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

[ChrisVer]

Why are they undetermined? You can always use them, even if you have to take the limit of m \rightarrow 0,afterall it's independent of m... These expressions are not good for defining the energy and momentum of the photon, but they seem fine in defining the velocity extracted from SR.

 

[Dale]

The simplicity of it strikes me as profound, and it's amazing because even though the relation is rather obvious no one seems to have paid any attention to it before.

I think many people have noticed it. In fact, it is something that we occasionally talk about here and sometimes try to get people to calculate on their own:

https://www.physicsforums.com/showthread.php?t=719625
https://www.physicsforums.com/showthread.php?t=589457

I am sure that there are other examples. I remember calculating it, being surprised, and then realizing that it was a necessary consequence of the Lorentz transform.

If you are interested in that, then I would definitely focus on the Lorentz transform stuff more than the magnetic/electric properties stuff. The Lorentz transform part is probably more fundamental anyway.

 

[bahamagreen]

...I was hoping there is more that can be said about it.

"For doubt can exist only where a question exists,
a question only where an answer exists,
and an answer only where something can be said." (original emphasis)
Ludwig Wittgenstein, 1921 Tractatus 6.51 2nd paragraph

 

[256bits]

q2/(4πεR2)=μq2v2/(4πR2)
v0=1/√(ε0μ0),

The simplicity of it strikes me as profound, and it's amazing because even though the relation is rather obvious no one seems to have paid any attention to it before. Unfortunately, as usual, it's not quite clear what it really means or whether it is a part of the reason or just a consequence itself. Still, it actually tell us more about the whole thing, not much perhaps, but it's something.

Can anyone make some more sense out this relation and explain why would these two forces "need" to be balanced in an electromagnetic wave, and whether this could be a part of the reason for the speed of light or just a consequence of it and a side-effect itself?

It means that when charge distribution changes, the effect cannot be felt instantaniously, but spreads out as a wave at the speed of light.

 

[KatamariDamacy]

I think many people have noticed it. In fact, it is something that we occasionally talk about here and sometimes try to get people to calculate on their own:

https://www.physicsforums.com/showthread.php?t=719625
https://www.physicsforums.com/showthread.php?t=589457

I don't think a thread on a forum has any official significance. When Maxwell derived the speed of light from his wave equation it was a revolution in physics. Surely then this other and more direct derivation deserve more serious attention and treatment in some published peer review paper.

If you are interested in that, then I would definitely focus on the Lorentz transform stuff more than the magnetic/electric properties stuff. The Lorentz transform part is probably more fundamental anyway.

I don't see Lorentz transformation has anything to say about the connection between the speed of light and equality between electric and magnetic force.

 

[KatamariDamacy]

It means that when charge distribution changes, the effect cannot be felt instantaniously, but spreads out as a wave at the speed of light.

What does equality between electric and magnetic force have anything to do with any of that?

 

[ChrisVer]

about that thread, as I also mentioned there, even if you consider the particles to be massless just to be able to have them running at c, then they won't ever feel any force at all... that's a possible reason why the forces come out to be equal and opposite (in fact there is no force).
That's because the electromagnetic interaction coming from the particle 1, can never reach particle 2 and vice versa...
Also, as pointed out in that thread, your particles should be massless to run at c.

 

[KatamariDamacy]

about that thread, as I also mentioned there, even if you consider the particles to be massless just to be able to have them running at c, then they won't ever feel any force at all... that's a possible reason why the forces come out to be equal and opposite (in fact there is no force).

Only if "they" are parallel. But what are "they", force between what and what? It takes two. The problem is that thread was about two separate charges. The other problem is that "charge" implies mass, i.e. a "particle" like electron or positron.

But when we talk about EM waves those electric and magnetic fields seem to be on their own, and just one pair instead of two. How did those fields got stripped from their carrier particles in the first place? Where did that "charge" go from Maxwell's equations when they turned into the wave equation?

Also, as pointed out in that thread, your particles should be massless to run at c.

It seems to me the limit of c is a separate thing from what directly defines it. Take terminal velocity for example, acceleration will be defined by gravity, and only final velocity limit will be defined by atmosphere density. Two different things, one is primary and the other is secondary. Similarly electric and magnetic properties appear to be "defining" or "driving force", and mass on the other hand seems to be "secondary" and only related by setting the final limit.

 

[ChrisVer]

The thread's question and result was all about charges moving parallel ... of course charge implies mass, and that's why my answer is hypothetical and unphysical in that sense. Which charge? the charge in Maxwell equations acts as a source:
\partial_{\mu}F^{\mu \nu} = b j^{\nu} with b some constant I don't remember now (I think it's 4pi).
charged particles that are accelerated will radiate energy. I don't understand what you meant by the atmospheric density defining the final velocity limit. The problem with the masslessness appears because of what you also pointed out yourself- that you have charges. A massless particle will run at c, no acceleration needed. A massive particle will never reach c...

 

[KatamariDamacy]

Which charge? the charge in Maxwell equations acts as a source

Yes, in Maxwell equations there is a charge which carries, or is a source, of electric and magnetic fields. So when we reformulate those equations into EM wave equation, why do we only have fields and where is their charge they were originally a part of?

A massless particle will run at c, no acceleration needed.

How is it possible for something to go from zero to c without acceleration, and why would that be?

 

[ChrisVer]

In the vacuum there are no charges acting as sources... The Maxwell eqs for the vacuum take the form then:
\partial_{\mu}F^{\mu \nu}=0
This is one case of Maxwell eqs (charge free).. When you have charges/currents this equation is changed to the one I gave to my previous post. The 4current j^{\mu} contains the information for the charges and the currents. For light then, this will be like the wave equation with some source.

Look at post posts #9, #28 for the massless moving at c... and since you can't find a ref.frame at which it'll be at rest, you can't say it wasn't moving and suddenly it moved after a push...a massless particle will always move at c no matter what. It doesn't start from 0, it starts from c.

 

[KatamariDamacy]

In the vacuum there are no charges acting as sources... The Maxwell eqs for the vacuum take the form then:
\partial_{\mu}F^{\mu \nu}=0

All those equations are derived from basic electrical equations, about electric currents and wires, about electrons and their motion. There are no any electric or magnetic fields in those equations that are on their own and not of an electron, where electric field magnitude is proportional to electrons quantity and magnetic field magnitude proportional to both their quantity and velocity. There is no any mass in those equations either, mass is implied indirectly through F=ma.

So now we have Maxwell equations which are about electric and magnetic fields of electrons, then we shuffle those symbols around and suddenly we shake off those electrons and are left only with their fields. It's no more electric and magnetic field of an electron, it's now field of itself, and for some reason F=ma doesn't apply anymore. It doesn't follow, where did those electrons go?

a massless particle will always move at c no matter what.

Yes, but zero mass doesn't explain why would they do such thing. How can something with zero value be a reason for something that has specific non-zero value? It does not compute, such equation can not exist.

 

[ChrisVer]

You've never seen the Maxwell eqs in vacuum? Don't they have solutions for the vacuum? what are those solutions?
You are left with a wave that propagates, the way it propagates is given by the Max eqs solution. If in the mean that it propagates, there are no sources, it won't be affected. The electrons might be anywhere, it can be on the other side of the universe and now stopped- what you need is starting with non-trivial E or B fields... Otherwise indeed you are having nothing (no light)... The thing is that light, when propagating in vacuum, is not affected if it doesn't meet any sources/charges.
You have a rock, you throw it in the water, and the waves then propagate in the water...are you asking me what happened to the rock?... the thing with light is that it can propagate in vacuum-it doesn't need a medium.

What is then the velocity of a massless particle? The reason is in the Lorentz transformations... A massless particle will travel at c, and it will do so in any reference frame.

 

[Doc Al]

How is it possible for something to go from zero to c without acceleration, and why would that be?

It's always moving at c, never zero or anything less than c.

 

[Dale]

I don't think a thread on a forum has any official significance. When Maxwell derived the speed of light from his wave equation it was a revolution in physics. Surely then this other and more direct derivation deserve more serious attention and treatment in some published peer review paper.

You are correct that threads here have no official significance. I was only pointing out that this is not a new concept, as you seem to believe.

Also, since it is a derivation based on a wrong assumption leading to a self contradictory conclusion I doubt that it would pass peer review. I suspect that threads on internet forums are all that it can expect. I think that it is interesting for pedagogical purposes, but not for serious treatment by professionals.

I don't see Lorentz transformation has anything to say about the connection between the speed of light and equality between electric and magnetic force.

Then you definitely should focus there. I would start with Einstein's 1905 paper "On the electrodynamics of moving bodies" and
http://physics.weber.edu/schroeder/mrr/MRRtalk.html

You may also want to learn about how forces transform. I find the four vector treatment easiest.

 

[Dale]

All those equations are derived from basic electrical equations, about electric currents and wires, about electrons and their motion. There are no any electric or magnetic fields in those equations that are on their own and not of an electron

This is exactly wrong. The vacuum equation that ChrisVer posted contradicts this. It explicitly states that the fields can exist in regions without any sources.

 

[KatamariDamacy]

Also, since it is a derivation based on a wrong assumption leading to a self contradictory conclusion I doubt that it would pass peer review.

What do you mean "wrong assumption"? 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?

This is exactly wrong. The vacuum equation that ChrisVer posted contradicts this. It explicitly states that the fields can exist in regions without any sources.

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?

 

[KatamariDamacy]

What is then the velocity of a massless particle? The reason is in the Lorentz transformations... A massless particle will travel at c, and it will do so in any reference frame.

Equations can not be a reason for physical phenomena, they can only describe it. Zero value can not yield any specific non-zero value.


c = 1/√(ε0μ0)

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?

 

[ChrisVer]

I think the wrong assumption Dale refers to is that they can't travel at 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. Its speed varies from medium to medium... the photons always travel at c since they are massless. I made it clear in my previous posts, that I make a distinction between light as wave and photons as massless particles. What changes is that photons through a medium can be absorbed and re-emitted or scattered (but always traveling at c), thus the difference of speeds for the light waves.

What do you mean about the equations? 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.

 

[ChrisVer]

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)

 

[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.