Justification for no properties before measurement

[bahamagreen]

First question: what is the reason/evidence, EXACTLY, for the position that particles have no properties before they’re measured? I know it’s part of Copenhagen, but what justifies that particular feature of Copenhagen? I’m looking for an answer that I could present to, say, a roomful of non-physics people.

EXACTLY? :)

Perhaps those here that know more may answer whether this analogy is OK for "a roomful of non-physics people"... I offer it "as is" so feel free to comment and mark it up...

Fourier had a mathematical insight that waves might be decomposed into a collection of sine waves.
Fourier transformation is the name for this operation. Fourier synthesis is the inverse (using waves to compose another wave).

The wave forms used for decomposition and synthesis don't have to be sine waves; they may be any arbitrary wave themselves.
Sine waves are used because the math is less complex, but a wave may be decomposed into sine waves, triangle waves, saw-tooth waves, etc.
Likewise, sine, triangle, saw-tooth, etc. waves may be used to compose a wave.

The point here is that when one decomposes a wave, one has to chose a "measurement" wave, usually a sine wave.
If you chose the sine wave you are measuring the "sinewaveness" of the subject wave.
If you chose a square wave or impulse wave, you are measuring the subject wave's "squarewaveness" or "impulsewaveness".

The properties or attributes of the subject wave are depending on the "measurement" wave selected to decompose the subject wave.
The choice of measurement wave is like asking a specific question, and getting a particular answer.

The choice of measurement wave is the equivalent of the experimental design and conditions - determining the property measured.
The simple measurement waves allow for experiments that can be performed and properties that can be understood.
(As if sine waves measure momentum and impulse waves measure position - simple waves and simple properties).

There is an infinite list of possible measurement wave forms for which no possible real experimental design and construction can be imagined.
And the results would be the measurement of an indefinitely complex unimaginable abstract property of the subject wave.

So, if the subject wave has all potential decompositions (properties) corresponding to all potential measure wave selections (tests)...

Does it hold all potential properties waiting to be tested?
Does it have no properties until tested?
Does it have no properties; all properties being within the experimental setup?
Will the classical philosophical foundation meaning of "properties" need to be reviewed or updated?

 

[bhobba]

So, as I see it, at the finest level to which space is, point A is simply not distinguishable from point B. A point A, at x meters cannot exist as distinct and separate from a point B at x+0.000000000001 meters. Heisenberg uncertainty are actually coupled pairs so this is may be oversimplification. Never the less, points A and B cannot be distinct because if this were so, an object at point A could not move to point B. Points in space, A and B, are connected. We know they are connected. We can move from one place to the next. Quantum uncertainty is simply the natural outcome of space having an extent.

Your post has so many misconceptions I don't even know where to begin. But let's start with real numbers. Between any two real numbers lies another real number. A point can exist as distinct, separate and between one .000000000001 meters away. It's basic math. And QM places no limit whatsoever on the accuracy you can measure a particles position - but that is getting off topic and needs a thread to discuss exactly what the Uncertainty Principe says.

Time as we know it does not exist? In all measures you are aware it its simply a measure of distance - well we do have this thing called an atomic clock with a digital readout.

I think we pretty well know what time is:
http://www.informationphilosopher.com/solutions/scientists/feynman/past_and_future.html

Simply its what a clock measures - and as explained above what it measures is basically the tendency of things to go from order to disorder because there are many more disordered states than ordered ones. Entropy goes one way - and that is time.

There are many more misconceptions - but really it needs its own thread - so if you want to discuss it start a new one and try to stay on topic in this one.

Thanks
Bill

 

[ggraham76]

EXACTLY? :)

Perhaps those here that know more may answer whether this analogy is OK for "a roomful of non-physics people"... I offer it "as is" so feel free to comment and mark it up...

Fourier had a mathematical insight that waves might be decomposed into a collection of sine waves.
Fourier transformation is the name for this operation. Fourier synthesis is the inverse (using waves to compose another wave).

The wave forms used for decomposition and synthesis don't have to be sine waves; they may be any arbitrary wave themselves.
Sine waves are used because the math is less complex, but a wave may be decomposed into sine waves, triangle waves, saw-tooth waves, etc.
Likewise, sine, triangle, saw-tooth, etc. waves may be used to compose a wave.

The point here is that when one decomposes a wave, one has to chose a "measurement" wave, usually a sine wave.
If you chose the sine wave you are measuring the "sinewaveness" of the subject wave.
If you chose a square wave or impulse wave, you are measuring the subject wave's "squarewaveness" or "impulsewaveness".

The properties or attributes of the subject wave are depending on the "measurement" wave selected to decompose the subject wave.
The choice of measurement wave is like asking a specific question, and getting a particular answer.

The choice of measurement wave is the equivalent of the experimental design and conditions - determining the property measured.
The simple measurement waves allow for experiments that can be performed and properties that can be understood.
(As if sine waves measure momentum and impulse waves measure position - simple waves and simple properties).

There is an infinite list of possible measurement wave forms for which no possible real experimental design and construction can be imagined.
And the results would be the measurement of an indefinitely complex unimaginable abstract property of the subject wave.

So, if the subject wave has all potential decompositions (properties) corresponding to all potential measure wave selections (tests)...

Does it hold all potential properties waiting to be tested?
Does it have no properties until tested?
Does it have no properties; all properties being within the experimental setup?
Will the classical philosophical foundation meaning of "properties" need to be reviewed or updated?

Thx bahamagreen. I’ll consider your post very carefully.

 

[ggraham76]

Hi Graham

As promised here is my suggested reading list for your purposes.

1. Quick Calculus:
https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20
2. Theoretical Minimum
https://www.amazon.com/dp/0465075681/?tag=pfamazon01-20
3. Susskind - Quantum Mechanics::
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20
4. Structure And Interpretation Of QM:
https://www.amazon.com/dp/0674843924/?tag=pfamazon01-20
5. Quantum Probabilities:
https://www.scottaaronson.com/democritus/lec9.html
http://math.ucr.edu/home/baez/bayes.html
6. Consistent Histories - It'a a modern interpretation favored by Gell-Mann and towards the end by Feynman - sometimes categorized as Copenhagen done right:
http://quantum.phys.cmu.edu/CQT/index.html

I think that's enough to start with - get back with any questions.

Thanks
Bill

Bill, thank you so much: you went to a lot of trouble to help me. Very appreciative.

 

[SemM]

Hi. I’m a PhD student at University of Toronto, in philosophy of physics.
I have a number of questions which are quite fundamental: just trying to get everything clear in my head in the most succinct way possible, so I’m sorry if the questions seem remedial.

If a particle with it's wave-component travels through space, either in free state or bound state to a nucleus (oscillating), it has an energy that is unmeasured and cannot be measured unless it's state is excited by the measurement-equipment you might use (electron microscope or X-ray or similar). I think that is perhaps what some mean that it can't be measured. It's not like a tennis ball flying through the room, which you can track with light, an electron or a particle shifts state as soon as the observer (light) hits it and before you "saw it", so therefore it's really impossible to know what it was before. You can calculate what it was before though.

 

[Urs Schreiber]

Mathematically, the state space of quantum mechanics is not a simplex

Maybe you meant to say "point" or "0-simplex" instead of "simplex"? A 0-simplex is a point, a 1-simplex is an interval, a 2-simplex is a filled triangle, a 3-simplex is a filled tetrahedron, and so on. See simplex.

That said, the space of quantum states is a convex space (see here). While also each $n$-simplex is a convex space, the space of quantum states is not an $n$-simplex for any $n$. Unless indeed we have the completely trivial system for which there is only the zero-state, so that the state space is the point, hence the 0-simplex.

 

[atyy]

Maybe you meant to say "point" or "0-simplex" instead of "simplex"? A 0-simplex is a point, a 1-simplex is an interval, a 2-simplex is a filled triangle, a 3-simplex is a filled tetrahedron, and so on. See simplex.

That said, the space of quantum states is a convex space (see here). While also each $n$-simplex is a convex space, the space of quantum states is not an $n$-simplex for any $n$. Unless indeed we have the completely trivial system for which there is only the zero-state, so that the state space is the point, hence the 0-simplex.

What I wrote seems to be the same as what you wrote.

 

[Urs Schreiber]

What I wrote seems to be the same as what you wrote.

No, how? But it's not a big deal. I just thought you might not know the definition of "simplex", so I pointed it out.

 

[Fra]

(*)

"Absence of evidence is not evidence of absence" - Carl Sagan

I would like to defend PeterDonis original comment and object to this response as I think it trivializes away a possibly deeper aspect that is relevant to the OT.

The Statement(*) is only unambigously true in the context of deductive logic, where by evidence we mean "proof", in the sense that absense of a proof of statement, surely does not disproove it. And think this is what you meant as well.

But to what extent is this relevant to QM?

In a more general inference (induction or abduction), such as when you need to determine the odds for certain events, in order to choose a rational action, then absense of certain information certainly influenes the chosen action in a way that does imply that "absense of events" simply render these these events less probably as per the condtitional inference and thia has observable consequences.

Moreover, we do not know if understanding the causal parts of laws of physics in its most fundamental sense as "deductive logic" is right. My personal insights tell me rather that this is likely wrong, in fact it
makes no sense to me at all.

Surely insights is not a formal argument but others fringes these ideas as well. See Lee Smolin (reality of time and evolution of law). Also check out his the principle of precedence. https://arxiv.org/abs/1205.3707.

What I am hinting is that the ACTION of a quantum system, might be determined by this quantum systems lack of confirmed information about its own environment (read lack of a specfic interation history, lack of preparation etc). And vice versa. In this case, the absense or presence of certain information might even be the key to understand quantum causality.

Or maybe not - my point in any case is i
expect subtle things like to not escape any philsophical analysis of QM foundations. This issue may be neither black nor white.

/Fredrik

 

[Lord Jestocost]

... the position that particles have no properties before they’re measured? I know it’s part of Copenhagen, but what justifies that particular feature of Copenhagen?

Such a position was never part of the Copenhagen approach. The "Copenhagens" would merely ask: What is a PARTICLE? I hope the following will help:

"In classical physics the aim of research was to investigate objective processes occurring in space and time, and to discover the laws governing their progress from the initial conditions. In classical physics a problem was considered solved when a particular phenomenon had been proved to occur objectively in space and time, and it had been shown to obey the general rules of classical physics as formulated by differential equations. The manner in which the knowledge of each process had been acquired, what observations may possibly have led to its experimental determination, was completely immaterial, and it was also immaterial for the consequences of the classical theory, which possible observations were to verify the predictions of the theory.
In the quantum theory, however, the situation is completely different. The very fact that the formalism of quantum mechanics cannot be interpreted as visual description of a phenomenon occurring in space and time shows that quantum mechanics is in no way concerned with the objective determination of space-time phenomena." [Bold, LJ]

Werner Heisenberg in “The development of quantum mechanics”

 

[vanhees71]

I didn't know that Heisenberg was that "philosophical"... Sigh.

 

[A. Neumaier]

I didn't know that Heisenberg was that "philosophical"... Sigh.

You should read his book ''Der Teil und das Ganze''!
https://scholar.google.at/scholar?cluster=9928574072894946072

 

[atyy]

No, how? But it's not a big deal. I just thought you might not know the definition of "simplex", so I pointed it out.

Aren't these the same?

"the state space of quantum mechanics is not a simplex" = "the space of quantum states is not an n-simplex for any n."

I think the most common simplex that is not a simplex is the "simplex algorithm" (or at least I've never known why it's called that).

 

[vanhees71]

You should read his book ''Der Teil und das Ganze''!
https://scholar.google.at/scholar?cluster=9928574072894946072

I remember that I've read this book when I was at high school, but it didn't appeal too much to me at that time. Perhaps, I should indeed read it again.

 

[bhobba]

I didn't know that Heisenberg was that "philosophical"... Sigh.

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

 

[bhobba]

I remember that I've read this book when I was at high school, but it didn't appeal too much to me at that time. Perhaps, I should indeed read it again.

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

 

[A. Neumaier]

most of the founders, could at least in part, be described as a mob of mystics

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.

 

[microsansfil]

In the quantum theory, however, the situation is completely different. The very fact that the formalism of quantum mechanics cannot be interpreted as visual description of a phenomenon occurring in space and time shows that quantum mechanics is in no way concerned with the objective determination of space-time phenomena." [Bold, LJ]
Werner Heisenberg in “The development of quantum mechanics”

it's surprising from Werner Heisenberg. I didn't know he had a philosophical position based on naïve realism. If you don't give a visual description of a space-time phenomenon (vawe, corpuscle, trajectory, ..., from our first-person experience) this shows that the description is in no way concerned with the "objective" (inter-subjective) determination of space-time phenomena !

Best regards
Patrick

 

[dextercioby]

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.

 

[bhobba]

The philosophy-free position of @vanhees71 is possible only since the subject has matured such a lot since its inception.

Yes. When something genuinely mystifying turns up one does find philosophy more prominent. Von-Neumann was no mystic - yet was the promulgator of consciousnesses causes collapse in his famous textbook.

Except for the measurement problem, where most of the discussion is still on the level of the dark ages.

Oh dear - do tell

Of course. What do you say to someone like Penrose - if he gets caught up in it anyone is vulnerable.

Thanks
Bill

 

[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.