What is the Universe expanding into..

[SNR]

Well, don't worry, if someday would result that c it is not constant, it shouldn't be the end of physics, just some changes.

Very well said.

The problem with the speed of light in a vacuum, is that a vacuum is not empty.
It is full of short-lived positron/electron and quark/antiquark pairs. This is what makes a vacuum polarized and magnetic.

Cheers.

 

[popilin]

I think you will find that gravitational lensing is ample evidence that the velocity of light changes in a gravitational field.

No, gravitational lensing is ample evidence that space-time is curved by matter.

In GR the speed of light is locally invariant, i.e. if you measure the speed of light at your location you will always get the same value c; if you measure the speed of light at another location, with another gravitational field, your rule and clock will be affected and you will always get the same value c.

You seem to confuse coordinate speed with locally measured speed.

 

[popilin]

The problem with the speed of light in a vacuum, is that a vacuum is not empty.

I think that this is the key, Casimir effect, experimentally checked, is a real challenge to understanding of vacuum.

 

[esgigt]

In GR the speed of light is locally invariant, i.e. if you measure the speed of light at your location you will always get the same value c; if you measure the speed of light at another location, with another gravitational field, your rule and clock will be affected and you will always get the same value c.

You seem to confuse coordinate speed with locally measured speed.

That's one of the major points of confusion....

The coordinate speed and locally measured speed can differ.... no problem, unless one demands that the speed of light always has to be the same, no matter from which position it was measured.

C is always C in the position you are in.

 

[rayma]

No, gravitational lensing is ample evidence that space-time is curved by matter.

In GR the speed of light is locally invariant, i.e. if you measure the speed of light at your location you will always get the same value c; if you measure the speed of light at another location, with another gravitational field, your rule and clock will be affected and you will always get the same value c.

You seem to confuse coordinate speed with locally measured speed.

Yes, light always follows a geodesic. In empty space, that's a straight line. Near a large mass, it's a curved path. We could say that light's path defines the geodesic.

 

[NorthStar]

Perhaps Alfred (Einstein) was doing his calculations inside a vacuum? ...And looking outside of it?

 

[NorthStar]

...No wonder all the outlaws want to shoot the sheriff, drinking his glass of milk at the saloon's bar.

 

[rayma]

Perhaps Alfred (Einstein) was doing his calculations inside a vacuum? ...And looking outside of it?

That's "Albert" to you.

 

[chrisb]

a confabulation of Alfred E Newman, no doubt - if anything like my own misspent youth, one of Bob's heros

 

[popilin]

Yes, light always follows a geodesic. In empty space, that's a straight line. Near a large mass, it's a curved path. We could say that light's path defines the geodesic.

Totally agree!

 

[popilin]

Most UK EE graduates may not have been told that a magnetic field is just a Lorentz-transformed electric field; those that have been told may not understand what they have been told

Interesting. I'm just a dumb chemist and we had to derive this.

For the good of most UK EE graduates, you might never have derived such a result, because it is totally wrong.

The electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another as

E∥’ = E∥​

B∥’ = B∥​

E⊥’ = γ [E⊥ + (1/c) v x B]​

B⊥’ = γ [B⊥ – (1/c) v x E]​

Where

γ = 1/ √(1 – v²/c²)​

Maxwell's Equations are Lorentz covariant, i.e. they have the same form after a Lorentz transformation, then, fields are interrelated the same form.

 

[JacquesToo]

Hmm, Wikipedia

 

[popilin]

Hmm, Wikipedia

No, Jackson's Classical Electrodynamics, first edition.

Wikipedia is also wrong.

 

[rayma]

No, Jackson's Classical Electrodynamics, first edition.

Wikipedia is also wrong.

You could edit the Wiki entry.

 

[NorthStar]

That's "Albert" to you.

What kind of dark space was I in?

 

[NorthStar]

Hmm, Wikipedia

MinusIQ | The pill to lower your IQ permanently - YouTube

 

[rayma]

For the good of most UK EE graduates, you might never have derived such a result, because it is totally wrong.

The electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another as

E∥’ = E∥​

B∥’ = B∥​

E⊥’ = γ [E⊥ + (1/c) v x B]​

B⊥’ = γ [B⊥ – (1/c) v x E]​

Where

γ = 1/ √(1 – v²/c²)​

Maxwell's Equations are Lorentz covariant, i.e. they have the same form after a Lorentz transformation, then, fields are interrelated the same form.

Notice that c in Maxwell's equations is just c, and not qualified in some way.
It is c in all reference frames, at all times. I think this may be how Einstein was first led to take the constancy of c literally.

 

[NorthStar]

Yes, I did make a mistake; Albert instead of Alfred, thank you for correcting me Ray.

 

[popilin]

Notice that c in Maxwell's equations is just c, and not qualified in some way. It is c in all reference frames, at all times.

That's the beauty of Maxwell's equations, and that's why I love cgs units.

Sadly, most today books used mks units, even worse, authors confuse the fields, E and D, B and H.

I think this may be how Einstein was first led to take the constancy of c literally.

Totally agree, because I always thought the same, even more, it is said over there that Einstein said that constancy of c lies implicit on Maxwell's equations.

 

[nezbleu]

So all you guys who reject C as a constant, when you look at the equation E=mC**2, what do you see? Does that mean that the energy equivalent of a mass depends on where you are standing? Or that mass is location-dependent? Or do we have to redefine "2"? Or do you reject the equation all together, and all its derived results and experimental confirmations? In which case, what have you to offer?