What does the probabilistic interpretation of QM claim?

[A. Neumaier]

I collect here info from another thread, to have a more focussed discussion.

The probability interpretation says that _if_ you can set up an experiment that measures a self-adjoint operator for a system in state psi then the probability of observing the k-th eigenvalue is psi^* P_k psi, where P_k is the projector to the k-th eigenspace. It says _nothing_ at all about which particular operators are observable in this sense.

Everything beyond that is interpretation, and hence (at the current state of affairs) a matter of philosophy. In particular, which operators can be measured is not part of the probability interpretation but a matter of theoretical and experimental developments.

Regarding what is arbitrarily _precisely_ measurable, there is a no go theorem by Wigner (I can give references if you want to check that) that states that _only_ quantities commuting with all additive conserved quantities are precisely measurable. The position operator is not among these.

Nobody comparing QM with experiments is making use of this particular assumption.

''this particular assumption'' refers to the assumption that |psi(x_1,...,x_n|^2 is the probability density of observing simultaneously particle k at position x_k (k=1:N).

It is stated in the beginning as an interpretation aid without proof, and never taken up again in the context of real measurements where the claim would have to be justified. It is very common to make this sort of idealized assumption to get started; but once the formalism is established, this assumption is never used again.

For example, Landau & Lifgarbagez begin in Section 2 of their Vol. 3 with such a statement, but immediately replace it in (2.1) and (3.10) by the more correct version about the interpretation of the expectation value <K> = Psi^* K Psi, where K is an arbitrary observable (linear integral operator) depending on the form and values of the measurement. From then on, only the latter interpretation is used; never the fictitious, idealized introductory remark.

And it cannot be different, since quantum mechanics is used in many situations where the state vectors used in the formalism have no interpretation as a function of position - the whole of quantum information theory and the whole of quantum optics belonging to this category.

For nonrelativistic particles, absolutely everyone comparing QM with experiments does make use of the wave-mechanics interpretation of |\psi(x)|^2 as a probability density.

Please show me a comparison with experiment that does this.

Nonrelativistic particles have no different interpretation than relativistic ones.

Particle detectors respond to the momentum of a particle, not to its position.
Scattering experiments are interpreted in the momentum picture. Nobody is interested in the position of particle tracks, only in their momentum (which tells about masses).

Yes, this is true. QM does not talk about the specifics of observations and measuring devices. For example, P_k can be a projection on the k-th eigenvalue of the position operator.

It could be this _only_ if you can prepare an experiment that realizes such a P_k. But this is a matter of experimental technique and not one about the interpretation of quantum mechanics. But there are no such operators since the spectrum of position is continuous.

Yes, this is true. QM does not talk about the specifics of observations and measuring devices. For example, P_k can be a projection on the k-th eigenvalue of the position operator. Then psi^* P_k psi is the probability (density) for measuring position k in the state described by psi. QM tacitly assumes that some ideal precise measuring device can be constructed, which does exactly that

No. This unrealistic assumption is needed _only_when one wants to insists on a probability density interpretation of |psi(x)|^2. And for the position representation of an N-particle state, one would need an even more ideal precise measuring device that can measure the simultaneous presence of N particles in N different, arbitrarily small regions
covering the size of an uranium atom (N=92), say.

This is ridiculous - such measurement devices are impossible!

Whereas the form in which I stated the probability interpretation assumes nothing. it makes claims only for those projectors that are actually realizable. it is therefore much more realistic.

 

[_PJ_]

there are no such operators since the spectrum of position is continuous.

Quantum uncertaqinty rules out continuity in position.

 

[A. Neumaier]

Quantum uncertainty rules out continuity in position.

Wigner's theorem (p.298 in: Wheeler & Zurek, Quantum theory and measurement, Princeton 1983) even rules out projective measurements of a particle being in a given region, since the corresponding projector does not commute with all additive conserved quantities.

 

[meopemuk]

Particle detectors respond to the momentum of a particle, not to its position.
Scattering experiments are interpreted in the momentum picture. Nobody is interested in the position of particle tracks, only in their momentum (which tells about masses).

Would you then agree that |\psi(p)|^2 is the probability (density) of finding the particle with momentum p? Of course, \psi(p) is the wave function in the momentum representation.

Eugene.

 

[meopemuk]

For nonrelativistic particles, absolutely everyone comparing QM with experiments does make use of the wave-mechanics interpretation of as a probability density.

Please show me a comparison with experiment that does this.

The double-slit experiment is a good example. See Feynman's Lectures on physics.

Eugene.

 

[Avodyne]

I also reproduce what I wrote on this point in the other thread:

Experimenters have been recording particle tracks in position space with cloud chambers, bubble chambers, spark chambers, and drift chambers for many decades. The experiments are typically done in a strong magnetic field, which allows for measuring the momentum of charged particles by measuring the curvature of a track in position space. Modern experiments also have calorimeters at the boundaries of detectors that measure energy deposited; this does give a direct measurement of a particle's energy, but not its momentum.

For some recent pictures of particle tracks in position space from the LHC see

http://public.web.cern.ch/press/pressreleases/Releases2010/PR15.10E.html

 

[StevieTNZ]

I certainly believe that the superposition principle even applies when you can consider a quantum object in a definite state (Quantum Enigma, pg. 191; Entanglement, pg. 79; Absolutely Small, 371-372). So if it is in a definite state (this is obviously determined through what you see) then you can also consider all the other states it COULD be in as potentials (as you cannot see those other states). Of course, we can only talk about what we see. Perhaps those potentials ARE really real too, we just can't see them? But such questions are pointless as what we work with is from what we see.

The Mental Universe -> http://henry.pha.jhu.edu/The.mental.universe.pdf

 

[_PJ_]

When the particles in these chambers pass the medium, they ionise their surroundings. This interaction itself causes a collapse of the wafefunction.
The resultant ionised particles of media are what is detected, the momentum can be calculated as can the energy of the particle, but since there is delay between the initial ionisation and the detectoin of the ionised media particles, the initial particle is no longer in that state and cannot be correlated with the measurement of its energy (velocity).

 

[A. Neumaier]

Would you then agree that |\psi(p)|^2 is the probability (density) of finding the particle with momentum p? Of course, \psi(p) is the wave function in the momentum representation.

Definitely yes! Momentum is measurable, and (in direction, often also in magnitude) measured in every scattering experiment. And this doesn't contradict Wigner's theorem since momentum is one of the additively conserved quantities.

 

[A. Neumaier]

The double-slit experiment is a good example. See Feynman's Lectures on physics.

It cannot, since photons (usually used in the double slit experiment) have no Schroedinger position picture.

If it doesn't in the most important case, there is no reason to believe it should in other cases.

 

[A. Neumaier]

I also reproduce what I wrote on this point in the other thread:

Experimenters have been recording particle tracks in position space with cloud chambers, bubble chambers, spark chambers, and drift chambers for many decades. The experiments are typically done in a strong magnetic field, which allows for measuring the momentum of charged particles by measuring the curvature of a track in position space.

Yes; one measures the momentum by finding the curvature of the track. Nobody is interested in the position of the particle. Just as the photon in a double slit experiment is a spherical wave which leaves a detector click at a random detector position, so
the particle is a spherical wave which leaves a track in the detector (according to Mott's famous analysis) in a random initial direction - the scattering direction and the particle energy (which together give the momentum) form the observables, not the position.

 

[Physics Monkey]

I don't think its really correct to say that no one is interested in particle tracks. Although I'm not a particle experimentalist, I certainly think they're interesting to look at!

More seriously, detailed reconstruction of particle tracks is important for determining interaction vertices. For example, interesting unstable particles may decay after traveling some macroscopic distance, thus leading to an offset in the positions of the decay products. Deciding whether certain decay products came from a "primary vertex" or from some "secondary vertex" is critical for determining the nature of the unstable particles. For example, it helps in deciding what invariant mass to compute. At least that's my understanding from chatting with my experimentalist friends.

See here: http://lhcb-public.web.cern.ch/lhcb-public/ for an example. The April 21, 2010 entry.

 

[Avodyne]

Yes; one measures the momentum by finding the curvature of the track. Nobody is interested in the position of the particle.

Whether or not anyone is interested in the position of the particle is irrelevant. The point is that position of the particle has been measured. You had claimed that "Particle detectors respond to the momentum of a particle, not to its position." This is wrong. Particle detectors at the LHC respond to, and record, the position of a particle at a sequence of times, and then infer the momentum from the path of that the particle took.

 

[meopemuk]

Definitely yes! Momentum is measurable, and (in direction, often also in magnitude) measured in every scattering experiment. And this doesn't contradict Wigner's theorem since momentum is one of the additively conserved quantities.

So, you are not against probabilistic interpretation per se. You are against probabilistic interpretation of position measurements.

But experimentalists do measure particle positions all the time. They use rulers, photographic plates, bubble chambers and other not-so-sophisticated devices to do so. Then they can specify a certain volume in space and count how many times particle passed through that volume (e.g., using a Geiger counter). So, experimentalists can calculate the probability of the particle being in that volume. Probabilistic interpretation of position measurements exists experimentally. However, for some reason, you do not allow us to do the same in theory.

I would appreciate if you give an original reference to the "Wigner theorem", which, as you say, does not allow us to measure position and interpret it probabilistically. This claim sounds unbelievable to me.

Eugene.

 

[meopemuk]

It cannot, since photons (usually used in the double slit experiment) have no Schroedinger position picture.

When a photon hits the photographic plate or a CCD detector it leaves a clear trace, whose position is well-defined (at least in our macroscopic world). So, it seems that there is no problem in measuring photon position with the precision of few micrometers, or so. We must have a theory, which would explain these kinds of measurements. Quantum mechanics is exactly this kind of theory, and the probabilistic interpretation of measurements of position (and all other obervables) is the cornerstone of quantum mechanics. If you deny that, then you invite a major revision of the entire foundation of quantum mechanics.

I don't know what would happen if we tried to determine photon's position with the precision of, say, less than 1 Angstrom. Perhaps, in this case we would meet some difficulties that you are referring to. However, there are no experimental devices, which can measure photon's position so precisely. So, the issue of the absence of a photon's position operator is an academic issue, in my opinion.

You do not deny the existence of photon's momentum eigenstates. And I can always form linear combinations of these eigenstates (with factors like exp(ipx)) which would behave *almost* like position eigenstates. For example, the linear combinations with different x and x' will be (almost) orthogonal. A space translation of an x-combination will move it to the x+a-combination. So, all properties characteristic to position will be approximately satisfied.
This should be sufficient for defining position measurements and related probabilities at least in our macroscopic world with micrometer-or-so-precision measurements.

All these problems are absent for massive particles, like electrons. So, to keep our discussion simple, let us focus on the double-slit experiment with electrons.

Eugene.

 

[A. Neumaier]

I don't think its really correct to say that no one is interested in particle tracks. Although I'm not a particle experimentalist, I certainly think they're interesting to look at!

More seriously, detailed reconstruction of particle tracks is important for determining interaction vertices.

Yes. particle tracks _are_ important; but because they allow one to measure the momentum of a particle. But particle position is irrelevant, and doesn't exist on the quantum field level.

 

[A. Neumaier]

Whether or not anyone is interested in the position of the particle is irrelevant. The point is that position of the particle has been measured. You had claimed that "Particle detectors respond to the momentum of a particle, not to its position." This is wrong. Particle detectors at the LHC respond to, and record, the position of a particle at a sequence of times, and then infer the momentum from the path of that the particle took.

No. The position of a particle has been ''measured'' only in the same sense as the position of a photon has been ''measured'' when a photodetector clicks. But neither of them exists at the quantum field theory level.

For photons one not even has a Schroedinger picture in which photon position would be well-defined, hence clicks cannot be said to measure a photon position. Instead, the analysis in the book by Mandel & Wold shows that the clicks in the photodetector are produced by the photodetector already for a classical external e/m radiation field, showing that photodetection is a random measurement of the intensity of the incident radiation field, and nothing else. See the thread https://www.physicsforums.com/showthread.php?t=474537

For alpha particles, the corresponding analysi analysis is given in Mott's 1929 paper (reprinted in pp.129-134 in: Wheeler & Zurek, Quantum theory and measurement, Princeton 1983). He shows that the tracks formed in a cloud chamber are already produced by the cloud chamber in a classical external radial charged field - in which case the quantum system considered does not contain an alpha-particle at all. Thus the tracks cannot be said to measure a particle position. Instead they form a random measurement of the intensity and direction of the incident charged field, and nothing else.

 

[A. Neumaier]

So, you are not against probabilistic interpretation per se. You are against probabilistic interpretation of position measurements

Yes. In quantum field theory and hence in multiparticle quantum mechanics where particles are indistinguishable, position is a mere parameter, like time, that cannot be measured. Only for a single massive particle it seems to be different - but even here it causes the typical qauntum weirdness of propertyless particles suddenly materializing when measured.

But experimentalists do measure particle positions all the time. They use rulers,

How do you measure a particle position by a rule? Rules only serve to measure local discontinuities or maxima of a macroscopic color field.

photographic plates, bubble chambers and other not-so-sophisticated devices to do so.

These never measure particles, but macroscopic distributions of silver atoms or bubbles.

I would appreciate if you give an original reference to the "Wigner theorem", which, as you say, does not allow us to measure position and interpret it probabilistically. This claim sounds unbelievable to me.

The most accessible reference (in English translation) is the one I gave already; the book is a very useful reprint volume. The original is in German: Z. Phys. 133, 101-108.

 

[A. Neumaier]

When a photon hits the photographic plate or a CCD detector it leaves a clear trace, whose position is well-defined (at least in our macroscopic world). So, it seems that there is no problem in measuring photon position with the precision of few micrometers, or so. We must have a theory, which would explain these kinds of measurements. Quantum mechanics is exactly this kind of theory, and the probabilistic interpretation of measurements of position (and all other obervables) is the cornerstone of quantum mechanics. If you deny that,

I deny that a photodetector measures the position of photons, or that a bubble chamber measures the position of charged quantum particles. (The trace is a trace of particle excitations as the result of the external charged field and a constant magnetic field in case of curved traces.) They measure the incident fields, nothing else.

then you invite a major revision of the entire foundation of quantum mechanics.

In my lecture http://arnold-neumaier.at/ms/optslides.pdf , I call this revision the thermal interpretation of quantum mechanics. It does not require the slightest alteration of quantum mechanics or quantum field theory. I only changed the currently accepted weird way of talking about quantum system (a long tradition introduced by many years of brainwashing) into one which matches common sense much better. So it is not a change in the foundations but only a change in the interpretation - one that is more consistent with the mathematics (such as the nonexistent of a photon position operator, and Wigner's theorem).

You do not deny the existence of photon's momentum eigenstates.

Indeed, photon momenta are measurable if they are large enough. (Only soft photons cannot be measured, because of the infrared problem.)

 

[dx]

Do you deny that the position of an electron can be measured by letting it fall on a photographic plate?

 

[A. Neumaier]

Do you deny that the position of an electron can be measured by letting it fall on a photographic plate?

According to the quantum field theoretic view, position is only a field label, not an observable.

The plate responds to the field strength of the beam containing the electrons: Random atoms are ionized, with a rate proportional to the field strength. This effect that is subsequently magnified and becomes visible.

What is measured is therefore the field strength, although because of the randomness involved, the measurement becomes reliable only if the exposure is sufficiently long.

 

[JK423]

Mr Neumaier,

I'm also suprised to read such a statement! (That the tracks in a bubble chamber are not a position measurement). I don't deny this immediately, i just want to understand what you're saying.
Let me say first how i would define a position measurement. If the incident field/particle has a state |Ψ>, and expand this state on the basis of position eigenstates, then i would call a position measurement something that would make the wavefunction of the particle in the position representation "gather" around a point. So that, we will be able to say that it was here, in that box, and not in the andromeda galaxy. Knowing that the field/particle is located in a subregion of space, i think defines a position measurement.
When charged fields/particles interact with the bubble chamber we see a trajectory. This trajectory has dimension, for example 0.5x0.5 mm^2 and that defines a subregion of space. I agree that what we see is the effect of the interaction of the particle with the atoms of the liquid, but there can be an interaction only if the paticle's wavefunction is nonzero at the point of the interaction with an atom. The fact that we see only a small trajectory -to my mind- means that the wavefunction of the particle is non-zero only in that subregion of space. It doesn't interact with the rest of the chamber, and its not in my house either.
So, that fits my definition of position measurement, the wavefunction is 'gathered' in a subregion of space.
Am i wrong?


John

 

[A. Neumaier]

On Wigner's no-go theorem for exact measurement:

The most accessible reference (in English translation) is the one I gave already; the book is a very useful reprint volume. The original is in German: Z. Phys. 133, 101-108.

The paper J. Math. Phys. 25 (1984), 79 -87 by Ozawa might also be of interest.

 

[dx]

According to the quantum field theoretic view, position is only a field label, not an observable.

The position is of course a field label, since the quantum field is essentially the position version of momentum mode creation operators. But why does that imply that the position of an electron cannot be measured? As far as I know, the fact that momentum is a label of the creation operators for momentum modes does not imply that the momentum of an electron cannot be measured, so what's the difference?

 

[JK423]

In my opinion, we should first define what we mean by a 'position measurement' and then see if the tracks in a bubble chamber, for example, qualify.

 

[A. Neumaier]

The position is of course a field label, since the quantum field is essentially the position version of momentum mode creation operators. But why does that imply that the position of an electron cannot be measured? As far as I know, the fact that momentum is a label of the creation operators for momentum modes does not imply that the momentum of an electron cannot be measured, so what's the difference?

The difference is that momenta (like other conserved additive quantities) are asymptotic quantities, and quantum particles have meaning in an asymptotic sense only.

Things start to get semiclassical (where the particle concept begins to be applicable) only when field concentrations are so large that their density peaks at reasonably well-defined locations in phase space. At this point, these peaks behave like particles, and position and momentum of the peak behaves approximately classically.

 

[A. Neumaier]

In my opinion, we should first define what we mean by a 'position measurement' and then see if the tracks in a bubble chamber, for example, qualify.

Why don't you start with a proposal for a definition what _you_ mean by a 'position measurement'?

 

[JK423]

Why don't you start with a proposal for a definition what _you_ mean by a 'position measurement'?

I've done it at post #22.

 

[dx]

The difference is that momenta (like other conserved additive quantities) are asymptotic quantities, and quantum particles have meaning in an asymptotic sense only.

Could you expand on this part a bit. What's an asymptotic quantity?

 

[A. Neumaier]

Could you expand on this part a bit. What's an asymptotic quantity?

An observable still visible at times t-->inf or t-->-inf, so that scattering theory says something interesting about it. This is relevant since quantum dynamics is very fast but measurements take time. Measuring times are already very well approximated by infinity, on the time scale of typical quantum processes. Thus only asymptotic quantities have a reasonably well-defined response.

That's why information about microsystems is always collected via scattering experiments described by the S-matrix, which connects asymptotic preparation at time t=-inf with asymptotic measurement at time t=+inf.

 

[A. Neumaier]

I've done it at post #22.

Ah, I missed the details in that post.

Let me say first how i would define a position measurement. If the incident field/particle has a state |Ψ>, and expand this state on the basis of position eigenstates, then i would call a position measurement something that would make the wavefunction of the particle in the position representation "gather" around a point. So that, we will be able to say that it was here, in that box, and not in the andromeda galaxy. Knowing that the field/particle is located in a subregion of space, I think defines a position measurement.

This recipe cannot cover a photon position measurement since the photon disappears upon exciting an electron. Do you want to improve upon your definition of a position measurement, or do you want to treat photons and electrons on a different footing?

When charged fields/particles interact with the bubble chamber we see a trajectory. This trajectory has dimension, for example 0.5x0.5 mm^2 and that defines a subregion of space. I agree that what we see is the effect of the interaction of the particle with the atoms of the liquid, but there can be an interaction only if the particle's wavefunction is nonzero at the point of the interaction with an atom.

In the quantum field view, one would say that there can be a response only if the field intensity is nonzero at the point of interaction. This works independent of the number of particles present.

The fact that we see only a small trajectory -to my mind- means that the wavefunction of the particle is non-zero only in that subregion of space. It doesn't interact with the rest of the chamber, and its not in my house either.
So, that fits my definition of position measurement, the wavefunction is 'gathered' in a subregion of space.
Am I wrong?

If you assume the collapse postulate, your view is consistent, as long as you don't claim that position can be measured arbitrarily well. This is just the Copenhagen interpretation.

The problem with this is that there is no known mechanism for causing the collapse. (Decoherence reduces the pure state to a mixture, but we don't observe a mixture of tracks - only a single one. This accounts correctly for the long-term average, but not of the collapse at each single instance.)

The quantum field picture doesn't need to assume a collapse; ordinary randomness is enough.

 

[meopemuk]

Yes. In quantum field theory and hence in multiparticle quantum mechanics where particles are indistinguishable, position is a mere parameter, like time, that cannot be measured. Only for a single massive particle it seems to be different - but even here it causes the typical qauntum weirdness of propertyless particles suddenly materializing when measured.

I agree with you that parameter x in quantum field \psi(x,t) has absolutely no relationship to physically measurable position. However, this does not mean that the observable of position cannot be defined in quantum field theory. We've discussed this point with you already. In any n-particle sector of the Fock space I can define a state in which one particle has position x_1, second particle has position x_2, third particle ... etc. You were correct to point out that in the case of indistinguishable particles this does not allow to form a Hermitian "particle position" operator. But the above construction of n-particle localized states is sufficient to describe position measurements in the Fock space.

You would possibly object that the Fock space is not valid for interacting particles. But this has no relevance, because we've been discussing the measurements of position of a single electron, which is not interacting with anything.

Another point is that refusing the measurability of positions you are are not saving yourself from the "weird" quantum collapse. You've mentioned elsewhere that the momentum-space wavefunction \psi(p) does have a measurable probabilistic interpretation. So, it does require a collapse. This time in the momentum space.

photographic plates, bubble chambers and other not-so-sophisticated devices to do so.

These never measure particles, but macroscopic distributions of silver atoms or bubbles.

Our difference is that I believe that the blackening of silver atoms or the formation of bubbles are direct local effects of incident particles. So, by measuring positions of exposed grains of photoemulsion or bubbles we measure (albeit indirectly) positions of particles, which created these effects.

If I understand correctly, your position is that the blackened grain of photoemulsion or the formed bubble is not a proof that the particle really hit that spot. You invoke a (rather strange, in my opinion) detection theory from Mandel & Wolf, where they represent the particle by an extended continuous field. Then creation of the local photographic image or a small bubble is "explained" by a sequence of non-trivial condensation events happening in the bulk of the detector. These events require migration of charge to macroscopic distances, entanglement, and other complicated and not fully explained things.

If I understand correctly, your motivation for applying these non-trivial models of particle detection is to avoid using the quantum-mechanical wave function collapse. So, you replace the collapse with some chaotic and yet mysteriously choreographed (condensation of the originally distributed particle energy at one fixed but random point) processes inside the macroscopic detector.

Eugene.

 

[strangerep]

[...] the analysis in the book by Mandel & Wold shows that the clicks
in the photodetector are produced by the photodetector already for a
classical external e/m radiation field, showing that photodetection is
a random measurement of the intensity of the incident radiation field,
and nothing else. [...]

For alpha particles, the corresponding analysi analysis is given in
Mott's 1929 paper (reprinted in pp.129-134 in: Wheeler & Zurek, Quantum
theory and measurement, Princeton 1983). He shows that the tracks
formed in a cloud chamber are already produced by the cloud chamber in
a classical external radial charged field - in which case the quantum
system considered does not contain an alpha-particle at all. Thus the
tracks cannot be said to measure a particle position. Instead they form
a random measurement of the intensity and direction of the incident
charged field, and nothing else.

To others who may be interested in studying the latter (formation of
tracks by charged particles) in more detail...

There's an extended treatment in Schiff's textbook, pp335-339. He uses
2nd-order perturbation theory to consider the probability of a fast
electron participating in an ionizing interaction with the electrons in
two separate atoms. The result is that the probability is very small
unless the atoms are on a line parallel to the momentum of the incident
electron (approximated as an incident plane wave field).

Thus, Mandel & Wolf are not the only ones who treat the subject in
this more careful way.

 

[meopemuk]

To others who may be interested in studying the latter (formation of
tracks by charged particles) in more detail...

There's an extended treatment in Schiff's textbook, pp335-339. He uses
2nd-order perturbation theory to consider the probability of a fast
electron participating in an ionizing interaction with the electrons in
two separate atoms. The result is that the probability is very small
unless the atoms are on a line parallel to the momentum of the incident
electron (approximated as an incident plane wave field).

Thus, Mandel & Wolf are not the only ones who treat the subject in
this more careful way.

strangerep,

I agree that some aspects of particle detection can be explained by Mandel & Wolf type arguments. However, there are situations, where these arguments fail completely. I think the most spectacular failure is related to electrons registered by a photographic plate. If you describe the incident electron by a plane wave or other continuous charge density field, you will have a hard time to explain how this distributed charge density condenses to a single location of one emulsion grain. I think it is well established that after "observation" the entire electron charge is located in the neighborhood of the blackened emulsion grain. Apparently, there should be a mechanism by which the distributed charge density condenses to a point and overcomes a strong Coulomb repulsion in the process. This doesn't look plausible even from the point of view of energy conservation.

Eugene.

 

[Physics Monkey]

Yes. particle tracks _are_ important; but because they allow one to measure the momentum of a particle. But particle position is irrelevant, and doesn't exist on the quantum field level.

I'm sorry, but this statement is simply false. I just gave an example where particle position is relevant. One can mention quantum fields all one wants, but that doesn't change the fact that as a practical matter particle positions can be meaningful and useful approximations. Even in quantum field theory.

 

[A. Neumaier]

I'm sorry, but this statement is simply false. I just gave an example where particle position is relevant. One can mention quantum fields all one wants, but that doesn't change the fact that as a practical matter particle positions can be meaningful and useful approximations. Even in quantum field theory.

I have nothing against particle positions as meaningful and useful semiclassical _approximations_, as is appropriate for particles assumed to have collapsed already, and hence described by an effective particle picture along a track. This is a change of the representation, simplifying the picture and the analysis in cases where the physics allows this.

Nevertheless, even in a track, one only has a measurement of the projection of the position on the plane transversal to the momentum.

But before the detector is reached, there is just a radially expanding quantum field for each particle kind involved in the decay (before and after), and Mott's analysis applies. The secondary bubble traces start at random positions along the track, for the same reason that the primary trace start at a random position anywhere at the surface of the detector where the field density is large enough and continues inside the detector.

 

[A. Neumaier]

the most spectacular failure is related to electrons registered by a photographic plate. If you describe the incident electron by a plane wave or other continuous charge density field, you will have a hard time to explain how this distributed charge density condenses to a single location of one emulsion grain.

Mott even explains how a complete particle track appears in a bubble chamber - caused by a classical external electromagnetic field reaching the detector from a particular direction.

 

[A. Neumaier]

I agree with you that parameter x in quantum field \psi(x,t) has absolutely no relationship to physically measurable position.

We completely disagree. There is indeed no relation to an alleged particle position.

But the parameters x and t in a quantum field have the definite meaning of position and time - not of a particle, but of the point where the field strength is measured. The rate of response of the detector at position x at time t is for a photon proportional to the intensity <|E(x,t)|^2>, where E(x,t) is the complex analytic signal of the electric field operator, and for an electron proportional to the intensity <|Psi(x,t)|^2>, where Psi(x,t) is the Dirac field operator.

You were correct to point out that in the case of indistinguishable particles this does not allow to form a Hermitian "particle position" operator. But the above construction of n-particle localized states is sufficient to describe position measurements in the Fock space.

The radial wave produced by a double slit is not a localized state.

Another point is that refusing the measurability of positions you are are not saving yourself from the "weird" quantum collapse. You've mentioned elsewhere that the momentum-space wavefunction \psi(p) does have a measurable probabilistic interpretation. So, it does require a collapse. This time in the momentum space.

There is only an apparent collapse due to changing the description before and after reaching the detector. Discontinuities caused by changes in the description level are ubiquitous in physics - whether classical or quantum.

Our difference is that I believe that the blackening of silver atoms or the formation of bubbles are direct local effects of incident particles. So, by measuring positions of exposed grains of photoemulsion or bubbles we measure (albeit indirectly) positions of particles, which created these effects.

I know. Whereas I interpret it in terms of quantum fields, which have a much more benign intuitive interpretation, and also apply to electromagnetic radiation, where your interpretation breaks down.

If I understand correctly, your position is that the blackened grain of photoemulsion or the formed bubble is not a proof that the particle really hit that spot.

Instead, it is proof that there is an incident quantum field.

creation of the local photographic image or a small bubble is "explained" by a sequence of non-trivial condensation events happening in the bulk of the detector. These events require migration of charge to macroscopic distances

Of charge density. But charge density migrates over macroscopic distances also during the flight from the source to the detector - there is nothing strange about it.

If I understand correctly, your motivation for applying these non-trivial models of particle detection is to avoid using the quantum-mechanical wave function collapse.

No. My motivation is to have a consistent intuitive view of quantum field theory, which since over half a century is regarded as the correct description of microscopic physics, with ''particles are just bundles of energy and momentum of the fields'' (Weinberg).

That one doesn't need the collapse is just a welcome byproduct of this view.

 

[meopemuk]

I know. Whereas I interpret it in terms of quantum fields, which have a much more benign intuitive interpretation, and also apply to electromagnetic radiation, where your interpretation breaks down.

Is there a single example, where the corpuscular interpretation "breaks down", as you say?

Of charge density. But charge density migrates over macroscopic distances also during the flight from the source to the detector - there is nothing strange about it.

I can understand a charge wave that propagates and spreads out. However, I have a difficulty to imagine a wave that collapses to a point spontaneously. Which physical mechanism can be responsible for such a collapse?

That one doesn't need the collapse is just a welcome byproduct of this view.

I think that the discovery of the quantum nature of things, sometimes dubbed "collapse", was the single most important discovery in 20th century physics. I know that we disagree about that.

Eugene.

 

[A. Neumaier]

Is there a single example, where the corpuscular interpretation "breaks down", as you say?

Photons have no position; they disappear upon the attempt to measure any of their properties. It is only continuous brain washing that calls such ghost-like objects particles.

I can understand a charge wave that propagates and spreads out. However, I have a difficulty to imagine a wave that collapses to a point spontaneously. Which physical mechanism can be responsible for such a collapse?

In my understanding there is no collapse and there need not be one. The collapse is an artifact of the point particle interpretation of quantum mechanics.

I think that the discovery of the quantum nature of things, sometimes dubbed "collapse", was the single most important discovery in 20th century physics. I know that we disagree about that.

Collapse is not the quantum nature of things, but the least understood aspects of quantum mechanics. QM is an extremely successful description of Nature no matter whether one believes in collapse.

 

[meopemuk]

Photons have no position; they disappear upon the attempt to measure any of their properties. It is only continuous brain washing that calls such ghost-like objects particles.

There is nothing strange in the fact that photons can be created and absorbed easily. This is described naturally in QFT, which is a theory designed to work with systems, where the number of particles can change.

In my understanding there is no collapse and there need not be one. The collapse is an artifact of the point particle interpretation of quantum mechanics.

Collapse is not the quantum nature of things, but the least understood aspects of quantum mechanics. QM is an extremely successful description of Nature whether one believes in collapse.

I think we agree that in the double-slit setup the locations of marks on the photographic plate are random. I hope we also agree that the clicks produced by a Geiger counter attached to a piece of radioactive material occur at random times. At least, it is fair to say that nobody was able to predict locations of individual marks or timings of individual clicks.

In my understanding, quantum mechanics says that these kinds of events are not predictable as a matter of principle. Nature has an inherently random component, which cannot be explained. The best we can do is to calculate probabilities of these random events. That's what quantum mechanics is doing and it is doing it brilliantly. Once we agreed on the fundamental randomness of quantum events, there is no other way, but to accept the idea of collapse: The outcomes are not known to us before observations, they are described only as probability distributions. After the observation is made a single outcome emerges, so the probability distribution collapses.

There is nothing there to understand about the collapse. Things that are fundamentally random cannot be explained or understood any better than simply saying that they are random.

From my discussions with you I've understood that you have a different view on the origin of randomness. You basically believe that nature obeys deterministic field-like equations. The appearance of a mark on the photographic plate has a mechanistic explanation in which the impacting electron field interacts with the fields of atoms in the plate. This interaction leads to some physical migration of the field energy and charge density to one specific point, which appears to us as a blackened AgBr microcrystal. These migration processes involve huge number of atoms, so they are "stochastic" or "chaotic", and their outcomes cannot be predicted at our current level of knowledge. Nevertheless, you maintain that at the fundamental level there are knowable field equations as opposed to the pure chance.

These are two different philosophies, two different world views, which could be completely equivalent as far as specific experimental observations are concerned. In general, I find it not fruitful to argue about ones philosophy, religion or political preferences. These kinds of convictions cannot be changed by logical arguments. So, perhaps we should agree to disagree.

Eugene.

 

[A. Neumaier]

There is nothing strange in the fact that photons can be created and absorbed easily. This is described naturally in QFT, which is a theory designed to work with systems, where the number of particles can change.

An entity about which we can say nothing at all during its flight from the source to the detector, which never has a position, produces a spot on a plate and at this moment disappears forever. This is a perfect description of a ghost, whereas calling it a particle is an unfortunate historical accident. Everyone beginning to study quantum mechanics finds this extremely strange and un-particle-like. Not to find that strange is the result of years of indoctrination by famous and less famous kindergarden storytellers. That the most famous of them had won a Nobel prize helped in making the brainwashing more efficient.

Nature has an inherently random component, which cannot be explained.

I explain is as microscopic chaos in the detector.

The best we can do is to calculate probabilities of these random events. That's what quantum mechanics is doing and it is doing it brilliantly. Once we agreed on the fundamental randomness of quantum events, there is no other way, but to accept the idea of collapse: The outcomes are not known to us before observations, they are described only as probability distributions. After the observation is made a single outcome emerges, so the probability distribution collapses.

Nobody but you calls the change of prior probabilities into posterior certainties a collapse.

Collapse _always_ refers to the collapse of the state - that after the measurement, the state of the measured system is in an eigenstate of the measured observable!

You basically believe that nature obeys deterministic field-like equations.

No. Nature obeys the rules of QFT, and all macroscopic information arrives in the form of expectation values of appropriate fields, as given by statistical thermodynamics, the quantum theory of macroscopic matter. This is enough to explain everything without assuming a collapse of the state. (What you call collapse, but what others label a change of probabilities into certainties is fully explained by the subjective inability to predict a chaotic system with zillions of degrees of freedom.)

Nevertheless, you maintain that at the fundamental level there are knowable field equations as opposed to the pure chance.

Field equations are operator equations. What is knowable are the field expectations at macroscopic resolutions. Engineers measure them routinely.

These are two different philosophies, two different world views, which could be completely equivalent as far as specific experimental observations are concerned. In general, I find it not fruitful to argue about ones philosophy, religion or political preferences.

I find it _very_ fruitful to argue about ones philosophy, religion or political preferences.
This is the only way to influence people's convictions.

These kinds of convictions cannot be changed by logical arguments. So, perhaps we should agree to disagree.

We always agreed that we disagree, from the start of this thread. But we draw different consequences from this fact.

 

[meopemuk]

Nobody but you calls the change of prior probabilities into posterior certainties a collapse.

Collapse _always_ refers to the collapse of the state - that after the measurement, the state of the measured system is in an eigenstate of the measured observable!

I've forgotten to mention that I am not interested in the state of the quantum system after it has "interacted" with the measuring device and produced the measurement outcome. So, I am agnostic about the state after the measurement. Yes, I understand that there are situations when one can measure repeatedly different things on the same copy of the system. However, I would like to avoid discussions of such situations. So, I would prefer to think that after the measurement is done and its result is recorded, the system is discarded. Dealing only with such one-time measurements makes my life a bit easier.

So, I agree that collapse = "the change of prior probabilities into posterior certainties". However, I disagree that the collapse ever happens in classical physica, because in classical physics everything is determined and predictable. If somebody has encountered a "probability" in classical physics, that's only because this somebody was too lazy or ignorant to specify exactly all necessary initial conditions. Somebody's ignorance and laziness cannot be accounted for in a rigorous theory. "Zillions of degrees of freedom" is also not a good excuse to introduce probabilities, because we are talking about principles here, not about practical realizations.

Eugene.

 

[unusualname]

It should be pointed out that A Neumaier's suggestion that a deterministic chaotic dynamics may underly quantum randomness is not the standard view, and to even be consistent with modern experimental results requires some additional weird assumptions such as explicit non-locality (Bohm) or information loss behind event horizons ('t Hooft).

http://www.nature.com/news/2007/070416/full/news070416-9.html

 

[A. Neumaier]

I've forgotten to mention that I am not interested in the state of the quantum system after it has "interacted" with the measuring device and produced the measurement outcome. So, I am agnostic about the state after the measurement.

But this means that you are agnostic about collapse, as the term is traditionally understood: ''In quantum mechanics, wave function collapse (also called collapse of the state vector or reduction of the wave packet) is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer.'' http://en.wikipedia.org/wiki/Wavefunction_collapse

So, I agree that collapse = "the change of prior probabilities into posterior certainties".

You only agree to your own nonstandard interpretation of the word ''collapse''. I don't agree at all with this usage.

"Zillions of degrees of freedom" is also not a good excuse to introduce probabilities, because we are talking about principles here, not about practical realizations.

''Unperformed experiments have no results'' (A. Peres, Amer. J. Phys. 46 (1978), 745).
This holds even more for unperformable measurements or preparations.

 

[A. Neumaier]

It should be pointed out that A Neumaier's suggestion that a deterministic chaotic dynamics may underly quantum randomness is not the standard view, and to even be consistent with modern experimental results requires some additional weird assumptions such as explicit non-locality (Bohm) or information loss behind event horizons ('t Hooft).

It is enough to assume information loss to the part of the universe not visible from our planetary system (where all our experiments are done). Radiation goes there all the time; so this assumption is satisfied.

http://www.nature.com/news/2007/070416/full/news070416-9.html

The paper says nothing about requiring weird assumptions. But the author states: ''But for objects governed by the laws of quantum mechanics, like photons and electrons, it may make no sense to think of them as having well defined characteristics. Instead, what we see may depend on how we look.''

depend on how wee look = depend on the measurement apparatus (here our eye).

Thus his statement confirms my hypothesis.

 

[unusualname]

It is enough to assume information loss to the part of the universe not visible from our planetary system (where all our experiments are done). Radiation goes there all the time; so this assumption is satisfied.

Radiation travels via a local mechanism, are you saying your deterministic model is local and real?

The paper says nothing about requiring weird assumptions. But the author states: ''But for objects governed by the laws of quantum mechanics, like photons and electrons, it may make no sense to think of them as having well defined characteristics. Instead, what we see may depend on how we look.''

depend on how wee look = depend on the measurement apparatus (here our eye).

Thus his statement confirms my hypothesis.

Shouldn't you say that statement doesn't contradict your model, rather than asserting it confirms it.

I added that link to a mainstream science article to point out the mainstream view on quantum interpretation, just in case people think your "science advisor" tag adds credibility to your nonstandard view.

But I'm not saying you're wrong, just that it's an an unusual model to be promoting.

 

[meopemuk]

But this means that you are agnostic about collapse, as the term is traditionally understood: ''In quantum mechanics, wave function collapse (also called collapse of the state vector or reduction of the wave packet) is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer.'' http://en.wikipedia.org/wiki/Wavefunction_collapse

I've possibly created a confusion by using my own definition of collapse, which is different from the wikipedia's one. To clarify, I would like to mention that I am interested only in single measurements of observables. I am not interested in what is the state of the system after the measurement is completed. I am not sure if wave function is a good description for such states.

Eugene.

 

[strangerep]

I agree that some aspects of particle detection can be explained by Mandel & Wolf type arguments. However, there are situations, where these arguments fail completely. I think the most spectacular failure is related to electrons registered by a photographic plate. If you describe the incident electron by a plane wave or other continuous charge density field, you will have a hard time to explain how this distributed charge density condenses to a single location of one emulsion grain. I think it is well established that after "observation" the entire electron charge is located in the neighborhood of the blackened emulsion grain. Apparently, there should be a mechanism by which the distributed charge density condenses to a point and overcomes a strong Coulomb repulsion in the process. This doesn't look plausible even from the point of view of energy conservation.

In that case, what is wrong with Mott's or Schiff's analyses (which apply for incident
field carrying charge)? To me these seem adequate to account for the experimental
observations.

 

[A. Neumaier]

Radiation travels via a local mechanism, are you saying your deterministic model is local and real?

My interpretation is not deterministic, since it is based on standard QFT. But like the latter it is local.

By the way, there are no no-go theorems against deterministic field theories underlying quantum mechanics. Indeed, local field theories have no difficulties violating Bell-type inequalities. See http://arnold-neumaier.at/ms/lightslides.pdf , starting with slide 46.

Shouldn't you say that statement doesn't contradict your model, rather than asserting it confirms it.

If a key statement that wasn't known to the proposer of some model doesn't contradict this model, it is usually considered as a confirmation of the model. In the present case, since you brought the paper as argument to caution readers against my views, and my main assumption was that the results of measurements depend on the detector, and the author of the paper made precisely this point (for the special detector called us - or our yes), it is a significant confirmation.

I added that link to a mainstream science article to point out the mainstream view on quantum interpretation, just in case people think your "science advisor" tag adds credibility to your nonstandard view.

I am not reponsible for having this tag.

But I'm not saying you're wrong, just that it's an an unusual model to be promoting.

I am only taking quantum field theory seriously. It is not that unusual: People working on dynamic reduction models have a very similar view:

G. Ghirardi,
Quantum dynamical reduction and reality:
Replacing probability densities with densities in real space,
Erkenntnis 45 (1996), 349-365.
http://www.jstor.org/stable/20012735

My only new point compared to them is that one doesn't need the dynamic reduction once one has the field density ontology.