HUP & Non conservation of energy

[JK423]

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.

 

[meopemuk]

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?

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."

Eugene.

 

[haushofer]

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.

 

[humanino]

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 = $p^2-m^2$ so it's infinity (pole) for on-shell particles, and will realize just what the hand waving argument describes for off-shell particles.

 

[JK423]

@meopemuk
Can you explain it in other words? I don't think that i understood it.
How would you explain the virtual paticle creation/annihilation?

 

[humanino]

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

And where does the time-energy uncertainty relationship come in ?
It tells you esentially that *in order to perform an energy measurement with precision dE*, you will need to measure (to have your measurement apparatus interact with) the system for a time of at least dt.

In the pictured example, we consider an intermediate state with a virtual photon in it. It isn't classically possible for a charged particle to just emit a photon and remain unchanged (except for recoil) itself. The state with the photon in it has too much energy, assuming conservation of momentum. However, since the intermediate state lasts only a short time, the state's energy becomes uncertain, and it can actually have the same energy as the initial and final states. This allows the system to pass through this state with some probability without violating energy conservation.

Some descriptions of this phenomenon instead say that the energy of the system becomes uncertain for a short period of time, that energy is somehow "borrowed" for a brief interval. This is just another way of talking about the same mathematics. However, it obscures the fact that all this talk of virtual states is just an approximation to quantum mechanics, in which energy is conserved at all times. The way I've described it also corresponds to the usual way of talking about Feynman diagrams, in which energy is conserved, but virtual particles can carry amounts of energy not normally allowed by the laws of motion.

 

[meopemuk]

@meopemuk
Can you explain it in other words? I don't think that i understood it.
How would you explain the virtual paticle creation/annihilation?

"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.

Eugene.

 

[ThomasT]

"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.

Eugene.

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 ?

 

[humanino]

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 ?

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 ?

 

[humanino]

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.

 

[SpectraCat]

"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.

Eugene.

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.

 

[ThomasT]

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 ?

Probably so, sorry.

 

[Dmitry67]

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)

 

[humanino]

Depending of the frame, the same particle can appear 'real' or 'virtual'

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.

 

[Dmitry67]

I was talking about accelerating frames and Unruh effect

 

[humanino]

I was talking about accelerating frames and Unruh effect

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.

 

[Dmitry67]

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?

 

[humanino]

1. In any case, do you agree that 2 different observers do not agree on the number of real particles?

Sure !

12. 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?

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

 

[meopemuk]

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 ?

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.

Eugene.

 

[Dmitry67]

0. 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

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 :)

 

[Fredrik]

Dmitry, now you're just speculating wildly, and not making much sense. You seem to be confusing interpretations of QM with the question of whether Feynman diagrams describe what actually happens during an interaction. This last thing has nothing to do with the MWI.

 

[Dmitry67]

ok, 1 step at a time.
For you, what are the outputs from the Feynman diagrams? particles going to the measurement devices?

 

[Fredrik]

Not sure what you mean by the "output"? The result of the calculation? I'd say that a Feynman diagram represents "a function that you integrate to get a contribution to a term in a series which adds up to a probability amplitude". The result of the calculation is the probability amplitude, which isn't very interesting by itself, so you square its absolute value to get a probability.

I don't want to get dragged into another discussion about interpretations, so I probably won't have much more to say about this.