Recent content by Shaw1950

Alxm, look I really appreciate your input, but as regards my PhD I got that 37 years ago and haven't touched a physics text until a few weeks ago. As you can imagine, one forgets a lot in 37 years, so please bear with me. Physics is still a lot of fun and your help is very much appreciated...

Thanks, happy with all your comments. There seem to be two unresolved issues: 1) path integral: some commentators have referred to this formulation in terms of virtual "particles" - would they be more sensible to call them virtual "paths"? 2) bound states: Feynman repeatedly describes the...

Dear Bill, I am with you, please tell me more about the method(s) of solving the timelike (A0) component. I gather pertubation methods are out, so what alternatives are available? I also understand that the path integral solution was only published in 1979 by Duru and Kleinert, so what...

"Virtual particle" in path integral and perturbative approaches The term "virtual particle" is used in path integral and perturbative approaches. How do these "virtual particles" differ and how are they related? [For example, static, bound states such as the hydrogen atom are solvable by...

Thank you all for the comments and feedback it was most helpful and has spurred me on to do some of the maths for myself. One of my difficulties is that many textbooks "fudge" the solution by ignoring the fact that a point charge is essentially a delta distribution and they skip essential steps...

One way of looking at it is to look at Coulomb scattering of two negatively (or positively) charged particles. In the Classical (non-Quantum) picture the two particles slow down before rebounding; simultaneously, the energy in the electric field rises and then falls again (as does the field...

How would you think this specific result was viewed by Maxwell and his peers, if it was known? It surely would have seemed odd that in moving from a static particle to a frame at constant speed, a magnetic field mysteriously appeared yet the electric field was essentially the same. Did this get...

RedX, in terms of deeper insight, my suspicion is that the equations can be separated, perhaps Helmholtz decomposition, into parts that behave in different ways, and such a decomposition will explain the result. But I haven't figured out what that decomposition is yet.

Dale, thanks for all your feedback, much appreciated. An issue remains for the low speed approximation. At low speeds there are still electrodynamic and magnetodynamic terms dE/dt and dB/dt in Maxwell and yet the solution is a magnetostatic. So why is the low speed solution magnetostatic? (1)...

I agree. Now if you solve the multiple equations of Maxwell, you will also get Biot Savart. So two different sets of equations give you the same answer. What I'm asking is not about solving equations (for the result could be a coincidence) but what is the deeper insight into why the two...

Surely there is some significance that when you solve just Ampere's law with the point charge (and so just one equation  x B = J) you get the same answer as when you solve the full maxwell's equations (ie two vector equations  x B = J + dE/dt and  x E = -dB/dt). Why is the older formulation...

Another way of asking the question is why, for a moving point charge, is the Lienard Wiechert solution to the two vector equations :  x B = J + dE/dt and  x E = -dB/dt => => B = Q VxR/4πrrr (rrr=r cubed as symbols are unavailable, please excuse the poor symbols, the best I could do) the...

On Lorentz invariance I stand corrected, thanks all of you for putting me right. Thank you also for drawing my attention to Lienard Wiechert which is very helpful for following through the calculation. Can anyone give a simple explanation of why for the steadily moving particle, whose...

To clarify this, there seem to be 3 distinct situations that are widely studied: 1) currents in wires - zero net charge, no electrostic field - Biot-Savart only 2) particle beam - net charge, field is static so no displacement - Biot-Savart only 3) moving charge - net charge, dynamic field...

By "non-relativistic" I mean the equations that Maxwell originally formulated rather than the re-formulation on a relativistic basis. Getting back to my original question, which I'd love someone to answer, what is the magnetic field of a single charge moving at a constant velocity? It clearly...