Measurement of electron spin direction, assuming hidden variables

[b***@hotmail.com]

Assume that an electron spin direction vector, e, is its 'hidden variable'.

When the electron spin direction is measured along direction vector a, does
the measurement outcome of + or -1 necessarily conform to the sign of the
dot product e.a?

I am asking because the direction of motion of a gyroscope under a force
is not in the direction of the force. Any Bell simulation
(unsuccessful, of course) that I have previously done assumes that the
dot product e.a gives the measurement but if a gyroscopic effect could
override the dot product, to a small extent, that would be helpful in
perhaps explaining the breaking of Bell's Inequality.

[r***@gmail.com]

Post by b***@hotmail.com
Assume that an electron spin direction vector, e, is its 'hidden variable'.
When the electron spin direction is measured along direction vector a, does
the measurement outcome of + or -1 necessarily conform to the sign of the
dot product e.a?
I am asking because the direction of motion of a gyroscope under a force
is not in the direction of the force. Any Bell simulation
(unsuccessful, of course) that I have previously done assumes that the
dot product e.a gives the measurement but if a gyroscopic effect could
override the dot product, to a small extent, that would be helpful in
perhaps explaining the breaking of Bell's Inequality.

The MEAN, most PROBABLE result of the measurement result being +1 or -1
conforms to the sign of the dot product, but only the probability. For
example, if the vector 'a' differs from the previously selected spin
vector 'e' by an angle of 85 degrees, the dot product will have positive
sign, but the result of the measurement of many electrons will be nearly
54:46 for +1:-1 results, not all +1. The probability ratios will go as
(1+cos(theta))/2:(1-cos(theta))/2 for +1:-1 probabilities.

Rich L.

Rich L.

[b***@hotmail.com]

Thanks Rich and Jos

Yes, I know that QM explains average outcomes perfectly and, yes, I am
trying to think of matters in microscopic detail using hidden variables so
as to calculate an event-by-event simulation.

I follow Rich's formula for QM (and laboratory) giving probability ratio:
(1+cos(theta))/2:(1-cos(theta))/2 for +1:-1 probabilities.
That is OK.

An equivalent ratio for classical/ hidden variables is
(1+theta/180)/(1-theta/180) {where theta is measured in degrees}
which is based on the sawtooth curve of correlational outcomes.

The results for Rich's example of theta = 85 deg is
for QM 54.4/45.6 which agrees with Rich's figures
and for Hidden Variables is 52.8/47.2 which represent the Bell inequality
cut-off value.

So QM at 54.4 exceeds the inequality cut of value of HV.
which means that, in order to make a hidden variable simulation more
realistic, more +1 readings are needed than is given by HV. That is more +1
readings are needed than is given by sign(e.a)

Jos's formula (1 + e.a) / 2 is equivalent to Rich's value of
(1 + cos(theta))/2. But when using a single electron with a hidden variable
represented by vector e, The usual HV calculation for the outcome
measurement is given by the sign of e.a not by the exact value of e.a.
This is the nub of quantisation of the measurement. It is obviously wrong
to use sign(e.a) which is why I am trying alternatives.
For an individual electron, (1 + e.a) / 2 is in general neither +1 nor -1.
But if (1 + e.a) / 2 can be built into my HV measurement, in the form of
adding chance to the outcome, I will try it. This has given me an idea for
another simulation which will take a few days. Using e.a rather than
sign(e.a) will make the electron angle not a single constant value and hence
likely not a proper hidden variable.

I hope I never need to resort to a multiverse to bring chance into the
calculations. Once the electron is in the detector magnetic field it will be
turned away from vector e to point at vector a. This turning can bring
dynamism into the spin direction and hence add chance. My original question
was worrying that the initial value of e determined the outcome exactly.
Period. But that might imply infinitesimal effects. At what point in its
time of flight after leaving its source is the electron measurement decided?
If it is decided initially and infinitesimally (I mean a very weak magnetic
field far from the detector) then we have an HV measurement, which is known
to be unreal.

Thanks again for your help.


Austin Fearnley

[Jos Bergervoet]

Post by b***@hotmail.com
Thanks Rich and Jos
Yes, I know that QM explains average outcomes perfectly and, yes, I am
trying to think of matters in microscopic detail using hidden variables so
as to calculate an event-by-event simulation.
(1+cos(theta))/2:(1-cos(theta))/2 for +1:-1 probabilities.
That is OK.
An equivalent ratio for classical/ hidden variables is
(1+theta/180)/(1-theta/180) {where theta is measured in degrees}
which is based on the sawtooth curve of correlational outcomes.
The results for Rich's example of theta = 85 deg is
for QM 54.4/45.6 which agrees with Rich's figures
and for Hidden Variables is 52.8/47.2 which represent the Bell inequality
cut-off value.
So QM at 54.4 exceeds the inequality cut of value of HV.
which means that, in order to make a hidden variable simulation more
realistic, more +1 readings are needed than is given by HV. That is more +1
readings are needed than is given by sign(e.a)
Jos's formula (1 + e.a) / 2 is equivalent to Rich's value of
(1 + cos(theta))/2. But when using a single electron with a hidden variable
represented by vector e, The usual HV calculation for the outcome
measurement is given by the sign of e.a not by the exact value of e.a.

But that is just one (rather straightforward) choice! You use the
direction of the vector with a simple division of the outcome over
two half-spheres..

Post by b***@hotmail.com
This is the nub of quantisation of the measurement. It is obviously wrong
to use sign(e.a) which is why I am trying alternatives.
For an individual electron, (1 + e.a) / 2 is in general neither +1 nor -1.
But if (1 + e.a) / 2 can be built into my HV measurement, in the form of
adding chance to the outcome, I will try it.

You could also take a fine-grained sandpaper-like mosaic for your
"+1 and -1 outcome pattern". Such a mosaic might follow the precise
cos(theta) probability of QM, and still be deterministic (formally,
that is.. not practically predictable of course. But in principle
still free of 'chance').

Doing that for another direction as well (use the same jig rotated
to another axis or use an indepent one) gives you exactly the QM
outcome distributions. Of course it doesn't give the QM correlation,
Bell's theorem is proven mathematics, after all!

Post by b***@hotmail.com
This has given me an idea for
another simulation which will take a few days. Using e.a rather than
sign(e.a) will make the electron angle not a single constant value and hence
likely not a proper hidden variable.

Once you're ready with one particle, you should extend it to correlated
particles. At least the 'quantum teleportation' procedure should be
correctly described by it:
<https://en.wikipedia.org/wiki/Quantum_teleportation#Formal_presentation>
I'm not sure how a pure 'classical' variant of this process actually
could be presented.. It looks as if you'll have to transmit 2 real
numbers by sending only 2 bits [*]

Post by b***@hotmail.com
I hope I never need to resort to a multiverse to bring chance into the
calculations.

You are mistaken. The multiverse *removes* chance from QM. The chance
concept only appears if you insist that one 'true' reality is at some
point selected instead of all the others. The multiverse never does
that.

[*] PS: Transmitting real numbers by sending only 2 bits is also very
poorly described by 'collapse-based' QM pictures. It requires a kind of
'complete universe collapse' where this collapse is in fact transferring
the information needed from one place to the other. And since the
collapse is exactly the part of the time evolution in QM *without* any
exact description, this is in fact a total non-explanation! The more
correct descriptions omit the measurement by describing the 'classical
transport' also by QM (where the complex numbers only decohere to one
real number per particle, but not to one single bit!)

[b***@hotmail.com]

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[r***@gmail.com]

...
...Unless .... and this is anathema to all bona fide=20
physicists, but I am currently wondering if time for an antiparticle is
travelling backwards, as nominally shown in a Feynmann diagram. So a Bell
test starts at say Alice's measurement and ends at Bob's measurement. Or
vice versa. ...

This would not be relativisticly consistent. That is, if we are to say
that \the causal chain starts with Alice's measurement which eventually
causes Bob's, then to be consistent with the relativity principle there
must not be any observer who sees Bob's measurement happening first,
thus "causing" Alice's result. It has been demonstrated that entangled
correlation does occur between two spatially separated events (i.e.
Alice's and Bob's measurements) and so there would be observers who can
see either Alice's or Bob's measurement happening first. If causality
is to have meaning we can't accept this.

If you only allow forward causality (i.e. the result of a measurement
only depends on events within its past light cone), then the moment of
emission of the entangled particles is the only time common to both
Alice and Bob. This requires hidden variables (as you are trying to make
sense of). The Bell Inequality applied to such experiments, however,
proves that the results of the measurements at Alice and Bob cannot be
solely determined by a local hidden variable on the particle. The
statistics are wrong and the inequality is violated.

The solution I subscribe to is retro causality. That is, the particle
is not emitted until its destination is determined and is consistent
with the constraints of polarization/spin/etc. This requires some sort
of communication cannot be used to communicate information beyond the
fact that out there, from the future, hence the term "retro causality".
This communication somewhere, is something that can accept the
photon/particle w/spin.

This is a somewhat controversial idea. I'm not sure how many mainstream
physicists subscribe to this, but it is discussed by serious physicists.

BTW, I too abhor the idea of the multiverse. The number of entire
universes spawned every instant is unimaginable, and I think fails the
Occam's Razor test.

Rich L.

[b***@hotmail.com]

Post by r***@gmail.com

...
...Unless .... and this is anathema to all bona fide=20
physicists, but I am currently wondering if time for an antiparticle is
travelling backwards, as nominally shown in a Feynmann diagram. So a Bell
test starts at say Alice's measurement and ends at Bob's measurement. Or
vice versa. ...

This would not be relativisticly consistent. That is, if we are to say
that \the causal chain starts with Alice's measurement which eventually
causes Bob's, then to be consistent with the relativity principle there
must not be any observer who sees Bob's measurement happening first,
thus "causing" Alice's result. It has been demonstrated that entangled
correlation does occur between two spatially separated events (i.e.
Alice's and Bob's measurements) and so there would be observers who can
see either Alice's or Bob's measurement happening first. If causality
is to have meaning we can't accept this.

If an observer saw Alice's measurement for the positron travelling backwards
in time to the Source, then that observation/measurement would render the
pair of particles to be no longer entangled, and so not a pair entitled to
be in a Bell experiment. I admit that I either do not understand 'weak
measurement' or believe it to be a measurement which is not provable to be
on a single particle. A non-weak measurement to me is one which changes
the spin sign of a particle.

Post by r***@gmail.com
If you only allow forward causality (i.e. the result of a measurement
only depends on events within its past light cone), then the moment of
emission of the entangled particles is the only time common to both
Alice and Bob. This requires hidden variables (as you are trying to make
sense of). The Bell Inequality applied to such experiments, however,
proves that the results of the measurements at Alice and Bob cannot be
solely determined by a local hidden variable on the particle. The
statistics are wrong and the inequality is violated.

Causality? Knowing Alice's measurement, even in a time reversal setting for
Alice, does not imply that we know what Bob's measurement will be. In the
analysis of the results after the experiment, the measurements are inputted
into a 2x2 table and that associates A and B measurements post-experiment.
Knowing what the row (A value) is for a particle pair gives no information
on what the column (B value) is. Well, we could maliciously somehow ensure
that Bob's measurement is fixed once we know the A result. But I do not
know how to do that with an HV formula. At least not a formula that would
withstand scrutiny for fairness by independent scrutineers.

Post by r***@gmail.com
The solution I subscribe to is retro causality. That is, the particle
is not emitted until its destination is determined and is consistent
with the constraints of polarization/spin/etc. This requires some sort
of communication cannot be used to communicate information beyond the
fact that out there, from the future, hence the term "retro causality".
This communication somewhere, is something that can accept the
photon/particle w/spin.

Yes, I agree, and this is what I meant by time reversal not helping at first
impression.

Superdeterminism as I understand it uses forward causality, as does
determinism. IMO it relies on the future eventually becoming what it will
be, and that will not correspond to countless particles available in all
places and HV vector directions. But that seems to me to lead to failing to
break the inequalities just as often as breaking them. In a similar way,
deliberately having missing data in the data sets can lead to breaking
inequalities, or not, depending on the bias introduced in the snipping of
the data.

I am not sure about retro-causality as you describe it. It seems to imply
information of some kind is travelling backwards in time. It also at first
glance seems to suffer from the same problem that IMO superdeterminism
suffers from. That is why should the particular measurement break the
inequalities?

My idea has IMO the advantage that the whole stream of antiparticles in a
Bell experiment has its distributions of HVs moulded by Alice and those are
passed on to particles beamed at Bob. This means that there is no point in
making a simulation with say 1 million pairs (as I often have done) with HVs
random on a sphere. As the HVs in my time-reversed scenario are not random.

I do not yet know why the moulding of the HVs for Bob does break the
inequalities. But it seems to me that superdeterminism has no mechanism for
breaking the inequalities except by chance outcomes.

Post by r***@gmail.com
This is a somewhat controversial idea. I'm not sure how many mainstream
physicists subscribe to this, but it is discussed by serious physicists.
BTW, I too abhor the idea of the multiverse. The number of entire
universes spawned every instant is unimaginable, and I think fails the
Occam's Razor test.
Rich L.

[Jos Bergervoet]

Post by b***@hotmail.com
Assume that an electron spin direction vector, e, is its 'hidden variable'.
When the electron spin direction is measured along direction vector a, does
the measurement outcome of + or -1 necessarily conform to the sign of the
dot product e.a?

No it does not. The chance[*] for measuring +1 is not zero if e.a < 0,
as you probably know very well.. but instead is:

(1 + e.a) / 2

Post by b***@hotmail.com
I am asking because the direction of motion of a gyroscope under a force
is not in the direction of the force. Any Bell simulation
(unsuccessful, of course) that I have previously done assumes that the
dot product e.a gives the measurement but if a gyroscopic effect could
override the dot product, to a small extent, that would be helpful in
perhaps explaining the breaking of Bell's Inequality.

The breaking is perfectly explained already by QM, of course. But here
you want to do it, presumably, with some local microscopic description
of the system based on classical mechanics? For two entangled particles
that approach clearly breaks down, for zero particles it doesn't, so for
one particle you still may be able to do something! :-)

[*] If you still want to use the 'chance' concept, that is. If you do
not believe in collapse of the wave function then a 'density' concept,
for relative populations in a multiverse, would also be appropriate..

[Sylvia Else]

Post by b***@hotmail.com
Assume that an electron spin direction vector, e, is its 'hidden variable'.
When the electron spin direction is measured along direction vector a, does
the measurement outcome of + or -1 necessarily conform to the sign of the
dot product e.a?
I am asking because the direction of motion of a gyroscope under a force
is not in the direction of the force. Any Bell simulation
(unsuccessful, of course) that I have previously done assumes that the
dot product e.a gives the measurement but if a gyroscopic effect could
override the dot product, to a small extent, that would be helpful in
perhaps explaining the breaking of Bell's Inequality.

If you apply a force to a gyroscope other than through its centre of
gravity, then you will be applying a torque. The angular momentum of a
gyroscope changes in the direction of the applied torque, so there is
nothing unusual about its behaviour. It looks odd only because humans
are not used to taking angular momentum into account.

Sylvia.

[r***@gmail.com]

...

Post by b***@hotmail.com
If an observer saw Alice's measurement for the positron travelling backwards
in time to the Source, then that observation/measurement would render the
pair of particles to be no longer entangled, and so not a pair entitled to
be in a Bell experiment. I admit that I either do not understand 'weak
measurement' or believe it to be a measurement which is not provable to be
on a single particle. A non-weak measurement to me is one which changes
the spin sign of a particle.

I am not talking about time reversal. There is no attainable speed
at which an observer would see a positron travelling from Alice
back to the source.

What I mean by retro-causality is that a particle (photon or a
massive particle) will not be emitted until, by some as yet mysterious
process, there is a definite location in the future for it to end
up. As I said, this is a very controversial idea, but not unrecognized,
and I hesitate to assert it too forcefully as there is much unknown
about how this would work.

One justification for it is inhibition of emission of photons by
atoms in certain situations. For example, an atom in a resonant
cavity that does not support a mode at the photon frequency will
not emit that photon. Emission is suppressed. This is related to
so called "hole burning" in lasers where a population of atoms that
can emit a wide range of wavelengths will show dips in the population
on the resonant modes of the laser cavity. I have read of experiments
demonstrating this in a more direct way, where the decay of atomic
states is extended when atoms are in a suitable cavity.

What I'm suggesting is something very similar to what Feynman and
Wheeler were suggesting in the early 1940s where the emission of a
photon is a process that involves a transaction between the emitter
and absorber. The "retro-causality" reference here is that if that
future absorber atom does not exist, the photon will not be emitted.
There is no transmission of information from future to past, only
that there exists, somewhere in the future, something capable of
accepting that photon.

Rich L.

[b***@hotmail.com]

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