Criteria for a good quantum interpretation

[stevendaryl]

The math shows that they are not different in principle. There is nothing more than a purely "quantum mechanical" von Neumann measurement chain.

If there is no in-principle difference, then I don't see how we get from: "The electron is in a superposition of spin-up in the x-direction and spin-down in the x-direction" to "The measurement device is either in the state 'measured spin-up' or 'measured spin-down' with 50/50 probability of each."

Von Neumann explicitly put in a non-deterministic "collapse" that did not follow from Schrodinger's equation.

 

[stevendaryl]

Perhaps not. But I don't think it's nonsensical to at least consider the possibility.

I don't think it's nonsensical to believe that there is some difference in the macroscopic and microscopic situations, some effect (such as spontaneous collapse) that is negligible in the microscopic case. But I do think it's nonsensical to say that both that there are no in principle differences, and also that superpositions exist in the one case but not the other.

 

[vanhees71]

Let me expand on why I think that interpretations of QM are either nonsensical or wrong.

Suppose I prepare an electron to be spin-up in the z-direction, and thereafter, nothing interacts with the electron. What is the probability that at a later time, the election has spin-up in the x-direction? It's a nonsensical question, because if nothing interacts with the electron, it will never be spin-up in the x-direction. It will continue to be spin-up in the z-direction forever.

Let's just look at this statement. It's not what QT (the formalism) says. If you have prepared the electron to be in the state
$$\hat{\rho}=|\sigma_z=1/2 \rangle \langle \sigma_z=1/2|,$$
this tells you everything also about measurements on all other spin components. Particularly it tells you that the spin-x component is indetermined and what the probability is to find the one or the other possible outcome. It's of course
$$P(\sigma_x)=\langle \sigma_x|\hat{\rho}|\sigma_x \rangle=\frac{1}{2}, \quad \sigma_x \in \{1/2,-1/2\}.$$
There's no other meaning in the states than the probabilities for the outcomes of all possible measurements on that system (in this sense reduced to just the spin observables of an electron).

 

[vanhees71]

I don't think it's nonsensical to believe that there is some difference in the macroscopic and microscopic situations, some effect (such as spontaneous collapse) that is negligible in the microscopic case. But I do think it's nonsensical to say that both that there are no in principle differences, and also that superpositions exist in the one case but not the other.

Of course, but there's not the slightest hint to some "cut", i.e., that there are differences between "macro physical" and "micro physical" principle laws. To the contrary, the better the technical possibilities get the more the experimentalists can demonstrate "quantum properties" on macroscopic objects, e.g., the kg heavy mirrors of the gravitational LIGO/VIRGO detectors.

 

[Demystifier]

My opinion about interpretations of QM is that there are no good ones. I would distinguish between two different ways that an interpretation can be flawed:

1. Wrong.
2. Nonsensical.

I consider all collapse interpretations to be wrong, while I consider all non-collapse interpretations nonsensical.

(Actually, Bohmian mechanics is sort of an oddball here. It bears some similarity with non-collapse interpretations, but I consider it wrong, rather than nonsensical.)

Would you agree with the following? All realist interpretations are wrong, all non-realist interpretations are nonsensical. The realist interpretations (Bohm, GRW, many worlds, ...) are wrong because we don't know what is real and chances that our guesses are right are too slim. The non-realist interpretations (Copenhagen, QBism, statistical ensemble, relational, ...) are nonsensical because it does not make sense to think about things without imagining that they are real.

 

[stevendaryl]

Would you agree with the following? All realist interpretations are wrong, all non-realist interpretations are nonsensical. The realist interpretations (Bohm, GRW, many worlds, ...) are wrong because we don't know what is real and chances that our guesses are right are too slim. The non-realist interpretations (Copenhagen, QBism, statistical ensemble, relational, ...) are nonsensical because it does not make sense to think about things without imagining that they are real.

Yes, that sounds about right. I would lump many worlds in with nonsensical, though. Not that I object in principle to the possibility of alternate worlds where things happened differently than they did in our world, but I don't think that probabilities make a lot of sense in many-worlds (and without probabilities, QM makes no testable predictions at all).

 

[stevendaryl]

Of course, but there's not the slightest hint to some "cut", i.e., that there are differences between "macro physical" and "micro physical" principle laws. To the contrary, the better the technical possibilities get the more the experimentalists can demonstrate "quantum properties" on macroscopic objects, e.g., the kg heavy mirrors of the gravitational LIGO/VIRGO detectors.

That illustrates the wrong versus nonsensical conundrum. Interpretations with a macro/micro distinction are (probably) wrong. Interpretations without such a distinction are nonsensical.

 

[stevendaryl]

Let's just look at this statement. It's not what QT (the formalism) says. If you have prepared the electron to be in the state
$$\hat{\rho}=|\sigma_z=1/2 \rangle \langle \sigma_z=1/2|,$$
this tells you everything also about measurements on all other spin components.

[STUFF DELETED]
There's no other meaning in the states than the probabilities for the outcomes of all possible measurements on that system (in this sense reduced to just the spin observables of an electron).

That's what I consider nonsensical. The last statement.

To me the conjunction of these two claims is contradictory:

1. There is nothing special about macroscopic systems.
2. The only meaning to QM is the predictions it makes about macroscopic systems.

 

[vanhees71]

1. is of course true.
2. QM makes predictions of single electrons and other single particles. These I'd not consider macroscopic.

 

[stevendaryl]

1. is of course true.
2. QM makes predictions of single electrons and other single particles. These I'd not consider macroscopic.

How can you measure a single electron without having it interact with a macroscopic system?

I thought you said that QM only makes predictions about measurement results. Measurement results are states of macroscopic systems.

 

[vanhees71]

That's of course true, but why does this imply for you that QT is "nonsensical"? The only criterion for the quality of a physical theory is whether it describes the observations correctly, and that's what QT does for nearly 100 years now!

 

[stevendaryl]

That's of course true, but why does this imply for you that QT is "nonsensical"?

You contradict yourself within two sentences. That means what you're saying is nonsensical. On the one hand, you say that QM only makes predictions about measurements. Since measurements are macroscopic results, then it logically follows that QM only makes predictions about macroscopic results, not microscopic results. But then you say that QM doesn't treat macroscopic and microscopic systems differently. That's a contradiction.

The only criterion for the quality of a physical theory is whether it describes the observations correctly,

That's philosophy, not physics.

 

[martinbn]

Would you agree with the following? All realist interpretations are wrong, all non-realist interpretations are nonsensical. The realist interpretations (Bohm, GRW, many worlds, ...) are wrong because we don't know what is real and chances that our guesses are right are too slim. The non-realist interpretations (Copenhagen, QBism, statistical ensemble, relational, ...) are nonsensical because it does not make sense to think about things without imagining that they are real.

I don't understand the last bit. Why can I not talk about something that isn't real. Before i toss a coin the value of the observable isn't real. After i toss it and see head or tail, then it is real. Why is it nonsense to talk about it before the toss?! I can say that there is a 50-50 chance of getting head.

 

[Sunil]

To me the conjunction of these two claims is contradictory:

1. There is nothing special about macroscopic systems.
2. The only meaning to QM is the predictions it makes about macroscopic systems.

Good observation. But requires some more detailed considerations to become a contradiction.

Let's note: (2) is essentially what QT says. QT predicts probabilities for measurement results of macroscopic measurement devices, for states prepared by macroscopic preparation procedures.

In itself, these statistical predictions hold for macroscopic states too. If you measure macroscopic states prepared by macroscopic preparation procedures with macroscopic measurement devices, you obtain the statistical predictions of QT too. Which, because of decoherence, are the same as classical predictions. In Ballentine's ensemble interpretation, there would be no conflict between (1) and (2).

But, of course, one implicitly adds to QT all those "no hidden variables" or "completeness" Copenhagen metaphysics. Then, Schrödinger's cat gives us something additional to QT. Namely, the actual state of the cat, which obviously existed even before we have looked at it. A configuration of the cat with a trajectory $q(t) \in Q$.

We can, of course, interpret QT in such a way that the Schrödinger equation, which gives us a continuity equation for $\rho(q)=|\psi(q)|^2$, contains such a trajectory too. But this goes already beyond minimal QT.

With these implicit assumptions added, one can defend (1) only in two ways: Either deny the existence of the macroscopic world as we know it (many worlds and similar ...), or add trajectories to QT (realistic interpretations).

Those who argue for (1) usually presuppose a) the completeness of QT, b) its universal, fundamental character. So, to add trajectories to QT is, for them, out of discussion. But nonetheless, (1) is obligatory. So, they essentially have to reject the world as we see it. They will not do it, that would be too obviously nonsensical. It remains to develop mystical philosophy about the strangeness of QT (rejection of realism, causality, probability theory, logic) so that it becomes possible to hide the absurdity behind that strangeness.

 

[Demystifier]

Why can I not talk about something that isn't real.

Read again what I wrote, I used words "think" and "imagine". When I think of heads before I toss the coin, I imagine how heads would look like if it was real.

 

[martinbn]

Read again what I wrote, I used words "think" and "imagine". When I think of heads before I toss the coin, I imagine how heads would look like if it was real.

Why are they nonsense then?

 

[Demystifier]

Why are they nonsense then?

I can't explain it in a way you would understand.

 

[martinbn]

I can't explain it in a way you would understand.

Sounds like an excuse.

 

[vanhees71]

You contradict yourself within two sentences. That means what you're saying is nonsensical. On the one hand, you say that QM only makes predictions about measurements. Since measurements are macroscopic results, then it logically follows that QM only makes predictions about macroscopic results, not microscopic results. But then you say that QM doesn't treat macroscopic and microscopic systems differently. That's a contradiction.

I still don't understand what you mean. QM makes probabilistic predictions for the outcome of measurements on all kinds of systems, no matter whether they are microscopic, mesoscopic, nanoscopic, femtoscopic or macroscopic.

If one performs the double-slit experiment with single electrons, what quantum mechanics predicts is the probability for registering an electron at a point on a screen behind the slits, $P(x)=|\psi(x)|^2$. There's nothing nonsensical in this. I'd say a single electron can be regarded as pretty "microscopic" ;-)).

Quantum mechanics together with basic principles of statistical physics (the maximum-entropy principle) also predicts the single-particle phase-space distribution of an ideal (or even real) gas in a container at a given temperature and chemical potential (grand-canonical approach). I'd consider this a pretty macroscopic system, and there's no nonsensical element in this either.

I don't understand the statement on philosophy either. Is it already philosophy to define what theoretical physics is supposed to do, namely describe observations in terms of mathematical models.

 

[stevendaryl]

I still don't understand what you mean. QM makes probabilistic predictions for the outcome of measurements on all kinds of systems, no matter whether they are microscopic, mesoscopic, nanoscopic, femtoscopic or macroscopic.

You have two different systems involved: (1) The system being measured, and (2) the system doing the measurement. You're saying that there is no reason in principle that the first type of system can't be macroscopic. That may or may not be true, but it's not my point is that the second type of system, the measuring device must be classical---macroscopic for QM to make any predictions at all. So QM makes a big distinction between microscopic systems and macroscopic systems. You're arguing exactly the wrong side of this---to the extent that QM only says things about measurements, it only says things about macroscopic systems.

f one performs the double-slit experiment with single electrons, what quantum mechanics predicts is the probability for registering an electron at a point on a screen behind the slits, P(x)=|ψ(x)|2. There's nothing nonsensical in this. I'd say a single electron can be regarded as pretty "microscopic" ;-)).

In this situation, QM isn't making a prediction about the electron---it's making a prediction about the future state of the detector. You say "we're making a measurement of the electron's spin, or location, or whatever", but that's sort of nonsensical, since electrons don't have spins or locations (unless they are in eigenstates of those operators).

I don't understand the statement on philosophy either. Is it already philosophy to define what theoretical physics is supposed to do

That's what I mean--your statement is philosophy, and is therefore off-topic in this thread.

 

[Lord Jestocost]

The non-realist interpretations (Copenhagen, QBism, statistical ensemble, relational, ...) are nonsensical because it does not make sense to think about things without imagining that they are real.

Non-realist interpretations seem to be nonsensical because we feel the inner impulse to think of phenomena as experiences of objects; and objects – per definition – can be given descriptions in their own right.

In „Niels Bohr, 1913-2013, Poincaré Seminar 2013”, Michel Bitbol and Stefano Osnaghi write:

“Bohr restricts his definition of ‘phenomenon’ to ‘observations obtained under specified circumstances, including an account of the whole experimental arrangement' [Bohr 1958, p. 64]. The task of complementarity is then to bring phenomena occurring in incompatible situations together, as if they referred to the same object.” [bold by LJ]

Or, as Nick Herbert puts in in his book “Quantum Reality: Beyond the New Physics”:

“The separate images that we form of the quantum world (wave, particle, for example) from different experimental viewpoints do not combine into one comprehensive whole. There is no single image that corresponds to an electron. The quantum world is not made up of objects. As Heisenberg puts it, ‘Atoms are not things.’

This does not mean that the quantum world is subjective. The quantum world is as objective as our own: different people taking the same view point see the same thing, but the quantum world is not made of objects (different viewpoints do not add up). The quantum world is objective but objectless.

An example of a phenomenon which is objective but not an object is the rainbow. A rainbow has no end (hence no pot of gold) because the rainbow is not a ‘thing’. A rainbow appears in a different place for each observer—in fact, each of your eyes sees a slightly different rainbow. Yet the rainbow is an objective phenomenon; it can be photographed.”

 

[stevendaryl]

Let me go through this again:

If you prepare an electron so that it is spin-up in the z-direction, then it simply does not have a spin in the x-direction. It's not that we don't know what that spin is --- it doesn't have one. (At least in a minimalist interpretation without hidden variables...)

If you set up a Stern-Gerlach device oriented in the x-direction the prediction "50% spin up/50% spin down" is NOT a statement about the electron. There is no more to say about the electron beyond "It is spin-up in the z-direction". The Stern-Gerlach device is not going to tell us anything more about the electron. Instead, the interaction of the electron with the device makes the evolution of the DEVICE nondeterministic; it has a 50% chance of ending up in one macroscopic state, and a 50% chance of ending up in the other macroscopic state.

The probabilistic predictions of QM are therefore only predictions about macroscopic systems. The predictions aren't about electrons or protons, they are predictions about measurement devices. At least in the minimalist interpretation.

 

[vanhees71]

You have two different systems involved: (1) The system being measured, and (2) the system doing the measurement. You're saying that there is no reason in principle that the first type of system can't be macroscopic. That may or may not be true, but it's not my point is that the second type of system, the measuring device must be classical---macroscopic for QM to make any predictions at all. So QM makes a big distinction between microscopic systems and macroscopic systems. You're arguing exactly the wrong side of this---to the extent that QM only says things about measurements, it only says things about macroscopic systems.

No it doesn't. It says things about single elementary particles which are comparable to experiment. The classical behavior of macroscopic systems, including measurement apparati, is an emergent phenomenon understandable from quantum theory. There is no distinction between microscopic and macroscopic systems. It's only hard to reveal specifically quantum phenomena for macroscopic systems, but it is possible for larger and larger systems. So far there's not the slightest hint that there is a limit for the validity of QT depending on system size.

 

[stevendaryl]

No it doesn't.

You say that, but you also say contradictory things.

It says things about single elementary particles which are comparable to experiment.

No, it doesn't. If an electron is prepared to be spin-up in the z-direction, and you perform a measurement of the spin in the x-direction (so that there will be a dot on the left side of a photographic to indicate spin-up in the x-direction, and a dot on the right side to indicate spin-down), you aren't learning ANYTHING about the electron. You already knew everything that there was to know about the electron's spin before you performed the measurement. (According to an interpretation without hidden variables.) The prediction "there will be a dot on the left side of the photographic plate with probability 50% and there will be a dot on the right side with probability 50%" is NOT a prediction about the electron. It's a prediction about photographic plates.

 

[stevendaryl]

The prediction "there will be a dot on the left side of the photographic plate with probability 50% and there will be a dot on the right side with probability 50%" is NOT a prediction about the electron. It's a prediction about photographic plates.

In a "collapse" interpretation, a measurement does tell you something about the particle, because after the measurement, the particle is assumed to be in an eigenstate of whatever was measured. In a "hidden variables" interpretation, a measurement tells you something about the values of hidden variables.

But in the interpretation in which there are no hidden variables, and no collapse, a measurement doesn't tell you anything about particles. That's the nonsensical (as opposed to wrong) interpretation.

 

[vanhees71]

I don't understand why an unobservable collapse makes the measurement telling me something about the electron while in the statistical interpretation it doesn't. The collapse is unobservable because the electron is not prepared in the state you assume by the collapse conjecture but it's absorbed by the photoplate (or CCD cam nowadays).

 

[stevendaryl]

I don't understand why an unobservable collapse makes the measurement telling me something about the electron while in the statistical interpretation it doesn't.

If you prepare an electron to have spin-up in the z-direction, and then you perform a measurement of spin in the x-direction, what does the result tell you about the electron? Nothing, in the no-collapse interpretation.

In the collapse interpretation, after the measurement, you know the electron's spin in the x-direction.

 

[vanhees71]

I don't need a collapse to state that I measured the value of the spin-x component. It's just done by measuring precisely enough where the electron was registered (assuming we do a usual Stern-Gerlach experiment), because the spin-x component is entangled with the position of the electron, which is measured. I don't need a collapse, and it doesn't even tell you the right state of the electron, because it's simply absorbed and just becomes thermalized with the plate and its spin state is just that it's unpolarized ;-)).

 

[stevendaryl]

I don't need a collapse to state that I measured the value of the spin-x component.

You can state it, but it's not true. If the electron has no spin in the x-direction, then you can't measure it.

The most you can say is a counterfactual: IF the electron had been prepared to be spin-up in the x-direction, THEN there would be a dot on the left side of the photographic plate. IF the electron had been prepared to be spin-down in the x-direction, THEN there would be a dot on the right side. But in the case where the electron is prepared to be spin-up in the z-direction, what does the dot tell you about the electron? Nothing.

 

[vanhees71]

An electron always has a spin in $x$ direction, because an electron is a spin-1/2 particle. Maybe its value is indetermined but it always has a spin observable.

The 2nd paragraph I also don't consider correct. All you can say in QT is that, if the electron is prepared in the (spin) state $\hat{\rho}$ then the probability to get the value $\sigma_x \in \{1/2,-1/2\}$ when measuring the spin-x component is given by $\langle \sigma_x|\hat{\rho}|\sigma_x \rangle$.

 

[stevendaryl]

An electron always has a spin in $x$ direction, because an electron is a spin-1/2 particle. Maybe its value is indetermined but it always has a spin observable.

If the value is indetermined, then it doesn't have a value.

Once again, if the electron is prepared to be spin-up in the z-direction, and then your Stern-Gerlach device oriented in the x-direction gives the result "spin up", what does that tell you about the electron that you didn't already know? Nothing (in the interpretation without collapse and without hidden variables). Calling it a "measurement of the x-component of the electron's spin" is misleading to the point of being nonsense.

 

[Lord Jestocost]

... what does that tell you about the electron that you didn't already know? Nothing (in the interpretation without collapse and without hidden variables).

To my mind, the discussion suffers from the missing definition regarding the role of the wave function: Does the quantum mechanical formalism refer to particular quantum systems or to only a very large number of such systems?

In case the wave function gives a complete account of the physical situation of a single quantum entity, there is no escape from the reduction/collapse postulate.

Of course, one doesn’t need the collapse or state reduction postulate in case one believes in Einstein’s ensemble/statistical interpretation. However, as Amit Goswami puts it in a nutshell: “What lurks behind the statistical interpretation is the notion that quantum mechanics is not the final story, but must be supplemented by some kind of hidden variables that operate from behind the scenes and manipulate the fate of single quantum objects……”.

 

[Tendex]

An electron always has a spin in x direction, because an electron is a spin-1/2 particle. Maybe its value is indetermined but it always has a spin observable.

Always? what's the point of "having" a certain quantum observable between measurements when its value cannot be supposed to exist precisely due to qm's incompatibility with HV theories per Bell?

 

[Fra]

No it doesn't. It says things about single elementary particles which are comparable to experiment. The classical behavior of macroscopic systems, including measurement apparati, is an emergent phenomenon understandable from quantum theory. There is no distinction between microscopic and macroscopic systems. It's only hard to reveal specifically quantum phenomena for macroscopic systems, but it is possible for larger and larger systems. So far there's not the slightest hint that there is a limit for the validity of QT depending on system size.

Do you reject that QM requires a classical context (observer/measurement device etc) to be properly formulated and corroborated?

This suprises me a bit, as I interpret you as defending the experimental/empirical side of thigs? I myself see myself as defend the conceptully consistent reasoning side of things, but even as such an some what armchair position, I take the "principle" of empirical and experimental "practical details" seriously. This is why it will not do IMO, to just "imagine" a reduction of the whole universe. Such scale of things can never be corroborated, and especially when you think of unification with gravity, these details are important. For me, it's clear the quantum theory and its principles are only corroborated for small subsystems taking place on very short time scales, monitoring from classical laboratory. To extrapolate those principles to cosmological times and cosmological scales is speculative.

/Fredrik

 

[vanhees71]

To my mind, the discussion suffers from the missing definition regarding the role of the wave function: Does the quantum mechanical formalism refer to particular quantum systems or to only a very large number of such systems?

In case the wave function gives a complete account of the physical situation of a single quantum entity, there is no escape from the reduction/collapse postulate.

Of course, one doesn’t need the collapse or state reduction postulate in case one believes in Einstein’s ensemble/statistical interpretation. However, as Amit Goswami puts it in a nutshell: “What lurks behind the statistical interpretation is the notion that quantum mechanics is not the final story, but must be supplemented by some kind of hidden variables that operate from behind the scenes and manipulate the fate of single quantum objects……”.

The trouble with hidden variables is that so far nobody has found which kind of hidden-variable theory works, because behind this, as we know from Bell's theory and the experimental decision in favor of quantum theory, lurks non-locality. AFAIK there's no consistent non-local theory compatible with relativity.