Answering Mermin’s Challenge

Hi Georgina,

Mermins puzzle is a description of the SG entanglement experiment, so we are talking about the same experiment. Only that Mermin handles the whole experiment as a kind of black box and invites us to figure out what the inner workings of the box are to produce the reported results. Moreover, he challenges us with his suggestion that there is no way to classically, mechanically explain the results.

The angles 0, 90 and 180 degrees always refer to the magnets' orientations relative to each other. As you can imagine, one can turn one magnet around its axis by 90 degrees, leaving the other magnet unchanged. This then would result in a relative angle of 90 degree between these two magnets.

"RE. "Though by probability still giving each same/matched state outcome 1/4 of the time. " I added 'each' to make clear for up/up and for down/ down. As you say 1/2 for both."

The 1/4 are exactly the case when the relative angle is 90 degrees.

But this is not the same as Mermin's case b) - read Mermin's paper here:

https://www.informationphilosopher.com/solutions/scientists/mermin/Mermin_short.pdf

Mermin's case b) is for the case of a relative angle of 45 degrees (or alternatively 315 degrees).

Mermin's puzzle confronts us with the assumption that each particle has a set of instructions that tells the particle how to react when switch 1, 2 or 3 is on. The switches symbolize the 3 possible measurements axis' x, y and z in the SG experiment.

His case a) is equivalent to the 180 degree case of the SG experiment: both spins either are up/up or down/down.

Mermin's conundrum is (although he doesn't mention a Bell curve or orange or red lines) that fixed instruction sets should produce the red line depicted in the plot i gave you (or the blue line of the plot here: https://en.wikipedia.org/wiki/Bell%27s_theorem#/media/File:Bell.svg).

But Mermin's devices produce the orange line (or blue line for the wikipedia picture) - and that is not compatible with a fixed set of instructions.

You are right that Mermin's conundrum - at first sight - only applies to the assumption that there are fixed instruction set in play. Take the wording "instruction set" as equivalent with "physical law". The particle has a magnetic moment with a certain orientation. the physical law is how this orientation is altered when a well defined influence acts on that magnetic moment directly (or alternatively on some other property indirectly which in turn again acts directly on the magnetic moment). So your scheme aims to explain the Mermin-cases a) and b) by instruction sets (means physical laws that dictate how the magnetic moment should be altered when influenced by a certain amount of force from the magnet).

The essence of Bell's considerations is that a theory without fixed instruction sets is physically impossible - except for the strange world of quantum mechanics. Whatever mechanical, physical forces along the chain of events produce the Bell curve, it must be instructions how to react when a particle's property x in a state of orientation y relative to a magnet encounters a force z of some environment (the magnet). I think you would agree on that, otherwise we are left with randomness in your scheme.

Since your scheme explains things by a pre-existing magnetic moment that can be changed via a measurement, it is in conflict with the assumption that the particle does *not* have a definite orientation prior to the mesurement.

What is this conflict? the conflict arises about whether or not particles have well defined spin states (up or down) in all 3 directions prior to a measurement. It is possible to *imagine* a scheme like yours where these spin states aren't detected but altered via measurement. But nonetheless your scheme says that until altered via such a measurement, the spin orientations remain unaltered. This does mean that they are unaltered between their production at the source until they are "measured" for the first time.

The question now is in which direction around the axis of flight these spin orientations leave the source. If these orientations are evenly distributed around 360 degrees in a statistical sense (but surely pairwise always correlated), how can a fixed set of two magnets in a row (means they are oriented identically in space) always give anti-correlated results (means up/down or down/up, but never up/up or down/down)? To assume that the source prefers only one direction around the axis of flight is evenly absurd. So both possibilities are likewise absurd and that is another reason why the orthodox interpretation of QM says that the particle's spin orientations aren't predetermined by the source until measured for the first time.

Hope that clears some misunderstandings.

Greetings,

Stefan

Stefan and Georgina,

It's fun to go back to the source and browse the many video presentations of 'what is spin'. It is entirely observer dependent, yet at the same time deemed an intrinsic property. What seems to be missing is the distinction that while it is true enough that a moving charge produces a magnetic field, what is actually being observed is a differentiated magnetic field similar to the shape of a bar magnet. That does not mean that a magnetic field is dependent on the charge moving, only that a measurable dipole moment is differentiated by that motion of a charge. A point charge, will have an accompanying magnetic field, moving or not. So given the uniform negative charge of an electron, the vectors would all be pointing either inwardly towards the center of mass, or outwardly away from the center of mass (we really don't know which) until it is measured with an external dipole magnetic field and then it exhibits an orthogonal differentiation. Remove that dipole and apply one at a different angle of incidence, and the electron forgets the first measurement, and aligns orthogonally with the second. Given an unpaired electron in the outer shell of a silver atom, I think it shouldn't be surprising that ALL the results of any Stern-Gerlach type experiment, would be averaged and equi-partitioned in probability. The magnetic field is already there, the act of applying a dipolar observing system induces a differentiated dipole moment. jrc

John,

"Remove that dipole and apply one at a different angle of incidence, and the electron forgets the first measurement, and aligns orthogonally with the second."

If that dipole sits in the outer shell of the silver atom at a definite place, the problem i spoke of in my last reply remains. If that dipole's vectors are smeared out somewhat uniformly over the whole silver atom, how can the well known deviations (violations of the Bell inequality) from equi-partitioned probabilities then come about?

Stefan, thanks for clarifying that we are talking about the same experiment. "Mermin's puzzle confronts us with the assumption that each particle has a set of instructions that tells the particle how to react when switch 1, 2 or 3 is on. The switches symbolize the 3 possible measurements axis' x, y and z in the SG experiment." Stefan.

"I don't think I'm arguing for instruction sets. The particle does not have the capacity to carry them. The apparatus encounters the particles however they are oriented relative to it. The orientation of the magnetic moment does not change unless it encounters an environment that makes it do so. That can be known from experiments where particles are collected after a fist run through the apparatus and retested with the same orientation of analyzer.. Which produces same spin outcome as previous test. A different orientation of analyzer-random spin outcome. The field encountered in the SG apparatus is inhomogeneous and so each individual particle will have its unique experience according to its orientation and position of entry and trajectory though the apparatus. There are not set instructions as to how it must behave but ad hoc (not generalizable, as it happens) response. This fits with an 'open' unwritten material future rather than the outcomes already within space-time. What is generalizable is- treat the 'entangled' particles to the same environmental influence, they will respond in the same way. Treat them differently correlation is lost,

Hi Georgina,

thanks for your reply.

The term "instruction sets" is just an alternative shorthand to say that all what happens physically in those experiments is governed by some classical laws of physics - known or unknown. So in this view, all the components of those experiments and all their laws of motion and interaction *are* the complete "instruction set" that determines every outcome. Of course no particle or other component of these experiments has some kind of list to look at for how to react to specific encounters.

"The apparatus encounters the particles however they are oriented relative to it."

Yes, this would be the view of classical physics.

"There are not set instructions as to how it must behave but ad hoc (not generalizable, as it happens) response. This fits with an 'open' unwritten material future rather than the outcomes already within space-time."

This is of course an ad hoc explanation. I think it falls under the category about Bell said it would be local, but unrealistic. You know Einstein insisted on a theory where all elements of the physical mechanics that lead to the results have a counterpart in the theory. Remember "God does not play dice". Surely Einstein's view was a deterministic one, all outcomes then had to be predetermined in space-time.

If there are no "set instructions" (aka physical laws) as to how it must behave, then we are left with bottomless randomness that somewhat manages to be generalizable, because it follows the Bell curve. Even without explicitely naming that kind of randomness as generically non-local, implicitely it seems to be just that - because how can some local random events (by random i mean here events out of the blue, ad hoc and without classical or other laws dictating the events) produce the regularity of the Bell curve?

The term "realistic", in my opinion, is always used to characterize a physical system as behaving classically, means mechanically, with the ususal pictures like forces, properties, interactions. Boiled down i think "realistic" and "classical" are another shorthand for "cause and effect" as we as humans are used to. The question for me is then, is it possible that there could be unphysical (immaterial) causes that can have physical (material) effects?

Stefan, I think it is not quite right to think of the laws of physics as instructions that must be obeyed. Instead I think they are a distillation of what happens, from observation. Like Kepler's laws. There are no instructions telling the planets what to do. But from observation of what they do a pattern can be found.

The results are not what would be expected for a fixed property which seems to be the classical assumption. If change of orientation. potentially altering output state, can happen that is like blue socks turning pink- and Bell's inequalities don't apply

Hi Georgina,

thanks again for the reply. I agree sofar as blue socks can turn pink. Mermin's challenge is to explain how and why they do it. Or in other words, what goes on in Mermin's boxes to produce the results. Classically, blue socks *must* turn pink under some specific influences. Your attempt seems to be that they can, but they must not. What decides then that it nonetheless happens, that is the question nobody could answer me yet.

Stefan, classically socks are either blue or pink they can not change.[ that of course is an analogy for any fixed classical characteristic; excluding laundry accidents!]. I'm proposing the idea that the orientation of thee magnetic moment is not like that but responds to the environment encountered. What the outcome will be is not preordained or pre-written but develops as the relationship of particle and magnets evolves. A pair can either undergo the same environmental 'journey' or undergo different 'journeys'. Same journey they produce same state outcomes. Different journeys-different or same state outcome, ie, not necessarily the same.

Why 0 degrees and 180 degrees give matched outcome all the time.

lets call the phase of the particles vibration and that of the magnets electrons I for in and O for out. (Into the magnet/out of the magnet. Imagine too the magnetic moment as a magnet.

Lets have output ports that divide the electrons exiting the machine. Instead off calling them up and down lets call them R and G ,R taking those closest to N pole facing in to center of apparatus magnet and G those closest to S pole facing center of apparatus magnet. When the device is inverted relative to the other, of course, the ports are too. Which is why the names up and down would be confusing. The following lines refer to phases of; top magnet (first), test particle, and bottom magnet.

Alice's apparatus, attraction to top, repulsion by bottom R outcome

1 0 1 0 1

0 1 0 1 0

0 1 0 1 0

Bob's apparatus (160 degrees cf. Alice's) Repulsed by top attracted by bottom. Also R outcome as ports inverted with apparatus. This is for correlated particles

0 1 0 1 0

0 1 0 1 0

1 0 1 0 1

If anti correlated ( meaning a pair of opposite orientation of phase) particles is used the anticorrelation is preserved as can be seen by drawing out more phase interaction diagrams, and thinking carefully about what I and O mean on each line.

The particles are responding to their local environment-relationship of the apparatus to Earth's gravity doesn't matter.

Pink and Blue,

socks don't change themselves.

Neither do the poles of a magnet. It is purely a matter of convention that North and South are platted from the archaic traditions of early civilization and the mysterious 'lodestone' before the earth's magnetic field was known. So in practice a compass needle points N but that's the south end of the magnetized needle and customarily painted red, though Blue is commonly attributed to N. And, by convention, the direction of magnetic field lines of flux (really arbitrary isobars of the same level of intensity) are commonly shown with arrows as 'moving' from the North pole and looping around (usually diagrammed as upwardly) past parallel to loop again around to the south pole. Still, you'll find many diagrams that label a magnet end 'N' colored red. And there is no detectable direction other than that isobaric shape. Also by convention if you look 'down' onto the north pole, rotation is Clockwise and is really due to the fact that most people are right-handed and twisting a screwdriver that direction has greater strength than CCW. So in diagrams with N Up, the direction of the horizontal arrow showing is pointing leftward, and UP is Negative torque. Two common bar magnets oriented on a plane at right angles will display an attraction of the S end of one magnet from the right angle plane of the S end of the other, all the way to the N loop, and vice-versa. Equilibrium is 'superposition' made physically evident in the macroscopic realm. Nothing mystical about it, no spooky action. Just real easy to get confused, Like the same equilibrium displayed by opposite electric charge.

So Mermin's device holds not hidden variables. An electron is like a 2sphere, there is no cowlick, the hairs on that coconut all stand on end! The orthogonal relationship is freely gimballed, it doesn't matter if the electron is rotating or any surface discrete region is circling an equatorial plane. There are an infinite possible number of possible equatorial planes. It is the shape of the external magnet group producing a non homogenous field that becomes less intense towards one element which influences the flight of the electron. And ON AVERAGE the electron's freely gimballed propensity to be oriented either UP or DOWN will be equally distributed. Superposition of both electric charge and magnetic moment has no preference and persists throughout. Half of 'em will go one way, and the other half will just as likely go the other, they need not be all uniform, just basically the same. But the electron does not need change at all. jrc

The simplest electric motor has no preferred direction of rotation that isn't designed into it.

Can't edit at the moment - bother I think the diagrams are wrong

. There's more to take account of. 1. that the vibration is two sided, a dipole -out one side is in the other. 2, The two apparatus magnets have opposite poles facing each other.

Try again

To differentiate magnets and particles: A and I for away and into magnet body

Alice's

1 0 1 0 1 ( 1 into magnet body) I A I A I

0 1 0 1 0 0 1 0 1 0 Two phases for each end of

1 0 1 0 1 1 0 1 0 1 the dipole magnetic moment

1 0 1 0 1 I A I A I

(I into magnet body) So I's moving in the opposite direction to other magnet.

To differentiate A and I for away and into magnet body

Bob's

0 1 0 1 0 A I A I A

0 1 0 1 0 0 1 0 1 0

1 0 1 0 1 1 0 1 0 1

0 1 0 1 0 A I A I A Opposite direction of first line

If anti correlated ( meaning a pair of opposite orientation of phase) particles is used the anticorrelation is preserved as can be seen by drawing out more phase interaction diagrams, and thinking carefully about what I and O mean on each line.

I think that's right now. I'll leave it there as it's' doing my head in'. -You have to picture what the magnets and particles are doing. '

John, I agree. Blue socks do not classically change into pink socks. A magnetic pole labelled North does not turn into a South .But orientation of the magnet (or a magnetic moment) can change. I'm associating the phase of vibration of particle with the poles to try and explain what is happening. It may be out of the box, but will also explain why magnets come as dipoles. A single electron being the smallest.

Bother again . I didn't check how my post would appear on screen.

Again

Alice's

1 0 1 0 1 ( 1 into magnet body) ..I A I A I

0 1 0 1 0 ..................................0 1 0 1 0

1 0 1 0 1,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,1 0 1 0 1

1 0 1 0 1 ...............................I A I A I

Two middle lines phases for particle magnetic moment ends

(I into magnet body) So I's moving in the opposite direction to other magnet.

To differentiate A and I for away and into magnet body

Bob's

0 1 0 1 0........................... A I A I A

0 1 0 1 0........................... 0 1 0 1 0

1 0 1 0 1........................... 1 0 1 0 1

0 1 0 1 0............................ A I A I A Opposite direction of first line

Should line up but you can see what I meant now.

John,

"An electron is like a 2sphere, there is no cowlick, the hairs on that coconut all stand on end! The orthogonal relationship is freely gimballed, it doesn't matter if the electron is rotating or any surface discrete region is circling an equatorial plane. There are an infinite possible number of possible equatorial planes."

I am not sure if i understood this correctly.

Quantum theory says that there is a 100% anti-correlation for our entanglement experiment when both the magnets have the same field-orientation in space (of course also with the same field forces).

Means, if the spin of the electron referring to magnet A is "down", then the spin of the electron referring to magnet B is "up" - and vice versa. That's the anti-correlation i spoke of. How does this anti-correlation come about if each of the two electrons are

"a 2sphere, there is no cowlick, the hairs on that coconut all stand on end! The orthogonal relationship is freely gimballed, it doesn't matter if the electron is rotating or any surface discrete region is circling an equatorial plane."???

If the measurement devices (magnets) at each side are identical in orientation and strength, the cause for the anti-correlation at a relative angle of 0 degrees must be found in a difference between electron A and electron B. What difference is that???

Sorry, what a pigs ear I've made of that attempt to elucidate. Got muddled with inversion of Alice and Bob's apparatus and the orientation of the magnets in each. The two in each are of course the same orientation and would if able attract. I thought it might have more explanatory power but I end up with just a exceedingly tiny magnet passing through a magnetic field. The inhomogeneity of that field could play a part in selecting which polarity the particle moves towards. In Bob's apparatus the same inhomogeneity is encountered but inverted leading to the same output port, though spatially inverted too.

.I A I A I Alice's............. A I A I A Bob's

A I A I A....................... I A I A I

What would happen if the orientation of the source was altered?

John. maybe they need to be different from your description, if the characteristics and behaviour can not account for experimental results. Reimagining the electron is less of a big deal compared to faster than light communication. Is the idea that something has a definite state or value even if not measured even classically realistic? (Rhetorical). A heads or tails bit cannot be associated with a coin until the measurement protocol has been decided. Read by opening the palm and calling it? Or is the coin to be flipped -giving opposite state? The outcome state associated with a second particle of correlated or anticorrelated pair can only be accurately predicted if the same test x. y or z is selected. The isolated outcome bit is not a particle, or condition of it, pre -testing. The outcome only happens when it happens.

Georgina,

I can follow what you are saying, it's just that there is always that loop-hole of a coin not being associated with a heads or tails bit outcome until a measurement protocol is chosen. From a technical experimentalist perspective, the assumption that two, and only two, individual electrons are selectively prepared as a singlet pair, is itself a theoretical probability. It's a choice to accept that just such a micro-managed sequence of events has been accomplished. In short; we choose to accept that anti-correlation is observed in the initial detection, thence forward.

In refreshing as this discussion has progressed, I realized I was thinking in terms that had simply followed from the usual accepted norms. In particular the induction of a dipolar magnetic moment. And the more I puzzled, the more it became apparent that there are reasons why not only is it not necessary, but there are problems if spin is physically what QM theoretically assumes. To whit; Up and Down are both CCW rotations, yet if that is what physically happens that orients an electron then we have to accept that there is a preferred physical direction for rotation. Shouldn't anti-correlation be CCW, UP, North and CW, UP, North, and CCW, DN, North, and CW, DN, North? (;- jrc