# Propagation speed of Coulomb fields

meopemuk
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weirdoguy

## Answers and Replies

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2022 Award
R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella, "Measuring propagation speed of Coulomb fields", Eur. Phys. J. C 75 (2015), 137. arXiv:gr-qc/1211.2913v2

Eugene.
It's sufficient to read the abstract to see that this is nonsense. The Lienard Wiechert solutions for the fields are by construction the retarded fields, and so it must be because otherwise you'd violate causality in the relativistic context of Minkowski spacetime. There's nothing propagating with infinite speed.

There's much confusion about the retarded solutions in the literature, mostly due to sloppy handling of partial derivatives. It's also well known that the Jefimenko equations for the fields indeed are identical to the equations derived from the Lienard Wiechert potentials (i.e., the retarded solution for the four-vector potential in Lorenz gauge) and also from the solutions to the potentials in the Coulomb gauge, which is no surprise due to gauge invariance.

Also the expression in the Feynman lectures is equivalent with the Jefimenko equations. See the following comment to the cited paper (it's open access btw!):

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Dale, bhobba, Delta2 and 1 other person
meopemuk
Delta2, Motore and weirdoguy
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The nonsense is not in the experiment (I've not checked what they really did, I just read the abstract) but the entire intepretation to begin with. It simply doesn't make sense to ask, how fast a "Coulomb field propagates". The Coulomb field is simply there, and nothing propagates. Nothing can be a-causal, because Maxwell's electrodynamics is a causal theory (as the dynamics of the electromagnetic and continuous charge-current distributions). As far as I understand the just quoted paper by Stefanovich by also glancing only over it that's what has been confirmed by these experiments in his interpretation of them.

bhobba and Delta2
meopemuk
It simply doesn't make sense to ask, how fast a "Coulomb field propagates".

When a relativistic electron beam leaves the accelerator pipe and enters the experimental hall, the electric field of the beam is going to change somehow in order to fill the room. This propagation speed is exactly what was measured in the Pizzella experiment. Maxwell-Lienard-Wiechert theory predicts that the electric field buildup occurs only gradually with the speed of light. But the experiment showed that the electric field of the beam filled the room immediately as if the Coulomb field propagated faster than light.

This sharp contradiction between theory and experiment is the reason why I believe the speed of propagation of EM interactions is the most important open question in modern physics.

Eugene.

weirdoguy and Motore
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No, the Lienard-Wiechert solutions precisely predict that there's not only a radiative piece which you seem to describe but that there's also the electrostatic piece. As far as I understand the paper the meausured fields are consistent with Maxwell theory and thus the Lienard-Wiechert solutions. The speed of propagation of the em. interaction in a vacuum is among the best established phenomena in both theory and experiment ever.

bhobba
meopemuk
As far as I understand the paper the meausured fields are consistent with Maxwell theory and thus the Lienard-Wiechert solutions.

No, this is not what this paper claimed. Their results directly contradict the Lienard-Wiechert solution. Though, this paper is not well written, and the contradiction is not formulated in clear terms. Perhaps the authors didn't want to stir up too much controversy?

The speed of propagation of the em. interaction in a vacuum is among the best established phenomena in both theory and experiment ever.

After Pizzella's experiment, I am not so sure about that.

Eugene.

weirdoguy and Motore
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The authors are, however, self-contradictory in their own conclusion section. On the one hand they claim their measurement is consistent with the results from the Lienard-Wiechert potentials. In the next paragraph, however they claim that would contradict the predictions from the retarded potentials, but the Lienard-Wiechert potentials are the retarded potentials for a moving point charge, given by Eq. (4) of that paper. For the simple derivation see p62-62 of

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

Dale
weirdoguy
This sharp contradiction between theory and experiment

We once had this "contradiction" with superluminal neutrinos.

The word "nonsense" cannot apply to (properly made) experiments.

Properly made - yes. Did they repeat their experiment a couple of times?

Motore
meopemuk
We once had this "contradiction" with superluminal neutrinos.

The OPERA setup was unique and very complicated. Nobody could find/fix the problem but those involved in that project.

In contrast, Pizzella's experiment looks very basic and inexpensive (to my untrained eye). I think it can be repeated easily at any lab that has a decent particle accelerator. Even if this rerun doesn't find the claimed superluminal effect, it will be very valuable as the first experimental measurement of the speed of the velocity part of Lienard-Wiechert fields.

Properly made - yes. Did they repeat their experiment a couple of times?

As far as I know, they made multiple runs with varying conditions (like the addition of the "beam stop").

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I've read the paper under debate in more detail, and I don't see any contradiction to standard Maxwell theory and SRT. Note that the claim that the Feynman expression for the retarded fields of moving charges is in contradiction to the standard theory. It's mathematically identical [1]. Thus the statement in the paper that the predicted signals to be measured by the experiment is wrong, and what they've shown is that their measurement is consistent with the standard expression and thus the retarded-potential aka. Lienard-Wiechert potential.

[1] https://link.springer.com/article/10.1140/epjc/s10052-016-4108-7 (it's open access!)

Motore and weirdoguy
meopemuk
It is well-known that the electric field of a fast-moving charge has the form of a "pancake" that is perpendicular to the direction of motion. To get this result, you can use Lienard-Wiechert formulas or you can simply Lorentz-contract the spherical electric field of a charge at rest. You'll get the same result quoted in many textbooks. There is no controversy here.

However, the above result refers to a charge that was moving uniformly in empty space for infinitely long time before the observation was made. The surprise of the Pizzella experiment was that the same pancake-shape field was found around an electron bunch which just emerged from the accelerator pipe, so the bunch was not moving uniformly in empty space for long time before the observation.

According to Maxwell-Lienard-Wiechert theory, the fast electron bunch entering the experimental room from the accelerator pipe initially does not have any electric field around it. The pancake field forms only gradually as the bunch moves away from the accelerator pipe into the free space.

A simple estimate shows that for the 500 MeV beam the radius of the pancake would grow to only 0.5 cm at the distance of 5m from the accelerator pipe's exit. Contrary to this expectation, Pizzella et al. registered rather healthy electric fields as far as 55 cm from the beam's axis. Moreover, they didn't see any predicted "pancake formation" effect. The field pancake was fully formed as if the beam was moving uniformly without obstruction for hundreds of meters before being measured.

In other words, it appears that the fully formed pancake electric field around the beam appeared immediately after the beam left the pipe. This strongly suggests a superluminal propagation speed of the Coulomb field.

Eugene.

weirdoguy
Gold Member
2022 Award
Of course the electron has always its electric field around it, also when being in a pipe. I guess, it's not an easy task to solve the full time-dependent problem of an electron moving in a cavity and then exiting at its end, but given the fact that the experiment was made not too close to this end of the cavity, for me it's intuitively not too surprising that what they measure is the Lorentz-boosted Coulomb field. It's only amazing that a paper with the theory part being completely wrong (claiming that two mathematical identical formulae can yield completely different predictions for the expected outcome of the measurement) could appear in a well-established physics journal like EPJC. As a referee, I'd already stumbled over the title, because for me the idea that a static field has a "propagation speed" is already absurd. Using Google Scholar you can find a bunch of papers commenting this paper which are also partially quite mediocre, but some are very good, among them the one quoted above correcting this absurd wrong claim about two identical formulae being different.

Dale and Vanadium 50
meopemuk
I agree that theory is not the strongest part of this paper.

You can find IMHO the best available Maxwell-Lienard-Wiechert theoretical description of the charge electric field formation after exiting the accelerator pipe in
Carron N.J. Fields of particles and beams exiting a conductor. Prog. Electromagn. Res. 28 (2000), 147.

But Pizzella's effect is rather dramatic and its explanation does not require detailed field calculations. Roughly speaking, classical theory predicts that the radius of the field "pancake" is equal to ##R=L/\gamma##, where ##L## is the distance traveled by the beam after exiting the pipe and ##\gamma## is the usual relativistic factor. In our case ##L = 92 - 552 ## cm and ##\gamma \approx 1000##, so the expected extension of the field is only 1-6 mm. But the pancake field was seen as far as 55 cm from the beam axis. This is a huge discrepancy between the experiment and classical theory.

Eugene.

Staff Emeritus
The position that the Pizzella paper is confused theoretically, confusing as to exactly what their measurement entails, deliberately obfuscating the results to avoid controversy but provides unequivocal evidence of faster-than-light field propagation is...well...hard to swallow.

But the experiment showed that the electric field of the beam filled the room immediately as if the Coulomb field propagated faster than light.

I don't think Pizzella et al. are saying that. Maybe you're right and that they are obfuscating that; the paper is too confused to tell. As you know, if the speed is infinite in one frame, it can be Lorentz transformed to a frame where the signal arrives before it is sent.

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vanhees71 and bhobba
meopemuk
the paper is too confused to tell.
You can probably find some clarifications of authors' claims in their other articles:

R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella, Why the interpretation of Measuring propagation speed of Coulomb fields'' stands, Eur. Phys. J. C, 77 (2017), 75. arXiv:gr-qc/1611.06935v1

R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella, Experimental result on the propagation of Coulomb fields, J. Phys. Conf. Series, 845 (2017), 012015.

As you know, if the speed is infinite in one frame, it can be Lorentz transformed to a frame where the signal arrives before it is sent.

This is true if we assumed exact applicability of Lorentz transformations to all events, including events involving interacting particles. However, this assumption remains a subject of a long-standing controversy called the "no interaction theorem."

D. G. Currie, T. F. Jordan, E. C. G. Sudarshan, Relativistic invariance and Hamiltonian theories of interacting particles, Rev. Mod. Phys., 35 (1963), 350.

If we relaxed the strict "worldline invariance" rule and allowed interaction-dependence of boost transformations, we could both avoid the pitfall of the "no interaction theorem" and explain the Pizzella experiment without violating the principle of causality.

E. V. Stefanovich, Does Pizzella's experiment violate causality?, J. Phys. Conf. Series, 845 (2017), 012016.

Eugene.

weirdoguy
Mentor
Did they repeat their experiment a couple of times?

And by different groups. And get a theorist to look at it. I remember the story of a group that thought they had found a new particle in an experiment, but, correctly as it turned out, decided to show the evidence to Feynman. He had a look at the accelerator pictures and said - you will find a bolt right there - and guess what - they did.

Thanks
Bill

weirdoguy
Mentor
There's nothing propagating with infinite speed.

And nothing can. I could give the reference to the paper deriving SR without the speed of light being constant assumption - but will not here because anyone advanced enough to read that paper should know it, or be able to dig it up. The fact is the constant c that appears in the Lorentz Transformations (which of course implies nothing can travel faster than that c) can be determined as the speed of light in many different experiments, a lot of which have nothing to do with EM. If it was possible it would turn physics on its head. Extraordinary claims require extraordinary evidence (I wish I said it - but it was good old Issac Asimov). One experiment that has been heavily criticized here is not extraordinary evidence.

Thanks
Bill

Dale, vanhees71 and weirdoguy
Mentor
This is true if we assumed exact applicability of Lorentz transformations to all events, including events involving interacting particles. However, this assumption remains a subject of a long-standing controversy called the "no interaction theorem."

That's news to me. I thought Wigner's No Interaction Theorem was a cornerstone of why we need fields - since if you move say a charged particle a nearby charged particle will only move a bit later by SR (the theorem itself is about Hamiltonian's etc getting into trouble with interactions - so they can't strictly be allowed relativistically - its real issue as I will mention later is Newtons Third Law). So something is needed if you believe in Noether and all that to preserve momentum etc. That something is a field. Of course by some rather weird shenanigans one can get by without fields as Wheeler and Feynman showed, but its so weird it sort of died out - except maybe in the transactional interpretation of QM - but that is another story.

Sometimes you see discussions about it and Newtons Third Law - I think those that wish to discuss it in that context need to read Landau - Mechanics where he explains the reason in his usual short - terse - but correct style (hint - think Galilean Transformations)

It also just occurred to me its possibly the reason you need QFT - but that's just a thought that struck me while penning this.

Thanks
Bill

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vanhees71 and weirdoguy
meopemuk
Extraordinary claims require extraordinary evidence (I wish I said it - but it was good old Issac Asimov). One experiment that has been heavily criticized here is not extraordinary evidence.

On the other hand, one good experiment is worth a thousand theories. (Don't remember who said this.)

You are right, there are lot of papers where Lorentz transformations are derived with full mathematical rigor. Here are a couple examples:

A. R. Lee, T. M. Kalotas, Lorentz transformations from the first postulate, Am. J. Phys., 43 (1975), 434.
D. A. Sardelis, Unified derivation of the Galileo and the Lorentz transformations, Eur. J. Phys. 3 (1982), 96.

But you may notice that all these derivations share one common feature: they assume from the beginning that the desired transformations are universal, i.e., they apply not to specific physical events, but to abstract space-time points. So, in fact it is supposed that if two events (perhaps of different physical nature) occupy the same space-time point, then they will remain coincident in space and time for all observers. I could find a few textbooks where this idea is mentioned explicitly:

This is a "principle of the invariance of coincidences". When one observer says two events coincide in space and time, so will all other observers. D. Mermin "Space and time in special relativity" (1968).

The sole assumption we make is that the conception of the 'simultaneity (time coincidence) of two events occurring at the same place' (viz. the reading of the clock and the beginning of the event) has an absolutely definite meaning. We may make the assumption, although we cannot define the conception or express its content more clearly; it belongs to those ultimate data, which become directly known to us as an experience of our consciousness. M. Schlick "Space and time in contemporary physics" (1963).

But most of the time this "principle" is deemed so obvious as not even deserving a mention. However, I think this principle is just as important for the foundations of special relativity as the two Einstein's postulates. So, it deserves a rigorous scrutiny both theoretically and experimentally.

Eugene.

zoki85
But Pizzella's effect is rather dramatic and its explanation does not require detailed field calculations. Roughly speaking, classical theory predicts that the radius of the field "pancake" is equal to ##R=L/\gamma##, where ##L## is the distance traveled by the beam after exiting the pipe and ##\gamma## is the usual relativistic factor. In our case ##L = 92 - 552 ## cm and ##\gamma \approx 1000##, so the expected extension of the field is only 1-6 mm. But the pancake field was seen as far as 55 cm from the beam axis. This is a huge discrepancy between the experiment and classical theory.

Hmm.. I would investigate very carefully if that pipe (supposed to be an *ideal* EM shield) doesn't get charged to some extent long before the beam exits it

Dale and vanhees71
Gold Member
2022 Award
I agree that theory is not the strongest part of this paper.

You can find IMHO the best available Maxwell-Lienard-Wiechert theoretical description of the charge electric field formation after exiting the accelerator pipe in
Carron N.J. Fields of particles and beams exiting a conductor. Prog. Electromagn. Res. 28 (2000), 147.

But Pizzella's effect is rather dramatic and its explanation does not require detailed field calculations. Roughly speaking, classical theory predicts that the radius of the field "pancake" is equal to ##R=L/\gamma##, where ##L## is the distance traveled by the beam after exiting the pipe and ##\gamma## is the usual relativistic factor. In our case ##L = 92 - 552 ## cm and ##\gamma \approx 1000##, so the expected extension of the field is only 1-6 mm. But the pancake field was seen as far as 55 cm from the beam axis. This is a huge discrepancy between the experiment and classical theory.

Eugene.
Thanks for the reference. I'll have a look at it.

Your last paragraph confuses me completely since the authors say in the final conclusion of their paper that their measurements confirm the quoted Lienard-Wiechert result for a uniformly moving point charge(which of course is identical with the result simply achieved by Lorentz boosting a Coulomb field). The only "surprise", if there is any, is that the fact that the charge of course was not uniformly moving in free space but ejected from a cavity and still they got the result without taking this into account, but as far as I understand there statement is that there's no discrepancy between the Lienard-Wiechert field of a uniformly moving charge and their measurement (and thus also no violation of relativity or any mysterious "propagation speed"; one should note that there is no clear definition of "propagation speed" for (boosted) static fields to begin with).

Dale
Staff Emeritus
On the other hand, one good experiment is worth a thousand theories.

How many is a crap experiment worth?

bhobba, Dale, phinds and 2 others
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2022 Award
Another question is whether an experiment based on crap theory can ever be a good experiment to begin with?

All the great experiments, that lead to the development of SR (most prominently the Michelson-Morley experiment) were based on a solid understanding of the contemporary theories (Maxwell's equations, interpreted in terms of "aether theory" based on the Newtonian spacetime model), and only this lead after a lot of interaction between theory and experiment to the modification of the old theory and the discovery of the necessity of the relativistic spacetime for all of physics (it took quite a while from Maxwell 1865 till Einstein 1905!).

Dale, bhobba and weirdoguy
Staff Emeritus
This is true if we assumed exact applicability of Lorentz transformations to all events

Hey, you want to claim that this paper shows SR is wrong, more power to ya'.* I note that the authors of the experiemental paper did not make such a claim, even though if their data supported this they would get a plane trip to Stockholm. But, as explained above several times, the paper is a hot mess.

* But not on PF.

vanhees71 and weirdoguy
meopemuk
Your last paragraph confuses me completely since the authors say in the final conclusion of their paper that their measurements confirm the quoted Lienard-Wiechert result for a uniformly moving point charge(which of course is identical with the result simply achieved by Lorentz boosting a Coulomb field). The only "surprise", if there is any, is that the fact that the charge of course was not uniformly moving in free space but ejected from a cavity and still they got the result without taking this into account, but as far as I understand there statement is that there's no discrepancy between the Lienard-Wiechert field of a uniformly moving charge and their measurement (and thus also no violation of relativity or any mysterious "propagation speed"; one should note that there is no clear definition of "propagation speed" for (boosted) static fields to begin with).

As a cartoon is worth a thousand words, I'll show you one here:

Frames (a), (b), (c) on the right hand side show how the electric field of the ejected electron bunch must be formed according to classical theories: (a) there is no field in the room before the bunch has left the accelerator pipe. The pipe is shown by the rectangle on the left; (b)+(c) as the bunch (red dot) emerges from the pipe there are two components of the field: a sphere of the transient radiation (dashed line) which expands with the speed of light and the quasistatic "pancake" electric field (light blue lines) whose transversal dimension gradually increases.

You are right that "propagation speed of a static field" is a misnomer. Perhaps a better name would be "the speed of field's formation or field buildup." Obviously, in this case this speed is equal to the speed of light.

Frames (d), (e), (f) show Pizzella observations. The pancake electric field was fully formed immediately after the bunch left the pipe. Obviously, the pancake field penetrates far beyond the light cone.

Eugene.

weirdoguy
meopemuk
But, as explained above several times, the paper is a hot mess.

You could probably dismiss this work if it were alone, but there are few other respectable experimental groups who observed various superluminal electromagnetic effects in open space. Though these effects were not as clear and dramatic as the Pizzella's one.

G. C. Giakos, T. K. Ishii, Anomalous microwave propagation in open space, Microw. Opt. Techn. Let. 4 (1991), 79.

A. Ranfagni, P. Fabeni, G. P. Pazzi, D. Mugnai, Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time, Phys. Rev. E 48 (1993), 1453.

A. L. Kholmetskii, O. V. Missevitch, R. Smirnov-Rueda, Measurement of propagation velocity of bound electromagnetic fields in near zone, J. Appl. Phys. 102 (2007), 013529.

Eugene.

Staff Emeritus