# A How does the thermal interpretation explain Stern-Gerlach?

#### PeterDonis

Mentor
The point is that for $N_e=1$ only one spot will appear. How does the thermal interpretation explain this?
Conservation of mass, together with the instability of macroscopic superpositions and randomly broken symmetry forces this, just as a classical bar under vertical pressure will bend into only one direction.
This exchange does raise a follow-up question that I didn't ask at the time (because I was focused on the case of a high intensity beam): the explanation given is basically spontaneous symmetry breaking. But spontaneous symmetry breaking occurs because a single equation that has a certain symmetry has multiple solutions that, taken individually, do not share that symmetry. For example, the classical bar under vertical pressure obeys an equation that is symmetrical about the bar's axis: but each individual solution of that equation describes a bar that is bent in one particular direction, i.e., not symmetrical. There is no individual solution that describes a bar bent in all directions at once.

However, in the case of the SG experiment for $N_e = 1$, we don't have that. We have a single solution of the equation describing the system that shares the equation's symmetry: it describes a superposition of a spot in the "up" position and a spot in the "down" position. We don't have two solutions, one of which describes a spot in the "up" position and one of which describes a spot in the "down" position. So how can spontaneous symmetry breaking explain why we only observe one spot?

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#### charters

I don't see how the explanation can be both the instability of superpositions and inaccurate devices. The point of saying devices are inaccurate is so the superposition is actually stable - it is just that the detectors are bad, so detector 1 didn't register any of the incident (N=1) beam, while detector 2 registered too much of it. But the beam is ontologically at both detectors before and after each measurement or non-measurement, and in a single world.

The issues are A) how it can be reasonable for these bad detectors to be perfectly correlated in their inaccurate clicks and non-clicks and B) how is it plausible to think so many different types of detectors are bad in just the right way so that a sum over histories and collapse/MWI-branching explanation has coincidentally worked all along, given the infinite ways for a detector to be inaccurate. Superdeterminism is the only live option here, imo.

And I don't think one can invoke spontaneous symmetry breaking, given III.4.2, where the interpretation seems to be presented as a deterministic hidden variable theory, All SG results and bent metal bars should be functions of the pre-existing fine grained hidden variables.

#### A. Neumaier

The second reason is the need to explain correlations between detectors.

Under this account, it is not clear why there is never a simultaneous click in both the up and down detectors. It is difficult to understand how the SG detectors can be so inaccurate as to wrongly report +1 or -1 when the true value is 0, yet at the same time so reliable that A) one or the other detector always misreports on every single experimental run and B) they never both misreport at the same time.
See this post and the subsequent discussion.

#### A. Neumaier

it is always an option to dismiss inconvenient and hard to interpret problems by claiming the theory and measurements are simply not really telling us the truth. It seems to me far more interesting to ask: assuming our measurements are telling the truth, what is the universe like?
I am not doing the first. Regarding the second, I ask instead: assuming our measurements are telling the truth, what is the right way to interpret this truth?

#### A. Neumaier

This exchange does raise a follow-up question that I didn't ask at the time (because I was focused on the case of a high intensity beam): the explanation given is basically spontaneous symmetry breaking. But spontaneous symmetry breaking occurs because a single equation that has a certain symmetry has multiple solutions that, taken individually, do not share that symmetry. For example, the classical bar under vertical pressure obeys an equation that is symmetrical about the bar's axis: but each individual solution of that equation describes a bar that is bent in one particular direction, i.e., not symmetrical. There is no individual solution that describes a bar bent in all directions at once.

However, in the case of the SG experiment for $N_e = 1$, we don't have that. We have a single solution of the equation describing the system that shares the equation's symmetry: it describes a superposition of a spot in the "up" position and a spot in the "down" position. We don't have two solutions, one of which describes a spot in the "up" position and one of which describes a spot in the "down" position. So how can spontaneous symmetry breaking explain why we only observe one spot?
Instead of the continuous syymmetry breaking for the bar let us discuss the same issue in a sequence of technically simpler problems.

1. Symmetry breaking of a classical anharmonic oscillator in a double well potential. All positions are possible states. An initial state at the location of the local maximum of the potential is unstable under tiny random prturbations, and the small amount of dissipation associated with the randomness (fluctuation-dissipation theorem) forces the state to move intto one of the two minima. Note that the symmetry only needs to be local (in a neighborhood of the stationary point) for this to hold; the potential itself needs not be symmetric.

2. Classical symmetry breaking in a multimodal potential energy surface with two degrees of freedom, such as a little ball moving in a bowl with an uneven bottom. Again all positions are possible states. An initial state at the location of a stationary point is unstable and moves into one of the local minima of the potential energy surface. This clearly generalizes to any number of degrees of freedom.

3. Classical symmetry breaking in a multimodal potential energy surface on the 3-dimensional unit ball, with forces on the boundary pointing inwards or tangential. Now the positions are constrained to lie in the closed unit ball, but otherwise nothing changes, except that now local minima may occur on the boundary. It is easy to construct potentials that have just two local minima, located at the north pole and the south pole of the ball. As a result, tiny dissipative and stochastic prturbations force the dynamics to settle at one of the poles.

4. An isolated quantum spin in the thermal interpretation is described by a deterministic linear dynamics of its density matrix $\rho$. The latter can be mapped 1-to-1 onto the unit ball, with pure states being mapped to its boundary, the Poincare sphere or Bloch sphere. One can choose this mapping such that the up state and the down state are represented by the noth pole and the south pole. For a nonisolated quantum spin, the reduced density matrix is again represented on the Bloch sphere but has a nonlinear, dissipative dynamics obtained by coarse-graining. If the environment is such that it corresponds to a spin measurement with collapse to an up or down state, this dynamics is expected to have just two stable fixd points, both located on the boundary. local minima on the boundary and no interior minimum. Thus we have essentially a generalization of the siuation in case 3, except that the detailed dynamics is different. Again, tiny dissipative and stochastic prturbations force the dynamics to settle at one of the poles. Thus we obtain collapse of an arbitrary (pure or mixd) spin state to the up state or the down state.

#### PeterDonis

Mentor
For a nonisolated quantum spin, the reduced density matrix is again represented on the Bloch sphere but has a nonlinear, dissipative dynamics obtained by coarse-graining.
This would appear to be the fundamental difference between the treatment you are giving and the "standard" QM treatment, which uses the linear dynamics of the Schrodinger equation combined with the obvious assumption about how the interaction Hamiltonian between the SG apparatus, with its inhomogeneous magnetic field, and the spin-1/2 passing through it acts on spin states that are parallel to the field inhomogeneity (e.g., +x and -x spins for an apparatus oriented in the x direction). In the standard treatment, the action of the Hamiltonian on a +z spin is given by simple superposition (which is allowed due to the linearity of the Schrodinger equation) of the actions on the +x and -x spins.

But the dynamics you are attributing to the system + apparatus is nonlinear, so the simple standard linear superposition picture does not work and there is no solution to the nonlinear dynamics that describes a superposition of a spot at the +x position and a spot at the -x position. Instead, there are two solutions, one describing a +x spot and one describing a -x spot, and which solution gets realized in a particular case depends on random and unmeasurable fluctuations.

Is this a fair description of what you are saying?

#### A. Neumaier

This would appear to be the fundamental difference between the treatment you are giving and the "standard" QM treatment, which uses the linear dynamics of the Schrodinger equation [...]

But the dynamics you are attributing to the system + apparatus is nonlinear, so the simple standard linear superposition picture does not work.
Standard quantum mechanics also has lots of nonlinear approximations. Prime examples are the Hartree-Fock equations and the quantum-classical dynamics discussed in Part III of my series of papers. Nothing is really new in the thermal interpretation except for the reintepretation of what a measurement means.

The instantaneous collapse in the standard interpretation mimicks the nonlinearities by ignoring details of what happens during the measurement, which in fact tkes a finite time. it is like mimicking the classical continuous dynamics of an electric switch by treating it as an instantaneous discontinuity.

Objective-collapse theories introduce such nonlinearities explicitly into the dynamics of the universe. But they are not needed since they arise automatically through the well-knon coarse-graining procedures.

there is no solution to the nonlinear dynamics that describes a superposition of a spot at the +x position and a spot at the -x position.
The solutions are time-dependent. The trajectories started anywhere (e.g., in a superposition) move within a very short time (the duration of the measurement) towards one of the distinguished up and down states.

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#### PeterDonis

Mentor
Standard quantum mechanics also has lots of nonlinear approximations.
Yes, but the standard description of what happens if you make a SG measurement oriented in the x-direction on a single +z spin-1/2 does not, as I understand it, use them. It uses the linear Schrodinger equation and superposition. As I understand it, you are saying that that is wrong. In fact, it would seem that the thermal interpretation implies that it is always wrong--that as soon as you include any kind of macroscopic apparatus to make a measurement (which in practice you always will), the dynamics are no longer linear and so the Schrodinger Equation is not correct.

#### PeterDonis

Mentor
The solutions are time-dependent.
If this just means that the starting state is not preserved by the dynamics, of course this is true; but it's just as true for the linear Schrodinger Equation as for the nonlinear dynamics you appear to be using.

The trajectories started anywhere (e.g., in a superposition) move within a very short time (the duration of the measurement) towards one of the distinguished up and down states.
But that's not what happens with the linear Schrodinger Equation. The linear Schrodinger Equation says that if the spin-1/2 starts in the +z spin state, which is a 50-50 superposition of +x and -x spin (for a SG apparatus oriented in the x direction), the solution is a superposition of a +x spot and a -x spot. There is no such solution of the nonlinear dynamics, as you say; every solution ends up with either a +x spot or a -x spot, not a superposition of both.

#### A. Neumaier

If this just means that the starting state is not preserved by the dynamics, of course this is true; but it's just as true for the linear Schrodinger Equation as for the nonlinear dynamics you appear to be using.
Yes.
But that's not what happens with the linear Schrodinger Equation. The linear Schrodinger Equation says that if the spin-1/2 starts in the +z spin state, which is a 50-50 superposition of +x and -x spin (for a SG apparatus oriented in the x direction), the solution is a superposition of a +x spot and a -x spot. There is no such solution of the nonlinear dynamics, as you say; every solution ends up with either a +x spot or a -x spot, not a superposition of both.
Yes, but traditional interpretations claim the validity of the linear Schrodinger Equation only for isolated systems. A detector is never isolated, hence the linear Schrodinger Equation does not apply.

Traditional interpretations claim nothing during the measurement, which is usually thought of being instantaneous, and only claim that the state of the system after the measurement collapsed. This is obviously a nonlinear stochastic process.

The thermal interpretation explains this nonlinear stochastic process as an effect of the neglected environment.

#### charters

If the environment is such that it corresponds to a spin measurement with collapse to an up or down state, this dynamics is expected to have just two stable fixd points
Hmm...I think I might get it. Let me try my own words again and see if you agree. The appearance of Copehagen style collapse is inextricably bound up in the physical construction of the device itself. We should think of the incident field as causing the device to transition from its (sort of metastable) "ready" configuration to 1 of its 2+ possible (sort of "ground state") "clicked" configurations, which represent inaccurate TI measurements (as opposed to Copenhagen projections).

But the key is that not all transitions to all arbitrary clicked configurations can be induced by an N=1 field. In particular, such a field cannot induce a transition to a clicked configuration where the device has clicked 2+ times at different cells of the device.

Is that the idea?

#### PeterDonis

Mentor
traditional interpretations claim the validity of the linear Schrodinger Equation only for isolated systems. A detector is never isolated, hence the linear Schrodinger Equation does not apply.
Just to be clear: you are saying that the linear Schrodinger Equation does not apply to the detector and the spots that appear on it, correct? The linear Schrodinger Equation seems to work fine for explaining how the interaction of the spin-1/2 with the inhomogeneous magnetic field splits one trajectory into two. But the spin-1/2 is not an isolated system in this interaction: the system also includes the magnetic field.

#### A. Neumaier

Hmm...I think I might get it. Let me try my own words again and see if you agree. The appearance of Copehagen style collapse is inextricably bound up in the physical construction of the device itself. We should think of the incident field as causing the device to transition from its (sort of metastable) "ready" configuration to 1 of its 2+ possible (sort of "ground state") "clicked" configurations, which represent inaccurate TI measurements (as opposed to Copenhagen projections).

But the key is that not all transitions to all arbitrary clicked configurations can be induced by an N=1 field. In particular, such a field cannot induce a transition to a clicked configuration where the device has clicked 2+ times at different cells of the device.

Is that the idea?
Yes. Which transitions are possible is constrained by conservation laws and by selection rules.

#### charters

Yes. Which transitions are possible is constrained by conservation laws and by selection rules.
So, it seems these detector transitions are restricted at the holistic level, requiring a top down definition of the overall detector, which can be a highly nonlocal object in space and time.

Consider a detector made of multiple, widely separated components, such as arbitrarily many quad cell photodetectors, each at the end a of different arm of a Mach Zender interferometer. How do photodetectors A and B (which can be kilometers or lightyears apart) know if and when they are part of the same overall MZI detector, such that their transitions have to be constrained by each other? How do they know if/when they are meant to act as one non-local detector?

#### A. Neumaier

So, it seems these detector transitions are restricted at the holistic level, requiring a top down definition of the overall detector, which can be a highly nonlocal object in space and time.
Yes. In the thermal interpretation, the whole is more than its parts. In mathematical terms, a composite system has more independent beables (q-expectations) than the beables of its parts. This is a consequence of the formal apparatus of quantum mechanics, which the thermal interpretation does not change.
Consider a detector made of multiple, widely separated components, such as arbitrarily many quad cell photodetectors, each at the end a of different arm of a Mach Zender interferometer. How do photodetectors A and B (which can be kilometers or lightyears apart) know if and when they are part of the same overall MZI detector, such that their transitions have to be constrained by each other? How do they know if/when they are meant to act as one non-local detector?
I don't know how they know. This seems to be a secret of the creator of the universe.

But other interpretations of quantum mechanics also have no explanation for long-distance correlations violating Bell-type inequalities. One can only say that the dynamics assumed predicts these phenomena, and that Nature conforms to these predictions.

#### charters

But other interpretations of quantum mechanics also have no explanation for long-distance correlations
In Bohm, you have the pilot wave making the necessary trajectory corrections to the particle HVs. In MWI you have local decoherence and branching. In GRW you have the stochastic collapse mechanism. In superdeterminism, you have it all baked into the initial conditions. Retrocausal interpretations have the backwards evolving state vector. I don't know what equivalent story you want to tell here, esp if the TI is meant to be non-random.

I also would note most of these other interpretations require the above stories specifically to deal with Bell violations. You appear to need this for even a basic MZI. It is sort of like even when the quanta is unentangled, the entire macroscopic world of all detectors is still highly entangled (and at long distances, to a stronger degree than implied by something like Reeh Schlieder).

#### A. Neumaier

In Bohm, you have the pilot wave making the necessary trajectory corrections to the particle HVs. In MWI you have local decoherence and branching. In GRW you have the stochastic collapse mechanism. In superdeterminism, you have it all baked into the initial conditions. Retrocausal interpretations have the backwards evolving state vector.
They have stories, not explanations. They all assume an unexplained nonlocal dynamics from the start.
I don't know what equivalent story you want to tell here, esp if the TI is meant to be non-random.
The existence of multilocal q-expectations, which provide the potentially nonlocal correlations and evolve deterministically.
I also would note most of these other interpretations require the above stories specifically to deal with Bell violations.
So does the thermal interpretation, but without artificial baggage (no additional micropositions, no multiple worlds, no postulated collapse, no causality violations). Though it is superdeterministic in the sense that every deterministic theory of the universe has its complete fate encoded in the initial condition. (I don't really know what the extra 'super-' is about.)
You appear to need this for even a basic MZI.
No. If one does MZI with coherent light there are no correlations between the different detector results; each one fires independently according to its own locally incident field intensity, and the observed coincidence statistics (no bunching or antibunching) comes out. The apparent nonlocality is due to looking at the five detectors only at the random times where one of the detector fires, and observes that at this exact time no other detector fires. In fact, the collection of all five detectors responds with an all zero result almost all the times and occasionally with a 100% (in your setting), exact coincidencde has zero probability. Thus nothing nonlocal happens.

#### charters

(I don't really know what the extra 'super-' is about.)
The super in superdeterminism means that the interpretation is set up such that, for a generic choice of initial conditions, the standard equations/laws we use to make predictions will not work.

So, in this case, you explain the TI as relying on:

The existence of multilocal q-expectations, which provide the potentially nonlocal correlations and evolve deterministically.
But I can imagine different initial conditions with arbitrary/different multilocal q-expectations and therefore different non-local correlations between detector components. These detector correlations won't reproduce the correct experimental outcomes, eg in EPR experiments. It's only a special subclass of conceivable multilocal q-expectations which have to be assumed/baked into the initial conditions in order to reproduce QM.

This is not really anything to do with the TI in particular. It is just a consequence of Bell's theorem that any single world, deterministic interpretation will feature either a pilot wave+preferred foliation, retrocausality, or superdeterminism. Based on what you've written (and since you don't seem to adopt the former two concepts) superdeterminism seems like the choice the TI makes here.

#### A. Neumaier

The super in superdeterminism means that the interpretation is set up such that, for a generic choice of initial conditions, the standard equations/laws we use to make predictions will not work.
But this is the case for any deterministic dynamics of a specific system. For a generic choice of initial conditions, Nwton's law for our Solar system is not predictive. Would you therefore call Newton's mechanics superdeterministic?

On the other hand, the universe is a single system, so has to be treated on par with our Solar system.
Based on what you've written (and since you don't seem to adopt the former two concepts) superdeterminism seems like the choice the TI makes here.
Sure, the TI is deterministic, and applies only for our single universe.

By the preceding it is superdeterministic in your sense, just like Newton's mechanics for our Solar system.
But I can imagine different initial conditions with arbitrary/different multilocal q-expectations and therefore different non-local correlations between detector components. These detector correlations won't reproduce the correct experimental outcomes, eg in EPR experiments
But these detector and environment preparations would also not reproduce the actual detector and environment preparations needed to guarantee the correct performance of these experiments.

Thus TI is predictive without the need for assuming more about the initial conditions than is assumed in the analysis of the experiment.

#### charters

Would you therefore call Newton's mechanics superdeterministic?
Yes, in a limited sense. Newtonian mechanics does have to assume restriction to the set of initial conditions where nonrelativistic physics is valid. But this is not really something to worry about for emergent theories only valid in some restricted regime. In contrast, QM is claimed to be universal and fundamental, so if the validity of its equations/laws are claimed to be contingent on initial conditions in this way, a lot of people experience some heartburn and doubt.

But these detector and environment preparations would also not reproduce the actual detector and environment preparations needed to guarantee the correct performance of these experiments.
This is begging the question/assuming the superdeterminist methodology. The anti-superdeterminism worldview is that you can't look to outcomes to decide which initial conditions are valid.

I'm not really trying to say superdeterminism is an unacceptable philosophy. It doesn't work for me, but it does for many people smarter than me, most prominently t'Hooft. I guess I just wanted to highlight what I see as *the* major philosophical wedge issue/commitment in the TI, which doesn't get much attention in the papers.

#### A. Neumaier

In contrast, QM is claimed to be universal and fundamental, so if the validity of its equations/laws are claimed to be contingent on initial conditions in this way, a lot of people experience some heartburn and doubt.
Well, in the TI, the universal laws approximately follow from the law for the full universe, for all small subsystems of the universe that physicists find (by Nature or by special equipment, which is just human-manipulated Nature) prepared in the initial states they use to make successful predictions. To produce these approximations, the initial state of the universe is irrelevant; only the initial state of the subsystem and some general features of the universe known to be valid at the time of performing the experiment matter.

Thus no fine-tuning of the universe is needed beyond perhaps a low entropy state of the early universe. And even that might perhaps come about through coarse-graining.
This is begging the question/assuming the superdeterminist methodology. The anti-superdeterminism worldview is that you can't look to outcomes to decide which initial conditions are valid.
I don't see the problem.

It is obvious that one can predict states of a subsystem of a big deterministic system only when the initial conditions of this subsystem actually have the values assumed for the prediction! One does not have to look at the outcomes but at the preparation!

#### stevendaryl

Staff Emeritus
But this is the case for any deterministic dynamics of a specific system. For a generic choice of initial conditions, Nwton's law for our Solar system is not predictive. Would you therefore call Newton's mechanics superdeterministic?
The distinction between deterministic and superdeterministic theories is basically in what can be considered "free variables". For example, in the EPR experiment, we have two experimenters, Alice and Bob, who choose what measurements to perform (so that's one source of variability) and then we have the experimental results themselves, which is another source of variability. In Bell's analysis of EPR, he treats Alice's and Bob's choices as "free variables", and considers the measurement results to be functions of those choices (plus the "hidden variable", which is another free variable). In contrast, if you consider Alice's and Bob's choices to be constrained so that there is a hidden relationship between the three variables--(1) Alice's choice, (2) Bob's choice, and (3) the hidden variable value--then Bell's analysis doesn't apply. You can certainly match the predictions of EPR with local hidden variables if you assume that Alice's and Bob's choices are predictable (or are determined by the hidden variable $\lambda$). That loophole is the superdeterminism loophole.

It might seem at first that determinism implies superdeterminism. If Alice and Bob are described by deterministic laws, then their choices should be predictable, right? But they're not really the same. Alice might decide to make her choice based on some external event, such as whether she sees a supernova explosion in a certain region of the sky right before her measurement. Bob might decide to make his choice based on whether a basketball player makes his shot. Their choices can depend on absolutely anything. So in order for Alice's and Bob's choices to be reliably correlated, it's not enough that things be deterministic, but that the whole universe (or at least the part that is observable by Alice and Bob) be set up precisely in order to make that correlation. Such superdeterminism is not just a matter of having the future determined by current conditions (ordinary determinism), but would require that current conditions of the entire universe be fine-tuned.

#### A. Neumaier

The distinction between deterministic and superdeterministic theories is basically in what can be considered "free variables".
Would a Laplacian classical multiparticle universe in which observers (taken to be machines to avoid problems with consciousness) are also multiparticle systems be superdeterministic in this sense?

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#### DarMM

Gold Member
Would a Laplacian classical multiparticle universe in which observers (taken to be machines to avoid problems with consciousness) are also multiparticle systems be superdeterministic in this sense?
Consider such a world where the gravitational potential is $r^{-1+a}$, for some constant $a > 0$ let's say.

Then imagine that the initial state of the universe is such that your machines are "destined" to never obtain the accuracy or sufficient statistical certainty to confirm the $a$ correction and are thus "doomed" to believe gravity has a $r^{-1}$ potential. That would be superdeterminism.

In essence a deterministic world where the initial conditions never evolve into states corresponding to observers obtaining an accurate determination of the physical laws.

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#### stevendaryl

Staff Emeritus
Would a Laplacian classical multiparticle universe in which observers (taken to be machines to avoid problems with consciousness) are also multiparticle systems be superdeterministic in this sense?
As I said in my previous post, being deterministic does not imply being superdeterministic. Classical mechanics is not superdeterministic.

"How does the thermal interpretation explain Stern-Gerlach?"

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