# I A special relativity explanation for the Lorentz Force?

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1. Mar 14, 2016

### tim9000

I am still a bit puzzled by this video:

Does this mean that force exerted on an electrically charged particle facilitated by moving through magnetic field B is due to special relativity, and not virtual photons acting as magnetic force carriers?

Thanks

2. Mar 14, 2016

### bhobba

You have to differentiate between a QM explanation and a classical explanation.

First as many threads here explain virtual particles do not exist but a QM explanation is not required for this.

SR and Coulombs law implies Maxwell's equations:

Thanks
Bill

3. Mar 14, 2016

### tim9000

Thanks for the pdf Bill, I look forward to reading through it.

Ah, so is this one of those, where SR and QM both explain the same thing in totally different ways, but the two models don't meet?

Thanks

4. Mar 14, 2016

### bhobba

Of course QED can explain EM phenomena. But for classical phenomena is simply not required.

Thanks
Bill

5. Mar 14, 2016

### Staff: Mentor

It does not mean that, because the two explanations are not mutually exclusive. Electricity and magnetism are, as the video says, connected by special relativity. Virtual photons acting as force carriers appear in the math when you quantize this theory of electromagnetic fields to get to quantum electrodynamics.

6. Mar 15, 2016

### tim9000

Thanks for the replies.
I understand that QED and SR are not mutually exclusive.
Excuse my ignorance, but a simple electromagnet, is that covered by what you mean by classical phenomena?
I infer you're telling me not to make things more complicated than they need to be, but was I right when I said SR and QED can explain EM phenomena (a 'classical aspect' in this case) but they do it in different ways? (Like was I right when I said they're both sound theories but no one can figure out how they work together?)

Thanks!
Hmm, could one say something like 'from the reference of SR the EM (virtual photon) force carriers are electric, and from the reference of QM the (virtual photon) force carriers are magnetic?

Thanks

P.S. I found the part "quantize this theory of electromagnetic fields to get to quantum electrodynamics." particularly enlightening.

7. Mar 15, 2016

### bhobba

Yes and no. Yes using a simple model of the electrons like spinning tops classical EM theory (Maxwell's equations) can explain it. They are not really like spinning tops though so to be exact you need QED - but its more complicated. Depending on your application that compilation may or may not be required. Mostly it isn't.

QED has SR already built into it. So does Maxwell's equations for that matter - but that is whole new story. Start a new thread if you are interested but read the link I gave first.

No. At the beginner level see Feynmans classic (an oldy but one of the very best lay books on QM ever written):
https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

I also like the following:
https://www.amazon.com/Fields-Color-theory-escaped-Einstein/dp/0473179768

Thanks
Bill

Last edited by a moderator: May 7, 2017
8. Mar 15, 2016

### tim9000

I always imagined virtual photons shooting out the axis of a spinning electron. From what I remember from quantum mechanics (years ago). Electrons are probabilistic clouds, of standing waves.
Is there any simple QED analogy of magnetic force carrier, that you could throw at me? Just out of curiosity, no biggie if not.

I wish I had the time to read through those in depth (child on the way and looking for work). That Feynman book does ring a bell, probably already on my endless to-do list.
If you could humour me for a sec, could we break this down into parts:
What about the first part? from the reference of SR is the force on the charge an 'electric force carrier' / virtual photon, or did I just make that up?

Thank you

9. Mar 15, 2016

### bhobba

Last edited by a moderator: May 7, 2017
10. Mar 15, 2016

### tim9000

Last edited by a moderator: May 7, 2017
11. Mar 15, 2016

### Staff: Mentor

No. There is no "electrical" and "magnetic". There is just one electromagnetic field and the apparent distinction between electricity and magnetism is caused by the observer's velocity relative to the sources of that field. That's the real point of the "special relativity explanation for the Lorentz force": how an observer divides the electromagnetic force into electrical and magnetic bits depends on the observer's motion.

So we have this one electromagnetic field, described by relativity and classical electrodynamics. How do we treat this field quantum mechanically? Standard undergraduate quantum mechanics, with wave functions and particles as probability clouds and Schrodinger's equation and all that, is not up to the job. The problem is that this basic QM ignores relativistic effects so it only applies when the velocities involved are small compared with the speed of light and the energies involved are small compared with the mass of the particles involved. Neither condition applies to electromagnetism - disturbances in the electromagnetic field propagate at the speed of light, and they can be arbitrarily small.

So we need to extend QM to allow for relativistic effects, and this leads to quantum field theory (QFT; quantum electrodynamics is QFT applied to the electromagnetic field). In QED, all transfers of energy and momentum to and from the field happen in discrete lumps at a single point in space-time (that's space-time, not space - remember that this is a relativistic theory) and we call these lumps "photons". And since a classical force is something that transfers energy and momentum.... We have photons, whether virtual or real, as the carriers of the electromagnetic force.