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HUP & Non conservation of energy

  1. Jan 20, 2010 #1


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    There is one thing i always wanted to ask.
    Since when HUP is so 'easily' allowed to explain the obvious non-conservation of energy?
    With what justification we say with such an ease that a particle can borrow(wtf does that mean?) energy ΔΕ but it must return it(what...??) in time Δτ?
    I really please someone with real knowledge of these things to explain it to me, because all the introductory books use such arguments but none really explains why they should hold.
  2. jcsd
  3. Jan 20, 2010 #2
    This kind of language is sometimes used in bad popular books, whose authors pretend to suggest "intuitive" explanations of quantum-mechanical effects. These "explanations" are often confusing and misleading.

    For example, one can find an "explanation" of the tunneling effect as "borrowing" and then "returning" energy that is required to overcome the barrier in a finite time interval. This is just plain nonsense.

    In fact, the energy conservation law remains valid in quantum mechanics. To be more precise this law can be formulated as follows: "the probability distribution for the total energy of any isolated system does not depend on time."

  4. Jan 20, 2010 #3


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    What I never really understood is the justification of virtual particles by the "Heisenberg uncertainty principle dE*dt > constant". But I agree, the meaning of this principle is not always properly explained, and it's important to note that it's quite something else than the principle which concerns non-commuting operators like x and p.
  5. Jan 20, 2010 #4
    Halzen & Martin "Quarks & Leptons" has a nice section 4.8 entitled "the origin of the propagator" if you have access to it. The basic idea is that virtual particles appear in the amplitude as a factor 1/virtuality where virtuality = [itex]p^2-m^2[/itex] so it's infinity (pole) for on-shell particles, and will realize just what the hand waving argument describes for off-shell particles.
  6. Jan 20, 2010 #5


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    Can you explain it in other words? I dont think that i understood it.
    How would you explain the virtual paticle creation/annihilation?
  7. Jan 20, 2010 #6
    JK423 : we do not know your background so we have to guess which level is appropriate. Have your read https://www.physicsforums.com/showpost.php?p=986037&postcount=5 [Broken]

    Last edited by a moderator: May 4, 2017
  8. Jan 20, 2010 #7
    "Virtual particles" is just another misleading and confusing concept. There are no virtual particles in nature, just as there are no angels. This idea was invented to give some "intuitive feel" to quantum field theory. (I think, Feynman started it, but it is not his best contribution to science, unfortunately).

    In fact, QFT provides some formulas (integrals) for scattering amplitudes. Feynman invented an ingenious way to simplify book-keeping and calculation of these integrals by representing them in a graphical form. The Feynman graphs resemble "photographs" of particle trjectories. They create an impression that particles are moving, emitting and absorbing other particles in a complex web of events. It is very easy to take these abstract graphs as a realistic mechanism of particle scattering. In fact this interpretation is misleading. Feynman graphs are nothing but an exotic way of writing usual integrals. "Virtual particles" and internal lines in Feynman graphs are nothing but certain factors in the integrands of these integrals.

    In general, it is wrong to think that quantum mechanics or QFT gives us a picture of mechanisms of micro-events. They don't. QM and QFT are just mathematical tools that allow us to calculate probabilities of measurements. These tools operate with formal abstract notions like wave functions, Hermitian operators, Hilbert spaces, propagators, Feynman diagrams, quantum fields, etc. These notions do not have counterparts in nature. They are not more real than the square root of -1.

    So, it is completely useless to contemplate "virtual photons" being "exchanged" between two charges. "Virtual photons" do not exist, they cannot be observed, their energy has no meaning.

  9. Jan 23, 2010 #8
    I agree with what you're saying, but shouldn't it be noted that the energy-time uncertainty relation and the associated notion of virtual particles (re: Yukawa 1934, Wick 1938) led to the discovery of the mu and pi mesons in the 1930's and 1940's, respectively ?
  10. Jan 23, 2010 #9
    Maybe I misunderstand, but I remember the mu was experimentally discovered and first thought to be the pi. So I agree with you for the pi, but isn't the mu's only role in this affair to bring confusion ?
  11. Jan 23, 2010 #10
    You will note that according to the quotes I provided above, saying that the virtual particles are off mass-shell is strictly speaking impossible. The all point is that they are sufficiently short lived for the uncertainty on their energy to prevent you from claiming that they are off mass-shell. Please note that, I am not trying to push towards Feynman diagrams being little pictures of what really happens, I'm just pointing out to an interpretation compatible with the original question.
  12. Jan 23, 2010 #11


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    Huh! I always thought that virtual particles were rather useful for explaining how physical forces are able to create "action at a distance" while remaining consistent with relativity, but I guess this is just a fuzzy, lay conceptualization without any rigorous justification.

    Another take on this is that I guess it was ok for Feynman to use virtual particles to follow his intuition, since he understood the underlying physics and mathematics, and was therefore less likely to use them improperly.
  13. Jan 23, 2010 #12
    Probably so, sorry. :redface:
  14. Jan 23, 2010 #13
    the claim that 'virtual particles is just math' is misleading
    It comes from narrow Copenhagen view that 'virtual particles can not be registered'
    Depending of the frame, the same particle can appear 'real' or 'virtual'
    So in fact the only difference between them is energy 'on the long run' (beyond HUP)
  15. Jan 23, 2010 #14
    No. The invariant mass of a particle is given by the square of its four-momentum, and whether it's not on mass shell (= to the PDG mass for this particle) does not depend on the frame.
  16. Jan 23, 2010 #15
    I was talking about accelerating frames and Unruh effect
  17. Jan 23, 2010 #16
    I see. Thanks for the clarification. In an accelerated frame undergoing Unruh frame, real particles are recorded leading to a thermal bath. Whether those particles are really there virtually in a non-accelerated frame is rather a philosophical question, and if I deny those particle actually are there while I'm not accelerated, you'll have trouble proving me wrong experimentally.
  18. Jan 23, 2010 #17
    1. In any case, do you agree that 2 different observers do not agree on the number of real particles?

    2. I scanned thru several different definitions of what "virtual" particle is, could you provide an interpretation-free definition, without words "measured", "registered", "output", "only inside feynmann diagram" etc?
  19. Jan 23, 2010 #18
    Sure !

    A virtual particle is off-mass-shell : it's mass is not as defined in PDG database. It is used as an intermediate step in a perturbative expansion of the amplitude, and indeed if you will insist to ask whether the virtual particle was "really there" with the energy attributed in the intermediate of the calculation
    1) I will be forced to admit that it could have had the energy corresponding to its mass-shell because of the HUP
    2) I will also be forced to admit that there could be other means of calculation for the same amplitude which would not have used the concept of virtual particle
  20. Jan 23, 2010 #19
    Yes, this is true. The idea of virtual particles played some positive role in heuristic guessing of right theories. However, this is not sufficient to claim that such particles exist.

    When Maxwell formulated his equations he believed in the idea of ether, which is completely discredited now. So, wrong ideas can often lead to important discoveries.

  21. Jan 24, 2010 #20
    0. That I was talking about. There are 3 different views:
    A. For macroscopic realism, both virtual and real particles are “just math” to explain the correlations between the macroscopic events. Only macroscopic events are real
    B. For collapse theories, real particles are real, and virtual are “just math”
    C. For MWI, there are no particles, but what is usually called particles, are excitations of the “omnium”. Both real and virtual “particles” are real and have the same properties, except the energy. (I am not ready to discuss other non-collapse interpretations like BM as I don’t know how virtual particles are explained there)

    Personally I can accept A or C, while B looks the most illogical for me: I can not believe that always minimalist nature would create math which mimics the reality in all details: including a list of particles, conservation laws etc. But in any case, Unruh effect leaves no choice but A or C: you agreed that different observers don’t agree on the number of real particles. So if for Bob particle is “real” and for Alice it is not, then how can you call it “pure math”?

    Regarding your definition. Virtual particles exist only short time, allowed by HUP, so their energy is not well defined, we both agree there. You probably meant their invariant mass. But how do you know they don’t have invariant mass? You can not ‘register’ virtual particles, so you can’t prove it experimentally. Also, probably ALL particles don’t have invariant mass, and there is an illusion of invariant mass because of their interaction with virtual Higgs particles :)
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