Against "interpretation" - Comments

[Ian J Miller]

If you introduce new premises, the maths are not the same. For my example above, I have introduced the phase velocity of the wave equalling the particle velocity. That does not occur in any book or paper on QM of which I am aware, apart from anything I have written, such as the above. What it does is provide a method for calculating properties that standard theory can not dowiht0put introducing "validation corrections" (See Pople's Noble lecture).

 

[PeterDonis]

If you introduce new premises, the maths are not the same.

True, but the math might also be inconsistent. See below.

For my example above, I have introduced the phase velocity of the wave equalling the particle velocity.

But you have not shown that this leads to a consistent model, or given a reference to one. In the pilot wave version of standard (non-relativistic) QM, you can't arbitrarily set the phase velocity of the pilot wave; it's not a free parameter, it's determined by the Schrodinger Equation.

 

[Ian J Miller]

True, but the math might also be inconsistent. See below.
But you have not shown that this leads to a consistent model, or given a reference to one. In the pilot wave version of standard (non-relativistic) QM, you can't arbitrarily set the phase velocity of the pilot wave; it's not a free parameter, it's determined by the Schrodinger Equation.

The Schrödinger equation defines the energy of the particle, and it applies even if there is no wave with physical properties. But if the wave is not at the slits, how can it affect what the particle does when it goes through? Accordingly, what I have written above is not the standard pilot wave, nevertheless it gives results in accord with observation for molecules.

 

[Dale]

If you introduce new premises, the maths are not the same.

What matters is whether or not the experimental predictions are the same. Same predictions -> same theory.

 

[Pleonasm]

If the model makes different predictions for some experiments, then it is a different theory, not an interpretation. But a model that just says "there are hidden variables", but keeps all of the experimental predictions the same, is an interpretation.

I suppose it depends on the context. In a philosophy context, a theory of the world is what one thinks constitutes the world. A world of hidden variables as opposed to no hidden variables would constitute two difference universes cosmetically. I write cosmetically, because they would in this case be operationally identical nevertheless. Perhaps a physics context doesn't give a damn about this, but it would seem overly reductionist.

Definitely not. A prime example is Lorentz aether theory which posits that nature has an additional feature (the aether), but is generally considered an interpretation of S.R. rather than a new theory precisely because it makes no new predictions.

How do you square "definitely not" with "generally concidered". Is statement 1 a personal opinion expressed?

 

[Dale]

In a philosophy context

This forum is a scientific context.

How do you square "definately not" with "generally concidered". Is statement 1 a personal expression?

Everything I write is a personal expression. I believe that expression to be consistent with the professional scientific literature as referenced earlier in this thread.

Btw, spell check might be helpful, or at least copy and paste. Both of your manual quotes introduced spelling errors that were not in my original. At first I thought you were trying to make fun of me.

 

[PeterDonis]

if the wave is not at the slits, how can it affect what the particle does when it goes through?

Because the pilot wave version of standard non-relativistic QM has an explicitly nonlocal interaction between the pilot wave and the particles. This feature is a key reason why nobody has yet been able to come up with a consistent relativistic version.

what I have written above is not the standard pilot wave

Then your model is under-specified, because you have not given the complete statement of all the entities and dynamics, and therefore we don't know what your model predicts for all experiments that we have predictions from standard QM for. So it's impossible to tell whether it is a different theory from standard QM, or just a different interpretation.

 

[PeterDonis]

I suppose it depends on the context.

Sure, it could, but in this context we care about the physics definition, not about any philosophical definition. This is a physics forum.

 

[Pleonasm]

This forum is a scientific context.

How one defines "theory" as opposed to "interpretation" is ultimately a philosophical question. It's just semantics at the end of the day.

My point was that your initial statements are contradictions. You wrote "definitely not" to my claim, only to follow it up with a "generally not" example. This is a contradiction.

 

[Pleonasm]

FWI, I know of a working physicist who is of the opinion that the pilot wave model is a theory, not just an interpretation. It doesn't seem to be self-evident to him at least.

 

[PeterDonis]

I know of a working physicist who is of the opinion that the pilot wave model is a theory, not just an interpretation.

Is he claiming that the pilot wave model makes different predictions from standard QM?

If he is, you should ask him to back up that claim (since AFAIK every other physicist agrees that the pilot wave model makes the same predictions as standard QM).

If he is not, then he's just using the words "theory" and "interpretation" differently from how we define them here at PF. That's a matter of choice of words, not physics.

 

[Dale]

How one defines "theory" as opposed to "interpretation" is ultimately a philosophical question

Nonsense. It is a semantic question as are all definitions. Philosophy does not own all definitions. Scientific definitions belong to the scientific community just as financial definitions belong to the financial community.

My point was that your initial statements are contradictions. You wrote "definitely not" to my claim, only to follow it up with a "generally not" example. This is a contradiction.

I said “generally considered” not “generally not”. Please don’t misquote me.

There is no contradiction. A definition is what a word is “generally considered” to mean by the community using the word. “Generally considered” indicates my belief that the terminology I am using is not my personal usage but is the usage by the general scientific community.

 

[Demystifier]

Because the pilot wave version of standard non-relativistic QM has an explicitly nonlocal interaction between the pilot wave and the particles.

More precisely nonlocal interaction between the particles, in the same sense in which Newtonian gravity is a nonlocal interaction between particles, not a nonlocal interaction between the gravitational field and particles.

 

[Demystifier]

This feature is a key reason why nobody has yet been able to come up with a consistent relativistic version.

In the paper linked in my signature below I argue that Bohmian mechanics predicts that the Standard Model is only an effective theory emergent from a more fundamental non-relativistic theory. In this way Bohmian mechanics becomes a "theory" (in the sense of making a new prediction) and the problem of relativistic Bohmian mechanics is avoided.

 

[martinbn]

More precisely nonlocal interaction between the particles, in the same sense in which Newtonian gravity is a nonlocal interaction between particles, not a nonlocal interaction between the gravitational field and particles.

But to me it doesn't seem to be the same as in the Newtonian case. There, if I move a particle here, it will result in a measurable effect to the particle over there. In the Bohmian case there is nothing you can do to a particle here that will have observational consequence to a particle over there, right?

 

[Demystifier]

But to me it doesn't seem to be the same as in the Newtonian case. There, if I move a particle here, it will result in a measurable effect to the particle over there. In the Bohmian case there is nothing you can do to a particle here that will have observational consequence to a particle over there, right?

You seem to be speaking as if, in the Newton case, a particle can move by a human will. But this is wrong. In Newtonian mechanics particles move by deterministic forces, not by human will. So one has to use a passive language: If a particle moves here, it will result to a measurable effect over there. When put in this form, the same can be said about Bohmian mechanics.

 

[martinbn]

You seem to be speaking as if, in the Newton case, a particle can move by a human will. But this is wrong. In Newtonian mechanics particles move by deterministic forces, not by human will. So one has to use a passive language: If a particle moves here, it will result to a measurable effect over there. When put in this form, the same can be said about Bohmian mechanics.

I move one of the particles, you can see that I've done something by measurering the other particle. Just like Alice can choose and measure spin in a direction (or whatever she wants), but here Bob cannot tell just looking at the other particle.

 

[Demystifier]

I move one of the particles, you can see that I've done something by measurering the other particle. Just like Alice can choose and measure spin in a direction (or whatever she wants), but here Bob cannot tell just looking at the other particle.

You don't seem to understand my objection. I insist on formulation that does not contain athropomorphic notions such as the bolded ones above.

 

[Dale]

I insist on formulation that does not contain athropomorphic notions such as the bolded ones above.

Why? Science is done by anthropomorphic entities such as Bob and Alice who do have wants. Seems counterproductive to insist otherwise.

 

[martinbn]

You don't seem to understand my objection. I insist on formulation that does not contain athropomorphic notions such as the bolded ones above.

That objection doesn't appear anywhere in Newtonian mechanics, why is it so essential in Bohmian mechanics?

Consider two different scenarios for one of the particles. Say it is stationary, or it moves back and forth. The two scenarios have different effect on the other particle. They (the two scenarios) are distinguishable. And that distinction is local for the other particle. In the Bohmian mechanics that is not the case. Same as standard quantum mechanics. Locally the behavior of one particle doesn't distinguish the two different behaviors of the second particle.

 

[PeterDonis]

I move one of the particles

Newtonian mechanics is deterministic, so you can't just arbitrarily choose to move one of the particles. Whatever any particle does is completely determined by the initial conditions of the universe; the same goes for what you do. I think that is the point that @Demystifier is trying to make.

 

[A. Neumaier]

I move one of the particles, you can see that I've done something by measurering the other particle. Just like Alice can choose and measure spin in a direction (or whatever she wants), but here Bob cannot tell just looking at the other particle.

Newtonian mechanics is deterministic, so you can't just arbitrarily choose to move one of the particles. Whatever any particle does is completely determined by the initial conditions of the universe; the same goes for what you do. I think that is the point that @Demystifier is trying to make.

But @martinbn is making a point different from @Demystifier, namely that in the conventional analysis of long-distance correlation experiments, one has to assume that Alice can make choices. Otherwise everything was determined according to @Demystifier at the big bang, and nothing at all needs to be explained, nothing baffling is left.

To be convincing with his argument, Demystifier has to explain is why the Bohmian universe behaves such that seeming choices can be made by Alice!

[In the original post I had also claimed: ''In a Bohmian universe, one can also consider two universes that are identical except for a difference in the initial conditions of some particle at a particular time. One finds that this difference in initial conditions does not influence the other particles.'' But this is not true; see the next two posts.]

 

[stevendaryl]

In a Bohmian universe, one can also consider two universes that are identical except for a difference in the initial conditions of some particle at a particular time. One finds that this difference in initial conditions does not influence the other particles - all beables of the two universes (except for the position of the one particle moved) behave exactly the same!

Maybe I'm misunderstanding something. In one formulation of Bohmian mechanics, the wave function gives rise to a "quantum potential" whose value depends on the locations of every particle in the universe. So changing the location of one particle potentially affects every other particle.

 

[A. Neumaier]

Maybe I'm misunderstanding something. In one formulation of Bohmian mechanics, the wave function gives rise to a "quantum potential" whose value depends on the locations of every particle in the universe. So changing the location of one particle potentially affects every other particle.

Oh, yes, you are right, sorry. The wave function is unaffected by the particles, but the motion of the other particles depends on its value at the particle whose position changed, thus the latter affects the former.

This answers the concern by @martinbn in a more direct way than the response by @Demystifier had suggested.

 

[martinbn]

Oh, yes, you are right, sorry. The wave function is unaffected by the particles, but the motion of the other particles depends on its value at the particle whose position changed, thus the latter affects the former.

This answers the concern by @martinbn in a more direct way than the response by @Demystifier had suggested.

Yes, this does answer my concern better. But I still have a question left. My point was that in Newtonian gravity I can by only observing one particle deduce something about the behavior of the other, without the need of me knowing the initial state of the universe, just local observations of one particle. That is not possible in quantum mechanics. Is it possible in Bohmian mechanics? If not, then the claim that the nonlicality of Bohmian mechanics is the same as that in Newton's gravity is simply incorrect. This was the only point that I wanted to make. If on the other hand it is possible, then it seems that Bohmian mechanics is substantially different from QM, not just an interpretation. So different that it is already ruled out.

 

[stevendaryl]

Yes, this does answer my concern better. But I still have a question left. My point was that in Newtonian gravity I can by only observing one particle deduce something about the behavior of the other, without the need of me knowing the initial state of the universe, just local observations of one particle. That is not possible in quantum mechanics. Is it possible in Bohmian mechanics? If not, then the claim that the nonlicality of Bohmian mechanics is the same as that in Newton's gravity is simply incorrect. This was the only point that I wanted to make. If on the other hand it is possible, then it seems that Bohmian mechanics is substantially different from QM, not just an interpretation. So different that it is already ruled out.

I'm not sure I understand what distinction you are making. Bohmian mechanics is deterministic, just as Newtonian mechanics is. Each particle affects every other particle, just as with Newtonian mechanics.

That is, in principle, different from standard QM, which is nondeterministic, but in practice they make the same predictions. If you don't know the exact positions of every particle, but only a probability distribution, then Bohmian mechanics only allows you to make probabilistic predictions.

 

[A. Neumaier]

in Newtonian gravity I can by only observing one particle deduce something about the behavior of the other, without the need of me knowing the initial state of the universe

You can say nothing exact without knowing the state of the universe at the particular moment, since the dynamics of each particle depends on all others. This is as in Bohmian mechanics.

 

[Demystifier]

Why? Science is done by anthropomorphic entities such as Bob and Alice who do have wants. Seems counterproductive to insist otherwise.

That's true for a large part of science (applied science, mainly), but not for all science. (For instance, in cosmology one does not ask what happens if Alice creates a new galaxy or Bob creates a new quantum fluctuation as a seed for a new inflationary Universe.) The point of Bohmian mechanics is to interpret quantum mechanics in a manner that does not involve observers. So if one wants to understand Bohmian mechanics, then referring to Alice and Bob is, well, counterproductive.

 

[Demystifier]

To be convincing with his argument, Demystifier has to explain is why the Bohmian universe behaves such that seeming choices can be made by Alice!

Well, that's a problem for any physical theory that claims to be fundamentally deterministic or fundamentally probabilistic. If so, then where does the human free will come from? The most physical answer is that free will is an illusion. Things just happen due to the laws of physics, but our brain then somehow interprets some of those as being "chosen by oneself". How exactly that happens in the brain is something that physics alone cannot answer.

 

[Demystifier]

My point was that in Newtonian gravity I can by only observing one particle deduce something about the behavior of the other, without the need of me knowing the initial state of the universe, just local observations of one particle. That is not possible in quantum mechanics. Is it possible in Bohmian mechanics? If not, then the claim that the nonlicality of Bohmian mechanics is the same as that in Newton's gravity is simply incorrect. This was the only point that I wanted to make.

It is not possible in Bohmian mechanics, but to understand where does the difference come from you have to ask the following question: How exactly one observes a particle in Newtonian gravity? The point is that one observes it by a local non-gravitational interaction. Typically, one observes the stars and planets by watching them, which involves interaction with light. For instance when you watch the Moon, the light interacts with the Moon (by reflecting from it) only when the light touches the Moon. It is this locality of interaction that allows one to determine the position of the Moon. In Bohmian mechanics, on the other hand, particles do not interact via any local interactions at all (see my "Bohmian mechanics for instrumentalists"). In this sense, there is no analogue of "light" in Bohmian mechanics. Bohmian particles are analogous to dark matter in astrophysics, which, as you might know, cannot be directly observed precisely because it does not interact with light.

Or to make the long story short, nonlocality in Newtonian gravity is very much like nonlocality in Bohmian mechanics, but the difference is that, in Newtonian gravity, there is something additional which is local and non-gravitational.

 

[martinbn]

It is not possible in Bohmian mechanics, but to understand where does the difference come from you have to ask the following question: How exactly one observes a particle in Newtonian gravity? The point is that one observes it by a local non-gravitational interaction. Typically, one observes the stars and planets by watching them, which involves interaction with light. For instance when you watch the Moon, the light interacts with the Moon (by reflecting from it) only when the light touches the Moon. It is this locality of interaction that allows one to determine the position of the Moon. In Bohmian mechanics, on the other hand, particles do not interact via any local interactions at all (see my "Bohmian mechanics for instrumentalists"). In this sense, there is no analogue of "light" in Bohmian mechanics. Bohmian particles are analogous to dark matter in astrophysics, which, as you might know, cannot be directly observed precisely because it does not interact with light.

Or to make the long story short, nonlocality in Newtonian gravity is very much like nonlocality in Bohmian mechanics, but the difference is that, in Newtonian gravity, there is something additional which is local and non-gravitational.

I am not so sure about this. I can sit at the seashore and watch the tides. If the moon disappears I will realize that by the tides. I don't need to look at the moon. Newtonian gravity allows instantaneous signal transmission, QM doesn't. Does BM? I guess not, so it is not the same as Newtonian gravity.

 

[stevendaryl]

Newtonian gravity allows instantaneous signal transmission, QM doesn't. Does BM? I guess not, so it is not the same as Newtonian gravity.

I think BM does allow instantaneous effects in the same sense that Newtonian gravity does. But it can't be used for communication unless you know the exact locations of every particle in the universe. Which you don't.

Let me illustrate with a very simplified version of EPR. Suppose that Alice is trying to transmit a single bit (0 or 1) to Bob. Alice has a device with two buttons labeled 0 and 1. Bob has a corresponding device with two LEDs, one labeled 0 and one labeled 1. Let's suppose that there is a bit-valued hidden variable $\lambda$ that is either 0 or 1, and that $\lambda$ depends in some sensitive way on the exact positions of every particle in the universe.

Let $A$ be Alice's choice, 0 or 1. Let $B$ be Bob's result, 0 or 1. Then the laws of the universe work so that:

$B = A + \lambda(1 - 2A)$

So if $\lambda = 0$, then $B = A$. If $\lambda = 1$, then $B= 1-A$.

I think it's clear that Alice can't dependably send a 0 to Bob unless she knows the value of $\lambda$. However, her choice does affect Bob's result, in the sense that if she makes the opposite choice, he will get the opposite value.

 

[Demystifier]

I am not so sure about this. I can sit at the seashore and watch the tides. If the moon disappears I will realize that by the tides. I don't need to look at the moon. Newtonian gravity allows instantaneous signal transmission, QM doesn't. Does BM? I guess not, so it is not the same as Newtonian gravity.

How would you make the Moon disappear? Which force would you apply for that? Gravitational force or some other force? If it is some other force, then, as I already pointed out, the difference emerges from the fact that in Newtonian gravity there are some additional forces.

 

[cube137]

Demystifier. Why does Bohmian Mechanics belong to "b) No" in the "Find Your Own Quantum Interpretation" chart for the question "Is the world completely described by the state in the Hilbert space? The "a) Yes" is for Many Worlds for example. You may argue the beabble in BM is only for the particles like tables or chairs. But what would be wrong by stating the wave function in BM is also real like in Many worlds? What theoretical conflict can occur?

 

[stevendaryl]

Demystifier. Why does Bohmian Mechanics belong to "b) No" in the "Find Your Own Quantum Interpretation" chart for the question "Is the world completely described by the state in the Hilbert space?

The answer is "no" because the world is described by the state in Hilbert space AND the instantaneous positions of every particle. The state alone is not a complete description.

 

[cube137]

The answer is "no" because the world is described by the state in Hilbert space AND the instantaneous positions of every particle. The state alone is not a complete description.

Why, in many worlds, there are no instantaneous positions of every particle since the world is conpletely described by the state in Hilbert space?

 

[stevendaryl]

Why, in many worlds, there are no instantaneous positions of every particle since the world is conpletely described by the state in Hilbert space?

I'm not sure how to answer a "why" question like that. It just doesn't. In the simplest case of one particle, you have a wave function $\psi(x,t)$. The particle has a probability of being here or there, but the wave function doesn't tell you where the particle is.

 

[cube137]

I'm not sure how to answer a "why" question like that. It just doesn't. In the simplest case of one particle, you have a wave function $\psi(x,t)$. The particle has a probability of being here or there, but the wave function doesn't tell you where the particle is.

I know. But why did you state that "the world is described by the state in Hilbert space AND the instantaneous positions of every particle"? Is this only for Bohmian Mechanics?

 

[stevendaryl]

I know. But why did you state that "the world is described by the state in Hilbert space AND the instantaneous positions of every particle"? Is this only for Bohmian Mechanics?

Yes, in Bohmian mechanics, the world is described by the wave function and the positions of every particle. In Many-Worlds, the world is described by just the wave function.

 

[cube137]

Yes, in Bohmian mechanics, the world is described by the wave function and the positions of every particle. In Many-Worlds, the world is described by just the wave function.

Ok. That's clear enough.

About many worlds. I'd like to know something. In a cat. How often are there quantum choices in the atoms and molecules of the cats enough to create different mixed states or worlds? And if the quantum choices affect the organs and endocrine system. So the cats can be in different moods in different worlds?

 

[Elias1960]

Back to the OP. The point that there is no physical theory without metaphysical elements so that it becomes difficult to give meaning to "theory" if one has several interpretations is a good one. But it is not strong enough to justify a change in the language.

A more interesting point is why it makes sense to consider different interpretations at all.

1.) With different interpretations, it is much easier to identify the metaphysical elements in all these interpretations (these are the things which differ) from physical elements (these have to be the same for all interpretations).
2.) Interpretations are starting points for theory development. Different theories define different programs for such theory development. A reasonable starting point for QG would be to start with different interpretations of the Einstein equations, instead of using only a single one for this purpose.
This happens in several ways:
a.) General theory development. The classical Lorentz ether and Minkowski spacetime are identical. Considering quantization, the spacetime interpretation allows proving Bell's theorem while the proof fails for the Lorentz ether. Thus, the quantization applied to different interpretations of the same theory can give different theories. Generalizing both to gravity has a similar effect. The Minkowski spacetime interpretation gives GR, the Lorentz ether interpretation of the Einstein equations requires a Newtonian background, excluding in this way wormhole solutions of GR, and requires that absolute time is a global time-like function, excluding solutions with causal loops.
b.) Healing particular problems of an interpretation. Some interpretations have problems that do not appear in other interpretations. There may be possibilities to solve these problems by minor modifications of the theory. The modified theory is already a different theory. Simply adding the harmonic condition as a physical equation to the Einstein equations, as done by the Lorentz ether interpretation of the Einstein equations, destroys the Lagrange formalism. This can be healed by adding terms to the Lagrangian which enforce harmonic coordinates. But these terms also modify the Einstein equations. The resulting theory has already different equations.
3.) What was initially thought to be an interpretation appears to be, nonetheless, a different theory, by subsequent research. The typical situation is that the interpretation adds structure to the theory, and this structure is not compatible with all solutions of the theory. Nelsonian stochastics was thought to be an interpretation of QT. Then Wallstrom objected that it is a different theory. The point was that the equations of Nelsonian stochastics are equations for probability density and the phase, and the phase has to be a global function. This excludes solutions of QT where the wave function has zeros in the configuration space representation.

To summarize, interpretations play an important role for theory development. Without considering different interpretations, one loses many interesting paths to the development of new theories. Moreover, some interpretations were found to be different theories later.

 

[Demystifier]

1.) With different interpretations, it is much easier to identify the metaphysical elements in all these interpretations (these are the things which differ) from physical elements (these have to be the same for all interpretations).

Take, for example, the Lagrangian and the Hamiltonian formulation of classical mechanics. Are they two interpretations? Are the Lagrangian and the Hamiltonian metaphysical elements?

 

[Dale]

Take, for example, the Lagrangian and the Hamiltonian formulation of classical mechanics. Are they two interpretations? Are the Lagrangian and the Hamiltonian metaphysical elements?

They are two equivalent mathematical frameworks which can be derived from one another through mathematical operations. Why should we use a definition of “interpretation” where a straight mathematical operation generates a new interpretation? Every line of every theorem or homework problem would then be using a unique interpretation. Is that what you want the word to mean?

 

[A. Neumaier]

They are two equivalent mathematical frameworks which can be derived from one another through mathematical operations.

They are not quite equivalent since the Legendre transform that relates the two is not always defined.

 

[Elias1960]

Take, for example, the Lagrangian and the Hamiltonian formulation of classical mechanics. Are they two interpretations? Are the Lagrangian and the Hamiltonian metaphysical elements?

That they are frameworks complicates the issue. In general they are not even equivalent, the equivalence is something which holds for usual Lagrangians but not in the general case. You have $p = \frac{L}{\dot{q}}$, but this formula (usually $p=m\dot{q}$ but in principle quite arbitrary for an arbitrary Lagrangian) should be invertible, else you cannot compute $H(p,q) = p\dot{q} - L(q,\dot{q})$. In the other direction, you have a similar problem for general Hamiltonians, $\dot{q}=\frac{\partial H(p.q)}{\partial p}$ in general does not allow to compute the reverse $p=p(q.\dot{q})$.

For the usual Lagrangians / Hamiltonians they are equivalent. But they are certainly metaphysical, if you have given the equations you have all that empirical evidence can give you, and the Lagrangian is not even completely defined by the equations.

 

[Dale]

They are not quite equivalent since the Legendre transform that relates the two is not always defined.

$F/a=m$ is also not always defined. Shall we make that a new interpretation?

The word "interpretation" is just a word so we can define it to mean anything we like. It has a standard definition, and for historical consistency it is best to stick with standard definitions unless there is a compelling reason to change. Frankly, the standard definition of "interpretation" is already trivial enough for my taste, so I don't find further trivializing it to be a compelling reason to change.

 

[Demystifier]

The word "interpretation" ... It has a standard definition ...

What is the standard definition of the word "interpretation"? I think it has different meanings in different fields such as (i) mathematical logic, (ii) applied experimental physics and (iii) quantum foundations. Only in (iii) it has some negative "non-scientific" connotations.

 

[Demystifier]

$F/a=m$ is also not always defined. Shall we make that a new interpretation?

It is not so innocent as it may look. Some physicists interpret the 2nd Newton law not as a law but as a definition of force, defined as $F\equiv ma$.

 

[Demystifier]

They are two equivalent mathematical frameworks which can be derived from one another through mathematical operations. Why should we use a definition of “interpretation” where a straight mathematical operation generates a new interpretation? Every line of every theorem or homework problem would then be using a unique interpretation. Is that what you want the word to mean?

No I don't. As you can see from the first post, I would like to ban the word "interpretation" completely from quantum foundations, because the meaning of it, in my opinion, is not well defined. It makes much more sense to talk about "observationally equivalent theories". Hamiltonian and Lagrangian mechanics are one example, Copenhagen QM and Bohmian mechanics are another.

 

[Dale]

I think it has different meanings in different fields

Of course. That is typical. Even the word field has different meanings in different fields