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

[KatamariDamacy]

Also what I wrote was that
u= \frac{1}{\sqrt{\epsilon_{0} \mu_{0}}} =c
u in general can be u \ne c (u \le c). It comes from the wave equation form:
∇^2 f = \frac{1}{u^{2}} ∂_t ^2 f
and depends on the medium.

and it's rational since in vacuum the light is going to propagate as fast as the photons do (no obstacles for the photons)

I don't see what's your point. How fast obviously depends on the value of electric and magnetic constant, which is not zero for vacuum, but specific constant numbers that naturally yield specific non-zero and constant number c. There are no obstacles in vacuum, but apparently there are still constraints. We don't need aether to have them, those constraints can simply be a default property of the fields themselves.

 

[KatamariDamacy]

I think the wrong assumption Dale refers to is that they can't travel at speed of light.

There is no any mass in neither of those two equations to prevent those fields to travel at the speed of light.

The equation for c you are giving describes the LIGHT and not the photons... the light is an EM wave which propagates, it can't have a mass.

What is the difference between photons and EM waves?

Its speed varies from medium to medium... the photons always travel at c since they are massless.

Zero can not yield any specific non-zero number. Zero mass can not be a reason for specific, non-zero and constant value c.

What do you mean about the equations?

I don't see what is that question related to.

The physical phenomenon is Special relativity itself. If you could find any other speed for a massless particle, you would be able to boost it in such a way that you bring it at rest. However that's not possible for a massless particle- thus it travels at c in all reference frames.

What equation are you talking about: c = ?

 

[Drakkith]

There is no any mass in this equation, so why do you think it is relevant? Also, if electric and magnetic constants were different they would clearly make c different as well, so how is it not these two constants the reason why the speed of light is exactly c and not more or less?

I don't think so. The velocity c is special in the universe in that nothing can surpass it and only massless objects can go c. Changing the electric and magnetic constants wouldn't appear to have any effect on how fast objects can travel through space, only EM waves. I think the reverse of what you've said is true. I think that the constants are what they are because c is approximately 300,000 km/s. Consider that any change in any field can only propagate at c, whether it's a change in the EM field, the gravitational field, or whatever.

In addition, when deriving the speed of light using electric and magnetic concepts as Maxwell did, you are forced to consider how magnetic fields are generated from moving charges, which can be explained using special relativity and depends, again, on c.

 

[KatamariDamacy]

I don't think so. The velocity c is special in the universe in that nothing can surpass it and only massless objects can go c. Changing the electric and magnetic constants wouldn't appear to have any effect on how fast objects can travel through space, only EM waves. I think the reverse of what you've said is true.

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.

I think that the constants are what they are because c is approximately 300,000 km/s. Consider that any change in any field can only propagate at c, whether it's a change in the EM field, the gravitational field, or whatever.

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.

I don't know about propagation of a field within the field itself, and so called "speed of gravity". I think it has been experimentally confirmed that electric fields travel along with their electrons without any lag, as if it was a rigid body, but I'm not sure if that's the same thing or actually related to what we are talking about.

 

[Doc Al]

I think it has been experimentally confirmed that electric fields travel along with their electrons without any lag, as if it was a rigid body,

Really? You think you can 'wiggle' an electron and have its field instantaneously changed at some distance?

 

[Nugatory]

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.

Why wouldn't it make sense? The permittivity, permeability, and speed of light of light are connected by a mathematical relationship so that specifying any two of them determines the value of the third. The history is that Maxwell started with permeability and permittivity and then made the connection to the speed of light, so it seemed natural to consider them to be more fundamental than the speed of light. But there's another line of thinking that just happened not to be discovered until after Maxwell's, that shows that there must be an invariant speed, that all waves (whether electomagnetic or gravitational or anything else) must propagate at this speed, we've measured that speed to be $2.998\times{10}^8$ m/sec, and therefore the permeability and permittivity are determined by that speed.

Indeed, it's a historical accident that we call the quantity $c$ "the speed of light" - it's just so happens that light was the first thing we knew about that moves at that speed.

 

[Nugatory]

I think it has been experimentally confirmed that electric fields travel along with their electrons without any lag, as if it was a rigid body, but I'm not sure if that's the same thing or actually related to what we are talking about.

That is true only for an observer who is, always has been, and always will be, moving in the same direction at the same speed as the electron - that is, for a stationary electron.

Any observer moving relative to the electron (or that the electron is moving relative to - it's the same thing) will observe a time-varying magnetic field and a time-varying electrical field, and the changes in these fields will propagate at the speed of light.

If you take an electron, and wiggle it back and forth, one wiggle per second, you'll be generating electromagnetic waves with a frequency of 1 Hz (and a wavelength of $3\times{10}^8$ meters) and the electrical field at any point away from the wiggling electron will be constantly varying - it will be proportional to sin($2\pi{t}$).

 

[KatamariDamacy]

Really? You think you can 'wiggle' an electron and have its field instantaneously changed at some distance?

I think that's what it means and I'm at least 80% sure that paper I saw was saying just that. I was not surprised, but then, I don't even care. Would that really be surprising? I better search for it then.

 

[Doc Al]

I think that's what it means and I'm at least 80% sure that paper I saw was saying just that. I was not surprised, but then, I don't even care. Would that really be surprising?

Yes, it would be quite surprising. And wrong.

I better search for it then.

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

 

[Nugatory]

I'm at least 80% sure that paper I saw was saying just that.

Then there's at least an 80% chance that either what you read was wrong or that you misunderstood it - see https://www.physicsforums.com/showpost.php?p=4818473&postcount=57 above.

 

[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.