# Speed of light in E field

Tags:
1. Aug 9, 2015

### HeavyWater

Without getting into a deep discussion about the vacuum, let's agree that c is the speed of light in a vacuum. If we direct a light beam in a vacuum to pass between the plates of a charged capacitor (perpendicular to the E field) will the speed of the light between the parallel plates of the capacitor be less than c?

Thanks,
Water boyWater boy

2. Aug 9, 2015

### Orodruin

Staff Emeritus
No. Maxwell's equations are linear.

3. Aug 9, 2015

### soothsayer

No. Light does not interact with E fields. This is because, as Orodruin said, Maxwell's equations are linear and thus allow for superposition.

4. Aug 10, 2015

### HeavyWater

Thank you both for your responses. I did not make myself clear...and I have thought about this so much I have confused myself.

In classical electrodynamics does an E-field exert a polarizing effect on free space (the vacuum)? That is where I am confused. We know that the classical wave equation for EM waves in free space shows that c^2= the inverse of epsilon-zero times mu-zero. In the context of classical electrodynamics, does an E-field polarize the vacuum (changing epsilon-zero to "epsilon")? If the beam of light is passing through a polarized media, then the beam of light would no longer be traveling through free space and its speed would be less than c.

5. Aug 10, 2015

### bcrowell

Staff Emeritus
As clarified in #4, this is a field theory question, not a relativity question.

6. Aug 10, 2015

### soothsayer

I think I can answer your question by pointing out that εr, your relative permittivity, is defined as the ratio of the capacitance of a capacitor that has the given medium as a dielectric, and the capacitance of that capacitor that with the vacuum as its dielectric.

Therefore, what you've just described, by my understanding, is a vacuum dielectric capacitor--the very definition of ε0. The speed of light in your experiment should be exactly c, regardless of the strength of the E field.

7. Aug 11, 2015

### bcrowell

Staff Emeritus
@soothsayer - As clarified in #4, the OP is asking about polarizing the vacuum, which would be a quantum field theory effect.

8. Aug 11, 2015

### tzimie

9. Aug 11, 2015

### soothsayer

1. Time dilation isn't applicable to photons. A gravity well would only effect photon frequency.
2. That is a purely hypothetical effect, and doesn't it say the photons would speed up? Also, it doesn't make much sense to me seeing as pair creation doesn't actually change the speed of light in a vacuum, it just may make it slightly longer for a signal to traverse a given distance in a vacuum, if anything. That's not really what the OP was asking.

10. Aug 12, 2015

### tzimie

1. It is applicable. Light bouncing between 2 mirrors forms a clock, clock is affected by time dilation, do you agree?
2. Correct
3. Correct - because vacuum energy is lower than in the 'normal' vacuum. In case of EM field pair production is, on the contrary, more probable. So the effect reverses it's sign.
4. Who cares )

11. Aug 12, 2015

### Orodruin

Staff Emeritus
I do not agree. What you are measuring here when you are referring to the speed of light slowing down is coordinate velocity, not actual velocity as measured by a local observer.

Please be aware that posting material which is not related to the OP is considered off-topic and subject to possible deletion. Thread hi-jacking and going off-topic in general is considered bad manners.

12. Aug 12, 2015

### tzimie

Agreed, but experimenter usually is too big to fit between plates of capacitor, so he/she is looking at it from the "outside", observing the coordinate velocity.