Why photons can't go any slower than the speed of light?

[rubi]

Electric permittivity and magnetic permeability is what defines how much are electric and magnetic fields permitted to permeate. Either they define c, as their names suggest, or c defines them, which doesn't make sense.

The vacuum permeability has been defined to be exactly $\mu_0 = 4\pi\times 10^7 \frac{\text{H}}{\text{m}}$. (I just wanted to throw this in.)

 

[KatamariDamacy]

You might want to read Nugatory's last post before you waste your time.

http://arxiv.org/abs/1211.2913

The problem of gravity propagation has been subject of discussion for quite a long time: Newton, Laplace and, in relatively more modern times, Eddington pointed out that, if gravity propagated with finite velocity, planets motion around the sun would become unstable due to a torque originating from time lag of the gravitational interactions.

Such an odd behavior can be found also in electromagnetism, when one computes the propagation of the electric fields generated by a set of uniformly moving charges. As a matter of fact the Li'enard-Weichert retarded potential leads to a formula indistinguishable from the one obtained assuming that the electric field propagates with infinite velocity. Feyman explanation for this apparent paradox was based on the fact that uniform motions last indefinitely.

To verify such an explanation, we performed an experiment to measure the time/space evolution of the electric field generated by an uniformely moving electron beam. The results we obtain on such a finite lifetime kinematical state seem compatible with an electric field rigidly carried by the beam itself.

 

[Doc Al]

http://arxiv.org/abs/1211.2913

I don't see that it has ever been published. I wonder why? (Do you have a journal reference?)

 

[Dale]

What do you mean "wrong assumption"?

The assumption that two charges can travel at c is wrong. If you allow that assumption then you get a contradiction, which is one way of proving that an assumption is false.

Are you saying those two force being equal at the point of the speed of light is some weird coincidence without any practical implication in reality?

Yes. Both the weird coincidence and the reason that it has no practical implication in reality are explained by relativity.

I was referring to equations that equation was derived from. Was it not derived from Gauss, Ampere and Faraday laws, which in turn are derived from Coulomb and Lorentz force laws, all of which are about electric and magnetic fields of electrons moving in wires or point charges? So at what point in derivation these fields cease to belong to those electrons or "point charges", and become entities on their own?

There is no mathematical operation of belonging. There is no sense in which Maxwell's equations assign ownership of the fields to the charges. This is a completely mistaken notion.

Maxwell's equations describe the relationship between the fields and the charges, but does not say that one belongs to the other. Maxwell's equations permit fields without charges, but not charges without fields.

 

[Dale]

I don't see any disagreement, I was talking about EM waves, not any "objects". I'm just saying that there must be a reason why it is exactly c and not more or less, and that reason can not be their zero mass because zero can not define any specific non-zero value.

Yes, it can.

What zero can and cannot define depends on the equation in which the zero occurs. If it is a proportionality then you would be right, but not all equations are proportionalities. In this case, the equation of interest is $m^2 c^2 = E^2/c^2-p^2$ which, if m=0 gives $E^2/c^2=p^2$, and any object with a four-momentum $(|p|,p)$ has v=c.

 

[Dale]

KatamariDamacy, please recognize that we are glad to help you learn, but if you just want to argue and not learn then your tenure on these forums will be brief. This is an educational forum, not a debate forum. You have been given a lot of good information, and seem to be trying desperately to avoid learning any of it.

 

[KatamariDamacy]

I don't see that it has ever been published. I wonder why? (Do you have a journal reference?)

I don't know. I just stumbled over it while I was looking for something else few months ago and didn't even care to read it except the abstract I quoted. It says those guys are from "Istituto Nazionale di Fisica Nucleare,Laboratori Nazionali di Frascati". I googled their web-page:

http://w3.lnf.infn.it/

I'm afraid that's all I can tell you about it. But if relativistic formulas end up reflecting the same expression as when field propagation is assumed to be instantaneous, then why would you be surprised the experiments measure just that? As I see it there is no contradiction either way, except instantaneous propagation equations are simpler to use.

 

[Dale]

For non-accelerating charges that is correct. The EM force from an inertial charge points towards its current location, not its retarded location. Of course, the magnitude of the field is different than would be predicted by Coulomb's law, which is kind of the whole point.

 

[KatamariDamacy]

For non-accelerating charges that is correct. The EM force from an inertial charge points towards its current location, not its retarded location.

I don't see what acceleration of the field has to do with how fast its change will be felt at some distance away from it. The speed of propagation of the change is either always c or always instantaneous, regardless of the speed or acceleration of the field itself.

 

[Chronos]

I am curious how the authors of http://arxiv.org/abs/1211.2913 managed to overlook a number of dissenting papers - e.g., http://arxiv.org/abs/gr-qc/9909087, Aberration and the Speed of Gravity. I was under the impression it was customary to take into account existing relevant papers before boldly leaping into the abyss.

 

[Dale]

I don't see what acceleration of the field has to do with how fast its change will be felt at some distance away from it.

Then maybe you should study more and argue less.

The speed of propagation of the change is either always c or always instantaneous, regardless of the speed or acceleration of the field itself.

Yes, but that isn't what the paper you cited showed. The paper you cited was showing the aberration of forces, not the propagation of changes in the field (despite some confusion on the part of the authors - which is probably why the paper didn't pass peer review).

It is well known that the free propagation speed of changes in the EM fields is c. It is also well known that there is no aberration in the forces from a uniformly moving charge. Please study the lecture below and ask questions.

http://www.mathpages.com/home/kmath562/kmath562.htm

 

[Doc Al]

Here's another treatment of that standard result for a uniformly moving charge: http://farside.ph.utexas.edu/teaching/em/lectures/node125.html

"Note that E acts in line with the point which the charge occupies at the instant of measurement, despite the fact that, owing to the finite speed of propagation of all physical effects, the behaviour of the charge during a finite period before that instant can no longer affect the measurement."​

 

[KatamariDamacy]

The assumption that two charges can travel at c is wrong. If you allow that assumption then you get a contradiction, which is one way of proving that an assumption is false.

There is no any mass in those equations, charge is not implied, only fields. Just like you said Maxwell's equations permit fields without charges, so Coulomb and Lorentz force equations must too. In this thread here:
https://www.physicsforums.com/showthread.php?t=765250

...jtbell explained EM wave and he mentioned not only one negative charge, but also the second positive charge, and even referred to Lorentz force equation: F= qv x B. You said it makes sense, and I passionately agree.

Yes. Both the weird coincidence and the reason that it has no practical implication in reality are explained by relativity.

How is such peculiar coincidence explained by relativity, what explanation is that?

 

[KatamariDamacy]

Yes, but that isn't what the paper you cited showed.

I believe the paper showed experimental results match both equations that assume instantaneous change propagation and relativistic equations. They only attack Feyman's explanation of that paradox.

The paper you cited was showing the aberration of forces, not the propagation of changes in the field (despite some confusion on the part of the authors - which is probably why the paper didn't pass peer review).

Why do you think the paper didn't pass peer review, or that they themselves are not peer review institution? The paper is given in Wikipedia for reference to this article about Coulomb's law, if that means anything:

http://en.wikipedia.org/wiki/Coulomb's_law

 

[Dale]

Since you continue to argue and spout misinformation rather than learn, this thread is closed. If you choose to start a new thread, I hope it is with the intention of learning.

There is no any mass in those equations, charge is not implied

Since the equations are calculating the force on a charge, clearly charge is implied.

Maxwell's equations permit fields without charges, so Coulomb and Lorentz force equations must too

No. If you take Maxwell's equations and set q and j to zero then you get some non-trivial solutions. If you take Coulomb's law and the Lorentz force equation and set q to zero then you have only the trivial solution. You cannot blindly take statements made about one set of equations and apply them to other sets of equations. You must actually do the math and see what it says.

How is such peculiar coincidence explained by relativity, what explanation is that?

Read the links I provided earlier, particularly the "Purcell Simplified" link. If you have questions after studying those links then come back and ask your questions. We are glad to help people learn, but don't tolerate people arguing for things that are incorrect as though they were fact.