Experimental proof of retardation in EM fields

[universal_101]

In the light that QED suggests the speed of interaction is infinite, are there any experiments which makes it clear that mediating fields are retarded in classical electrodynamics ? Whereas, on the theoretical grounds the causality requires time asymmetric interaction, but do we have any classical proof of the same for the so called bound fields ?

Thanks

 

[vanhees71]

Nothing in QED tells that there's faster-than-light signal propagation since it's a microcausal local relativistic QFT. The relativistic space-time structure is one of the best-tested theories in physics ever, not least through the high-precision successes of QED itself.

 

[Q-reeus]

In the light that QED suggests the speed of interaction is infinite, are there any experiments which makes it clear that mediating fields are retarded in classical electrodynamics ? Whereas, on the theoretical grounds the causality requires time asymmetric interaction, but do we have any classical proof of the same for the so called bound fields ?
Thanks

Universal_101 - Please check out this Wiki article: http://en.wikipedia.org/wiki/Antenna_measurement, especially the sub-section "physical Background". Near as well as far-field antenna measurements are a very well established practice. And theory - which absolutely relies on retardation of the near ('bound') as well as far (radiation) fields, is in excellent agreement with all such actual measurements.

 

[universal_101]

Universal_101 - Please check out this Wiki article: http://en.wikipedia.org/wiki/Antenna_measurement, especially the sub-section "physical Background". Near as well as far-field antenna measurements are a very well established practice. And theory - which absolutely relies on retardation of the near ('bound') as well as far (radiation) fields, is in excellent agreement with all such actual measurements.

I thought near field antenna measurement would match the simple coulomb's law, since it is retarded field plus the first order correction, especially in the light that near field has very low retardation and the drift speed of charge carriers in antenna is very limited.

But I don't know if there is any difference between near field measurement(bound fields) and the simple coulomb's law, if it deviates appreciably then certainly it is a valid proof.

 

[universal_101]

Nothing in QED tells that there's faster-than-light signal propagation since it's a microcausal local relativistic QFT. The relativistic space-time structure is one of the best-tested theories in physics ever, not least through the high-precision successes of QED itself.

Signal(radiation or photons) seems drastically different than mediating or bound (virtual photons), I just thought it would have NO point to make different types of photons if they have the same properties. But I'm not an expert in QM, so please, try to explain in simple words, and it would be nicer if we can discuss it in classical sense.

Thanks

 

[vanhees71]

I don't know, what you are talking about! By construction QED is a local, microcausal QFT and thus there's nothing that propagates with faster-than-light speed.

There are, even in classical electromagnetics, apparent violations of the "speed limit". The most famous are the phase and group velocity for waves with frequencies close to a resonance in the dielectric function (index of refraction), the socalled region of anomalous dispersion. This has been a famous debate in 1907 between one of the leading experimentalists, Willy Wien, and one of the leading theorist of their time, Arnold Sommerfeld. Sommerfeld answered this question in half a page with help of an elegant use of the residual theorem, and as expected Einstein causality is never violated by Maxwell theory, which is after all a fully relativistic classical field theory. Lateron Sommerfeld and also Brillouin worked out this problem in two famous articles in "Annalen der Physik", where they precisely show that the wave front of a wave packet proceeds precisely with vacuum (!) speed of light. They investigated also in great detail the shape of the head of the signal, the socalled Sommerfeld and Brillouin precursors. All this you can read in volume 4 of Sommerfeld's Lectures on Theoretical Physics.

There you also find the much less complicated elementary radiation solutions like the Hertz dipole in vacuum, which is of course precisely given by the retarded Green's function folded with the source (electric four current) of the em. field. There you explicitly see that the signal proceeds with the speed of light. Very close to the source you can approximate this solution by the quasistationary solution (the socalled "near-field region"), which means to neglect the displacement current and retardation. This of course doesn't prove the retarded solution wrong, because it's only an approximation to the latter that is valid only at distances smaller than the typical wavelength of the signal around the source. The full solution is still the retarded solution.

 

[Q-reeus]

I thought near field antenna measurement would match the simple coulomb's law, since it is retarded field plus the first order correction, especially in the light that near field has very low retardation and the drift speed of charge carriers in antenna is very limited.

But I don't know if there is any difference between near field measurement(bound fields) and the simple coulomb's law, if it deviates appreciably then certainly it is a valid proof.

On closer inspection, that linked article, while starting off referring to the retardation of all field components, dropped down to the far field approximation quickly. OK, please visit here and check the expressions for E and H fields under 'Elementary doublet' sub-section. Note in addition to 1/r³ retarded Coulombic field and 1/r radiation field, there is a 1/r² 'induction field' also. All components obey light speed propagation. it's true that in the very near zone, phase velocity can greatly exceed c, but that is an artifact of how the various components add there. No actual signal - i.e. a modulation of the otherwise unvarying sinusoidal driving current, in being conveyed - just motion of the wave crests. This same kind of feature applies to say hollow metallic wave guides - and it's the group velocity v_g, not phase velocity v_p, that determines signal propagation, and invariably is less than c according to v_gv_p = c². Back to the dipole oscillator case; without taking into account retardation, not just the observed phase relationships, but the field patterns would be quite different to what is actually measured. There is really no room for doubt that 'bound' fields obey the usual retardation relations.

 

[vanhees71]

It must be stressed again that also group velocity is not a general definition for signal propagation. That holds only true as long as the saddle-point approximation of the Fourier transform between frequency and time representation is applicable. Only then it is a good approximation to consider the wave packet traveling with the group velocity keeping it's shape. In region of strong anomalous dispersion (as occurs in media close to a resonance or also in wave guides; there particularly for evanescent-mode propagation) this approximation is not applicable, and the group velocity can become greater than the vacuum-speed of light or even negative. This does not contradict the Lorentz covariance and causality of Maxwell theory, because this approximation is simply invalid.

What, by the way, do you meant by "bound fields"? Are you referring to standing waves here or what?

 

[Q-reeus]

It must be stressed again that also group velocity is not a general definition for signal propagation. That holds only true as long as the saddle-point approximation of the Fourier transform between frequency and time representation is applicable. Only then it is a good approximation to consider the wave packet traveling with the group velocity keeping it's shape. In region of strong anomalous dispersion (as occurs in media close to a resonance or also in wave guides; there particularly for evanescent-mode propagation) this approximation is not applicable, and the group velocity can become greater than the vacuum-speed of light or even negative. This does not contradict the Lorentz covariance and causality of Maxwell theory, because this approximation is simply invalid.

Sure, in anomalous dispersion case 'group velocity' can exceed c, and it's something I have brought up myself in the past here. But as you said earlier, it tends to lose real meaning there, and leading wave front never exceeds c. Why throw up such overkill issues though when the basic matter of whether near/static/'bound' fields have finite propagation is at question? I noticed you did the same kind of thing here Quite impressive as a display of mathematical exactitude, but was it really apt for someone who didn't even understand transformer action?

What, by the way, do you meant by "bound fields"? Are you referring to standing waves here or what?

I take it this refers to myself rather than OP? Please actually quote to avoid such confusion. I will anyhow assume it does. I was merely adopting the parlance used by the OP in #1, otherwise it's not how I would term things, even though there nothing particularly wrong with that terminology in context.

Now, I bit my tongue responding to you at all. We have an issue that goes back to here
I considered it at the time simply a wise move on your part to decline answering me there, but that changed when you later came back with an unchanged position. So, to ignore a request for response is in my book downright disrespectful and basically a snub. I don't care how great someone's learning may be, if they don't show minimal respect and courtesy for their fellows, there is something basically amiss. So, please explain yourself, or if there is no satisfactory response, it will confirm to me you were indeed, for whatever reason I don't know, just outright snubbing me back then. And I emphasize the fundamental distinction between ignoring a comment, which can be quite ok, and ignoring a *request* for response, which imo is never ok. Which btw, apart from being ignorant, leaves the other party in a state of never knowing why.

 

[vanhees71]

I'm sorry that I'm not reading 24/7 your postings and that I missed to anwer questions brought up in some of your postings.

and I think one must answer as simple as possible but not simpler! If it comes to the issue of faster-than-light wave propagation, one has to answer immediately and correct any wrong statements right away!

Concerning the other thread about work/energy in electromagnetism, where you doubt the very foundations of Maxwell theory, particularly the validity of Poynting's theorem, I'm simply tired to repeating again and again the same very simple thing. The Poynting theorem holds generally, no matter whether there are superconductors involved or not. Work on charges and magnetic dipoles is done by the electric components of the em. field not the magnetic.

 

[Q-reeus]

I'm sorry that I'm not reading 24/7 your postings and that I missed to anwer questions brought up in all your postings.

and I think one must answer as simple as possible but not simpler! If it comes to the issue of faster-than-light wave propagation, one has to answer immediately and correct any wrong statements right away!

Concerning the other thread, I'm simply tired to repeating again and again the same very simple thing. The Poynting theorem holds generally, no matter whether there are superconductors involved or not.

While not imo a very satisfactory response, at least it is one. Let's just let it all rest here then and move on.

 

[universal_101]

I don't know, what you are talking about! By construction QED is a local, microcausal QFT and thus there's nothing that propagates with faster-than-light speed.

There are, even in classical electromagnetics, apparent violations of the "speed limit". The most famous are the phase and group velocity for waves with frequencies close to a resonance in the dielectric function (index of refraction), the socalled region of anomalous dispersion. This has been a famous debate in 1907 between one of the leading experimentalists, Willy Wien, and one of the leading theorist of their time, Arnold Sommerfeld. Sommerfeld answered this question in half a page with help of an elegant use of the residual theorem, and as expected Einstein causality is never violated by Maxwell theory, which is after all a fully relativistic classical field theory. Lateron Sommerfeld and also Brillouin worked out this problem in two famous articles in "Annalen der Physik", where they precisely show that the wave front of a wave packet proceeds precisely with vacuum (!) speed of light. They investigated also in great detail the shape of the head of the signal, the socalled Sommerfeld and Brillouin precursors. All this you can read in volume 4 of Sommerfeld's Lectures on Theoretical Physics.

There you also find the much less complicated elementary radiation solutions like the Hertz dipole in vacuum, which is of course precisely given by the retarded Green's function folded with the source (electric four current) of the em. field. There you explicitly see that the signal proceeds with the speed of light. Very close to the source you can approximate this solution by the quasistationary solution (the socalled "near-field region"), which means to neglect the displacement current and retardation. This of course doesn't prove the retarded solution wrong, because it's only an approximation to the latter that is valid only at distances smaller than the typical wavelength of the signal around the source. The full solution is still the retarded solution.

I apologize for the late response first,

First of all, the mediating mutual force between two charges are referred as bound fields, what I'm questioning is, suppose if the sun had a net charge on it, would we have the direction of force on a charge on Earth same as the aberration of light ?

Since, gravity surely does not seem to work this way,(I know one can always represent gravity as a curved space!) well, but it also has the finite speed of propagation, isn't it ? And if one expect the gravitation waves, then retardation in gravity(force field) must be present, but we don't measure it.

I wanted to clear the differences between the mediating mutual force field and the radiation(light, signal, group velocity etc.). I think that retardation in force fields are very obvious logically, but they seem difficult to measure.

Thanks

 

[universal_101]

On closer inspection, that linked article, while starting off referring to the retardation of all field components, dropped down to the far field approximation quickly. OK, please visit here and check the expressions for E and H fields under 'Elementary doublet' sub-section. Note in addition to 1/r³ retarded Coulombic field and 1/r radiation field, there is a 1/r² 'induction field' also. All components obey light speed propagation. it's true that in the very near zone, phase velocity can greatly exceed c, but that is an artifact of how the various components add there. No actual signal - i.e. a modulation of the otherwise unvarying sinusoidal driving current, in being conveyed - just motion of the wave crests. This same kind of feature applies to say hollow metallic wave guides - and it's the group velocity v_g, not phase velocity v_p, that determines signal propagation, and invariably is less than c according to v_gv_p = c². Back to the dipole oscillator case; without taking into account retardation, not just the observed phase relationships, but the field patterns would be quite different to what is actually measured. There is really no room for doubt that 'bound' fields obey the usual retardation relations.

Thanks Q-reeus, I think it is a very good explanation indeed. I think now I know what did I miss.

 

[Q-reeus]

Thanks Q-reeus, I think it is a very good explanation indeed. I think now I know what did I miss.

Glad to be of some help . There's stuff out there talking about 'infinite speed of virtual photons' etc., but it reminds me of Fourier analysis of a pulse that may be very short, yet mathematically is actually composed of an infinite number of infinitely long wave trains! We distinguish between mathematical creatures and what is physically real!