Why are 'virtual particles' allowed to be 'off-shell'?

In summary, the conversation touched on the concept of virtual particles and their behavior in quantum field theory. The participants questioned why virtual particles are allowed to be "off shell" and have a different propagator than real particles. They also discussed the idea of virtual particles not being "real" and the role of the vacuum fluctuation myth. The conversation also delved into the topic of mental images and popularizations in the context of understanding QFT. The question of whether lattice QFT is similar to the mattress picture model was also brought up.
  • #1
If virtual particles are supposed to be some sort of Green's function excitation of a field following a particular Lagrangian or PDE (induced by the presence of another particle, free or virtual), then why are they allowed to be "off shell"? (Especially: Why are they allowed to be nonzero outside the light cone). This doesn't seem right: First of all, if it doesn't evaluate to a delta-function at the origin, it isn't a Green's function to begin with. The behavior claimed for Feynman's propagator doesn't appear to fit. Second of all, why are influences allowed to propagate in ways that free particles are not if where you draw the boundaries of the diagram are arbitrary?

Why are "negative energy states" (negative time frequency components of a Green's function) forbidden for quantum field theory when we use them all the time for classical fields? (Water waves or classical radio waves don't seem to have any 'negative energy' instability problems. Why do quantum fields?)

If they're allowed to violate the fundamental equation they are supposed to represent, what rules *do* virtual particles follow?

Edit:
Another way of phrasing my question: If the dispersion relation for the motion of free and virtual particles comes from the same lagrangian leading to the same PDE, then how can the support for the Green's function for a virtual particle be any different than for a free particle?

I've heard the "virtual particle's aren't real, so we can do whatever we want" excuse before, but I don't buy it. There's still some way of weighting all (k,w)-vectors in your plane-wave decomposition that comes from somewhere - why is it different if it's virtual or free? If I were trying to invent semi-classical field theory, a virtual photon couldn't do anything an actual photon couldn't do since they would both be derived from Maxwell's equation (and fundamentally the same thing) - a disturbance in an EM field firmly nailed to a light-cone with zero support outside.
 
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  • #3
I read it briefly last night.

I appreciate the vacuum fluctuation myth portion - it meshes well with the impression I've formed so far beating my head against QFT. (PS - why are the popular mental pictures of what the math is supposed to be doing in QM so especially obscurantist and misleading? I've never encountered another area of engineering or physics where I've had to revise and re-revise my mental picture of what is going on so often due to misleading explanations.)

I still don't have a good answer for how the propagator (what I was calling a Green's function) for a real vs. virtual particle can be different. Also, insisting that virtual particles aren't real is a little silly - it's like insisting that static electric fields aren't real in the context of classical electrodynamics since they aren't plane wave solutions to homogenous Maxwell's equations - they still have to obey the equations!

In the context of a physical theory, any element that effects the outcome is "real" and better obey the fundamental laws!

Where does the propagator for a virtual particle come from? Why can you get away with using a different propagator than for a real particle? (Why, for example, in Feynman in Elementary Particles and the Laws of Physics) blithely integrate over invalid worldlines for virtual photons without any sort of weighting?) (Or a weighting that is nonzero outside the lightcone and inside it as well.)PPS - is lattice QFT similar in any way to the mattress picture model of QFT? (something which I think I understand.)
 
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  • #4
MadRocketSci2 said:
hy are the popular mental pictures of what the math is supposed to be doing in QM so especially obscurantist and misleading

One might as well ask, "how come QFT requires years of study and can't be easily understood by those who don't put the effort in?" Why should popularizations be accurate?
 
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1. What are virtual particles?

Virtual particles are particles that are not observable in the usual sense, as they do not have a definite mass or energy, and cannot be directly measured or detected. They are considered to be fluctuations in the quantum vacuum, and play a role in various physical processes, such as particle interactions and radiative corrections.

2. What does it mean for a virtual particle to be 'off-shell'?

When a particle is 'off-shell', it means that it does not satisfy the usual energy-momentum relation, E^2 = p^2 + m^2. This is because virtual particles do not follow the same rules as real particles and can temporarily have energy or momentum values that do not correspond to their mass.

3. Why are virtual particles allowed to be 'off-shell'?

Virtual particles are allowed to be 'off-shell' because they are not subject to the same restrictions as real particles. They exist for a very short period of time and do not have to follow the same laws of energy and momentum conservation. This allows them to have a greater range of energy and momentum values, including being 'off-shell'.

4. What is the significance of virtual particles being 'off-shell'?

The significance of virtual particles being 'off-shell' is that it allows for a greater range of possible interactions and processes in the quantum world. It also plays a role in quantum field theory and helps to explain various phenomena, such as the Lamb shift and the Casimir effect.

5. How are virtual particles used in scientific research?

Virtual particles are used in scientific research to explain and understand various phenomena in the quantum world, such as particle interactions, radiative corrections, and the behavior of the vacuum. They are also used in theoretical calculations and simulations to make predictions about the behavior of particles and their interactions.

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