Justification for no properties before measurement

[vanhees71]

The deeper reason for this is that in a situation where the right concepts are lacking and one has to grope in the dark, one needs a strong philosophical bend to make progress. All scientific subjects were rooted in philosophy before they matured to a science, and quantum mechanics is no exception.

The philosophy-free position of @vanhees71 is possible only since the subject has matured such a lot since its inception. Except for the measurement problem, where most of the discussion is still on the level of the dark ages.

Obviously there is no measurement problem, because theory and experiment agree to high accuracy, which means nothing less than that on the one hand the experimentalists can observe what's predicted by QT, i.e., the theory provides precise enough ideas for how to prepare and observe the phenomena it predicts and on the other hand theorists are able to use the theory to make such predictions and describe (hitherto all!) observations with the theory.

So what's "the measurement problem"?

 

[vanhees71]

Interesting to hear your reaction - especially the section with the philosopher Greta Herman (who actually was good enough to pick up the error Von-Neumann made in his no hidden variables proof) and the 'wonderful' discussion about what Kant would have thought of QM . It has a whole chapter, chapter 10 - Quantum Mechanics And Kantian Plilosophy - I am sure you will love it .

Basically most of the founders, could at least in part, be described as a mob of mystics - see attached.

Thanks
Bill

I've to look for the book in some corner of my bookshelf first, but Kant did already invent QT (according to a philsophy professor, whose lectures on Kant I've heard, because I wanted to fulfill the recommendation to listen to at least one philosophy lecture during my studies; fortunately there was no exam on it;-)), as die Lenin (read the appendix of Blokhintzev's QM textbook).

 

[vanhees71]

Perhaps W.Heisenberg was simpy trying to advocate the removal of the observer from the foundations of the theory, much like this is absent from any formulation of classical mechanics, or perhaps this is only what I want W.Heisenberg to mean by his quoted words.

It's not absent from classical theory. Already writing done $m \vec{a}=\vec{F}$ involves an observer, who prepares a reference frame and a clock, defining $\vec{x}(t)$ which is the basis for the whole mathematics of Newtonian mechanics condensed in this formula!

 

[SemM]

Basically most of the founders, could at least in part, be described as a mob of mystics - see attached.

Thanks
Bill

hahah!

 

[vanhees71]

Unfortunately he was - worse than Bohr even who actually wasn't too bad. The worst was the person you would least expect - Pauli - he was bad - really bad - just behind Wigner and Von-Neumann.

For me the only really sane one was Dirac - but he had other issues of a non-scientific nature.

Thanks
Bill

Well, Pauli was a great mystic, but he could keep it out of his scientific writings, which are always very clear and very similar to Sommerfeld's style, whose scientific pupil Pauli was. He was not only a follower of philosophical but, even worse, also psychological mysticism. I like Einstein more, who, after some conversation with Freud said, that he prefers to stay "unanalyzed". Pauli was a great "fan" of C.G. Jung.

Dirac was also very unmystical in his scientific writings. He had a pretty bad childhood due to his tyrranic father (see Farmelo's biography "The Strangest Man").

 

[SemM]

Dirac was also very unmystical in his scientific writings. He had a pretty bad childhood due to his tyrranic father (see Farmelo's biography "The Strangest Man").

Even Bohm had tendencies to Mysticism, but he also kept it out of science, and wrote an excellent book "Quantum Theory"

 

[vanhees71]

True, for me the most important original contribution to QM by Bohm is his work on the Aharonov-Bohm effect...

 

[A. Neumaier]

what's "the measurement problem"?

To define the meaning of ''measurement'' in a clean enough way that Born's rule becomes more than a heuristic principle, and the nearly hundred year old discussion comes to an end.

Kant did already invent QT

I only know that Thomas Aquina first discussed the Pauli exclusion principle.

 

[stevendaryl]

It's not absent from classical theory. Already writing done $m \vec{a}=\vec{F}$ involves an observer, who prepares a reference frame and a clock, defining $\vec{x}(t)$ which is the basis for the whole mathematics of Newtonian mechanics condensed in this formula!

I disagree with that completely. Classical mechanics (and by that, I mean non-quantum---I would include Special and General Relativity) give no special role to observers. Classical mechanics describes how particles and fields behave, given boundary conditions and initial conditions. Yes, you need an observer to know what the initial conditions are, and you need observers to discover what the forces are. But particles and fields don't require people to KNOW how they behave in order to do what they do. In classical mechanics, observers are just complex systems made up of the same particles and fields that everything else is. They play no role in the formulation of the laws of physics.

 

[stevendaryl]

I disagree with that completely. Classical mechanics (and by that, I mean non-quantum---I would include Special and General Relativity) give no special role to observers. Classical mechanics describes how particles and fields behave, given boundary conditions and initial conditions. Yes, you need an observer to know what the initial conditions are, and you need observers to discover what the forces are. But particles and fields don't require people to KNOW how they behave in order to do what they do. In classical mechanics, observers are just complex systems made up of the same particles and fields that everything else is. They play no role in the formulation of the laws of physics.

There is a distinction (in classical mechanics, anyway) between what is true and what we know. Observers and observations and measurements and so forth are certainly needed to know anything. But the universe doesn't care what we know. (Classically, anyway).

 

[Fra]

But particles and fields don't require people to KNOW how they behave in order to do what they do. In classical mechanics, observers are just complex systems made up of the same particles and fields that everything else is. They play no role in the formulation of the laws of physics.

In QM its the classical measurement device that "knows" and this is the key.

What the humans in the lab know doesn't matter. You are trying to bring back mysticism here.

In a very superficial way sure its the physicisy that invent or discover tha laws. But this superficial view holds also in classical mechanics.

/Fredrik

 

[Fra]

To define the meaning of ''measurement'' in a clean enough way that Born's rule becomes more than a heuristic principle, and the nearly hundred year old discussion comes to an end.

I think of the measurement problem as to unify the external an internal observer views of interactions.

The inside view is an information update. But consistency requires that in the small subsystem limit an external observer must be able to explain this process as an ordinary expected evolution.

This woulf have to restore the consistent coexistences of the evolving inside view with the timeless deductive causation that we see in the limit of a small subsystem observed by a classical dominant environment and I see two general strategies for this.

/Fredrik

 

[vanhees71]

There is a distinction (in classical mechanics, anyway) between what is true and what we know. Observers and observations and measurements and so forth are certainly needed to know anything. But the universe doesn't care what we know. (Classically, anyway).

The universe doesn't care about what we know also quantum theoretically, and I still think that physics is an empirical science, and to be able to write down mathematical formulae that have a meaning in the sense of physics you need an operational definition of the quantities you describe, and that implicitly uses the idea of observers who measure something, no matter whether you have a classical theory (no matter whether relativistic or non-relativistic) or QT in mind.

 

[vanhees71]

To define the meaning of ''measurement'' in a clean enough way that Born's rule becomes more than a heuristic principle, and the nearly hundred year old discussion comes to an end.

The meaning of measurement is defined what experimentalists do in their labs. Why you call Born's rule "heuristic" is not clear to me either since it clearly gives a probabilistic meaning of the state, and probabilities are measured via observations on ensembles and statistical analysis. Then, if you call Born's rule "heuristic", you'd also call the statistical meaning of probabilities (in this frequentist sense) "heuristic". If so, fine, because obviously the "heuristics" works with an amazing accuracy.

Concerning Thomas Aquina, I'd say he simply takes "angels" as being "usual matter" or "substance", and there it's empirically clear that two bodies cannot occupy the same space. Today we attribute this to the Pauli principle, but how one can conclude Thomas may have used the Pauli principle, is an enigma. He simply used everyday experience about matter.

 

[A. Neumaier]

In QM its the classical measurement device that "knows" and this is the key.

How does in classical mechanics a measurement device made up of many particles subject to the classical laws know the exact position of a particle whose position it is supposed to measure?

In classical mechanics, the measurement process is as ill-defined conceptually as in quantum mechanics. In both cases, an informal working definition exists in the head of experimenters and in calibration procedures, but not in a way that would be amenable to mathematical analysis, and hence to answer without doubt any questions about the meaning of a measurement.

 

[A. Neumaier]

Why you call Born's rule "heuristic" is not clear to me either

Well, this is because I have a philosophical bent and you don't. You sweep under the carpet of ''operational definition'' what for me is something to be clarified theoretically.

Then, if you call Born's rule "heuristic", you'd also call the statistical meaning of probabilities (in this frequentist sense) "heuristic".

I call everything heuristic that contains mathematically undefined terms. Born's rule contains the mathematically undefined term ''measurement'' that plays no role in the quantum formalism, hence is heuristic only, and with it Born's rule.

I have no difficulty with the formal Born rule that calls the modulus squared of a wave function a probability density. This is just mathematics. The heuristic comes in when it relates this probability to ''finding the particle on some region'', which is a theoretically undefined notion.

 

[vanhees71]

How can it be undefined? Experimentalists measure positions of subatomic particles in various ways. In Born's time by using a photoplate or scintillation screen, today some electronic detector. It's defined by the concrete setup in the lab, and that it matches with the mathematical definition of position in the theory is an empirical finding. How else do you want to justify that the theoretical and empirical notion of a quantity matches?

 

[A. Neumaier]

How can it be undefined? Experimentalists measure positions of subatomic particles in various ways. In Born's time by using a photoplate or scintillation screen, today some electronic detector. It's defined by the concrete setup in the lab, and that it matches with the mathematical definition of position in the theory is an empirical finding. How else do you want to justify that the theoretical and empirical notion of a quantity matches?

A very high precision position measurement is based on a lot of theory that goes into the construction of the measurement device and the calibration procedure. The theoretical analysis is the one that tells that the device actually measures the position. Thus everything about experimental measurement is actually encoded into the theoretical physics of the measurement device.

But Born's rule is device independent, relying on an undefined notion of measurement, that always delivers infinitely precise results - which is experimental nonsense.

 

[vanhees71]

I complete agree with your first paragraph, which contradicts the second one. Born's rule predicts probabilities, and you cannot get probabilities by measuring on an esemble but probabilities with some statistical (in practice also systematic) error, but Born's rule relies not on an undefined notion of measurement but on a well-defined notion of measurement as you explain yourself in the 1st paragraph. It's clear that theory and experiment are both needed to define the meaning of the mathematical theory. Pure math has no such meaning but is an invention of pure thought. This is the distinction between pure math and a physical theory which uses math as a language.

 

[SemM]

How does in classical mechanics a measurement device made up of many particles subject to the classical laws know the exact position of a particle whose position it is supposed to measure?

And how does, in quantum physics, a measurement device subject to the observer's choice? Never really. Only in time and place, but the result would still be the same, considering the same experiment.

 

[Lord Jestocost]

Maybe, the following statement makes Heisenberg‘s position clearer (compare #60); he sharply points to the underlying motivation the criticism of the Copenhagen approach was based upon:

„Finally, the criticism which Einstein, Laue and others have expressed in several papers concentrates on the question whether the Copenhagen interpretation permits a unique, objective description of the physical facts. Their essential arguments may be stated in the following terms: The mathematical scheme of quantum theory seems to be a perfectly adequate description of the statistics of atomic phenomena. But even if its statements about the probability of atomic events are completely correct, this interpretation does not describe what actually happens independently of or between the observations. But something must happen, this we cannot doubt; this something need not be described in terms of electrons or waves or light quanta, but unless it is described somehow the task of physics is not completed. It cannot be admitted that it refers to the act of observation only. The physicist must postulate in his science that he is studying a world which he himself has not made and which would be present, essentially unchanged, if he were not there. Therefore, the Copenhagen interpretation offers no real understanding of the atomic phenomena.

It is easily seen that what this criticism demands is again the old materialistic ontology.“Werner Heisenberg in „Physics and Philosophie“

 

[SemM]

Maybe, the following statement makes Heisenberg‘s position clearer (compare #60); he sharply points to the underlying motivation the criticism of the Copenhagen approach was based upon:
But even if its statements about the probability of atomic events are completely correct, this interpretation does not describe what actually happens independently of or between the observations. “

What happens in between observations in still subject to the law of Quantum Mechanics, whether it is a time-dependent excited state or an equilibrium state. This sums up to using the Schrödinger eqn for equilibrium processes, and a time-dependent eqn for non-equilibrium processes which would, altogether, describe what happens before, during and after observations.

 

[Lord Jestocost]

That would describe what happens between, within and after observations.

Again, quoting Heisenberg:

"When the probability function in quantum theory has been determined at the initial time from the observation, one can from the laws of quantum theory calculate the probability function at any later time and can thereby determine the probability for a measurement giving a specified value of the measured quantity. We can, for instance, predict the probability for finding the electron at a later time at a given point in the cloud chamber. It should be emphasized, however, that the probability function does not in itself represent a course of events in the course of time. It represents a tendency for events and our knowledge of events [a mental representation, but not a physical description - note by LJ]. The probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system."

Werner Heisenberg in „Physics and Philosophie“

 

[A. Neumaier]

Born's rule relies not on an undefined notion of measurement but on a well-defined notion of measurement as you explain yourself in the 1st paragraph.

I haven't seen any definition of measurement that is based on the mathematical formalism of QM alone.

It would have to be something that could be applied to a mathematical model of an imaginary world governed by the QM formalism, so that mathematical statements *theorems) are proved about measurements done according to that definition that tell that a particular multiparticle system actually measures what it is claimed to measure.

subject to the observer's choice

The observer's choice is also an activity of the physical system called observer, hence must be part of the model of the measurement process.

 

[SemM]

Again, quoting Heisenberg:

"When the probability function in quantum theory has been determined at the initial time from the observation, one can from the laws of quantum theory calculate the probability function at any later time and can thereby determine the probability for a measurement giving a specified value of the measured quantity. We can, for instance, predict the probability for finding the electron at a later time at a given point in the cloud chamber. It should be emphasized, however, that the probability function does not in itself represent a course of events in the course of time. It represents a tendency for events and our knowledge of events [a mental representation, but not a physical description - note by LJ]. The probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system."

Werner Heisenberg in „Physics and Philosophie“

That is fine, but it still does not contradict that everything is governed by equilibrium and non-equilibrium processes interchangingly, and QM describes both, whether we observe it or not.

 

[SemM]

The observer's choice is also an activity of the physical system called observer, hence must be part of the model of the measurement process.

Thanks Neumaier, but does this discussion end up in QFT eventually?

 

[A. Neumaier]

does this discussion end up in QFT eventually?

I guess so, since this is the way to model macroscopic equipment serving as the observer (consciousness is nowhere involved) as a quantum device.

 

[bhobba]

hahah!

Of course. The point was to read the attachment that explains what the early pioneers went through in grappling with these issues and how some of it even hangs about today.

Thanks
Bill

 

[bhobba]

I guess so, since this is the way to model macroscopic equipment serving as the observer (consciousness is nowhere involved) as a quantum device.

Well yes.

Varadarajan - Geometry Of Quantum Theory page 12 'Suppose L is an abstract Boolean σ-algebra. We shall define a Y-valued observable associated with L to be any σ-homomorphism B(Y) into L. If Y is the real line we call these observables real valued and refer to them simply as observables.'

Here B(Y) is the all the Borel subsets of Y into L.

The above is a very mathematically rigorous presentation of QM. But in doing so the concepts are defined mathematically. I think the issue isn't that the terms can't be rigorously defined in the theory, its like all physical theory's, matching the mathematics to the world so it can be applied is not defined in the theory, but built up from experience.

I think this is a key point - people like me and Vanhees simply accept that's the way mathematical descriptions are - but some want something deeper.

I think everyone knows I agree with Vanhees, but the essence of science is doubt - I could indeed be wrong. I wrote elsewhere in my youth I was influenced by Ayn Rand - but realized she fell for the trap of not doubting and thought of herself as the oracle or priestess of truth.

Thanks
Bill

 

[A. Neumaier]

its like all physical theory's, matching the mathematics to the world so it can be applied is not defined in the theory,

It is usually not very well defined, but in classical physics only for practical reasons, not for reasons of principle.

In classical physics you have complete control over the universe if a classical action for it is given. You can (in principle) define exactly what an observer is, by specifying which particles make it up. Then you can (in principle) define exactly how a proposed measurement of an observable X to be measure is done, by specifying which composite observable R - created solely from the observable making up the observer (a screen or a pointer) - defines the measurement result of measuring X. Then you can (in principle) analyze exactly to which extent the measurement result R agrees with the exact value of the observable X. It will never be exact, except by chance. But you can use statistical mechanics to work out (in principle) the mean (bias) and standard deviation (intrinsic uncertainty) of the error made. Then you can say with full mathematical clarity how accurate your measurement is.

Thus everything is well-defined in the classical theory - only practical considerations (keeping track of the atoms and doing the computations) prevent this for being actually done routinely. Instead one uses coarse approximations, like everywhere in physics, to simplify the burden. But there is no question of principle.

This is why deterministic classical mechanics does not suffer from the same philosophical problems as quantum physics. There are some with the stochastic version, due to the problem of saying what probability is, but this is no fundamental issue since classical mechanics is deterministic, and probability enters only through the approximation process.

 

[A. Neumaier]

What is a "momentum frame"?

The query "momentum frame" (with the quotation marks) entered into https://scholar.google.com yields nearly 10000 scientific papers.
The first one is:

Kogut, J. B., & Soper, D. E. (1970). Quantum electrodynamics in the infinite-momentum frame. Physical Review D, 1(10), 2901. [over 800 citations]

Finite momentum frames apppear, e.g., in:

Kim, Y. S., & Noz, M. E. (1977). Covariant harmonic oscillators and the parton picture. Physical Review D, 15(1), 335.

 

[PeterDonis]

The query "momentum frame" (with the quotation marks) entered into https://scholar.google.com yields nearly 10000 scientific papers.

All of the ones on the first page of results, at least, appear to be using the term "infinite-momentum frame", which does not appear to be what @mikeyork is talking about. If I filter out the term "infinite", I get other papers using terms like "center of momentum frame" and "zero momentum frame", which are also not what @mikeyork is talking about. Filtering those out doesn't seem to turn up anything useful. So I'm still not seeing any valid references using "momentum frame" the way @mikeyork is using it.

 

[A. Neumaier]

If I filter out the term "infinite",

The second reference I gave, cited 98 times, talks in Figure 1 about a zero momentum frame (= rest frame) and a large momentum frame, of which the infinite momentum frame is a limiting case. The following paper not even mentioning an infinite momentum frame but only a finite one is also cited 98 times:

Musch, B. U., Hägler, P., Negele, J. W., & Schäfer, A. (2011). Exploring quark transverse momentum distributions with lattice QCD. Physical Review D, 83(9), 094507.

But I agree with you, it is a coordinate system in spacetime, and not in momentum space, as @mikeyork thinks the term would be used.

 

[PeterDonis]

The second reference I gave, cited 98 times, talks in Figure 1 about a zero large momentum frame, of which the infinite momentum frame is a limiting case.

Ah, ok, I hadn't quite picked up on that.

 

[PeroK]

Well, this is because I have a philosophical bent and you don't. You sweep under the carpet of ''operational definition'' what for me is something to be clarified theoretically.

I call everything heuristic that contains mathematically undefined terms. Born's rule contains the mathematically undefined term ''measurement'' that plays no role in the quantum formalism, hence is heuristic only, and with it Born's rule.

I have no difficulty with the formal Born rule that calls the modulus squared of a wave function a probability density. This is just mathematics. The heuristic comes in when it relates this probability to ''finding the particle on some region'', which is a theoretically undefined notion.

How do you know what mathematical paths to follow? Unless experimental evidence tells you you are on the right track?

What is the point of quantum formalism if it doesn't tell you what you would measure?

Why is a paper on, say, prime number factorisation, which is pure mathematics not qualify as quantum theory? If it doesn't need to make measurable predictions?

Does QT not need to be explicit about the physical phenomena it is describing? And how else, other than by experiment, do you have any feedback about the applicability of the mathematical formalism?