# Why does light have a finite speed?

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1. Jun 14, 2014

hy,

there is nothing in Maxwells equations that would limit the speed of light.

the only way one can get light speed, is to assume that em waves solve Maxwells equations and then one gets c as the square root of something out from Maxwells equations.

the same goes for gravity waves, only observation makes one assume that space does not adjust immediately to change of mass distribution.

am i wrong in this assumption or is there something that comes out of the math, that limits light waves??

2. Jun 14, 2014

### HallsofIvy

The fact that the speed of light is finite, like any fundamental fact of physics, comes from experimental evidence, not any theory or formula. Maxwell's equations are based on the fact that the speed of light is constant, not the other way around.

3. Jun 14, 2014

### Staff: Mentor

The universe could have an infinite speed of light - it would have completely different physics then (because current quantum field theory would not work without special relativity), but I don't think this is an issue. We just do not happen to live in such a universe, as experiments show.

4. Jun 14, 2014

but isnt it strange that as you assume wavelike solutions for his equations that you get the speed of propagation for the wave as the speed of light?

5. Jun 14, 2014

### Staff: Mentor

No. Why?
As HallsofIvy explained, the Maxwell equations were made to match electromagnetism. It would be strange (or just bad physics) if electromagnetic waves would not agree with the wave-like solutions of those equations.

6. Jun 14, 2014

ok thanks you guys are the best

7. Jun 14, 2014

### stevendaryl

Staff Emeritus
It depends on what you mean by "based on". Maxwell's equations were not developed as a way of describing light--it wasn't known that light was electromagnetic. Maxwell's equations were developed as a way of describing electricity and magnetism in a unified way.

8. Jun 14, 2014

### stevendaryl

Staff Emeritus
But it wasn't known at the time of Maxwell that light was electromagnetic, was it?

9. Jun 14, 2014

### HallsofIvy

The question was about the fact that the speed of light is finite- that we do not instantaneously see what happens a long distance away. That was known by experimental evidence long before Maxwell's equations. Yes, you can argue that the speed with which any electromagnetic waves propagate at the speed of light (and so at finite speed) is due to Maxwell's equations but that was not the original question.

Last edited by a moderator: Jun 14, 2014
10. Jun 14, 2014

### phyzguy

Probably you know the history, but I think it is worth reviewing it. Maxwell himself hypothesized that light was electromagnetic in nature. After adding the displacement current term to the known equations of electricity and magnetism, he realized that the equations then supported transverse waves. He calculated the speed of such waves from the known electric and magnetic constants, and found it to be roughly equal to the speed of light, which as HallsofIvy said was known empirically. Maxwell said, "We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."

In my mind the fact that light "drops out" of the empirically determined equations of electricity and magnetism was one of the most fundamental syntheses in all of physics. I don't think it's true to say, as HallsofIvy did, that , "Maxwell's equations are based on the fact that the speed of light is constant, not the other way around." Maxwells' equations were developed to explain electricity and magnetism, and light (with a finite speed) "appeared" as a consequence.

11. Jun 14, 2014

### Staff: Mentor

You don't *assume* that em waves solve Maxwell's equations. You *discover* that em waves solve Maxwell's equations--more precisely, they solve Maxwell's equation with zero source. You don't have to assume it; you can prove it.

No, you don't assume that; you *discover* that gravitational waves solve the Einstein Field Equation--again, more precisely, they solve the source-free linearized EFE.

Yes. A signal propagating at infinite speed does not solve Maxwell's Equations.

Last edited: Jun 14, 2014
12. Jun 14, 2014

### HallsofIvy

But how do you "discover" that when no one has ever even detected "gravitational waves"?

13. Jun 14, 2014

### UltrafastPED

It was a discovery based on the model; Einstein (IIRC) found this solution early on. The calculations based on gravitational radiation match very well to the binary pulsars PSR B1913+16, discovered in 1974. See http://en.wikipedia.org/wiki/PSR_B1913+16

Gravitational waves have not yet been detected directly (except perhaps by the BICEP2 experiment), but are expected any time (year?) now.

So only direct verification is currently lacking.

14. Jun 14, 2014

### Staff: Mentor

As UltrafastPED says, I meant "discover" in the sense of discovering a mathematical solution. Maxwell discovered that electromagnetic waves traveling at the speed of light were solutions of the source-free Maxwell Equations the same way.

15. Jun 14, 2014

### atyy

As phyzguy and PeterDonis have pointed out - there is something that comes out of the Maxwell's equations that limits the speed of light waves.

16. Jun 14, 2014

### kurros

The speed of light in Maxwell's equations is inversely related to the product of the permeability and permittivity of the vacuum (constants). So it is interesting to see what happens if one of these is taken to zero, so that the speed of light goes to infinity.

If we take the permittivity to zero, then Gauss' law gets weird. It seems to say that the tiniest electric charge would create an infinitely strong electric field. So that seems bad.

If we take the permeability to zero, it looks like nothing could ever create a magnetic field. That seems more physically plausible at least. Electric fields would never have any curl either... slightly odd but maybe it is ok, since the electric field lines radiating from point charges would be always perfectly straight.

So in conclusion, I wager that if the speed of light were infinite, there would be no magnetic fields in our universe :). Which I guess means there would be no light either :p.

17. Jun 15, 2014

yes but that's strange isn't it.

basically what the displacement current says is that a rate of change of a electric field produces a magnetic field.
the same goes for Faradays law, a change in magnetic field makes an electric field.

the thing to see here is that the consequences of changing a magnetic or an electric field are manifested immediately. that is when the magnetic field changes i get immediately a electric field of some configuration and the same goes for changes of electric fields.

the only reason why a wave would propagate at a finite speed is if there would be a delay in the creation of both of those fields.

is this whats happening?

18. Jun 15, 2014

### Staff: Mentor

You are looking at it the wrong way.

The rock bottom essence of SR is symmetry, specifically the symmetries of the POR. From that alone you can derive SR:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

It predicts an invariant speed - it may be infinity - but it wasn't put in at the start, and it appears.

Now assuming this speed and the Coulomb law you can actually derive Maxwell's equations:

What this means is the the constant C in Maxwell's equations is the constant C of the Lorentz equations. It represents one of the most elegant determinations of the invariant speed in the Lorentz transformations confirmed by countless experiments.

Thanks
Bill

Last edited: Jun 15, 2014
19. Jun 15, 2014

lets say you have a point charge in empty vacuum and nothing else.

this charge will have associated with it a electric field witch is present in all of space.
an magnetic field will not be present if that particle is not moving.

1. first question, moving with respect to what? and that's a really good question.

now lets say it moves with respect to your frame of reference centered in you, that is with respect to you.

if this charge now moves an infinitesimal distance in one direction, then we will have immediately a magnetic field associated with it.

the induced magnetic field will depend on the particles speed and its charge, and it must build up gradually since the particle must still use an infinitesimal amount of time to travel the infinitesimal distance it cant do it immediately.

2. is this maybe the source for the finite speed of radiation, that it cant be infinite because one would have to move an object at infinite speed to create an immediate sensible change in the field?

but then again there is also a solution to Maxwells equations with no charges and no currents.

20. Jun 15, 2014

### Staff: Mentor

@kurros: No magnetic fields would also make Newtonian mechanics work exactly, and we would not need special relativity. That would be a universe where the low-velocity limit of our universe is exact for all speeds.
It would also mean no mass differences from binding energy. And it would not have protons or neutrons in the way we know them. Annihilation processes would not work in the same way they work in our universe, and basically everything else in particle physics would be different as well.

21. Jun 15, 2014

### Staff: Mentor

The consequences of a changing magnetic or electric field are only manifested immediately *at the point where the change occurs*. The effects of the change are *not* manifested immediately at a point spatially distant from the point where the change occurs; they propagate at the speed of light.

22. Jun 15, 2014

### Staff: Mentor

Moving with respect to the detector that is detecting the fields. A detector at rest relative to the charge will only detect an electric field. A detector moving relative to the charge will detect a magnetic field as well.

"Immediately" at the location of the charge, yes. But if the detector is spatially distant from the charge, then it will not detect a magnetic field until a time $t = d / c$, where $d$ is the distance from the charge to the detector. In other words, the information about the change in the field due to the change in the charge's state of motion propagates at the speed of light.

Yes, because, as you noted in a previous post, changes in the fields themselves produce changes in the fields: a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. But again, the information about these changes propagates at the speed of light. In fact, that's what an EM wave propagating at the speed of light *is*: information about changing fields.

23. Jun 15, 2014

### X338

I'm not sure the op's question was answered, but there's a hypothesis based on a paper published by European researchers last year that it's the quantum vacuum that determines the speed of light.

Basically as photons travel from point A to point B they have to interact with the virtual particles in their the way (kind of like a person on a crowded sidewalk) and while traveling they're continually absorbed and re-emitted by those virtual particles. And as a result have a certain speed in a vacuum, in this case c.

Last edited: Jun 15, 2014
24. Jun 17, 2014

### Staff: Mentor

Relativity is actually the origin of the magnetic force as shown by the fact relativity and coulombs law determines Maxwell's equations. But even aside from that simply consider a current. From relativity and length contraction its charge density in a moving frame is greater so a moving charge feels an extra force. This is the magnetic force and where it comes from.

You have put the cart before the horse. Relativity is a theory about space-time geometry. Obviously that is more fundamental than EM effects - its the very stage physical phenomena take place in. Its symmetry properties determines the Lorentz Transformations and its geometry - thats the import of the link I gave on its derivation from group theory which is the natural language of symmetry. It is that geometry (specifically 4 dimensional space-time geometry) that determines the properties of EM fields including the existence of magnetic fields.

Its not talked about much these days but there was once this very influential program called the Erlangen program:
http://en.wikipedia.org/wiki/Erlangen_program

Its ramifications are still being felt in physics to this day. In fact Einstein, although he probably didn't really realize it at the time, was really the first to place geometry and symmetry at centre stage in physics.

Thanks
Bill

25. Jun 17, 2014

### bcrowell

Staff Emeritus
Yep, bhobba has it right -- took the words out of my mouth :-)