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Tracks in particle detectors and quantum paths

  1. Jun 20, 2014 #1
    How are the track leftt say by an electron in a cloud chamber and its wave function undefined trajectory related exactly?
     
  2. jcsd
  3. Jun 20, 2014 #2

    Vanadium 50

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    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.
     
  4. Jun 20, 2014 #3

    CWatters

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    Very different scales.
     
  5. Jun 20, 2014 #4
    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?
     
  6. Jun 20, 2014 #5
    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.
     
  7. Jun 20, 2014 #6

    stevendaryl

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    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
     
  8. Jun 20, 2014 #7

    jtbell

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    Moved to Quantum Physics.
     
  9. Jun 20, 2014 #8
    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.
     
  10. Jun 20, 2014 #9

    ZapperZ

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    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.
     
  11. Jun 20, 2014 #10

    stevendaryl

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

     
  12. Jun 20, 2014 #11

    ZapperZ

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    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.
     
  13. Jun 20, 2014 #12

    stevendaryl

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    I thought the original question was about tracks in a cloud chamber, which is what the Bohr quote is about.
     
  14. Jun 20, 2014 #13

    ZapperZ

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    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.
     
  15. Jun 20, 2014 #14

    stevendaryl

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    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.

    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:

     
  16. Jun 20, 2014 #15

    ZapperZ

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    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.

    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.
     
  17. Jun 20, 2014 #16

    stevendaryl

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

    To quote from the conclusion:
     
  18. Jun 20, 2014 #17

    stevendaryl

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    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.

    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.

    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."

    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.
     
  19. Jun 20, 2014 #18

    atyy

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    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.
     
    Last edited: Jun 20, 2014
  20. Jun 20, 2014 #19
    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?
     
  21. Jun 20, 2014 #20

    ZapperZ

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    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.
     
  22. Jun 21, 2014 #21
    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, wich 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.
     
  23. Jun 21, 2014 #22

    Nugatory

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    "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.
    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.
     
  24. Jun 21, 2014 #23

    atyy

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    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).
     
    Last edited: Jun 21, 2014
  25. Jun 21, 2014 #24
    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.
     
  26. Jun 21, 2014 #25

    atyy

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