Does Maxwell's Equation independently show that the speed of light is constant for all observers?

Question

I have been on a debate with a guy who says Maxwell's equation alone shows the speed of light is constant.

I want to know the truth. In maxwells time, they believed in Galeilian relativity. In that case the speed of light is only calculated from our own frame. Assuming that, an object moving will emit light with a velocity of the object + velocity of light. In that case the speed of light is variant during maxwells time

But it has been made into a constant after a lot of experiments and deriving lorentz transformations. I leave that

So my question is, without lorentz transformation (without preassuming any constants) is the speed of light constant?

Answer 1

Maxwell's equations don't say anything on behalf of the velocity of light or relativity. Maxwell's Equations are a set of four equations that describe electromagnetic phenomena. These equations describe how electric and magnetic fields propagate, interact, and how they are influenced by objects.

Answer 2

You throw out the baby with the bath water when you say "So my question is, without lorentz transformation (without preassuming any constants) is the speed of light constant?". Sure teh speed of light is constant in whatever coordinate frame you do your calculation in - it has to be as it is a constant multiplier in the wave equation the results from Maxwell's equation. Whether it transofrms as a constant to another coordinate frame that is in motion relative to yours depends on the transformation you apply. One of the things that hints at the fact that c has the same value regardless of relative motion is that the wave equation is a second order partial differential equation which means you have second derivatives with respect to the time coordinate and the spaital coordinates. This implies that time and space are treated equally and that there is some transformation that allows us to have the form fo the equation remain unchanged.



Now the Galillean transformation doesn't work becuase it treats time differently than space - the spatial coordinate frames get linearly transformed but time does not. So it won't preserve the form of Maxwell's equations. The Lorentz transformation, on the other hand, treats time and spatial coordinates the same thus providing the opportunitiy to preserve the form of Maxwell's equations. In essence, Lorentz transformation provides a rotation of a four dimensional object in four dimensional space and scalars will be preserved as scalars under the transformation.

Answer 3

"Does Maxwell's Equation independently show that the speed of light is constant for all observers?"



Yes. c = 1 / sqrt( permittivity of free space * permeability of free space)

Nature provides the values of the constants.



"I have been on a debate with a guy who says Maxwell's equation alone shows the speed of light is constant."



Yep.



"I want to know the truth."



Try Religion, since Science is NOT about "Truth". All we have is what Nature shows us.



"In maxwells time, they believed in Galeilian relativity. In that case the speed of light is only calculated from our own frame. Assuming that, an object moving will emit light with a velocity of the object + velocity of light. In that case the speed of light is variant during maxwells time"



False. Maxwell's equations were written around an aether. Once the formulation was completed, the "aether-dependent" terms had fallen out. But he / they fully expected a constant light speed.



Keep in mind, the speed of light had been measured at least three different times by then (1865 when he published it):

http://www.speed-light.info/measurement.htm



"But it has been made into a constant after a lot of experiments and deriving lorentz transformations. I leave that"



It was not "made constant", Experiment showed it *is* constant.



"So my question is, without lorentz transformation (without preassuming any constants) is the speed of light constant?"



Only because Nature shows it to be so.

Answer 4

This is exactly what Maxwell realised when he formulated his equations: from the 3rd and 4th you can see that there could be an electromagnetic wave. The 3rd says that electric fields are equivalent to a changing magnetic field, and the 4th says that magnetic fields are equivalent to a changing electric field. The signs when combining these equations give a second order differential equation in both E and B who's solution is in the form sin(kx) or cos(kx) From these, you can calculate the speed of this electromagnetic wave, which is exactly what maxwell did. When his value was almost exactly the same as the accepted value for the speed of light, he realised EM radiation was in fact light. And the point is this calculation is reference frame independent. So light must be constant in every reference frame. So yes, the 3rd and 4th laws allow you to calculate the speed of an electromagnetic wave

Answer 5

No, and that was exactly Einstein's motivation in writing "The Electrodynamics of Moving Bodies". When you transform x and t by Galilean transformations, the form of the equations changes, and the predicted speed of light changes. Einstein asked what happens to x and t if you assume that Maxwell's Equations are valid in every frame, and got special relativity as a result.



@Kaynex: Light is an electromagnetic field.

Answer 6

As the others say about Maxwell's equation. I would like to add, the speed of light can vary in speed depending on the medium it travels on, this is why refraction exists. But the only constant value maybe is that the maximum speed that all things can achieve is the speed of light at its maximum velocity and that is the speed of light in vacuum.

Answer 7

Maxwells equations have nothing to do with light. They simply relate magnetic fields to electric fields in terms of their properties.



The speed of light was understood as constant through experimentation. As early as the mid 1800's they found ways to accurately measure the speed of light.

Answer 8

nope............bcoz he did not consider the fact that light gives information of the world around us



lorentz transformed maxwell eqn to satisfy the condition that sppennd of light is constant irrespective of observer