# The invariance of c

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"the invariance of the EM wave pops out of the Maxwell equations and is axiomatic to the most successful theories of physics"

That was imatfaal's post  in the above thread some two years ago.

Is it correct ? I have been under the impression that Relativity starts with the invariance of c as an axiom based on experimental evidence.. I am not aware that it can be derived from anything

I thought what popped out of the Maxwell equations was that  this value for the speed of the em wave and  the invariant  maximum speed,c were the same thing.

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Posted (edited)
1 hour ago, geordief said:

I thought what popped out of the Maxwell equations was that  this value for the speed of the em wave and  the invariant  maximum speed,c were the same thing.

Yep. One can derive the speed of light from the Maxwell equations, but it doesn't specify relative to what this speed is measured. A not quite historical reconstruction of Einstein's thought is that Galileo's principle of relativity also applies to electromagnetic phenomena: there is no experiment from which you can derive if you are in constant motion or not. Therefore the speed of light, as an EM phenomenon, can neither be used. You cannot measure the speed of light, and from there derive what your movement is. This means, everybody measures the same speed of light, independent of their (constant) velocity.

Einstein himself said he was not really aware of the Michelson-Morley experiment, and he was driven to the special theory of relativity by inconsistencies in describing electrical particles by different observers. For some, in the rest frame of the particle, there is only an electrical field. For others, moving in respect to the particles, there is also a magnetic field. This is the real historical basis of Einstein's thinking.

Edited by Eise
Typo

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As Eise notes, what Einstein noticed was that in electrodynamics the speed of light didn't depend on the frame of reference. The relativity paper applies that principle to kinematics. The title is (or translates to) "On the Electrodynamics of Moving Bodies"

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6 minutes ago, Eise said:

Yep. One can derive the speed of light from the Maxwell equations, but it doesn't specify relative to what this speed is measured.....................................

You cannot measure the speed of light, and from there derive what your movement is. This means, everybody measures the same speed of light, independent of their (constant) velocity.

Interesting  Maxwell's equations give  a speed  for em radiation without reference to any frame of reference.

I shall try and investigate that specific point , but I can see   that it shows that imatfaal was correct

I will have to attempt to go through the mathematical workings of Maxwell's equations

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15 minutes ago, geordief said:

I will have to attempt to go through the mathematical workings of Maxwell's equations

Not an easy job...

It turns out that from the basic Maxwell equations, one can derive a wave equation, which describes how 'ripples of magnetic and electric fields' move through space. On the place where in other wave functions the speed is, we find 1/sqrt(u0e0) (well a greek letter 'mu' and 'epsilon'). 'u0' is a measure for the strength of the magnetic field in vacuum, efor the strength of the electrical field in vacuum. The formula 1/sqrt(u0e0) exactly equals the speed of light, in vacuum.

See here for details.

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Posted (edited)
1 hour ago, Eise said:

Not an easy job...

It turns out that from the basic Maxwell equations, one can derive a wave equation, which describes how 'ripples of magnetic and electric fields' move through space. On the place where in other wave functions the speed is, we find 1/sqrt(u0e0) (well a greek letter 'mu' and 'epsilon'). 'u0' is a measure for the strength of the magnetic field in vacuum, efor the strength of the electrical field in vacuum. The formula 1/sqrt(u0e0) exactly equals the speed of light, in vacuum.

See here for details.

I had been thinking about those fields earlier.Does a magnetic wave affect the magnetic  field locally   and so change the way the local magnetic field affects the electric field?

Do the magnetic waves and the electric waves travel through the electric and magnetic fields  by pushing off each other in a similar way to a rocket  pushing a spacecraft through a vacuum?

Am I any way near understanding the process?

Edited by geordief

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13 hours ago, geordief said:

Do the magnetic waves and the electric waves travel through the electric and magnetic fields  by pushing off each other in a similar way to a rocket  pushing a spacecraft through a vacuum?

No, I am sorry.

From Faraday's experiments it is clear that a changing magnetic field causes an electrical field (induction), and a changing electrical field cause a magnetic field. So in an EM wave, a magnetic field is built up, and (because that is a changing magnetic field) it will cause an electric field. On its turn, the arising electrical field will build up a magnetic field, etc. etc. So there are no pre-existing electromagnetic fields in which EM waves propagate. EM waves are the fields themselves propagating.

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2 hours ago, Eise said:

No, I am sorry.

From Faraday's experiments it is clear that a changing magnetic field causes an electrical field (induction), and a changing electrical field cause a magnetic field. So in an EM wave, a magnetic field is built up, and (because that is a changing magnetic field) it will cause an electric field. On its turn, the arising electrical field will build up a magnetic field, etc. etc. So there are no pre-existing electromagnetic fields in which EM waves propagate. EM waves are the fields themselves propagating.

But do these newly created fields "push off" each other in the direction  the wave is traveling?

There seems to be an electric component and a magnetic component to this  moving electromagnetic  field.

Do they interact with each other in the way I have suggested? ( "pushing off" one another in turn)

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1 hour ago, geordief said:

Do they interact with each other in the way I have suggested? ( "pushing off" one another in turn)

No. Compare with water waves: there is no pushing in the direction in which the wave moves. It is the' unbalance' in the height of the water that moves. EM waves are disturbances where the electrical and magnetic forces are directed perpendicular to the direction that the wave travels.

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9 minutes ago, Eise said:

No. Compare with water waves: there is no pushing in the direction in which the wave moves. It is the' unbalance' in the height of the water that moves. EM waves are disturbances where the electrical and magnetic forces are directed perpendicular to the direction that the wave travels.

Thanks, I appreciate your patience. (I  take your point about those forces acting in a direction perpendicular to the direction of travel of the wave)

So what do those forces do? They just serve to maintain the mutual oscillation?

The direction of travel  is in all directions (an expanding sphere)?

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“Push” implies a force, so no.

A changing B field is an electric field, for example.

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Are the electric field and the magnetic field simply  constituent parts of the electromagnetic field?

Can the electric field  or the magnetic field exist in isolation ? When stationary?

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1 hour ago, geordief said:

So what do those forces do? They just serve to maintain the mutual oscillation?

I realise I used the word 'force', which is not quite correct: I'd better used 'field strength'.

As long as an EM wave is just travelling through the vacuum, yes, nothing else happens as a changing electrical field producing a changing magnetic field which in its turn produces a changing electrical field etc etc.

Only when EM waves interact with matter something else can happen: beating electrons from their orbitals (light and UV-light), transfer the changing EM-field to a changing current in an antenna (radio waves), or even trigger nuclear reactions (gamma rays).

1 hour ago, geordief said:

Can the electric field  or the magnetic field exist in isolation ? When stationary?

Of course they can: so they were discovered. Both electricity and magnetism are known at least since antiquity. Rub a plastic object with a woolen towel, and it will be electrically charged, and it can attract light objects, like small pieces of paper. Feed an electromagnet with a DC current, and you will have a static magnetic field. (Of course, in antiquity they discovered minerals that were permanently magnetic.) Only changing magnetic and electrical fields induce other fields, that change too.

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24 minutes ago, Eise said:

Only changing magnetic and electrical fields induce other fields, that change too.

Note that it is the time rate of change of these fields that is important.

It is this time rate that links the two of Maxwells equations that lead to the wave equation when combined.

$\frac{{\partial {E_x}}}{{\partial z}} = - \frac{{\partial {B_y}}}{{\partial t}}$

$- \frac{{\partial {H_y}}}{{\partial z}} = \frac{{\partial {D_x}}}{{\partial t}}$

Where

E, D are the electric vectors

B and H are the magnetic vectors

with subscripts denoting the direction relative to x, y, z axes and travel of the EM wave in the z direction.

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Thanks everyone. I think I may be more or less up to speed  now.

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2 hours ago, geordief said:

Can the electric field  or the magnetic field exist in isolation ? When stationary?

Yes, but that's true only in a particular frame of reference. When there is relative motion, it looks like a changing field, so you get both if you are moving relative to e.g. a static B field.

What it boils down to is that for any dynamic situation, there is electromagnetics. They are different aspects of one interaction. It's only in the case of statics where you can look at one or the other.

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On 10/1/2019 at 8:32 AM, geordief said:

"the invariance of the EM wave pops out of the Maxwell equations and is axiomatic to the most successful theories of physics"

That was imatfaal's post  in the above thread some two years ago.

Is it correct ? I have been under the impression that Relativity starts with the invariance of c as an axiom based on experimental evidence.. I am not aware that it can be derived from anything

I thought what popped out of the Maxwell equations was that  this value for the speed of the em wave and  the invariant  maximum speed,c were the same thing.

I recently found this video and became in awe of the simplicity of the explanation.

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4 hours ago, jajrussel said:

I recently found this video and became in awe of the simplicity of the explanation.

Thanks ,that was helpful for me to see how  c was related to the permittivity and permeability in Maxwell's equations ,but that only goes so far it seems to me.

Constancy does not necessarily show invariance and I think Special Relativity introduced this concept whereas Maxwell did not.

I  think I understand now that Einstein saw that Maxwell's equations  had an internal contradiction whereby the two observers (one moving along with the moving charge and the other at  rest with a stationary charge ) saw the same interaction differently.

I am still trying to understand  how the invariance of c sorted this out and am trying to go through the transcript from Feynman's  lecture on the subject as I think  he is considered  to be a clear educator.

Edited by geordief

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46 minutes ago, geordief said:

Constancy does not necessarily show invariance and I think Special Relativity introduced this concept whereas Maxwell did not.

If c was not invariant, then Maxwell's equations — specifically the wave equation – would only work in the rest frame. And we know that EM radiation still exists when frames are moving with respect to each other.

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52 minutes ago, swansont said:

If c was not invariant, then Maxwell's equations — specifically the wave equation – would only work in the rest frame. And we know that EM radiation still exists when frames are moving with respect to each other.

Is it better to think of em radiation as (more fundamentally) an expanding sphere than as following any particular trajectory?

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1 hour ago, geordief said:

Thanks ,that was helpful for me to see how  c was related to the permittivity and permeability in Maxwell's equations ,but that only goes so far it seems to me.

Constancy does not necessarily show invariance and I think Special Relativity introduced this concept whereas Maxwell did not.

I  think I understand now that Einstein saw that Maxwell's equations  had an internal contradiction whereby the two observers (one moving along with the moving charge and the other at  rest with a stationary charge ) saw the same interaction differently.

I am still trying to understand  how the invariance of c sorted this out and am trying to go through the transcript from Feynman's  lecture on the subject as I think  he is considered  to be a clear educator.

You are right to be somewhat skeptical of that presentation because it misrepresents what Einstein postulated.

He did not postulate that the speed of light is 'the same for all observers' as the narrator suggests.

(He actually proves this and something more which the narrator omitted).

Here are his original two postulates.

His proof of observer independence came after three pages of deductive reasoning on pages 6,7 and 8.

It is thus a consequence of of the original postulate of source independence.
I think he made it this way because his reasoning did not require light to be a wave phenomenon.
His original second postulate could have been taken from the already known properties of waves had he 'assumed' light to be a wave phenomenon.

Subsequent scholars simplified the postulates to include the observer.

Einstein also realised that the 'master postulate' is the principle of relativity and thus that he also had to prove that the second postulate is compatible with the first.
This he stated on page 8 and proceeded to verify.

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4 minutes ago, studiot said:

You are right to be somewhat skeptical of that presentation .....

Thanks.I will have to have a look at that later when I get home (on a bigger screen)

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1 hour ago, geordief said:

Is it better to think of em radiation as (more fundamentally) an expanding sphere than as following any particular trajectory?

For an isotropic point source, yes. But you can have other solutions, depending on your boundary conditions. You can get solutions for a wave in a waveguide, for example.

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Just thinking...

Consider Newton’s first law of motion.

Consider  Einstein’s set condition of empty space.

Then ask why c would not be invariant? Wouldn’t there need to be a change in the set condition (empty space) if you want to expect variety?

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2 hours ago, jajrussel said:

Just thinking...

Consider Newton’s first law of motion.

Consider  Einstein’s set condition of empty space.

Then ask why c would not be invariant? Wouldn’t there need to be a change in the set condition (empty space) if you want to expect variety?

It sounds like you are mixing up "constant" and "invariant".

The above might be enough to convince you that the speed of light is constant (after all, why would it change).

But it isn't obvious that if you are moving towards or away from the source, you will still measure the light to be moving at the same speed.

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