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Common quantum question

  1. May 21, 2007 #1
    I'm sure this has been asked before, but I've been searching for a clear answer as to why the Uncertainty Principle is a representation of physical reality and not just a result of our imperfect measuring techniques. Is an electron still considered to be a discrete particle orbiting the nucleus, or is the distribution of probability wave an accurate representation of how the atom physically exists? I understand that the act of measuring an electron's momentum will decrease the accuracy to which we can measure its position (and vice versa), but how does the electron cloud physically exist at any moment in time? With the electrons as discrete particles, or as a distribution of probability?

    Also, I'm pretty sure that protons and neutrons are actual spherical objects. Is the same true for electrons, or is this an unanswered question?
  2. jcsd
  3. May 22, 2007 #2
    Perhaps the wrong wording is confusing you. The Heisenberg “Uncertainty Principle” is the Heisenberg Dispersion Relation and has nothing to do neither with the measurements nor with the accuracy of the measurements.

    The dispersions are eigenvalues of the self adjoint operators (observables). They clearly indicate that the physical object under consideration is field and provide the parameters for description of the corresponding wave packets. For example, in case when the physical system (physical reality) contains the single (discrete,n=1) electron moving freely (v<<c) or bounded by external spherically symmetric EM field, it is spherical object. Indeed, the waveforms are entirely different in each case.

    How does the electron cloud physically exist at any moment in time? That QM is all about.

    The same true for free protons and neutrons. If v~c they more similar to pita (discus).

    Regards, Dany.
    Last edited: May 22, 2007
  4. May 22, 2007 #3

    Meir Achuz

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    The HUP is just the Fourier transform relation that (Delta k)(Delta x)>1/2 for any wave packet. This holds even for a classical light wave of finite extent.
    The connection of the HUP with measurement problems was just bad advice given to Heisenberg by Bohr.
  5. May 22, 2007 #4

    Meir Achuz

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    The proton and neutron are not spherical. The two u quarks in the proton are further apart than the u-d quark distance.
    The electron is believed to be a point particle, so its shape is not defined.
  6. May 22, 2007 #5
    The HUP isn't really the representation, the wave and states of the particles are more like it, but of course the HUP governs these.

    It isn't just a result of imperfect measurement. As it turns out, the probability functions are the only way to describe what is happening, and they describe it perfectly, as far as we can tell. Since Newtons laws of motion perfectly describe our classical world, we accept them as factual, and the same goes for QM.

    Electrons haven't been considered actual orbiting objects for 100 years, even before QM proper.

    Well, that's the mystery. QM doesn't make the distinction. It has a model that describes and predicts the electron in it's various possible situations, and calculates it as a wave or particle according to context. The function is the electron. You must first accept this. The reality of the particle in QM is the function. It's the only way it all works and makes sense. It's bizarre, but there you go. You can only convince yourself that it is true by reading and understanding the actual experiments yourself.

    It's not true of protons, neutrons, or even atoms, though by the time you start talking about atoms, the wave function fringes are so small that it begins to behave more predominately spherical. On the other hand, all particles have spherical probability domains, so the distinction is not a useful one.
  7. May 22, 2007 #6
    I think it might be OK to ask some basic questions in this thread...

    What do you mean? If the HUP defines the relative resolution of the probability components, how isn't it part of the accuracy of measurement?

    Could you state this in more conceptual terms, i.e. how an "observable" translates into the above?

    Could you explain more about "field" vs physical object? Are you talking about a mathematical, vector, or EM field?

    I'm having trouble looking up pita in this context, i.e. I keep getting "pita bread". Pointers?
  8. May 22, 2007 #7
    electrons have always been in orbit around the nucleous which is made up of protons and neutrons!
  9. May 22, 2007 #8
    The inequality has only qualitative meaning. To make it the quantitative statement you should consider the specific realization (R. Jackiw, JMP, 9, 339 (1968)).

    I have impression that it was much more than advice (W. Heisenberg as well as E. Schrödinger were ill after discussions with N.Bohr).

    At high energy region. At low energy it is coherent wave packet.

    Regards, Dany.
  10. May 22, 2007 #9
    HDR is the terminology used originally by W.Heisenberg. It expresses the experimental evidence that QM system is described by the dynamical variables which are not commuting in general (matrices). The measurement instruments are the macroscopic objects and obey the laws of the classical physics. The accuracy of measurement is well defined notion within the classical physics (statistical sampling, etc.).

    Delta A=<A^2>-<A>^2 for every A self-ajoint operator.

    OP asks about the single electron “orbiting the nucleus”. It described by the Dirac field or by Pauli-Schrödinger field in the non-relativistic limit (v<<c). I add the free electron consideration (the coherent wave packet) for completeness.

    Your questions make me feel that you arrived from Alpha Centauri half hour ago.

    Good morning!

    Regards, Dany.
  11. May 22, 2007 #10
    Ok, now I'm more confused than when I asked the question. Can someone explain this in understandable terms without using wave function math (and ideally with proper grammar)?
  12. May 22, 2007 #11


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    No. This well covered in the posts above. The HUP follows from the wave-particle duality. It can't be explained in 'billiard ball' terms.

    Completely answered by the posts above. You have to stop thinking classically, or none of this will ever make sense.
  13. May 23, 2007 #12
    You apparently discuss physics using English. I discuss physics apparently using English.

    When you write:” Is an electron still considered to be a discrete particle orbiting the nucleus, or is the distribution of probability wave an accurate representation of how the atom physically exists?”, it perhaps sounds for you meaningful in English, but it is nonsense physically, since you use undefined notions (for you) and it were already demonstrated that they are not adequate within the Quantum World.

    When I write:” the single (discrete, n=1) electron, I mean that in the discussed problem the operator of number of particles is observable (self-adjoint which commute with Hamiltonian and has eigenvalue equal to one).

    Physics is a science and not a philosophy, journalism or Hollywood movie. It based on the results of the measurements and uses the mathematics for its processing. In addition, the relevant math is simple, deep and much more beautiful than any science fiction book or movie.

    Regards, Dany.
  14. May 23, 2007 #13


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    Since QM has wave solutions, like analyzing any properties of a wave, there are relations. The Uncertainty Principle is taking those universal properties of waves and applying it to matter and energy. It is not a result of imperfection in equipment or interaction of particles, is has to do with that your experimenting on something that has wave properties.

    Based on my QM interpretation:
    And as far as what the electron looks like is entirely dependent upon what interpretation you have. I believe in matter waves. Just like if I took a wave from the ocean and changed its potential by putting it into my pool, it would change its form to the new conditions. A free electron with a Gaussian for a minimum wave packet, which appears localized, would change its form when encountering a proton. An electron in hydrogen is a trapped wave. The electron's matter wave has formed to the new potential and it no longer appears like a Gaussian wave that is localized.

    If you could actually measure the position of the electron as it flies around the proton, you would force the electron to localize into a Gaussian, somewhere within its probability cloud and then it would smear out again according to the Schrodinger equation. Having a Gaussian wave packet for the electron as the initial state for the hydrogen equation is do-able. But the actual act of measuring, causing the wave packet to become Gaussian or a delta function is what’s controversial.

    Overall, there is no true consensus on a QM interpretation. The Copenhagen Interpretation is the most popular and in that case, the electron is a point particle with properties that can be described by a mathematical wave equation.
  15. May 23, 2007 #14

    Meir Achuz

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    The wave packet describes the position of a particle, not the particle.
    A "point particle" is usually defined as one whose form factor is a constant:
  16. May 23, 2007 #15
    How you define and calculate form factor in case of the Schrödinger (Die Naturwissenschaften, 14,664,(1926)) coherent state?

    Regards, Dany.
  17. May 23, 2007 #16
    Can you explain me this better? You mean "coherence length" greater than source-detector distance or what exactly?
  18. May 23, 2007 #17
    Thanks, your response is the only one I've really understood so far. Are you saying that we don't actually know how the electron physically exists, and that using wave functions is the only way to accurately describe how it behaves at this point?
  19. May 23, 2007 #18
    I'm sure the physical state of the electron can be explained in words without using equations. I'm not asking for an analogy, but a straightfoward answer to a straightforward question: How does an electron exist physically? A) as a point particle with wave properties, B) just as a wave function, C) we don't know, D) something else.

    Also, doesn't all matter have wave properties? Don't people have wave properties? Why can macroscopic objects be thougt of as actual objects, while electrons can only be accurately represented by wave functions? Is it because of their small size, or is it because they HAVE NO actual size? And if the latter is true, how is that possible?
  20. May 23, 2007 #19


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    In different circumstances it can look like A) or B). Evidence from scattering experiments indicate that the electron has spatial extent. But it looks smaller when probed with higher energy particles. Evidence from diffraction experiments shows it is also a wave.

    I don't have a view about what it 'really' is because it is not relevant to making calculations.
  21. May 23, 2007 #20
    What about protons and neutrons, and other subatomic particles? Do any of these have defined sizes (I know they have defined masses) the way macroscopic objects do? Is there some fundamental difference between matter at the subatomic level and matter at larger scales? Since everything is made of this subatomic matter, why should macroscopic objects have defined sizes and shapes, but not the individual particles they are made of? I'm just trying to clear up whether there IS such a distinction, or if we simply don't understand what is going on at these small scales yet.
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