What mechanism enables interaction of the fields?

[Paul Woods]

In Quantum Field Theory, I am led to believe that there is a different field for each type of particle. When particles interact, it is an exchange of vibration between the fields. What mechanism is at play when one field influences another in this way?

It seems I've only ever found half-explanations of this which argue in circles, like saying that the electron is affected by the photon first then the photon affects the other electron (or whatever), but a photon is just another excitement of a field, so the question still isn't answered.

What's between the fields which communicates that one should use its vibrations to make another vibrate?

 

[Ian Mitchell]

The whole vibration concept is more of a way to visualize and mathematically model QFT, since it is so hard to imagine things that are that small at that amount of energy. The "photons as an excitement of another field" is mostly just for describing virtual particles.

Virtual particles are particles that appear for a brief second to really fill one single purpose, to interact with other particles. Take for example a famous Feynman diagram in QED: the diagram for electron-electron scattering. The photon between the two electrons isn't technically real, but it is. It's a way of quantifying the electric field into discreet packets; and so far, it's filled the bill.

I would suggest going and reading a bit more about the topic. At the moment I'm pretty tired, and I wasn't very good at explaining things in the first place.

 

[PeterDonis]

When particles interact, it is an exchange of vibration between the fields.

No, it isn't. Particles "interact" by exchanging other particles--for example, electrons interact by exchanging photons.

@Ian Mitchell gives good advice. A good, although informal, introduction is Feynman's popular book QED: The Strange Theory of Light and Matter.

 

[bhobba]

In Quantum Field Theory, I am led to believe that there is a different field for each type of particle. When particles interact, it is an exchange of vibration between the fields. What mechanism is at play when one field influences another in this way?

Well that is a very deep question we really don't know the answer to. Technically its because of an interaction term between the Lagrangian's of the two fields. You write it all down in Quantum Field Theory (QFT) language and you get the standard model. You have virtual particles and all that stuff you likely have read about in pop-sci literature - forget about those - that they exist in a real sense is one of a number of common myths about QM:
https://arxiv.org/abs/quant-ph/0609163

That aside where do these equations come from?

What you do, theoretically, is you write down the Lagrangian of both fields - the combined Lagrangian is simply the addition of the two Lagrangian's and doesn't really tell us anything - the fields simply behave their same separate ways but you have one equation instead of two. Then you notice something - they have this thing called global U(1) symmetry. Its simply the well known phase symmetry of quantum states - you multiply a pure state by a phase factor and you get the same state. But this is global - relativity teaches us it should really be local. So you check local symmetry - bummer it does not have this symmetry locally - not great from a theoretical point of view if the symmetry is more than just a mathematical curiosity. So let's insist it be local - the reason it's not local is these terms appear in the Lagrangian when you transform it under local U(1) symmetry. Ok - let's write the Lagrangian with terms to counter these other terms. How to do that almost stares you in the face. You do that - and lo and behold - its now locally U(1) invariant - great. But we now have this other term that appears in the Lagrangian. Its an interaction term between the two fields. We chug through the math to see how it affects it - and - to our surprise it predicts electromagnetism. Amazing. But while highly suggestive it does not prove anything - its very beautiful and all that - but why is nature like that - we as yet do not know.

All the other forces, the weak and the strong, can be done in a similar way - its way way beautiful, and all part of the standard model.

And even more amazing is the separate field Lagrangian's themselves are determined by symmetries - it's based on so called representations of the Lorentz group - but I won't go into the details of that one. If you are interested in the technical detail here is a book that gives it:
http://physicsfromsymmetry.com/

As one wit says - the standard model has parts of dazzling beauty like the above, and other parts downright ugly. For example why should we have a separate symmetry for each force - shouldn't there be one symmetry overall - and exactly where does gravity fit in. And we have to put constants in by hand such as the strength of the EM interaction. Right now things just do not look right - we need another Einstein.

If you want to pursue this a bit further see the following:
http://philsci-archive.pitt.edu/3662/

He also wrote a book about it:
https://www.amazon.com/dp/1591024242/?tag=pfamazon01-20

Thanks
Bill

 

[strangerep]

Ian Mitchell gives good advice.

...except for the bit about virtual particles.

 

[weirdoguy]

And with that, I would recommend (for you @Ian Mitchell too) to read those insights
https://www.physicsforums.com/insights/misconceptions-virtual-particles/
https://www.physicsforums.com/insights/physics-virtual-particles/

 

[Paul Woods]

Hey, Bill, that's a superb answer. Thank you very much! Have you written any books? I shall enjoy the reading you have suggested.

 

[bhobba]

Hey, Bill, that's a superb answer. Thank you very much! Have you written any books? I shall enjoy the reading you have suggested.

Hi Paul.

No mate - I haven't written anything.

But yes those sources I gave are fun.

However first read Stengers stuff, then a very great book by the equally great Landau - simply called Mechanics:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Its not talked about a lot - except by me - but will change how you view physics - it did me.

Then read the book - Physics From Symmetry.

Once you have done that get back to us with what you think and some further suggestions can be made.

Thanks
Bill

 

[Ian Mitchell]

Yeah, that explanation was flat out wrong. I was really tired, but that was honestly no excuse.