Tracks in particle detectors and quantum paths

[TrickyDicky]

How are the track leftt say by an electron in a cloud chamber and its wave function undefined trajectory related exactly?

 

[Vanadium 50]

Related exactly? Pretty much the same way they are related approximately.

This is a terribly vague question. You'll need to be more specific if you want any hope of getting the answer you are looking for. If it helps, the laws of quantum mechanics apply to baseballs and planets too.

 

[CWatters]

How are the track leftt say by an electron in a cloud chamber and its wave function undefined trajectory related exactly?

Very different scales.

 

[TrickyDicky]

Related exactly? Pretty much the same way they are related approximately.

This is a terribly vague question. You'll need to be more specific if you want any hope of getting the answer you are looking for. If it helps, the laws of quantum mechanics apply to baseballs and planets too.

Hi V50, I was specifically concerned about the quantum picture of particles such as electrons not having a defined trajectory, i.e. double slit settings(thus my placing the question in the QM subforum) in contrast with the clear path followed by an electron as shown in the tracks left in cloud chambers. What is the commonly given explanation to this apparent contrast?

 

[TrickyDicky]

I was interested in a discussion about collapse, the measurement problem or even the quantum Zeno effect, but I can see that it is going to be mighty hard here in general physics.

 

[stevendaryl]

Hi V50, I was specifically concerned about the quantum picture of particles such as electrons not having a defined trajectory, i.e. double slit settings(thus my placing the question in the QM subforum) in contrast with the clear path followed by an electron as shown in the tracks left in cloud chambers. What is the commonly given explanation to this apparent contrast?

The question of why linear tracks appear in cloud chambers is known as the Mott problem, named after the physicist who first investigated it in the 1920s. I found two discussions of it:
http://arxiv.org/pdf/1209.2665.pdf
http://en.wikipedia.org/wiki/Mott_problem

 

[jtbell]

Moved to Quantum Physics.

 

[TrickyDicky]

The question of why linear tracks appear in cloud chambers is known as the Mott problem, named after the physicist who first investigated it in the 1920s. I found two discussions of it:
http://arxiv.org/pdf/1209.2665.pdf
http://en.wikipedia.org/wiki/Mott_problem

Thanks for the pertinent reference to the Mott problem, I very vaguely remember having read about it but had completely forgotten it. I'll take some time to read the references through.

 

[ZapperZ]

Hi V50, I was specifically concerned about the quantum picture of particles such as electrons not having a defined trajectory, i.e. double slit settings(thus my placing the question in the QM subforum) in contrast with the clear path followed by an electron as shown in the tracks left in cloud chambers. What is the commonly given explanation to this apparent contrast?

This is a terrible concept. There are large number of situations where the classical picture of electron trajectory works! Look at the description we use to describe the beam physics for particle accelerators! They are all classical! Beam physics codes that we use, such as PAMELA, to track electron beams all consider them to be classical particles. The electron analyzers that are used to measure and detect photoelectrons, all considered these electrons having classical trajectories from the emitting surface all the way to the CCD plate!

Why would the description for the tracks in such particle detectors be any different?

Zz.

 

[stevendaryl]

This is a terrible concept. There are large number of situations where the classical picture of electron trajectory works! Look at the description we use to describe the beam physics for particle accelerators! They are all classical! Beam physics codes that we use, such as PAMELA, to track electron beams all consider them to be classical particles. The electron analyzers that are used to measure and detect photoelectrons, all considered these electrons having classical trajectories from the emitting surface all the way to the CCD plate!

Why would the description for the tracks in such particle detectors be any different?

Zz.

Well, let me quote Bohr's paraphrase of Einstein's statement of the problem:

Mr. Einstein has considered the following problem: A radioactive sample emits α-particles in all directions; these are made visible by the method of the Wilson cloud chamber. Now, if one associates a spherical wave with each emission process, how can one understand that the track of each α-particle appears as a (very nearly) straight line? In other words: how can the corpuscular character of the phenomenon be reconciled here with the representation by waves?

 

[ZapperZ]

I'm not sure I understand the point in relation to what I wrote.

A laser makes a very predictable path for the photons in its beam. Do you represent that with "spherical waves"? Why spherical waves? Why not plane waves as we would normally consider?

Secondly, I don't see how this has anything to do with the "wavefunction" that we use to describe a quantum system.

Zz.

 

[stevendaryl]

I'm not sure I understand the point in relation to what I wrote.

A laser makes a very predictable path for the photons in its beam. Do you represent that with "spherical waves"? Why spherical waves? Why not plane waves as we would normally consider?

Secondly, I don't see how this has anything to do with the "wavefunction" that we use to describe a quantum system.

Zz.

I thought the original question was about tracks in a cloud chamber, which is what the Bohr quote is about.

 

[ZapperZ]

I thought the original question was about tracks in a cloud chamber, which is what the Bohr quote is about.

It was, but you quoted that in relation to my response. I don't know what the point is in that context. Bohr's quote offered no insight into how to treat this problem other than rephrasing what Einstein has said.

It doesn't change the FACT that we do treat electrons as classical particles in many instances, with sufficient accuracy that the very device that we use to study elementary/high energy physics particles (particle colliders), were modeled with classical trajectories.

Zz.

 

[stevendaryl]

It was, but you quoted that in relation to my response.

I was trying to get back to what the actual puzzle was. I was trying to say that I think your response didn't actually address it.

I don't know what the point is in that context. Bohr's quote offered no insight into how to treat this problem other than rephrasing what Einstein has said.

It's a statement of what the puzzle is, it's not a statement of the solution. Your remarks, bringing up lasers, for instance, don't seem relevant. The explanation for why lasers seem to have definite tracks doesn't apply to particles in a cloud chamber. Or at least, I don't see any connection.

Once again, quoting one of the original researchers, Mott:

It is a little difficult to picture how it is that an outgoing spherical wave can produce a straight track; we think intuitively that it should ionise atoms at random throughout space.

 

[ZapperZ]

I was trying to get back to what the actual puzzle was. I was trying to say that I think your response didn't actually address it.

Why not? If I can model electron trajectory classically in an accelerator, what's the difference with doing it in a detector or cloud chamber? It is the same thing.

It's a statement of what the puzzle is, it's not a statement of the solution. Your remarks, bringing up lasers, for instance, don't seem relevant. The explanation for why lasers seem to have definite tracks doesn't apply to particles in a cloud chamber. Or at least, I don't see any connection.

Once again, quoting one of the original researchers, Mott:

I brought up lasers because the statement you quoted brought up "spherical waves", which was odd if that is the ONLY way to describe things. I brought up the instance where we DO have waves, i.e. light, in a laser, and we can still describe its trajectory very well when we have plane waves. So the laser was a counter example of a "wave" with definite trajectory. Waves do not always have to be spherical where the path diverges.

Take note that if the particles that we detect at the detectors can't be modeled classically as far as its trajectories are concerned, the whole concept of path reconstruction that is so common in elementary particle physics experiments can be thrown out of the window.

Zz.

 

[stevendaryl]

It's a statement of what the puzzle is, it's not a statement of the solution.

The link that I gave describes how the problem has been tackled
http://arxiv.org/pdf/1209.2665.pdf

To quote from the conclusion:

As it was pointed out before, according to Born and Heisenberg, it is definitely equivalent to consider the atom of the vapor as a (classical) measurement device (case a) or as a part of the quantum system to be described by Schrodinger dynamics (case b). Such a position is meant to guarantee the consistency of the standard interpretation of quantum theory. In particular, the authors are interested in stressing the unavoidable role of wave packet reduction as the crucial rule ensuring the right correspondence between theory and observed physical world. From a purely foundational point of view their reasoning aims to make the axiomatic scheme work in any chosen way to address the cloud chamber dynamical problem and, as such, it has been adopted and shared by the majority of the physics community for a long time. However, from the concrete point of view of the physical description of quantum systems, the equivalence of the two approaches a) and b) seems difficult to be maintained. In fact, one may find hard to accept the claim that an atom of the vapor is a classical measurement device of the position of the α-particle. After all, the atom is a microscopic system on the same ground of the α-particle and there is no a priori reason to regard it as a classical system. Agreeing with this point of view, one should concede that approach b) is surely more natural. In particular, it has the important advantage to allow a quantitative analysis taking into account explicitly the physical parameters characterizing system and environment. It is only on the basis of such a quantitative investigation that it is possible to clarify the conditions under which the interaction with the environment produces the appearance of classical trajectories.

 

[stevendaryl]

Why not? If I can model electron trajectory classically in an accelerator, what's the difference with doing it in a detector or cloud chamber? It is the same thing.

Well, there might be a similar question as to why it's possible to model electron trajectories classically in an accelerator. So maybe they are related.

I brought up lasers because the statement you quoted brought up "spherical waves", which was odd if that is the ONLY way to describe things.

The point is that, at least with a simplified model of alpha decay, the alpha particle leaves the nucleus in a spherical wave. Nobody was suggesting that ALL problems are spherically symmetric.

I brought up the instance where we DO have waves, i.e. light, in a laser, and we can still describe its trajectory very well when we have plane waves.

The Mott problem is about reconciling a spherically symmetric model with outcomes that very much are not spherically symmetric. I just don't see the relevance of bringing up lasers. It's as if I said "How can a needle float on water, when it's made of steel?" and you answered by saying "Corks float, too, and they're not made of steel."

Take note that if the particles that we detect at the detectors can't be modeled classically as far as its trajectories are concerned, the whole concept of path reconstruction that is so common in elementary particle physics experiments can be thrown out of the window

I don't think that there is any doubt about the use of particle tracks. The question is how to reconcile the observations of tracks and definite trajectories with the theory, which does not appear to have definite trajectories.

 

[atyy]

The problem can be treated as continuous approximate measurement of a quantum wave function.

http://arxiv.org/abs/math-ph/0512069
A Dynamical Theory of Quantum Measurement and Spontaneous Localization
V. P. Belavkin

We develop a rigorous treatment of discontinuous stochastic unitary evolution for a system of quantum particles that interacts singularly with quantum "bubbles" at random instants of time. This model of a "cloud chamber" allows to watch and follow with a quantum particle along the trajectory in the cloud chamber by sequential unsharp localization of spontaneous scatterings of the bubbles. Thus, the continuous reduction and spontaneous localization theory is obtained as the result of quantum filtering theory, i.e., a theory describing the conditioning of the a priori quantum state by the measurement data. We show that in the case of indistinguishable particles the a posteriori dynamics is mixing, giving rise to an irreversible Boltzmann-type reduction equation. The latter coincides with the nonstochastic Schroedinger equation only in the mean field approximation, whereas the central limit yields Gaussian mixing fluctuations described by stochastic reduction equations of diffusive type.Side note: Why can a single free particle often be treated as if there is a classical distribution of trajectories, without resorting to a Bohmian interpretation? In general this is not possible. The closest thing to a classical probability distribution is the Wigner function, but it is not a probability distribution because it is not positive. However, for a Gaussian wave function, the Wigner function is positive, and if the particle is free, the time evolution of the function is the same as the classical Liouville equation. This is why a single free particle can often be treated as if there is a classical distribution of trajectories.

Furthermore, even when the wave function is not Gaussian, although it is wrong to consider classical trajectories, the fully quantum derivation and the classical derivation sometimes lead to the same formula. This should be considered a lucky accident, just like Rutherford scattering for an inverse-square potential gives the same results whether it is treated classically or quantum mechanically.

 

[StrangeCoin]

This is a terrible concept. There are large number of situations where the classical picture of electron trajectory works! Look at the description we use to describe the beam physics for particle accelerators! They are all classical! Beam physics codes that we use, such as PAMELA, to track electron beams all consider them to be classical particles. The electron analyzers that are used to measure and detect photoelectrons, all considered these electrons having classical trajectories from the emitting surface all the way to the CCD plate!

Why would the description for the tracks in such particle detectors be any different?

Zz.

So for example in bubble chambers, is there any reason to believe the electron is not exactly in the center of those bubbles and not travailing over continuous path those bubbles describe?

Every time we can measure it we see defined continuous trajectories, every time we can not measure it, we assume it's doing something else. Inability to measure with some desired precision is usually referred to as "margin of error", it's a property of measuring tools, not really a property of what is being measured. Why then in QM this "margin of error" is considered to be an actual property of what is being measured, rather than just a consequence of inadequate measuring tools?

 

[ZapperZ]

So for example in bubble chambers, is there any reason to believe the electron is not exactly in the center of those bubbles and not travailing over continuous path those bubbles describe?

Every time we can measure it we see defined continuous trajectories, every time we can not measure it, we assume it's doing something else. Inability to measure with some desired precision is usually referred to as "margin of error", it's a property of measuring tools, not really a property of what is being measured. Why then in QM this "margin of error" is considered to be an actual property of what is being measured, rather than just a consequence of inadequate measuring tools?

I have no idea what you are talking about.

If you are referring to instrumentation uncertainty versus the Heisenberg uncertainty, this has been discussed and described numerous times already on here. They are not the same thing.

Otherwise, I see no relevance with the topic of this thread.

Zz.

 

[TrickyDicky]

The problem has been now well formulated by Steven. About the apparently preferred solution since it was proposed by Mott of introducing the environment in the analysis to solve the paradox, I have some doubts. The way I see it it is only a superficial solution in the sense that it doesn't address the bottom of the problem, for instance it doesn't really give a hint towards solving the measurement problem, it doesn't explain collapse,and it would seem this is really behind the Mott problem.
Besides, saying that integrating the environment clarifies why we observe classical linear tracks intead of what it would be expected in theory from spherically symmetric wavefunctions might give some insight but it basically defeats the concept of quantum particles as individual microscopic objects related to spherical wavefunctions, which is the starting point of the quantum theory.

FWIW the problem is IMO intimately related with the unitarity-non unitarity problem that is being discussed in a parallel thread.

 

[Nugatory]

The way I see it it is only a superficial solution in the sense that it doesn't address the bottom of the problem, for instance it doesn't really give a hint towards solving the measurement problem, it doesn't explain collapse,and it would seem this is really behind the Mott problem.

"Superficial" is somewhat in the eye of the beholder. If you don't demand more of QM than that it provide statistical predictions of the results of measurements, the Mott solution is altogether satisfactory and even provides a great deal of insight into how the microscopic and the macroscopic worlds are connected in the formalism of QM. It's not at all clear to me that the formalism of QM is the place to be looking if you want anything more.

Besides, saying that integrating the environment clarifies why we observe classical linear tracks intead of what it would be expected in theory from spherically symmetric wavefunctions might give some insight but it basically defeats the concept of quantum particles as individual microscopic objects related to spherical wavefunctions, which is the starting point of the quantum theory.

Wave descriptions (not necessarily spherical) of individual microscopic particles may be where quantum mechanics started, but it long ago grew beyond that early formulation of the problem. Quantum mechanically two entangled particles in the singlet state are not two microscopic particles; they're a single quantum system with a single wavefunction and two sets of observables on that system. Including the environment increases the complexity of the system (enough that completely different computational methods may be needed) but even before we include it, we've lost any sense of individual microscopic particles.

 

[atyy]

The question of why linear tracks appear in cloud chambers is known as the Mott problem, named after the physicist who first investigated it in the 1920s. I found two discussions of it:
http://arxiv.org/pdf/1209.2665.pdf
http://en.wikipedia.org/wiki/Mott_problem

The problem can be treated as continuous approximate measurement of a quantum wave function.

http://arxiv.org/abs/math-ph/0512069
A Dynamical Theory of Quantum Measurement and Spontaneous Localization
V. P. Belavkin

It's interesting to compare these two approaches. The review by Figari and Teta http://arxiv.org/abs/1209.2665v1 says that conceptually Born and Heisenberg thought the problem could be treated in two equivalent ways. One in which (a) the molecules are considered to measure the system causing wave function collapse, the other (b) in which the molecules decohere the system. Mott's approach and updates like Dell'Antonio, Figari and Testa's http://arxiv.org/abs/0907.5503 and Blasi, Pascazio and Takagi's http://www.ba.infn.it/~pascazio/publications/Particle_tracks_and_the_mechanis.pdf seem to follow (b), while Belavkin's http://arxiv.org/abs/math-ph/0512069 seems to follow (a).

 

[Jilang]

I don't think any of the above answers have really addressed the question as asked. The cloud chamber relies on a series of interactions which cause ionisation. These events are frequent in the path of the particle and constitute a series of measurements. The trajectory is only undefined between those interactions.

 

[atyy]

I don't think any of the above answers have really addressed the question as asked. The cloud chamber relies on a series of interactions which cause ionisation. These events are frequent in the path of the particle and constitute a series of measurements. The trajectory is only undefined between those interactions.

My understanding is that that is essentially Belavkin's approach.

 

[StrangeCoin]

If you are referring to instrumentation uncertainty versus the Heisenberg uncertainty, this has been discussed and described numerous times already on here. They are not the same thing.

I am referring to instrumentation uncertainty being misinterpreted as an actual property of what is being measured. I believe that's exactly what the OP question is about. You don't say electron position is undefined because you measured that to be true, but because you couldn't measure any better. Isn't that right?

So now on one hand we have the thing we can actually measure, the bubble chamber trajectories, which are apparently continuous and very well defined. And on the other hand we have QM theory which wants us to believe the opposite, that electron is actually doing something else, but it sneakily only does so when we are not looking. Apart from being funny, is there any actual reason to believe this theory based on unsuccessful measurements, rather than to believe what is obvious from those measurements that were successful?

 

[TrickyDicky]

Including the environment increases the complexity of the system (enough that completely different computational methods may be needed) but even before we include it, we've lost any sense of individual microscopic particles.

Yes, that might be so and we could debate what that loss means for the theory, but when I say I'm not convinced by the explanatory power of introducing the environment to explain the classical behaviour of a quantum system I'm referring for instance to the fact that if we apply this same logic to electrons in an atom we find serious problems not to conclude that this electrons should also follow classic trajectories within the atom and they probably should crash into the nucleus they orbit. We don't because we know well that the uncertainty principle forbids it. I'm not sure exactly how the HUP is avoided in the solution of the Mott problem.

The cloud chamber relies on a series of interactions which cause ionisation. These events are frequent in the path of the particle and constitute a series of measurements. The trajectory is only undefined between those interactions.

Here what happens "between interactions" is such a key factor wrt the trajectory that is actually measured as the outcome of those interactions compared to what the theory implies that nothing is really explained by referring to it with "only undefined".

 

[atyy]

The track in a cloud chamber is not a precise measurement of position. It consists of successive imprecise position measurements. Heuristically, this is why the track can be considered a precise momentum measurement.

As for what happens in between these imprecise measurements, the time between them can be taken to zero, such that the process describes continuous imprecise measurement.

 

[Nugatory]

I'm referring for instance to the fact that if we apply this same logic to electrons in an atom we find serious problems not to conclude that this electrons should also follow classic trajectories within the atom and they probably should crash into the nucleus they orbit. We don't because we know well that the uncertainty principle forbids it.

What does the uncertainty principle have to do with the observation that electrons do not "crash into the nucleus"? And how does applying "this same logic" about including the environment in the Hamiltonian of a bound electron lead to the conclusion that the electron should follow a classical trajectory?

These are questions not arguments, because I honestly don't understand what you're saying well enough to argue with it.

 

[TrickyDicky]

The track in a cloud chamber is not a precise measurement of position.

The track describes the classical trajectory of a quantum system, this is what Mott, Heisenberg, Born and Darwin as explained in the rerence provided by stevendaryl were trying to explain within the quantum formalism. A classical trajectory has well defined momentum and position, that is what's classical about it and what seems to clash with quantum theory in the context of the yet unsolved measurement problem.

It consists of successive imprecise position measurements.

Yes, that's the premise, Mott et al. are trying to explain, how do we go from individual imprecise measurements that should lead to not definite trajectories to a classical trajectory. The arguments used by these authors: the classical detectors and the environment. If they are valid it seems like they could be also applied in principle to situations where we don't observe clasical trajectories, like electrons in an atom, but here it is not used basically on the grounds that the HUP forbids well defined orbits(see for instance PF physics FAQ footnote on why electrons don't crash into the nucleus).

Heuristically, this is why the track can be considered a precise momentum measurement.

Too heuristic, as I said in as much as it is considered a classical trajectory the track can be considered to have position as precisely measured as momentum.

 

[stevendaryl]

I am referring to instrumentation uncertainty being misinterpreted as an actual property of what is being measured. I believe that's exactly what the OP question is about. You don't say electron position is undefined because you measured that to be true, but because you couldn't measure any better. Isn't that right?

No, not really. You seem to be suggesting that quantum uncertainty only reflects our ignorance of the true position of particles. That was certainly what Einstein thought. But subsequent experiments and analysis show that that claim is doubtful. That's a hidden-variables theory, which isn't COMPLETELY ruled out, but there are reasons to be skeptical. It seems that there is no such hidden-variables theory that doesn't involve strange instantaneous interactions between distant particles.

So now on one hand we have the thing we can actually measure, the bubble chamber trajectories, which are apparently continuous and very well defined. And on the other hand we have QM theory which wants us to believe the opposite, that electron is actually doing something else, but it sneakily only does so when we are not looking. Apart from being funny, is there any actual reason to believe this theory based on unsuccessful measurements, rather than to believe what is obvious from those measurements that were successful?

Yes, because even though quantum mechanics seems weird, it CORRECTLY describes every experiment ever performed, while the common-sensical belief that holds that particles really do have precise positions, we just don't know what those are unless we measure them, has not been successful.

If it were really the case that bubble-chamber results contradicted quantum mechanics, that would be big news, and we would throw out quantum mechanics. But they don't contradict quantum mechanics (even though it is a little work to see why not).

 

[TrickyDicky]

What does the uncertainty principle have to do with the observation that electrons do not "crash into the nucleus"?

I'm just referring to the usual argument that HUP is incompatible with well defined orbits to begin with so it wouldn't allow even the starting point for considering that an "orbiting" electron could crash into the nucleus since it doesn't follow a defined path, just has a probability cloud for its position in the atom, which might even coincide with the nucleus position with some not vanishing probability.(See PF FAQ on this https://www.physicsforums.com/showthread.php?t=511179 )

And how does applying "this same logic" about including the environment in the Hamiltonian of a bound electron lead to the conclusion that the electron should follow a classical trajectory?

If one includes the electron's environment(photon cloud, nucleus, polarized vacuum, other quantum particles...) in the analysis or uses these elements surrounding the electron in the atom as classical measurement devices and performs the same operations Mott does for the setting of the quantum particle in the cloud chamber, one might naively expect to also compute a classical trajectory for the electron in a stable ground state atom. It would be interesting to list the main differences in the scenarios that prevent this.

 

[stevendaryl]

What does the uncertainty principle have to do with the observation that electrons do not "crash into the nucleus"?

I consider that one of the primary issues that led to the development of quantum mechanics: A classical model of a positive electron orbiting a negatively charged nucleus is unstable; the electron would radiate and fall into the nucleus. The uncertainty principle implies a minimum value for the electron's energy. So there is a connection between the two. I assume that's what TrickyDicky meant.

 

[stevendaryl]

Yes, that's the premise, Mott et al. are trying to explain, how do we go from individual imprecise measurements that should lead to not definite trajectories to a classical trajectory. The arguments used by these authors: the classical detectors and the environment. If they are valid it seems like they could be also applied in principle to situations where we don't observe clasical trajectories, like electrons in an atom...

I don't think there is any necessary conflict between the two. The environment of an electron within an atom is very different from the environment of a high-energy particle in a bubble or cloud chamber. The way I understand it, the appearance of definite trajectories in a bubble/cloud chamber is due to collisions of the particle in question with much more massive atoms.

 

[Nugatory]

I'm just referring to the usual argument that HUP is incompatible with well defined orbits to begin with so it wouldn't allow even the starting point for considering that an "orbiting" electron could crash into the nucleus since it doesn't follow a defined path, just has a probability cloud for its position in the atom, which might even coincide with the nucleus position with some not vanishing probability.(See PF FAQ on this https://www.physicsforums.com/showthread.php?t=511179 )

ZapperZ edited that FAQ, so maybe you should listen to him not me... But it seems pretty clear to me that you're misunderstanding it. The uncertainty principle is (literally) just a footnote and the essential part of the explanation is the QM prediction of stable states as the solution to Schodinger's equation.

If one includes the electron's environment(photon cloud, nucleus, polarized vacuum, other quantum particles...) in the analysis or uses these elements surrounding the electron in the atom as classical measurement devices and performs the same operations Mott does for the setting of the quantum particle in the cloud chamber, one might naively expect to also compute a classical trajectory for the electron in a stable ground state atom. It would be interesting to list the main differences in the scenarios that prevent this.

You would have to be very naive indeed to expect that. The main difference is that in the case of a bound electron, the contribution of these environmental factors to the Hamiltonian is small compared with the central force. In the cloud chamber case the interaction of the particle with the environment isn't negligible - it's the only interaction present for the unbound particle.

 

[TrickyDicky]

If it were really the case that bubble-chamber results contradicted quantum mechanics, that would be big news, and we would throw out quantum mechanics.

This way of putting it I think it dramatizes it unnecessarily. Certainly it is not the purpose of this thread to throw out anything, on the contrary QM as a theory is robust enough to tackle all these only apparent contradictions. It makes little sense that particle detectors and scattering in general contradicts in any way QM, particle physicists would be quite amused.

It is in the nature of the theory not to cling to a unique graphical representation like it was the case in classical mechanics, and to allow different sometimes apparently contradictory approximate and relative representations that together with the mathematical formalism conform QM.

The environment of an electron within an atom is very different from the environment of a high-energy particle in a bubble or cloud chamber. The way I understand it, the appearance of definite trajectories in a bubble/cloud chamber is due to collisions of the particle in question with much more massive atoms.

Yes, it is different in many aspects, I'm not sure that the mass of the environment microparticles is the main one though.

 

[stevendaryl]

ZapperZ edited that FAQ, so maybe you should listen to him not me... But it seems pretty clear to me that you're misunderstanding it. The uncertainty principle is (literally) just a footnote and the essential part of the explanation is the QM prediction of stable states as the solution to Schrodinger's equation.

It might be a matter of semantics, but I don't consider the Schrodinger equation to be an alternative to reasoning using the uncertainty principle. It's a mathematically precise way of doing that reasoning. The Schrodinger equation in some sense already incorporates the uncertainty principle, since the primary mathematical object, the wave function, is interpreted probabilistically.

 

[stevendaryl]

This way of putting it I think it dramatizes it unnecessarily. Certainly it is not the purpose of this thread to throw out anything, on the contrary QM as a theory is robust enough to tackle all these only apparent contradictions. It makes little sense that particle detectors and scattering in general contradicts in any way QM, particle physicists would be quite amused.

I'm agreeing with you--bubble chamber physics certainly doesn't contradict QM.

Yes, it is different in many aspects, I'm not sure that the mass of the environment microparticles is the main one though.

I'm not sure. I was thinking that the particle collides with much more massive (and therefore, more localized) atoms, and that was responsible for the appearance of tracks, but the masses of the atoms might not be important.

 

[mfb]

Instead of electrons or alpha particles, you can shoot a grain of sand through the detector, physics will be the same: quantum effects are negligible. Even between bubbles, the particle interacts so much with the environment that quantum effects vanish.

 

[stevendaryl]

Instead of electrons or alpha particles, you can shoot a grain of sand through the detector, physics will be the same: quantum effects are negligible. Even between bubbles, the particle interacts so much with the environment that quantum effects vanish.

As I said, the original puzzle about bubble chambers was why a spherically symmetrical situation (the emission of alpha particles by a nucleus is approximately modeled as spherically symmetric) should lead to linear tracks, which are certainly not spherically symmetric.

If the alpha particle were initially given an approximately definite trajectory (a wave packet centered on a classical trajectory), it wouldn't be too surprising to find linear tracks. Of course, the uncertainty principle limits how classical its trajectory can be, but in the case of sand, its path can be pretty close to classical.

 

[mfb]

I just don't see what is puzzling about it. You measure the approximate position and momentum of the particle with every single atom that is close to it. Of course repeated measurements give a consistent result.

 

[TrickyDicky]

You would have to be very naive indeed to expect that. The main difference is that in the case of a bound electron, the contribution of these environmental factors to the Hamiltonian is small compared with the central force. In the cloud chamber case the interaction of the particle with the environment isn't negligible - it's the only interaction present for the unbound particle.

I really doubt this is a problem of free(unbound) vs bound particles. First of all a quantum particle is not exactly free in the sense a classical particle is, no matter how small the environment factors they can't be neglected in the same way in the quantum system case as in the classical. And in the case of the cloud/bubble chamber one could set up a strong central potential that would make the environment contribution small in comparison and still have a classical path result.

 

[TrickyDicky]

I just don't see what is puzzling about it. You measure the approximate position and momentum of the particle with every single atom that is close to it. Of course repeated measurements give a consistent result.

Generating a multitude of different trajectories(one for each interaction) would be the expected outcome for a spherical wave function, and it would be an equally consistent result, but it is not what is observed. That's why it is not so straightforward to give the answer you give,(wich is by the way the first thing that comes to mind or at least it was for me). One of the reasons it is not so straight forward I supposed is related to the fact that the measurement problem is still considered an usolved one in QM.

 

[stevendaryl]

I really doubt this is a problem of free(unbound) vs bound particles. First of all a quantum particle is not exactly free in the sense a classical particle is, no matter how small the environment factors they can't be neglected in the same way in the quantum system case as in the classical. And in the case of the cloud/bubble chamber one could set up a strong central potential that would make the environment contribution small in comparison and still have a classical path result.

I'm not clear about whether people are using the word "environment" with respect to a bubble/cloud chamber to mean the stuff filling the chamber (water vapor, or whatever it is), or the rest of the universe that is outside of the chamber. If the interaction with the stuff inside the chamber were negligible, then you wouldn't see tracks, I don't think. That's the whole point of filling the chamber with stuff.

 

[stevendaryl]

I just don't see what is puzzling about it. You measure the approximate position and momentum of the particle with every single atom that is close to it. Of course repeated measurements give a consistent result.

Well, sort of. If the atoms themselves have a definite location, then interacting with the atoms would localize the particle. But why should the atoms themselves have definite locations?

It's hard to know exactly how puzzled to be about something until after you thoroughly understand it (at which point, you're no longer puzzled, I guess).

 

[atyy]

The track describes the classical trajectory of a quantum system, this is what Mott, Heisenberg, Born and Darwin as explained in the rerence provided by stevendaryl were trying to explain within the quantum formalism. A classical trajectory has well defined momentum and position, that is what's classical about it and what seems to clash with quantum theory in the context of the yet unsolved measurement problem.

Heruristically, the atoms of the cloud chamber are the "pointer" of the instrument. These give a well-defined reading. But this reading is not necessarily correct or "accurate". For example, let's take a spin pointing up. A measurement will always yield a definite answer - either "up" or "down". But since the spin is in a definite up state, these well-defined readings are inaccurate if the measurement yields either answer with some non-zero probability. In contrast, an accurate measurement will always tell you the particle is in an up state.

In the same way, the definite trajectory you assign is only the definite reading of the instrument. It does not tell you that the measurement was accurate. This distinction is important, because definite but inaccurate measurements do not leave the quantum system in the definite state indicated by the measurement outcome.

Yes, that's the premise, Mott et al. are trying to explain, how do we go from individual imprecise measurements that should lead to not definite trajectories to a classical trajectory. The arguments used by these authors: the classical detectors and the environment. If they are valid it seems like they could be also applied in principle to situations where we don't observe clasical trajectories, like electrons in an atom, but here it is not used basically on the grounds that the HUP forbids well defined orbits(see for instance PF physics FAQ footnote on why electrons don't crash into the nucleus).

In quantum mechanics, the answer you get depends on what you measure. Heuristically, if you were to measure the position of the electrons in an atom, you would localize the electron. (I say heuristically, because I don't know if this can be done non-relativistically, and relativistically, position is not a good measurement operator).

Too heuristic, as I said in as much as it is considered a classical trajectory the track can be considered to have position as precisely measured as momentum.

The mathematical details behind the idea of continuous imprecise measurement are given in http://arxiv.org/abs/math-ph/0512069. This article also mentions the cloud chamber.

A general introduction to continuous imprecise measurement is given in http://arxiv.org/abs/quant-ph/0611067.

Note on my sloppy terminology: Here I have used "precise" and "accurate" to mean the same thing, ie. "correct". Others would prefer to reserve "precise" to mean "well-defined", and "accurate" to mean "correct".

 

[TrickyDicky]

Instead of electrons or alpha particles, you can shoot a grain of sand through the detector, physics will be the same: quantum effects are negligible.

We know quantum effects are negligible for macroscopic objects(sand grains, pick-up trucks,... but not for say buckyballs). But they shouldn't be for electrons or alpha particles, or else we wouldn't need quantum theory to explain them. Besides the base of the solutions given to the Mott problem relies on the quantum effects of the environment rather than they're being negligible.

Even between bubbles, the particle interacts so much with the environment that quantum effects vanish.

Again, I think all quantum systems interact significatively with the environment.

 

[Vanadium 50]

TrickyDicky, what you wrote is utterly, completely and totally false. I write this in such a strong manner because you will be tempted to hold on to as much of that as you can, and so long as you do, you will never, ever understand the right answer. You have to let go.

Quantum mechanics applies to everything: sand grains, baseballs and pickup trucks. In the limit of large quantum number n, the behavior approaches the classical limit. But what matters is n, not whether this is a baseball or an electron. An electron in a bubble chamber is at very large n - millions or more - so its behavior is very close to classical.

What matters is n.

 

[stevendaryl]

TrickyDicky, what you wrote is utterly, completely and totally false. I write this in such a strong manner because you will be tempted to hold on to as much of that as you can, and so long as you do, you will never, ever understand the right answer. You have to let go.

Quantum mechanics applies to everything: sand grains, baseballs and pickup trucks. In the limit of large quantum number n, the behavior approaches the classical limit. But what matters is n, not whether this is a baseball or an electron. An electron in a bubble chamber is at very large n - millions or more - so its behavior is very close to classical.

What matters is n.

I don't quite understand that. The quantum number n isn't well-defined for an unbound particle. Or maybe you want to say that n is infinite in that case? What is n for a baseball?

 

[TrickyDicky]

TrickyDicky, what you wrote is utterly, completely and totally false. I write this in such a strong manner because you will be tempted to hold on to as much of that as you can, and so long as you do, you will never, ever understand the right answer. You have to let go.

Quantum mechanics applies to everything: sand grains, baseballs and pickup trucks. In the limit of large quantum number n, the behavior approaches the classical limit. But what matters is n, not whether this is a baseball or an electron. An electron in a bubble chamber is at very large n - millions or more - so its behavior is very close to classical.

What matters is n.

Hmmm, I'm ready to let go of anything but I have not made any claim in the sense that QM doesn't apply to everything, in the post you seem to refer to as being utterly wrong I was quoting mfb to disagree with him that quantum effects are negligible, maybe that confused you.

On the other hand my layman understanding coincides with stevendaryl's about free particles not having the defined quantum numbers of particles in an atom, is this not correct?