Against "interpretation" - Comments

[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

 

[Demystifier]

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

So in the field of quantum foundations, what is the standard definition of "interpretation"? In the first post I have argued that neither of the possible definitions makes much sense.

 

[A. Neumaier]

$F/a=m$ 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.

Sure. I didn't imply with my comment that I would want to redefine the standard notion of interpretation.

For me, the formalism of classical mechanics to be interpreted in terms of reality consists of both the Lagrangian and the Hamiltonian view, their theoretical relations, and their generalizations. Interpretation only begins when one gives the potential, momentum, etc. meaning in terms of experiments.

 

[Demystifier]

Interpretation only begins when one gives ... meaning in terms of experiments.

Isn't interpretation in quantum foundations supposed to be the exact opposite, beginning only when giving meaning in terms of something not subject to experiments?

 

[A. Neumaier]

Interpretation only begins when one gives the potential, momentum, etc. meaning in terms of experiments.

Isn't interpretation in quantum foundations supposed to be the exact opposite, beginning only when giving meaning in terms of something not subject to experiments?

This would be interpretation of experiments, not interpretation of quantum mechanics.

Interpreting A in terms of B always means showing how aspects of A can be understood using concepts known from B. Thus to interpret quantum mechanics one need to explain the meaning of its concepts using concepts from outside quantum mechanics - i.e., from experimental practice in the widest sense.

On the other hand, to interpret experiments one needs theory; and both kinds of interpretation must mesh consistently to be acceptable.

 

[Dale]

So in the field of quantum foundations, what is the standard definition of "interpretation"?

To my knowledge in QM the standard definition of "interpretation" is as described in Wikipedia:

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

 

[vanhees71]

Isn't interpretation in quantum foundations supposed to be the exact opposite, beginning only when giving meaning in terms of something not subject to experiments?

I think that's the great misunderstanding between physicists and mathematicians. For a physicist there are quantifiable and thus measurable phenomena, to begin with. Experience shows that we find certain patterns, which we call natural laws, and from this we can try to make mathematical models or theories. The quantities/observables and states are defined empirically from the phenomena and mathematical descriptions use empirically useful primitive notions. The mathematician of course tries to make these primitive notions a system of axioms to seek for sharp definitions of the mathematical model and, if successful, then constructs even a theory. Then the mathematician forgets about the empirical foundation of the theory and thinks one has to rederive the empirical foundation from the theory.

In QT it's even worse, because there not only physicists and mathematicians are involved but also philosophers, making the quite complicated subject even more complicated by using a completely different language than the two languages already introduced by the physicists and mathematicians.

In other words: For a physicist QT is a probabilistic description for phenomena which are probabilistic to begin with, and the phenomena (observables and states) are defined empirically. There's nothing to be derived from the formalism, because the formalism is based on the empirically defined basic notions of observables (a measurement procedure) and states (a preparation procedure/observation of an initial condition).

For a mathematician there's an abstract formalism, from which the phenomena have to be derived, i.e., if it comes to the measurement problem the problem consists in the question, how there can be definite outcomes in a measurement given the "QT universe" only, where only probabilities exist. Usually one can settle the issue by using statistical arguments (though that seems not to be always the case).

For philosophers the problems become even more problematic, because there's some vague idea about "reality". The notion of "reality" differs from philosopher to philosopher, and you cannot make heads and tail of it. Then you discuss over thousands of pages problems that are not even well defined in either a physicist's nor a mathematician's way. You need a genius like Bell who can make out of philosophical unsharp problems a sound and solid scientific question, approachable by the scientific method of objective and quantitative observation by first finding a clear definition of "reality" or "realism" and finding a way to disprove either "local realistic hidden-variable theories" or "quantum theory". The result is known, and it's "quantum theory" that survived all these tests, and it's quantum theory in the clear and simple "minimal interpretation" just taking the standard textbook definitions of state and observables as the physical theory and accept that from a physicist's point of view nature is on a fundamental level behaving randomly and not deterministically.

 

[ftr]

Experience shows that we find certain patterns, which we call natural laws, and from this we can try to make mathematical models or theories. The quantities/observables and states are defined empirically from the phenomena and mathematical descriptions use empirically useful primitive notions.

I think this was more true in the past but for more than 100 years with mathematical sophistication physicists tend to deduce models based on specific and general understanding of concepts like what could work and try many until some prediction is obtained or matched by known observation (experiment play a kind secondary but important part). Schrödinger equation is a perfect example, not to mention QG, string, Unified ...etc.

 

[Elias1960]

For a physicist there are quantifiable and thus measurable phenomena, to begin with. Experience shows that we find certain patterns, which we call natural laws, and from this we can try to make mathematical models or theories. The quantities/observables and states are defined empirically from the phenomena and mathematical descriptions use empirically useful primitive notions. The mathematician of course tries to make these primitive notions a system of axioms to seek for sharp definitions of the mathematical model and, if successful, then constructs even a theory.

No. It is the theory that defines what is observable. And theories are free inventions of the human mind. They are empirical theories if one can make empirical predictions based on them. And in this case one can test if these predictions are correct. If not, the theory is falsified.

What you describe sounds like a naive version of empiricism. Empiricism is dead, as dead as possible for a philosophical theory, since Popper's Logic of Scientific Discovery.

In other words: For a physicist QT is a probabilistic description for phenomena which are probabilistic to begin with, and the phenomena (observables and states) are defined empirically.

Don't forget that "the theory that defines what is observable" is what Einstein told Heisenberg, and this had some influence on Heisenberg, helping him to create quantum theory.

 

[A. Neumaier]

theories are free inventions of the human mind.

But good theories aren't. They are heavily constrained discoveries of the human mind, and cannot be falsified in their domain of validity.

 

[Elias1960]

But good theories aren't. They are heavily constrained discoveries of the human mind, and cannot be falsified in their domain of validity.

There is, of course, the obvious restriction that the resulting predictions have to fit reality. But this does not tell you much about that theory. From the point of view of philosophy, it was important to reject the empiricist notion that the theories are somehow derived from observation. There is no such possibility of derivation. Usually no domain of validity is known a priori, at the moment of the invention of some theory. And if it can be falsified or not is nothing the scientist is able to know at that moment too.

 

[A. Neumaier]

There is, of course, the obvious restriction that the resulting predictions have to fit reality. But this does not tell you much about that theory. From the point of view of philosophy, it was important to reject the empiricist notion that the theories are somehow derived from observation. There is no such possibility of derivation. Usually no domain of validity is known a priori, at the moment of the invention of some theory. And if it can be falsified or not is nothing the scientist is able to know at that moment too.

This does not affect the validity of my statement.It simply takes some time before a theory can be known to be good.

 

[bhobba]

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 $F\equiv ma$.

True. How its resolved I could not figure out until John Baez explained it to me. I have mentioned it in passing on ocassion, but really it needs a thread of its own which I will create. I will give the final answer now however. The true basis of Newtonian mechanics is QM.

Thanks
Bill

 

[Demystifier]

To my knowledge in QM the standard definition of "interpretation" is as described in Wikipedia:

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

It's fine, but my objection is that there is no sharp borderline between "interpretational" and "non-interpretational" aspects of a theory. For instance, if we accept the wiki definition that interpretations are about reality, then even a shut-up-and-calculate approach to measurable quantities can be considered an "interpretation", because it is about measurable quantities which are real.

 

[Demystifier]

True. How its resolved I could not figure out until John Baez explained it to me. I have mentioned it in passing on ocassion, but really it needs a thread of its own which I will create.

If you will create it in the classical physics forum, please make a note/link here!

 

[A. Neumaier]

even a shut-up-and-calculate approach to measurable quantities can be considered an "interpretation", because it is about measurable quantities which are real.

No, it is about calculations only. The interpretation that (and how) the results of the calculations refer to experiments is already outside strict shut-up-and-calculate (unless one includes in the latter Born's rule in one of its interpretations).

 

[Demystifier]

No, it is about calculations only.

No it isn't, there is no paper (published in a peer-reviewed journal) that is only about calculations. If you think there is, show me an example and I will explain you why this paper is not only about calculations. If someone tried to publish a paper which is only about calculations, the reviewer would object that the paper misses motivation and meaning of those calculations.

 

[zonde]

Now suppose that someone else develops another theory T2 that makes the same measurable predictions as T1. So if T1 was a legitimate theory, then, by the same criteria, T2 is also a legitimate theory. Yet, for some reason, physicists like to say that T2 is not a theory, but only an interpretation. But how can it be that T1 is a theory and T2 is only an interpretation? It simply doesn’t make sense.

You are missing one point. Chronology is important. Predictions have to be made before factual observations. That's because people are very good at cheating themselves. All the reasoning done after the facts are known are very error prone and you have to be much more careful about checking the soundness of such reasoning. So it stands to reason to give such after the fact reasoning a different name.

 

[A. Neumaier]

No it isn't, there is no paper (published in a peer-reviewed journal) that is only about calculations. If you think there is, show me an example and I will explain you why this paper is not only about calculations. If someone tried to publish a paper which is only about calculations, the reviewer would object that the paper misses motivation and meaning of those calculations.

The papers always combine shut-up-and-calculate with non-shut-up heuristics involving their personal interpretation appropriate to the particular application. The resulting freedom is the main reason why shut-up-and-calculate is so successful in practice. It is also the reason why the Copenhagen interpretation (which was so vague in its meaning that it could be adapted freely) was sufficient for 30 years (and for many is still sufficient now).

 

[vanhees71]

No. It is the theory that defines what is observable. And theories are free inventions of the human mind. They are empirical theories if one can make empirical predictions based on them. And in this case one can test if these predictions are correct. If not, the theory is falsified.

What you describe sounds like a naive version of empiricism. Empiricism is dead, as dead as possible for a philosophical theory, since Popper's Logic of Scientific Discovery.

Don't forget that "the theory that defines what is observable" is what Einstein told Heisenberg, and this had some influence on Heisenberg, helping him to create quantum theory.

I know this quote of Einstein's by Heisenberg. Nevertheless, history shows that with such a scholastic approach almost never good physics comes out. You need the, admittedly vague, notions of observations and experiments first to create physically successful theories. A really aesthetic argument for a theoretical physicist is not if there's a free invention (e.g., Bohr's model of the atom) but if there's almost no freedom given the empirical foundations (e.g., Einstein's GR, which is almost inevitable given the strong equivalence principle and relativistic spacetime structure).

 

[Demystifier]

The papers always combine shut-up-and-calculate with non-shut-up heuristics involving their personal interpretation appropriate to the particular application. The resulting freedom is the main reason why shut-up-and-calculate is so successful in practice. It is also the reason why the Copenhagen interpretation (which was so vague in its meaning that it could be adapted freely) was sufficient for 30 years (and for many is still sufficient now).

Yes, exactly. That's why I insist that it is impossible to sharply distinguish "interpretational" research from "non-interpretational" one.