Particle exchange explaining attractive forces

[Jrs580]

I understand, and have unwillingly come to terms with the fact that virtual particles can carry negative momentum. This explains how momentum can be conserved in attractive forces via particle exchange.
I have a problem with this that I cannot reconcile...wouldn't this imply that as a particle approaches another (say electron/positron), it would have to "know" what that particle is before releasing a photon? I know I am probably thinking of this way too classically, but the fact is, the photon that's exchanged is different if it's attraction/repulsion.
Can you help me find a good way to think about this?

 

[Orodruin]

That is, indeed, a way too classical viewpoint.

In the quantum world, the amplitude of a final state is the sum of the amplitudes of all paths to that state.

 

[malawi_glenn]

It is just a popular science explanation, it has no real physical bearing

 

[Vanadium 50]

I know I am probably thinking of this way too classically

That is correct. You are.

It's just a story told to people who don't know QM. That is not what "particle exchange" really means, and the diagrams you see are not cartoon representations of what is happening. They are mnemonic devices for calculations.

 

[phinds]

@Jrs580 you should check these out:

https://www.physicsforums.com/insights/misconceptions-virtual-particles/
https://www.physicsforums.com/insights/physics-virtual-particles/

 

[Jrs580]

That is correct. You are.

It's just a story told to people who don't know QM. That is not what "particle exchange" really means, and the diagrams you see are not cartoon representations of what is happening. They are mnemonic devices for calculations.

So are the particles that get "exchanged" actual quantized values of the field? Like the photon in the example.
My logical idea prior to this writeup was that each (charged in this case) particle perturbs the photon field in a certain way. When another charged particle is close by, each of the particles notice a change in their local photon field due to the others presences. Then, as particles do, they sample the field near to them, which governs how they act.

 

[vanhees71]

Indeed, it's better to think about the "virtual particles", depicted by internal lines of a Feynman diagram, as fields than as "particles". In any case "virtual particles" or the mediation of forces by "exchanging particles" is pretty misleading.

The Feynman diagrams suggest something like this when taken in the sense of the pop-science literature as literal pictures of a scattering process. They are, however, rather ingeniously condensed symbols for the mathematical formulae describing transition amplitudes (S-matrix elements) of these scattering processes. The internal lines depict socalled propagators and the vertex points interaction terms in the Lagrangian (Hamiltonian) defining the dynamics of the involved fields.

The only physical meaning is that their modulus squared are transition-probability rates for the scattering process under consideration, i.e., they describe a process with (usually 2) asymptotic free incoming "particles" (i.e., Fock states of the free field theory) resulting after the interaction of these particles in asymptotic free outgoing "particles" (i.e., Fock states of the free field theory), and only these asymptotic free Fock states can be in a specific sense be interpreted as "particle-like" entities. What's going on "during the collision" is pretty opaque in this formalism. For sure there is not a clear particle interpretation of the "transient state" during the interactions happen.

 

[PeroK]

So are the particles that get "exchanged" actual quantized values of the field? Like the photon in the example.

No particles are exchanged. Each Feynman diagram represents an integral in an infinite series of integrals that itself represents the calculation of some probability amplitude. Each Feynman diagram can be interpreted as an exchange of a certain number of virtual particles. But no particular diagram represents the entire calculation.

 

[snorkack]

Ask then what virtual particles are and why we think they "exist", or rather why we think they are useful description of anything.
In the simple case of electromagnetic fields...
You can have a charge which carries an electrostatic field. Electrostatic field extends to infinity from the charge, but is not carrying away any energy or momentum from the charge. Likewise, an electric current loop is a source of magnetostatic field which extends to infinity from the magnetic dipole, but does not carry away any energy or momentum.
But a fluctuating electric or magnetic dipole radiates electromagnetic waves which do carry away energy and momentum in propagation.
Electrostatic field can exert force. Although this is a question of definition: when two charges interact, does each charge feel the force of its own field, or of the other charge´s field? In any case, a third test particle will see a total of the field of two charges, with no distinction between multiple sources.
When two bodies exchange electromagnetic waves, the light pressure can only be repulsive. When they exchange electrostatic fields, these can be repulsive or attractive, freely.
Now, real photons derive from evidence that the electromagnetic waves are quantized when radiated and received.
But as for virtual particles - what types of observations are better explained when electrostatic field is viewed as a flow of discrete particles rather than a continuum field?

 

[Hornbein]

I have learned to not take the word "particle" very seriously. I don't expect them to have anything in common with billiard balls. Whenever you see that word in the quantum context you could mentally translate it to "weirdo thing" and do pretty well.

 

[phinds]

I have learned to not take the word "particle" very seriously. I don't expect them to have anything in common with billiard balls. Whenever you see that word in the quantum context you could mentally translate it to "weirdo thing" and do pretty well.

Better still, just think of them as what the are, not waves and not particles, but quantum objects.

 

[vanhees71]

Ask then what virtual particles are and why we think they "exist", or rather why we think they are useful description of anything.
In the simple case of electromagnetic fields...
You can have a charge which carries an electrostatic field. Electrostatic field extends to infinity from the charge, but is not carrying away any energy or momentum from the charge. Likewise, an electric current loop is a source of magnetostatic field which extends to infinity from the magnetic dipole, but does not carry away any energy or momentum.
But a fluctuating electric or magnetic dipole radiates electromagnetic waves which do carry away energy and momentum in propagation.
Electrostatic field can exert force. Although this is a question of definition: when two charges interact, does each charge feel the force of its own field, or of the other charge´s field? In any case, a third test particle will see a total of the field of two charges, with no distinction between multiple sources.

Yes, each charge "feels" its own field when accelerated, and that's a big problem in classical electrodynamics with point charges. It leads to the infamous "radiation-reaction problem" with all kinds of oddities. First of all there's a diverging contribution from calculating the total energy of the charge's Coulomb field, which of course is infinity. If you smear the charge to a little sphere you get something $\propto 1/a$, where $a$ is the radius of this fictitious sphere. Fortunately this most severe contribution can be absorbed into the mass of the particle. The idea is that you have a "bare mass" of a fictitious particle without taking its own Coulomb field into account and the "electromagnetic mass" due to its Coulomb field. Both are taken to be infinite such that the total contribution is the mass of the particle (everything, of course, defined in the rest frame of the charged particle). Then you get a contribution to the equation of motion which goes with the 3rd time derivative of its position, and this implies all kinds of oddities like self-accelerating solutions and "run-away solutions", where it seems as if there's be an action from the future, which is, of course, inacceptable. The best way out known today is to use an approximation to this Abraham-Lorentz-Dirac equation, known as the Landau-Lifshitz equation.

For a (not yet complete) first treatment, see my SRT notes, using the great regularization techniques of the textbook by Lechner quoted therein:

https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf

Another very lucid treatment with a very nice trick to derive the LAD as well as the Landau-Lifshitz approximation using very clever gauge transformations can be found in Landau&Lifshitz vol. 2

The situation is much better in the quantized theory, i.e., in QED. The reason is that there are no point-particle descriptions but only fields, and you can define the theory in the sense of perturbation theory. Then one can show that all the infinities occurring at higher orders (involving Feynman diagrams with closed loops) of the perturbation theory can be renormalized by a finite number of counter terms, leading to a finite result for the physical quantities. That are wave-function normalization, (electron-) mass, and coupling-constant/charge renormalization. All other diagrams (particularly also the superficially divergent four-photon vertex due to a Ward-Takahashi identity from local gauge symmetry) are finite.

When two bodies exchange electromagnetic waves, the light pressure can only be repulsive. When they exchange electrostatic fields, these can be repulsive or attractive, freely.
Now, real photons derive from evidence that the electromagnetic waves are quantized when radiated and received.
But as for virtual particles - what types of observations are better explained when electrostatic field is viewed as a flow of discrete particles rather than a continuum field?

"Virtual particles" are just a slang word for fields, mediating the interaction. In Feynman diagrams they are depicted by the internal lines, connecting two interaction vertices. One should not (only) read Feynman diagrams as pictures for scattering processes of relativistic particles but rather as a very concise and economic notation for the mathematical expressions calculating the time-ordered $n$-point functions (auto-correlation functions of field operators), which can be used to calculate S-matrix elements ("LSZ reduction formalism"). The internal lines stand for the (Feynman/time-ordered) propagators of the corresponding fields (in QED for electron-positron-Dirac and photon fields).

 

[Orodruin]

Although this is a question of definition: when two charges interact, does each charge feel the force of its own field, or of the other charge´s field?

I’d say they feel the effect of the electromagnetic field.