-axis, can be written as a linear sum of unit vectors along the y-axis in the plane. AG 

a]6

[John Clark]

On Sat, Jul 26, 2025 at 1:17 PM Alan Grayson <agrays...@gmail.com> wrote:

>> If you make a measurement with a Stern–Gerlach magnet and determine that an electron is spin up, that is equivalent to saying the electron is in a superposition of spin left PLUS spin right along the orthogonal axis. And it would be the same for spin down except that then, instead of being a superposition of spin left PLUS spin right, it would be a superposition of spin left MINUS spin right.

> What orientation of the axes are you using to get that result? Please be explicit. AG 

I'm not sure what you mean by that. Place a point at the center of a Stern–Gerlach magnet and place another point randomly at any point on the outside circumference, draw a line between those two points in extended in both directions to infinity, that is one axis, arbitrarily call one direction along that axis "up" and the other direction "down". Now draw another line 90° from the first one, that is your other axis, pick one direction along that axis at random and call it "left", and the other direction "right"    

> I don't follow. Isn't UP / DN along the path taken by the electrons when they exit the apparatus?

The direction you want to call UP/DN is entirely up to you, but whatever axis you pick if an unmeasured electron enters a Stern–Gerlach magnet that is oriented along that axis then there's a 50% chance it will go up and a 50% chance it will go down. 

And if you now rotate the magnet by 90° and call one end of that new axis left and the other end right and an unmeasured electron enters the magnet then there's a 50% chance it will go left and a 50% chance it will go right, and you'd get exactly the same result if the electron had not been unmeasured but instead had been measured to be spin up. 

> How is  RT / LT defined? AG 

 Spin left is defined as the superposition of spin up PLUS spin down.
 Spin right is the superposition of spin up MINUS spin down.

You might object that the minus sign makes no observable difference because the probability is the square of the absolute value of the quantum wave function and a minus times a minus is a plus; and that's true in some circumstances but not in others. If X interacts with Y and then I measure the outcome it makes no difference, BUT if  X interacts with Y and then I do NOT measure the result, but whatever the result is if I let it interact with Z and then measure it, then it does make a difference. That's why engineers who make quantum computers have to make sure that there's no way intermediate results of the machine can be determined, because if there is it would destroy the superposition and the computation. 

John K Clark    See what's on my new list at  Extropolis

otm

[Alan Grayson]

On Saturday, July 26, 2025 at 1:05:27 PM UTC-6 John Clark wrote:

On Sat, Jul 26, 2025 at 1:17 PM Alan Grayson <agrays...@gmail.com> wrote:

>> If you make a measurement with a Stern–Gerlach magnet and determine that an electron is spin up, that is equivalent to saying the electron is in a superposition of spin left PLUS spin right along the orthogonal axis. And it would be the same for spin down except that then, instead of being a superposition of spin left PLUS spin right, it would be a superposition of spin left MINUS spin right.

> What orientation of the axes are you using to get that result? Please be explicit. AG 

I'm not sure what you mean by that. Place a point at the center of a Stern–Gerlach magnet and place another point randomly at any point on the outside circumference, draw a line between those two points in extended in both directions to infinity, that is one axis, arbitrarily call one direction along that axis "up" and the other direction "down". Now draw another line 90° from the first one, that is your other axis, pick one direction along that axis at random and call it "left", and the other direction "right"    

> I don't follow. Isn't UP / DN along the path taken by the electrons when they exit the apparatus?

The direction you want to call UP/DN is entirely up to you, but whatever axis you pick if an unmeasured electron enters a Stern–Gerlach magnet that is oriented along that axis then there's a 50% chance it will go up and a 50% chance it will go down. 

Suppose I choose UP/DN axis along the path the electron moves when exiting the apparatus, and RT/LT perpendicular to that axis. In this case, you cannot write UP or DN as a linear combination of RT/LT. It's like the situation I previously cited in the plane using the orthogonal unit vectors as basis vectors. AG 

[Brent Meeker]

On 7/26/2025 12:04 PM, John Clark wrote:

On Sat, Jul 26, 2025 at 1:17 PM Alan Grayson <agrays...@gmail.com> wrote:

>> If you make a measurement with a Stern–Gerlach magnet and determine that an electron is spin up, that is equivalent to saying the electron is in a superposition of spin left PLUS spin right along the orthogonal axis. And it would be the same for spin down except that then, instead of being a superposition of spin left PLUS spin right, it would be a superposition of spin left MINUS spin right.

> What orientation of the axes are you using to get that result? Please be explicit. AG 

I'm not sure what you mean by that. Place a point at the center of a Stern–Gerlach magnet and place another point randomly at any point on the outside circumference, draw a line between those two points in extended in both directions to infinity, that is one axis, arbitrarily call one direction along that axis "up" and the other direction "down". Now draw another line 90° from the first one, that is your other axis, pick one direction along that axis at random and call it "left", and the other direction "right"    

> I don't follow. Isn't UP / DN along the path taken by the electrons when they exit the apparatus?

The direction you want to call UP/DN is entirely up to you, but whatever axis you pick if an unmeasured electron enters a Stern–Gerlach magnet that is oriented along that axis 

If it's an unmeasured electron the the chance of UP or DN could be anything.  Maybe it's an UP electron from a source that only produces UP electrons.

Brent

then there's a 50% chance it will go up and a 50% chance it will go down. 

And if you now rotate the magnet by 90° and call one end of that new axis left and the other end right and an unmeasured electron enters the magnet then there's a 50% chance it will go left and a 50% chance it will go right, and you'd get exactly the same result if the electron had not been unmeasured but instead had been measured to be spin up. 

> How is  RT / LT defined? AG 

 Spin left is defined as the superposition of spin up PLUS spin down.
 Spin right is the superposition of spin up MINUS spin down.

You might object that the minus sign makes no observable difference because the probability is the square of the absolute value of the quantum wave function and a minus times a minus is a plus; and that's true in some circumstances but not in others. If X interacts with Y and then I measure the outcome it makes no difference, BUT if  X interacts with Y and then I do NOT measure the result, but whatever the result is if I let it interact with Z and then measure it, then it does make a difference. That's why engineers who make quantum computers have to make sure that there's no way intermediate results of the machine can be determined, because if there is it would destroy the superposition and the computation. 

John K Clark    See what's on my new list at  Extropolis

otm

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[John Clark]

On Sun, Jul 27, 2025 at 12:29 AM Brent Meeker <meeke...@gmail.com> wrote:

>> The direction you want to call UP/DN is entirely up to you, but whatever axis you pick if an unmeasured electron enters a Stern–Gerlach magnet that is oriented along that axis

 

> If it's an unmeasured electron the the chance of UP or DN could be anything.  Maybe it's an UP electron from a source that only produces UP electrons.

If that is the case then somewhere and sometime in its lifetime the electron must've encountered something equivalent to a Stern–Gerlach magnet, and so the electron is NOT unmeasured. 

John K Clark    See what's on my new list at  Extropolis 

utc 

 

[John Clark]

On Sat, Jul 26, 2025 at 6:34 PM Alan Grayson <agrays...@gmail.com> wrote:

> Suppose I choose UP/DN axis along the path the electron moves when exiting the apparatus, and RT/LT perpendicular to that axis. In this case, you cannot write UP or DN as a linear combination of RT/LT. It's like the situation I previously cited in the plane using the orthogonal unit vectors as basis vectors. [...] Suppose I choose UP/DN axis along the path the electron moves when exiting the apparatus, and RT/LT perpendicular to that axis. In this case, you cannot write UP or DN as a linear combination of RT/LT.

Your reasoning would be perfectly correct if we were dealing with classical vectors where the components of directional vectors are real numbers in 3D space and orthogonal components are 100% independent. But quantum spin states are not like that, they're vectors in 2-dimensional Hilbert space and, unlike the sort of vectors that classical physics usually uses, they absolutely require imaginary numbers. And even though the experiment is being performed in 3-D space the electron only has two independent bases states not three. Regardless of if you choose to measure up-down or right-left you're working in the same 2D Hilbert space where any state expressible in one basis can be written in the other.

I know that everything I said in the above sounds very weird verging on the ridiculous, however the truth of it has been experimentally confirmed! If you prepare electrons in the up state and then measure them along the right left orthogonal axis you always get a 50-50 probability. That would be impossible with classical vectors made of independent components, but not if the vectors are composed of quantum states. And it's important to remember that although we use the words up, down, right and left they should be thought of as quantum states NOT directions. Your intuition is fine in classical physics but nobody's intuition is of much use in Quantum Mechanics. 

John K Clark    See what's on my new list at  Extropolis

tig

[Alan Grayson]

On Sunday, July 27, 2025 at 5:45:27 AM UTC-6 John Clark wrote:

On Sat, Jul 26, 2025 at 6:34 PM Alan Grayson <agrays...@gmail.com> wrote:

> Suppose I choose UP/DN axis along the path the electron moves when exiting the apparatus, and RT/LT perpendicular to that axis. In this case, you cannot write UP or DN as a linear combination of RT/LT. It's like the situation I previously cited in the plane using the orthogonal unit vectors as basis vectors. [...] Suppose I choose UP/DN axis along the path the electron moves when exiting the apparatus, and RT/LT perpendicular to that axis. In this case, you cannot write UP or DN as a linear combination of RT/LT.

Your reasoning would be perfectly correct if we were dealing with classical vectors where the components of directional vectors are real numbers in 3D space and orthogonal components are 100% independent. But quantum spin states are not like that, they're vectors in 2-dimensional Hilbert space and, unlike the sort of vectors that classical physics usually uses, they absolutely require imaginary numbers. And even though the experiment is being performed in 3-D space the electron only has two independent bases states not three. Regardless of if you choose to measure up-down or right-left you're working in the same 2D Hilbert space where any state expressible in one basis can be written in the other.

Vector spaces have associated fields such as complex numbers, and I never heard that Von Neumann changed the rules of vectors spaces when he applied them to QM.  Can you cite such a change? It's so radical that it must be clearly documented. AG

[John Clark]

On Sun, Jul 27, 2025 at 3:59 PM Alan Grayson <agrays...@gmail.com> wrote:

>> Your reasoning would be perfectly correct if we were dealing with classical vectors where the components of directional vectors are real numbers in 3D space and orthogonal components are 100% independent. But quantum spin states are not like that, they're vectors in 2-dimensional Hilbert space and, unlike the sort of vectors that classical physics usually uses, they absolutely require imaginary numbers. And even though the experiment is being performed in 3-D space the electron only has two independent bases states not three. Regardless of if you choose to measure up-down or right-left you're working in the same 2D Hilbert space where any state expressible in one basis can be written in the other.

> Vector spaces have associated fields such as complex numbers, and I never heard that Von Neumann changed the rules of vectors spaces when he applied them to QM.  Can you cite such a change? It's so radical that it must be clearly documented. AG

 

Von Neumann didn't change the rules of vector space nor did anybody else, what changed is what physical qualities correspond to what mathematical objects. To be consistent with experimental results, when dealing with the quantum world the physical interpretation has to be different than it is in classical physics. For example:

Classical: 3D objects spin components along x, y, z are 3 INDEPENDENT physical quantities.

Quantum: Spin-1/2 particles such as electrons only have 2 INDEPENDENT degrees of freedom, despite having measurable components along all three spatial axes, that's why any state expressible in one basis can be written in the other.

You wanted a reference for all this and you can find it in any textbook on quantum mechanics, such as the one by Dirac or Sakurai.

 John K Clark    See what's on my new list at  Extropolis

74d

[Alan Grayson]

On Sunday, July 27, 2025 at 2:34:46 PM UTC-6 John Clark wrote:

On Sun, Jul 27, 2025 at 3:59 PM Alan Grayson <agrays...@gmail.com> wrote:

>> Your reasoning would be perfectly correct if we were dealing with classical vectors where the components of directional vectors are real numbers in 3D space and orthogonal components are 100% independent. But quantum spin states are not like that, they're vectors in 2-dimensional Hilbert space and, unlike the sort of vectors that classical physics usually uses, they absolutely require imaginary numbers. And even though the experiment is being performed in 3-D space the electron only has two independent bases states not three. Regardless of if you choose to measure up-down or right-left you're working in the same 2D Hilbert space where any state expressible in one basis can be written in the other.

> Vector spaces have associated fields such as complex numbers, and I never heard that Von Neumann changed the rules of vectors spaces when he applied them to QM.  Can you cite such a change? It's so radical that it must be clearly documented. AG

 

Von Neumann didn't change the rules of vector space nor did anybody else, what changed is what physical qualities correspond to what mathematical objects. To be consistent with experimental results, when dealing with the quantum world the physical interpretation has to be different than it is in classical physics. For example:

Classical: 3D objects spin components along x, y, z are 3 INDEPENDENT physical quantities.

Quantum: Spin-1/2 particles such as electrons only have 2 INDEPENDENT degrees of freedom, despite having measurable components along all three spatial axes, that's why any state expressible in one basis can be written in the other.

If the rules of vector spaces haven't change, then what you claim above is mistaken. The UP state, which is specific, cannot be written as a sum of RT and LT states. I asked for specific references to any radical changes; not entire texts which won't prove what you allege. AG 

[Alan Grayson]

What I seek is a mathematical proof that the UP state can be written as a linear sum of LT and RT states. Short of that, what you write is just a rhetorical rationale for a dubious claim. AG 

[John Clark]

On Sun, Jul 27, 2025 at 6:01 PM Alan Grayson <agrays...@gmail.com> wrote:

> What I seek is a mathematical proof that the UP state can be written as a linear sum of LT and RT states.

 

Nobody can provide a mathematical proof of that, if it was possible mathematicians would have predicted the laws of quantum mechanics about the year 1800, maybe earlier. That's why physicists need to do experiments, and in this case there is a physical proof. Suppose I've measured a beam of electrons and know they are all spin up. If you're right and they are independent qualities then that information will be of no help whatsoever in predicting what I will get if I decide to measure that beam and see if the electrons in it are spin left or spin right, but it is of considerable help.

Thanks to that information I can predict that 50% of the electrons will be spin left and 50% will be spin right. And I can also predict that if I decide to recheck the spin left particles to make sure they are still spin up I will find that they are NOT, and the same is true if I measure the spin right particles. So I can know if an electron is spin up or spin down, OR I can know if an electron is spin left or spin right, BUT I can't know both, and I could if they were independent qualities. So you're wrong and I'm right, it's as simple as that.       

 John K Clark    See what's on my new list at  Extropolis

4s2

[Brent Meeker]

On 7/27/2025 3:50 AM, John Clark wrote:

On Sun, Jul 27, 2025 at 12:29 AM Brent Meeker <meeke...@gmail.com> wrote:

>> The direction you want to call UP/DN is entirely up to you, but whatever axis you pick if an unmeasured electron enters a Stern–Gerlach magnet that is oriented along that axis

 

> If it's an unmeasured electron the the chance of UP or DN could be anything.  Maybe it's an UP electron from a source that only produces UP electrons.

If that is the case then somewhere and sometime in its lifetime the electron must've encountered something equivalent to a Stern–Gerlach magnet, and so the electron is NOT unmeasured. 

So if I illuminate a piece of iron with some photons that knock out electrons via the photoelectric effect, then on passing them thru an SG magnet and detecting their distribution, you say they must necessarily be 50/50 UP/DN?

Brent

John K Clark    See what's on my new list at  Extropolis 

utc 

 

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[Alan Grayson]

I'm not disputing the experimental results, but it's hardly obvious that this means UP (or DN) can be written as a linear sum of RT and LT as it violates the basic rules of vector spaces. AG

[John Clark]

On Sun, Jul 27, 2025 at 9:14 PM Alan Grayson <agrays...@gmail.com> wrote:

> it violates the basic rules of vector spaces.

Only if you associate the quantum spin of an electron with a 3-D direction in classical space composed of three independent components, which for physical not mathematical reasons you can NOT do if you wish to be consistent with experimental results.  A quantum state is not what you think it is so you're using the WRONG mathematical object to represent it 

John K Clark    See what's on my new list at  Extropolis

wno

[Alan Grayson]

Really? If I understand correctly, IIUC, a quantum state is a linear sum of the possible states of a system after measurement. Do you disagree with this definition? What did Von Neumann say about this? I am skeptical that your words imply what you think they do. I await Brent's justification, if he has one. AG 

[Alan Grayson]

Measuring UP/DN is a different experiment than measuring RT/LT, so they have different bases, but by conflating the experiments causes a mistaken result, that UP (or DN) can be written as a linear sum of RT/LT. AG  

[Brent Meeker]

It's confusing because the linear sum is in Hilbert space not 3-space.  In Hilbert space |U> and |D> are not anti-parallel, they are orthogonal, <U|D>=0.  There are only 2-dimensions in the Hilbert space of a spin 1/2 particle.  So the space is spanned by any two orthogonal vectors; so |Left>=(|U>+|D>)/sqrt{2}  and |Right=(|U>-|D>)/sqrt{2}.  That's a mathematical proof if you believe in Hilbert space.

Brent

[Alan Grayson]

TY. Why are U and D orthogonal? A Hilbert space, IIUC, is like any vector space except that it's complete, meaning that it has a metric and Cauchy sequences converge. AG 

[John Clark]

On Mon, Jul 28, 2025 at 1:11 AM Alan Grayson <agrays...@gmail.com> wrote:

> Really?

Yes really, except when complex numbers are required.  

>  a quantum state is a linear sum of the possible states of a system after measurement. Do you disagree with this definition? 

I don't disagree with your definition but we know from experiment that quantum objects behave differently than classical objects, therefore they MUST be treated differently mathematically. A spinning electron is in a linear sum of complex quantum states in abstract 2D Hilbert space, BUT a spinning basketball is in a sum of real directions and magnitudes in real 3-D space. Your problem is not in the manipulation of mathematical symbols, your problem is knowing what mathematical device should be associated with what physical trait. To summarize: 

Quantum amplitudes are complex; classical vector components are real.

Electron spin lives in abstract 2D Hilbert space; classical angular momentum lives in real 3D physical space.

Quantum states are abstract mathematical objects; classical vectors represent measurable physical quantities in space.

And although it has some analogist behaviors, an electron isn't really "spinning" at all, it's a completely different beast. 

John K Clark    See what's on my new list at  Extropolis

akk

[John Clark]

On Sun, Jul 27, 2025 at 9:10 PM Brent Meeker <meeke...@gmail.com> wrote:

 

>>> If it's an unmeasured electron the the chance of UP or DN could be anything.  Maybe it's an UP electron from a source that only produces UP electrons.

 

>> If that is the case then somewhere and sometime in its lifetime the electron must've encountered something equivalent to a Stern–Gerlach magnet, and so the electron is NOT unmeasured. 

 

> So if I illuminate a piece of iron with some photons that knock out electrons via the photoelectric effect, then on passing them thru an SG magnet and detecting their distribution, you say they must necessarily be 50/50 UP/DN?

Not necessarily. Electrons in magnetic iron are not randomly oriented, so the electrons knocked out of the iron may have some preferential spin orientation. Also because angular momentum is conserved, circularly polarized light can preferentially eject electrons of one spin orientation over the other. But both the magnetic orientation of iron atoms and the amount of polarization of the light are known quantities, at least theoretically, therefore the electrons they eject cannot be considered "unmeasured" because sometime somewhere they have encountered something equivalent to a Stern–Gerlach magnet, just as I said.

John K Clark    See what's on my new list at  Extropolis 

ed4

 

[Brent Meeker]

Because they're modeling the physical state and the state can't be both |U> and |D>, <U|D>=0.  When you measure along some axis the result must be an eigen vector of the measurement (a repeat measurement must give 100% the same).  So a measurement along an axis (calling it Up and Down is arbitrary) must yield either |U> or |D> as the eigenvector.

Brent

[Alan Grayson]

ISTM that the orthogonal property is the usual application of QM, nothing particularly related to Hilbert spaces, where the wf before measurement is the linear sum of all possible states of the system BEFORE measurement, and are basis states. So, you seem to be assuming that U and D are basis states which span the space so they can't be anti-parallel. But if every linear combination is a legitimate state of the electron when exiting the SG apparatus before measurement, how can the continuous properties of these states be consistent with only two, U or D, being measured? Is this one of unsolved mysteries of QM? AG

[Brent Meeker]

On 7/28/2025 4:12 AM, John Clark wrote:

On Sun, Jul 27, 2025 at 9:10 PM Brent Meeker <meeke...@gmail.com> wrote:

 

>>> If it's an unmeasured electron the the chance of UP or DN could be anything.  Maybe it's an UP electron from a source that only produces UP electrons.

 

>> If that is the case then somewhere and sometime in its lifetime the electron must've encountered something equivalent to a Stern–Gerlach magnet, and so the electron is NOT unmeasured. 

 

> So if I illuminate a piece of iron with some photons that knock out electrons via the photoelectric effect, then on passing them thru an SG magnet and detecting their distribution, you say they must necessarily be 50/50 UP/DN?

Not necessarily. Electrons in magnetic iron are not randomly oriented, so the electrons knocked out of the iron may have some preferential spin orientation. Also because angular momentum is conserved, circularly polarized light can preferentially eject electrons of one spin orientation over the other. But both the magnetic orientation of iron atoms and the amount of polarization of the light are known quantities, at least theoretically, 

What's that supposed to mean, besides "I need it to be right."?

therefore the electrons they eject cannot be considered "unmeasured" because sometime somewhere they have encountered something equivalent to a Stern–Gerlach magnet, just as I said.

A bit of iron found in the ground is unlikely to have encountered an SG.  I think you're fudging the meaning of "measured" to cover your error.  You've just defined "unmeasured" to mean 50/50 distribution.  What's your definition of "measurement"?

Brent

[John Clark]

On Mon, Jul 28, 2025 at 3:50 PM Brent Meeker <meeke...@gmail.com> wrote:

>>> So if I illuminate a piece of iron with some photons that knock out electrons via the photoelectric effect, then on passing them thru an SG magnet and detecting their distribution, you say they must necessarily be 50/50 UP/DN?

 

>>Not necessarily. Electrons in magnetic iron are not randomly oriented, so the electrons knocked out of the iron may have some preferential spin orientation. Also because angular momentum is conserved, circularly polarized light can preferentially eject electrons of one spin orientation over the other. But both the magnetic orientation of iron atoms and the amount of polarization of the light are known quantities, at least theoretically, 

> What's that supposed to mean, besides "I need it to be right."?

Its meaning is self-evident. And I don't need to be right and often I'm wrong, but in this case I am right. And I think you're mad because I didn't fall for your trap.

 >You've just defined "unmeasured" to mean 50/50 distribution. 

That's the word I used to describe a single electron if I know nothing about its history. If it's not a single electron but there is a beam of them and I send many electrons through a Stern–Gerlach magnet then I may conclude that whatever the origin of the beam was, it's producing electrons in some distribution other than 50-50.

> What's your definition of "measurement"?

Rather than a definition of measurement I will give you something much better, an example. Producing an electron with a known spin state, as a piece of magnetized iron does when, thanks to the photoelectric effect, it's exposed to circularly polarized light; or when an electron passes through a Stern–Gerlach magnet.

> A bit of iron found in the ground is unlikely to have encountered an SG.

True, but it's not unlikely that something equivalent could have occurred.  

John K Clark    See what's on my new list at  Extropolis 

sqo

 

[Brent Meeker]

Who says it's only two?  Any two independent vectors in 2D complex Hilbert space can be used as a basis.

Brent

[Brent Meeker]

On 7/28/2025 1:38 PM, John Clark wrote:

On Mon, Jul 28, 2025 at 3:50 PM Brent Meeker <meeke...@gmail.com> wrote:

>>> So if I illuminate a piece of iron with some photons that knock out electrons via the photoelectric effect, then on passing them thru an SG magnet and detecting their distribution, you say they must necessarily be 50/50 UP/DN?

 

>>Not necessarily. Electrons in magnetic iron are not randomly oriented, so the electrons knocked out of the iron may have some preferential spin orientation. Also because angular momentum is conserved, circularly polarized light can preferentially eject electrons of one spin orientation over the other. But both the magnetic orientation of iron atoms and the amount of polarization of the light are known quantities, at least theoretically, 

> What's that supposed to mean, besides "I need it to be right."?

Its meaning is self-evident. 

It's far from self-evident that you know the magnetic orientation of the iron atoms before you measure anything?  Even "theoretically".

And I don't need to be right and often I'm wrong, but in this case I am right. And I think you're mad because I didn't fall for your trap.

 >You've just defined "unmeasured" to mean 50/50 distribution. 

That's the word I used to describe a single electron if I know nothing about its history. If it's not a single electron but there is a beam of them and I send many electrons through a Stern–Gerlach magnet then I may conclude that whatever the origin of the beam was, it's producing electrons in some distribution other than 50-50.

Exactly my point.  Your 50/50 just an epistemic assumption, which measurement may prove wrong.  Yet if you take the UP beam from the SG and measure Left/Right the distribution will be 50/50, which is not just epistemic.  

> What's your definition of "measurement"?

Rather than a definition of measurement I will give you something much better, an example. Producing an electron with a known spin state, as a piece of magnetized iron does when, thanks to the photoelectric effect, it's exposed to circularly polarized light; or when an electron passes through a Stern–Gerlach magnet.

So which step is the example of measurement, producing an electron with a known spin state, as when you first measure the magnetized direction of a piece of iron before ejecting an electron from it, or when the electron passes thru the SG and is detected as deflected up or down?

> A bit of iron found in the ground is unlikely to have encountered an SG.

True, but it's not unlikely that something equivalent could have occurred.  

That it cooled in the Earth's magnetic field?  Is that what you call equivalent to being separated in an SG?

Let me help you out.  A measurement is something that leaves a classical record of a value.   A classical record is one that can be read without disturbing its state.  So if you have piece of magnetized iron, its direction of magnetization is already measured...even though you don't know it; that's just because you haven't read the record.  If it's a single iron atom, it hasn't been measured.

Brent

[John Clark]

On Mon, Jul 28, 2025 at 6:55 PM Brent Meeker <meeke...@gmail.com> wrote:

 >>>You've just defined "unmeasured" to mean 50/50 distribution. 

>> That's the word I used to describe a single electron if I know nothing about its history. If it's not a single electron but there is a beam of them and I send many electrons through a Stern–Gerlach magnet then I may conclude that whatever the origin of the beam was, it's producing electrons in some distribution other than 50-50.

> Exactly my point.  Your 50/50 just an epistemic assumption,which measurement may prove wrong. 

If I'm dealing with a single electron no measurement will ever prove me wrong.  

 

> Yet if you take the UP beam from the SG and measure Left/Right the distribution will be 50/50,

Yes but I didn't know it came from the UP beam from a SG, all I knew is that the electron went up, and now that doesn't matter because I've sent that electron to a SG magnet again and I've made a Left/Right measurement so now, although I know if it's left or right, I no longer know anything about up/down except that the probability is 50-50. 

 

>> Rather than a definition of measurement I will give you something much better, an example. Producing an electron with a known spin state, as a piece of magnetized iron does when, thanks to the photoelectric effect, it's exposed to circularly polarized light; or when an electron passes through a Stern–Gerlach magnet.

> So which step is the example of measurement, producing an electron with a known spin state, as when you first measure the magnetized direction of a piece of iron before ejecting an electron from it, or when the electron passes thru the SG

Both processes produce an electron with a known spin state, so both are a measurement.  

 

>>> A bit of iron found in the ground is unlikely to have encountered an SG.

>>True, but it's not unlikely that something equivalent could have occurred. 

 

> That it cooled in the Earth's magnetic field?  Is that what you call equivalent to being separated in an SG?

Yes because that leaves a classical record, just like a SG does. 

John K Clark    See what's on my new list at  Extropolis 

we1

 

[Brent Meeker]

Which is close to what I explained was the definition of a measurement (and you elided).  But just an SG doesn't make a record; you need a detector for that.  SG's are interesting because you can split say an UP beam into Left/Right, block one, and then measure UP/DN and find them 50/50.  But if you don't block one, then on and then measure UP/DN you get all UP.



Brent

[John Clark]

On Mon, Jul 28, 2025 at 9:07 PM Brent Meeker <meeke...@gmail.com> wrote:

 

>>>> A bit of iron found in the ground is unlikely to have encountered an SG.

>>>True, but it's not unlikely that something equivalent could have occurred. 

 

>>Yes because that leaves a classical record, just like a SG does. 

>Which is close to what I explained was the definition of a measurement

I know, and that's precisely why I decided to use that phrase. 

 >But just an SG doesn't make a record; 

If after the electron's encounter with the SG magnet it ever runs into a magnetic field again then the electron's behavior will be different than it would have been if it had never had an encounter with that SG magnet. And that is a classical record.  

 John K Clark    See what's on my new list at  Extropolis 

lv/

[Brent Meeker]

No.  That's why I included the diagram of the SG experiment in which one blocks or doesn't block one side of a split beam.  Until the beam hits a detector the atoms (not electrons) are maintaining their coherence between beams and can be recombined in a way that is impossible classically.

Brent

[John Clark]

On Tue, Jul 29, 2025 at 2:37 PM Brent Meeker <meeke...@gmail.com> wrote:

>> If after the electron's encounter with the SG magnet it ever runs into a magnetic field again then the electron's behavior will be different than it would have been if it had never had an encounter with that SG magnet. And that is a classical record.  

> No.  That's why I included the diagram of the SG experiment in which one blocks or doesn't block one side of a split beam.  Until the beam hits a detector the atoms (not electrons) are maintaining their coherence between beams and can be recombined in a way that is impossible classically.

Two points:

1) In the above I was talking about an electron, not a beam of electrons. 

2) You say "an SG doesn't make a record; you need a detector for that". But after the electron (singular) encounters the magnetic field of the SG the electron is moving on a trajectory that is different from the one it would've had if it had no such encounter. And that is a classical record.

> Until the beam hits a detector the atoms (not electrons) are maintaining their coherence between beams 

I'm not sure what you mean by that. Neither an electron nor a beam of them ever encounters the atoms in a Stern–Gerlach device, the electrons only encounter a magnetic field. 

> and can be recombined in a way that is impossible classically.

Are you talking about quantum erasure? If so I don't see the relevance except to say that's the only way you can make a detection without also making a classical record. 

 John K Clark    See what's on my new list at  Extropolis 

6nk

[Brent Meeker]

On 7/29/2025 12:17 PM, John Clark wrote:

On Tue, Jul 29, 2025 at 2:37 PM Brent Meeker <meeke...@gmail.com> wrote:

>> If after the electron's encounter with the SG magnet it ever runs into a magnetic field again then the electron's behavior will be different than it would have been if it had never had an encounter with that SG magnet. And that is a classical record.  

> No.  That's why I included the diagram of the SG experiment in which one blocks or doesn't block one side of a split beam.  Until the beam hits a detector the atoms (not electrons) are maintaining their coherence between beams and can be recombined in a way that is impossible classically.

Two points:

1) In the above I was talking about an electron, not a beam of electrons. 

Which makes me think you don't know how an SG works.  Typically it's a beam (although one at a time is fine) of neutral atoms with a magnetic moment, e.g. silver atoms.  Electrons are charged, so the Lorentz force on them is very much bigger that the magnetic divergence.  I don't know that it's impossible, but using electrons would be like trying to measure a small effect in the presence of much bigger orthogonal effects.

2) You say "an SG doesn't make a record; you need a detector for that". But after the electron (singular) encounters the magnetic field of the SG the electron is moving on a trajectory that is different from the one it would've had if it had no such encounter. And that is a classical record.

Ok, I take your point.  If the atom (not electron) comes out the up channel you've measured it to be spin UP in the sense of an ideal preparation.  But you have to block the down channel or otherwise know it is in the up channel.  That's the point of the diagrams I posted, see below.

> Until the beam hits a detector the atoms (not electrons) are maintaining their coherence between beams 

I'm not sure what you mean by that. Neither an electron nor a beam of them ever encounters the atoms in a Stern–Gerlach device, the electrons only encounter a magnetic field. 

> and can be recombined in a way that is impossible classically.

Are you talking about quantum erasure? If so I don't see the relevance except to say that's the only way you can make a detection without also making a classical record.

No.  I'm talking about this.  If you block one channel then you've made a measurement. So first you measure (prepare) an atom in z+ then you measure (prepare) it in x+ and then you measure it in z+ and find it is 50/50.  And this applies to one atom at a time as well as a beam.

But if you leave both channels open after the x+ measurement, then the z+ measurement recombines them and produces z+. So simply putting an atom thru the second SG was not a measurement, as it was in the above example, because there was no determination of whether it went x+ or x-, even though it went thru an SG.



Brent

[John Clark]

On Tue, Jul 29, 2025 at 7:26 PM Brent Meeker <meeke...@gmail.com> wrote:

>> I was talking about an electron, not a beam of electrons. 

> Which makes me think you don't know how an SG works.  Typically it's a beam (although one at a time is fine) of neutral atoms with a magnetic moment, e.g. silver atoms. 

Stern and Gerlach used neutral silver atoms in their original 1922 experiment, however in 2015 Hosein Majlesi used their magnet to separate spin up electrons from spin down. 

Stern-Gerlach experiment by free electrons

Electrons are simpler than atoms and I like to use the simplest thing possible in thought experiments. In fact I could make the same point if I got rid of both atoms and electrons and replaced them with photons of light, and junked the Stern Gerlach magnet and replaced it with a simple pair of polarizing sunglasses. 

>> 2) You say "an SG doesn't make a record; you need a detector for that". But after the electron (singular) encounters the magnetic field of the SG the electron is moving on a trajectory that is different from the one it would've had if it had no such encounter. And that is a classical record.

> Ok, I take your point.  If the atom (not electron) comes out the up channel you've measured it to be spin UP in the sense of an ideal preparation.  But you have to block the down channel or otherwise know it is in the up channel. 

Regardless of if I or anybody else knows it's in the up channel, the electron (or if you prefer the neutral silver atom) will behave differently because of its encounter with the Stern Gerlach magnet, and that is a classical record; although it would be possible to erase that record by sending it through a Stern Gerlach magnet again that had been rotated by 90° into the left right direction. That is quantum erasure. 

> if you leave both channels open after the x+ measurement, then the z+ measurement recombines them and produces z+ 

As I said, measuring for up/down and then measuring for left/right is quantum erasure, you no longer have any idea of the electron's (or the neutral atom's or the photon's) up/down orientation, that information is no longer in the observable universe. 

John K Clark    See what's on my new list at  Extropolis 

3b1

6nk