Justification for no properties before measurement

[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?

 

[A. Neumaier]

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

One needs contact to reality to check whether a theory is about this reality. But this is independent of my argument.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

Thread reopened.

 

[Auto-Didact]

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.

I literally could not have said this any better.

This quote should be printed in every QM textbook, read aloud in every QM classroom and emphasized in every philosophy of physics programme.

 

[vanhees71]

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.

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.

Measurement is something an experimentalist is doing in the lab. It's not defined by mathematics but by real-world constructions in the lab! The observer's choice is as well defined by these real-world setups in the world. What's measured is due to the construction of the measurement device. Although the construction of the device indeed uses some theoretical input about what you want to measure to answer some question about phenomena finally the device defines what's measured.

 

[A. Neumaier]

Measurement is something an experimentalist is doing in the lab. It's not defined by mathematics but by real-world constructions in the lab!

That's why there is a measurement problem. It consists in formalizing the concept of measurement in a similar way same way as we know how to formalize the concepts of force, energy, information, etc..

Note that one can say the same about forces and fields as what you said about measurement. Forces and fields are something that experimentalists are measuring in the lab. It's not defined by mathematics but by real-world constructions in the lab!

But this describes the situation of 150 years ago.

In the mean time, forces and fields are defined by mathematics and not by real-world constructions in the lab! One needs the theoretical definition to find out what real-world constructions in the lab actually do measure, and how to calibrate the latter so that they measure as good as possible the quantities defined by the theory. One even changes the experimental meaning of basic procedures such as units of mass, time, and length in order that they fit better what theory predicts!

 

[Boing3000]

Measurement is something an experimentalist is doing in the lab. It's not defined by mathematics but by real-world constructions in the lab! The observer's choice is as well defined by these real-world setups in the world. What's measured is due to the construction of the measurement device. Although the construction of the device indeed uses some theoretical input about what you want to measure to answer some question about phenomena finally the device defines what's measured.

I find that statement very strange. A was undr the impression that there is no difference between the experimental apparatus for a classic double slit experiment (which does NOT need QM at all for explaining) that for a QM one. Unless you consider dialing down the intensity of the light some sort of "real-world construction".

What is measure is the very same "macroscopic/classic" thing. The real-world realization comes when quantum object are "resolved" one by one. Can't we say that the measurement problem comes from the fact that QM has zero power of prediction for one event, and start having more and more sense only to connect the "in between" behaviors of "identically prepared quantum" ?
Isn't the measurement problem the fact that reality is not made of ensemble (those exist only in the theory and your mind) but only of individual events ?

 

[vanhees71]

That's why there is a measurement problem. It consists in formalizing the concept of measurement in a similar way same way as we know how to formalize the concepts of force, energy, information, etc..

Note that one can say the same about forces and fields as what you said about measurement. Forces and fields are something that experimentalists are measuring in the lab. It's not defined by mathematics but by real-world constructions in the lab!

But this describes the situation of 150 years ago.

In the mean time, forces and fields are defined by mathematics and not by real-world constructions in the lab! One needs the theoretical definition to find out what real-world constructions in the lab actually do measure, and how to calibrate the latter so that they measure as good as possible the quantities defined by the theory. One even changes the experimental meaning of basic procedures such as units of mass, time, and length in order that they fit better what theory predicts!

Sure, but after all the quantities are defined operationally by real-world measurement devices. That's precisely what the metrological institutes do to define units for various quantities, and the basic definitions (representations by real-world measurement prescriptions) of the units change due to technological progress. E.g., the unit of mass, the kilogram, in the SI is not anymore accurately enough by the prototype kept in Paris, given the much better accuracy reached by redefining the unit via another measurement prescription, in this case by defining fundamental conversion factors like $\hbar$, $N_A$, etc.

 

[vanhees71]

I find that statement very strange. A was undr the impression that there is no difference between the experimental apparatus for a classic double slit experiment (which does NOT need QM at all for explaining) that for a QM one. Unless you consider dialing down the intensity of the light some sort of "real-world construction".

What is measure is the very same "macroscopic/classic" thing. The real-world realization comes when quantum object are "resolved" one by one. Can't we say that the measurement problem comes from the fact that QM has zero power of prediction for one event, and start having more and more sense only to connect the "in between" behaviors of "identically prepared quantum" ?
Isn't the measurement problem the fact that reality is not made of ensemble (those exist only in the theory and your mind) but only of individual events ?

Nowdays we can do real-world double-slit experiments with single photons or particles, and these experiments cannot be described by classical particle or field theories but only by quantum theory, confirming the predictions of this theory with high accuracy. Physics is an empirical science, and theories are modified or even completely new ones (but that's very rare; it happened only twice since Newton with the discovery of relativity and QT) due to newly discovered observational facts.

 

[PeroK]

In the mean time, forces and fields are defined by mathematics and not by real-world constructions in the lab!

There are two very distinct mathematical objects when it comes to physics. Pure mathematical objects, such as a Linear Operator. Nothing any physicist does will ever change the definition or properties of a linear operator. Then there are mathematically defined objects that map to real-world phenomena, such as a Force. Experimental physics may influence the definition of these things.

I would say that Force is not defined solely as a mathematical object. It has a dual definition in terms of mathematics on the one hand and its role in the real world on the other.

Even if you defined the measurement process mathematically, you'd still need to verify experimentally that your definition of the measurement process correctly mapped to the real world phenomenon of measurement!

 

[Boing3000]

Nowdays we can do real-world double-slit experiments with single photons or particles,

What I meant to say is that even 200 hundred years ago all double slits experiments were already done with "individual" photons, we just didn't knew it.

and these experiments cannot be described by classical particle or field theories but only by quantum theory,

Of course, only QT can explain how all these individual events coalesce to some ensemble behavior, and also explains so many other "spooky" ones. Nobody is disputing that.

confirming the predictions of this theory with high accuracy.

Isn't that THE measurement problem ? That you need to add an "s", an unspecified number of "s" before the measurements reach any significant accuracy.
As far as I know classical measurement have not that problem. Every single one of them is accurate (up to precision)

Physics is an empirical science, and theories are modified or even completely new ones (but that's very rare; it happened only twice since Newton with the discovery of relativity and QT) due to newly discovered observational facts.

Indeed, and the only new observational fact is that some part of nature "comes in packet". And QM brilliantly describe an ensemble of measurements. But observational data are made of series of events/facts. I may understand your view about when an ensemble measurement start, but not when it ends. I need a number of events, and "infinite" is not something I would accept without calling it a "problem".
Another way of saying that is I haven' read anywhere that some photons is "aware/causally" linked to the other photons of the "same" ensemble of measurements. Yet they are, because the "preparation procedure" put them in some "identical" state (which in itself is a bold statement). I think it definitely deserve to be called "a problem". Unless of course you just "don't care" about individual events, nor that the theory have zero accuracy (to be fair no more than the classical one) to predict what an event will be.

 

[A. Neumaier]

the quantities are defined operationally by real-world measurement devices.

and in addition they are defined theoretically by the theory. One does not replace the other. Both aspects must be present for a complete understanding.

What holds for concepts like forces or fields also holds for the concept of what counts as a measurement. If you can express it only in experimental terms and not in addition in theoretical terms, there are problems in interpretation.

For example, experimenters boldly assert that observing a single spot on a screen actually is a measurement of a single particle arriving at that position. I have never seen a convincing demonstration that the value of the classical observable actually measured is in some meaningful theoretical sense the measured value of a property of a single particle. The arguments use foggy - and hence philosophically debatable - language. If the language were as clear as in classical mechanics there would not be this continuing discussion about the (in your minority view nonexisting) measurement problem, which even involves Nobel prize winning experts of quantum mechanics such as Steven Weinberg,

The development of quantum mechanics in the first decades of the twentieth century came as a shock to many physicists. Today, despite the great successes of quantum mechanics, arguments continue about its meaning, and its future. [...]
It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means.

(quoted from here) and Gerard t'Hooft,

When used correctly, it was found that the outcome of an experiment can be predicted precisely, but the answer often comes in a statistical form: upon repeating the experiment many times, statistical distributions will be found, and only those can be predicted by the theory, not the outcome of a single observation. Finally then, one could ask: what is the cause of all these observed statistical fluctuations?

(quoted from here).

 

[vanhees71]

What I meant to say is that even 200 hundred years ago all double slits experiments were already done with "individual" photons, we just didn't knew it.

No, 200 years ago there were no one-photon sources available. It's not easy to prepare Fock states of photons!

 

[Boing3000]

No, 200 years ago there were no one-photon sources available. It's not easy to prepare Fock states of photons!

I didn't say anything about Fock State. Maybe you mean that the Taylor experiment of in 1909 is all about Fock state ?
I am quite sure that you are not saying that light is not "made of" individual photons (meaning un-entangled), so the only conclusion I can draw here is that QM predict a different interference pattern between ensemble of photons only being able to interfere with themselves (in a path integral way), or being able to interfere with some non-Fock "companion" in some more classical way (something I am unaware of, thus my "individual" photon statement).

 

[SemM]

I didn't say anything about Fock State. Maybe you mean that the Taylor experiment of in 1909 is all about Fock state ?
I am quite sure that you are not saying that light is not "made of" individual photons (meaning un-entangled), so the only conclusion I can draw here is that QM predict a different interference pattern between ensemble of photons only being able to interfere with themselves (in a path integral way), or being able to interfere with some non-Fock "companion" in some more classical way (something I am unaware of, thus my "individual" photon statement).

Boing, is there a ODE that describes light composed of entagled photons? If so, can you give it here?

Thanks!