Haelfix said:
I think the problem I have with that entry is that it leads to statements like this written by JK423.
"Real particles, no matter how SMALL a lifetime they have, you can in principle interact with them because they have a quantum state"
This is deeply wrong for a number of reasons. The first is that mathematically this is fantasy. Most Interacting particles in 4d do not have well defined quantum states, especially ones that are not well separated, that haven't undergone clustering and that have arbitrarily small lifetimes. So pathological example.. Low energy quarks do NOT have well defined particle number operators. This is completely independent of perturbation theory and is indeed a nonperturbative statement. If you insist that they do, and give them one anyway, for instance as you ramp up the energies of the collider during deep inelastic scattering experiments then I assure you the distinction between real and virtual really does become a matter of convention (in this case the convention of energetics to contrast to the usual convention of time explained in the other thread).
The second is you have to define what you mean by 'interaction'. You can rewrite all of the contributions of virtual particles in certain specific theories (like QED) as 'dressed' particle interactions. This 'dressing' absolutely, quantitatively makes a separate and very real contribution to physical processes like scattering cross sections, decay times and so forth. So again, you simply can't be consistent and argue that they have nothing to do with interactions at all.
Haelfix, your main argument -if i understand correctly- stems from Haag's theorem; all these mathematical difficulties that make QFT ill-defined.
I tell you once more, is this relevant? What you say is "Ok real particles may have a quantum state, but this quantum state is not mathematically well-defined", or something like that.
My immediate response is:
I agree that these mathematical difficulties are present. But the point is that virtual particles just do not have a quantum state in the first place, which means that your reference to the mathematical difficulties on quantum states is irrelevant. If you want to argue about what Haags theorem means for the real particles, let's make another thread! In this thread, let's just agree that virtual particles do not have a quantum state regardless of this issue. (But you have already agreed with that in the other thread, and i don't know why you disagree with the "virtual particles are not real" statement)
Consequently:
An internal line, in Feyman diagrams of perturbation theory, even if it had a lifetime of 10 years you wouldn't be able to interact with it in principle since there is no quantum state to interact with.
This thing would be right there, in front of you, for 10 whole years and you wouldn't be able to "touch" it no matter what you do. You can only "touch" quantum states.
Haelfix said:
The second is you have to define what you mean by 'interaction'.
It's simple: If a virtual particle had a quantum state \left| {virtual} \right\rangle, then i could sent a probe \left| {probe} \right\rangle to interact with it unitarily, via \hat U\left( t \right), during the time of its existence. The final state of the system will be \hat U\left( t \right)\left( {\left| {virtual} \right\rangle \otimes \left| {probe} \right\rangle } \right). In your example with the photon from the other galaxy (from the other thread) i can write down such an interaction while the photon is on its way to Earth. I can write down such an interaction for every real excitation, in principle. Yes, maybe it's mathematically ill-defined, but as i said let's argue about what that means in another thread.
In the case of virtual particles, such an interaction cannot even be written down. Not even in principle.
I am waiting for your response.
