Is theory of measurement an oxymoron?

[Demystifier]

TL;DR Summary

Why some theoretical physicists are not interested in the theory of quantum measurements?

This thread is inspired by the statement of @vanhees71 in https://www.physicsforums.com/threa...and-philosophy-of-physics.983540/post-6290970 :
"What a measurement is, is not defined by philosophers (not even by theoretical or mathematical physicists) but by the physicists in their labs."

I can perfectly understand that serious theoretical physicists (which @vanhees71 certainly is) do not value philosophical discussions of what measurement is. But I would expect that they at least value discussions of what measurement is from the point of view of theoretical and/or mathematical physics. Yet it seems that most theoretical/mathematical physicists do not value even that. Why? Do they perhaps think that theory of measurement is an oxymoron?

 

[Lord Jestocost]

"What a measurement is, is not defined by philosophers (not even by theoretical or mathematical physicists) but by the physicists in their labs."

Such remarks are completely irrelevant. Maximilian Schlosshauer/1/ clearly identifies the measurement problem in the following way:

“But what exactly is the measurement problem? I have found that everyone seems to have a somewhat different conception of the affair. One way of identifying the root of the problem is to point to the apparent dual nature and description of measurement in quantum mechanics. On the one hand, measurement and its effect enter as a fundamental notion through one of the axioms of the theory. On the other hand, there’s nothing explicitly written into these axioms that would prevent us from setting aside the axiomatic notion of measurement and instead proceeding conceptually as we would do in classical physics. That is, we may model measurement as a physical interaction between two systems called “object” and “apparatus” — only that now, in lieu of particles and Newtonian trajectories, we’d be using quantum states and unitary evolution and entanglement-inducing Hamiltonians.

What we would then intuitively expect — and perhaps even demand — is that when it’s all said and done, measurement-as-axiom and measurement-as-interaction should turn out to be equivalent, mutually compatible ways of getting to the same final result. But quantum mechanics does not seem to grant us such simple pleasures. Measurement-as-axiom tells us that the post-measurement quantum state of the system will be an eigenstate of the operator corresponding to the measured observable, and that the corresponding eigenvalue represents the outcome of the measurement. Measurement-as-interaction, by contrast, leads to an entangled quantum state for the composite system-plus-apparatus. The system has been sucked into a vortex of entanglement and no longer has its own quantum state. On top of that, the entangled state fails to indicate any particular measurement outcome.

So we’re not only presented with two apparently mutually inconsistent ways of describing measurement in quantum mechanics, but each species leaves its own bad taste in our mouth. When confronted with measurement-as-axiom, many people tend to wince and ask: “But ... what counts as a measurement? Why introduce a physical process axiomatically? What makes the quantum state collapse?” And so on. But measurement-as-interaction delivers no ready-made remedy either. As we have seen, the interaction leads to nothing that would resemble the outcome of a measurement in any conventional sense of the word.”
[bold by LJ]

/1/ M. Schlosshauer (ed.), Elegance and Enigma, The Quantum Interviews, Springer-Verlag Berlin Heidelberg 2011, pp. 141-142

 

[vanhees71]

The fact that it is a matter of opinion of the individual physicist or philosopher what the "measurement problem" is, is a clear indication that it is not a scientific but a purely philosophical problem. QT, as any other theory, describes in mathematical terms what's objectively observed by some "measurement device" (and be it just qualitatively directly by our senses like the retina of our eyes "measuring" light or our ears measuring "sound" etc.), and the mathematical description is deduced from observations in the past. On the other hand to define what useful observations/measurements are and how to construct measurement devices you need theory, but finally you have to build the device and perform the observation/measurement and compare it with the theoretical expecations. If there's no way to describe the observed facts, there's either a misconception about the functioning of the measurement device (in the majority of all cases, as far as well-estblished theory is involved) or the theory is wrong (which is usually what really leads to fundamental progress in physics).

So the answer to the question posed in the title of this thread for me is a clear "yes".

 

[Demystifier]

The fact that it is a matter of opinion of the individual physicist or philosopher what the "measurement problem" is, is a clear indication that it is not a scientific but a purely philosophical problem.

It is also a matter of opinion why exactly, and do we at all, need a quantum theory of gravity. Does it mean that it is also a clear indication that it is not a scientific but a purely philosophical problem?

 

[martinbn]

It is also a matter of opinion why exactly, and do we at all, need a quantum theory of gravity. Does it mean that it is also a clear indication that it is not a scientific but a purely philosophical problem?

The question of why it is needed is philosophical. The question of finding such a theory is scientific.

 

[A. Neumaier]

The question of why it is needed is philosophical. The question of finding such a theory is scientific.

The question of finding such a theory is still philosophical. Only having such a theory is scientific.

 

[martinbn]

The question of finding such a theory is still philosophical. Only having such a theory is scientific.

Why?

 

[A. Neumaier]

Why?

Because handling the question is dominated by values and hopes, trying to turn the vagueness into something clear - not by scientific arguments. Science begins when you have clear criteria by which to proceed.

 

[martinbn]

Because handling the question is dominated by values and hopes, trying to turn the vagueness into something clear - not by scientific arguments. Science begins when you have clear criteria by which to proceed.

Just because people are handling the question in such manner doesn't change anything. It is a problem of the people, not the question.

 

[A. Neumaier]

Just because people are handling the question in such manner doesn't change anything. It is a problem of the people, not the question.

The question is not precise, hence it needs a personal philosophy to interpret it.

 

[atyy]

Yet it seems that most theoretical/mathematical physicists do not value even that.

Is this true? Haag discusses it extensively, and Dimock does comment "In addition to this continuous unitary time evolution the system also changes in a discontinuous way when a measurement is made upon it. Roughly the state jumps to a state which is specified by the results of the measurement. This is known as “reduction of the wave function.” The question of which physical processes constitute measurements in this sense is rather unsettled, as well as the question of finding a correct mathematical description. Nevertheless it turns out that one can solve most practical problems without entering into these issues."

 

[Lord Jestocost]

The fact that it is a matter of opinion of the individual physicist or philosopher what the "measurement problem" is, is a clear indication that it is not a scientific but a purely philosophical problem.

To my mind, it's a physical problem. As Michael Esfeld puts it in “Physics and Causation” (Foundations of Physics volume 40, pages 1597–1610 (2010)):

“It is not possible to give a precise physical definition of a measurement process and a measurement apparatus, since there is no physical difference that distinguishes a measurement process from other physical interactions….

The measurement problem thus is not about measurement in particular. It is a placeholder for the general problem how to understand the transition from quantum systems in entangled states to systems that possesses classical properties….”

 

[martinbn]

The question is not precise, hence it needs a personal philosophy to interpret it.

I don't think that being precise or not makes a question philosophical or scientific. There are plenty of imprecise open questions in maths. I would be very surprised if anyone considered them philosophical.

 

[A. Neumaier]

I don't think that being precise or not makes a question philosophical or scientific. There are plenty of imprecise open questions in maths. I would be very surprised if anyone considered them philosophical.

I am a counterexample, so you should be surprised!

 

[Demystifier]

There are plenty of imprecise open questions in maths.

I'm curious, can you give some examples?

 

[martinbn]

Ii am a counterexample, so you should be surprised!

Can you give me an example of a maths question that you consider philosophical? Then I can be surprised.

I'm curious, can you give some examples?

Here is one related to physics. The cosmic censership conjectures should hold generically, but there is no precise statement about what is to be generic.

 

[A. Neumaier]

Can you give me an example of a maths question that you consider philosophical? Then I can be surprised.

First give me one of the plenty of imprecise open questions in maths that you claimed exist. You only gave a physics question.

there is no precise statement about what is to be generic.

Thus it is a matter of personal philosophy how to make it precise.

 

[Demystifier]

Here is one related to physics.

I know many examples in physics. I would like to know an example in pure mathematics.

 

[vanhees71]

It is also a matter of opinion why exactly, and do we at all, need a quantum theory of gravity. Does it mean that it is also a clear indication that it is not a scientific but a purely philosophical problem?

Sure, we need a quantum theory of gravity, because the classical GR is inconsistent with QT, and there are unavoidable "holes" (i.e., singularities in the solution of the Einstein-Hilbert equations) in our description, which hopefully should be remedied by quantizing the theory (as in the analogous case of quantum electrodynamics as compred to classical electrodynamics).

 

[martinbn]

The cosmic censorship conjecture is a mathematical problem. It doesn't matter if it was motivated by physics. For instance here is a fomulation of the weak conjecture : "For generic complete asymptotically flat vacuum initial data, the maximal Cauchy development has a complete null infinity $\mathcal{I}^+$. "

Here is another example: do you consider the Langlands conjectures as presice or not?

 

[A. Neumaier]

The cosmic censorship conjecture is a mathematical problem. It doesn't matter if it was motivated by physics. For instance here is a fomulation of the weak conjecture : "For generic complete asymptotically flat vacuum initial data, the maximal Cauchy development has a complete null infinity $\mathcal{I}^+$. "

As long as the hypothesis is not stated in unambigous terms, it is not a mathematical statement, hence not yet a mathematical problem. The unprecisely stated conjecture is a metamathematical research proposal; the conjecture may be true or false depending on the meaning given to the imprecise term. Metamathematics always has a philosophical component.

 

[Demystifier]

Here is another example: do you consider the Langlands conjectures as presice or not?

It's not that I understand what exactly this conjecture says, but from what I was reading about it, I also had impression that it's vague. Thanks for confirming it!

 

[Demystifier]

Sure, we need a quantum theory of gravity, because the classical GR is inconsistent with QT

By the same token, sure, we need a quantum theory of measurement, because the classical measuring apparatus is inconsistent with QT.

 

[EPR]

By the same token, sure, we need a quantum theory of measurement, because the classical measuring apparatus is inconsistent with QT.

Only if you insist that it's classical. Some don't and get by just fine on a half baked understanding of the intricacies involved. Classical is a laden word.

 

[Demystifier]

Only if you insist that it's classical. Some don't and get by just fine on a half baked understanding of the intricacies involved. Classical is a laden word.

The same can also be said about gravity.

 

[vanhees71]

By the same token, sure, we need a quantum theory of measurement, because the classical measuring apparatus is inconsistent with QT.

How can it be inconsistent with QT, given the fact that QT describes the experimental results so well and even enables to construct measurement devices which couldn't be constructed with the fundamental knowledge QT provides? As an example, take only the enhanced LIGO, using specific quantum-mechanical states of light to enhance its sensitivity!

 

[Demystifier]

How can it be inconsistent with QT, given the fact that QT describes the experimental results so well and even enables to construct measurement devices which couldn't be constructed with the fundamental knowledge QT provides? As an example, take only the enhanced LIGO, using specific quantum-mechanical states of light to enhance its sensitivity!

I think you are using double standards. You use one mode of thinking when you think about measurements, but another mode of thinking when you think about gravity. Try to use the same mode of thinking for both. For instance, in the example above, if this shows that classical measurements are enough, then it also shows that classical gravity (in LIGO experiments) is enough.

 

[vanhees71]

There's a very distinct difference between the issue of "measurements in quantum theory" and the description of "gravity in general relativity". In the former case there's no physical problem whatsoever. To the contrary QT is the solution to the problems to describe what's observed within classical mechanics, including theory-intrinsic discrepancies like, e.g., the stability of atoms given the fact that it consists of atomic nuclei surrounded by "far distant" electrons.

In the latter case GR contains its own limitations (singularities) in close analogy to the limitations of classical electromagnetics (Maxwell theory) in connection with the idea of classical point charges. These problems are solved by QED (or partially even semiclassical theory with the em. field treated classically and the particles making up matter being quantized). The hope is that in some yet unknown way, a consistent formulation of quantum effects concerning the gravitational interaction this intrinsic trouble with GR may be solved too. That's all, I'm saying.

 

[Elias1960]

I know many examples in physics. I would like to know an example in pure mathematics.

There was the monstrous moonshine conjecture, also known as 196884 = 196883 + 1.

Essentially, it was nothing but the hypothesis that there is some deep connection between the j-function from number theory and the Monster group. Vague enough?

 

[QLogic]

If there's no way to describe the observed facts, there's either a misconception about the functioning of the measurement device (in the majority of all cases, as far as well-estblished theory is involved) or the theory is wrong (which is usually what really leads to fundamental progress in physics)

There's a very distinct difference between the issue of "measurements in quantum theory" and the description of "gravity in general relativity". In the former case there's no physical problem whatsoever.

This does not mesh with my education on the subject I must say.

The problem as typically presented is that the measuring device, when modeled quantum mechanically, enters into a system-device-environment entangled state. This state doesn't allow one to ascribe a definitive outcome state to the device should one be in the position of an external observer measuring the device itself.

This directly contradicts the observed fact that our devices have outcomes. Obviously real lab equipment lights up and responds in some way.

It isn't really a problem practically since the contradiction is in the completeness of the theory in a regime far from observations. Just like General Relativity and the "Quantum Gravity Problem" the issue is with contradictions far from the current observable regime.

 

[AlexCaledin]

Hmmm it looks like, nature doesn't actually consist of quantum systems but rather uses the quantum math for self-organizing - so our childish approach "What's it made of?" gets stuck in a contradiction.

 

[A. Neumaier]

There was the monstrous moonshine conjecture, also known as 196884 = 196883 + 1.

Essentially, it was nothing but the hypothesis that there is some deep connection between the j-function from number theory and the Monster group.

At that time it was just that it wasn't mathematics but just a piece of data coupled with a philosophy of what it might possibly mean.

 

[martinbn]

No! It was actually very precise.

There was the monstrous moonshine conjecture, also known as 196884 = 196883 + 1.

Essentially, it was nothing but the hypothesis that there is some deep connection between the j-function from number theory and the Monster group. Vague enough?

 

[EPR]

If there are no particles as such, there are no discrete things per se(in and of themselves). How can measurement be an oxymoron if measurement is fundamental to the nature of said discrete things? This is bad philosophy.