How did Maxwell's theory predict that c is constant?

[ajay.05]

In the book, briefer history of time, hawking says that maxwell's theory of electromagnetism, concluded that speed of light is finite and constant, which made other physicists to give up the idea of absolute time, and think of newer concepts. How did maxwell, through his theories, correctly said that speed of light is constant?

 

[Vanadium 50]

Calculate $$\nabla \times \nabla \times E$$ or $$\nabla \times \nabla \times B$$ and it falls out.

 

[sophiecentaur]

Have a look at this link, which shows how the wave speed of an EM wave is the same for all frequencies.
(I don't think there is an arm waving proof of this so you just have to get into the Maths.)

 

[ajay.05]

Calculate $$\nabla \times \nabla \times E$$ or $$\nabla \times \nabla \times B$$ and it falls out.

It clears my mind, but the main problem faced by Maxwell, when he said speed of light is constant, was that of Newton's ideas. According to these, if speed of light is constant, one who could catch up with the speed of light, can see a stationary em wave(theoretically, he can see nothing).
Here is my question,
a)What happens if one sees a stationary wave(although, this is impossible, are there any other effects?), and also
b)Maxwell calculated the speed of the waves and said that they matched the speed of light and they are constant. But how did he do this?(that is, how did he came up with the idea that they are constant?)
Any fresh ideas?

 

[tech99]

There is an interesting account in "The Man Who Changed Everything", by Basil Mahon, published by Wiley. According to the book, Maxwell devised an imaginary mechanical analogue of free space - a complicated machine using rotating cells. With this he could find equations for the behaviour of electric and magnetic fields. He then realized that a mechanical wave could travel in his machine, and he calculated its speed. It depended on the ratio of elasticity to inertia, which for his model were the permittivity and permeability of free space. Their ratio had been found from experiments by Weber and Kohlrausch, and from this he found that a wave in his machine traveled at about the speed of light. So wherever there is free space, permeability and permittivity have the same ratio, and the speed of light is a constant.

 

[ajay.05]

Have a look at this link, which shows how the wave speed of an EM wave is the same for all frequencies.
(I don't think there is an arm waving proof of this so you just have to get into the Maths.)

Thank you for your reply.
But I didn't mean to ask, how did he prove speed of light is constant for any frequency, but I meant a different thing. Look out my reply for Vanadium50, on this forum.

 

[sophiecentaur]

Maxwell didn't just decide that c is constant. The speed came out of the ε and μ in the medium, which are in the final wave equation which is one solution to his basic equations. If you want to understand this then you have to look at the references and be prepared to get your feet wet with the Maths. You can hardly expect a good arm waving explanation.

I don't like the idea of 'catching up with' an em wave. SR tells us that you couldn't so what's the point?

 

[ajay.05]

There is an interesting account in "The Man Who Changed Everything", by Basil Mahon, published by Wiley. According to the book, Maxwell devised an imaginary mechanical analogue of free space - a complicated machine using rotating cells. With this he could find equations for the behaviour of electric and magnetic fields. He then realized that a mechanical wave could travel in his machine, and he calculated its speed. It depended on the ratio of elasticity to inertia, which for his model were the permittivity and permeability of free space. Their ratio had been found from experiments by Weber and Kohlrausch, and from this he found that a wave in his machine traveled at about the speed of light. So wherever there is free space, permeability and permittivity have the same ratio, and the speed of light is a constant.

Thank you, helped me a lot.
But what happens at different speeds? Did he do any experiment for that?

 

[ajay.05]

Maxwell didn't just decide that c is constant. The speed came out of the ε and μ in the medium, which are in the final wave equation which is one solution to his basic equations. If you want to understand this then you have to look at the references and be prepared to get your feet wet with the Maths. You can hardly expect a good arm waving explanation.

I don't like the idea of 'catching up with' an em wave. SR tells us that you couldn't so what's the point?

Yes, SR does say that. But Maxwell's time was when people believed in "absolute time", that is there were no ideas of time dilation. For "them", it was "possible" to catch up with the speed of anything!

 

[sophiecentaur]

Thank you, helped me a lot.
But what happens at different speeds? Did he do any experiment for that?

Is there really any point in revisiting what Maxwell did in the absence of Relativity - except for a bit of historical interest?
These giants of past Science could only work within the limits of what they knew. If they had been given the benefit of present knowledge, they would have done things differently.

 

[ajay.05]

Is there really any point in revisiting what Maxwell did in the absence of Relativity - except for a bit of historical interest?
These giants of past Science could only work within the limits of what they knew. If they had been given the benefit of present knowledge, they would have done things differently.

Ha, well said! Thank you.

 

[sophiecentaur]

Life's too short, young man, to worry about the past.
It could give you a warm glow to think you know stuff that even Einstein didn't!

 

[gleem]

What is wrong by noting simply that the general form of a wave equation is

Which is the same form as Maxwell's equation

where v is the velocity of the wave = (μ₀ε₀)^-½

Maxwell's equation shown no dependence on frequency or anything else (in a vacuum) therefore v is constant.