What is the significance of v/c factors in the Maxwell-Einstein conflict?

[thedude27]

Galileo-Maxwell conflict

Hey all.

I need to write a small essay on their conflict, and I can't seem to find any information anywhere.

If anyone can help me, I would truly appreciate it.

Thanks.

 

[quartodeciman]

What conflict? Einstein was born the year James Clerk Maxwell died.

link to James Clerk Maxwell bio --->
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Maxwell.html

link to Albert Einstein bio --->
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Einstein.html

 

[Integral]

The only possible conflict involving the 2 it the conflict Maxwell created in 1867 amounsts the world of Physics with his reveation that the speed of light is indpentdant of the motion of the observer. Einstein resolved that conflict in 1905 with his paper on Special Relativity

 

[thedude27]

My bad, it's Galileo-Maxwell, not Einstein-Maxwell

 

[chroot]

There really isn't a conflict with some specific, conventional name attached to it. What I think you're looking for is the difference between Galiliean relativity and Einsteinian relativity -- i.e. the difference between a Galilean and a Lorentzian coordinate transformation. Search the web for "Galileo Lorentz transform" and you'll probably find what you're looking for.

- Warren

 

[quartodeciman]

Maxwell wasn't yet 50 years old when he died. I wonder what might have happened if he had lived and worked longer. Would he have guessed the required transformation for preserving the form of his electromagnetic equations? He never considered them in a moving coordinate system, as far as I know. But he was one smart cookie and there's no telling what he might have scooped on the way toward a relativity theory. But, alas, he died.

Galileo never studied electrical or magnetic phenomena, as far as I know. He doesn't seem to have had any theory about light propagation either, except that he believed it was of finite speed and not instantaneous. This was demonstrated by danish astronomer Römer after Galileo was dead.

 

[HallsofIvy]

My bad, it's Galileo-Maxwell, not Einstein-Maxwell

Well, that's even worse! Galileo died centuries before Maxwell!

You probably are referring to Galileo's concept of "relativity"- that if you in a sealed carriage moving at a constant speed in a straight line, you cannot do any experiment that will show that you are not standing still. That's, in a sense, expressed by "F= ma". All we can feel are forces and they depend on acceleration, not speed.

Maxwell's equations for electro-magnetic force, however, make the force on a charged body by a magnetic field dependent on the speed of the electron. That is, a person in a sealed carriage, moving at a constant speed in a straight line, can theoretically do an electro-magnetic experiment (say on a light beam staying entirely inside the carriage) to determine the carriage's "absolute" velocity. That was the idea of the Michelson-Morley experiment whose null result led to Einstein's relativity.

 

[arcnets]

thedude27,
the conflict that you have in mind may be the one between 'Galilei-invariants' and 'Lorentz-invariants'. These were two sets of invariants which were in contradiction with each other around ~1900, the first stemming from mechanics, and the second from electrodynamics. HallsofIvy has pointed out some details...

 

[quartodeciman]

Galilean and Lorentz transformations are not actually in conflict for relative speeds that are very much smaller than lightspeed. The Lorentz reduces to approximately the Galilean in that case. Around 1900, nothing was known to go fast enough to challenge lightspeed in empty space, although radioactivity charged particles (beta rays) were getting closer to it than anything before.

 

[arcnets]

quartodeciman,
I think it's not a question of 'approaching light speed'. Just think about the effect of e.m. induction (discovered by Faraday in 1842 or so...). When the coil moves, and the magnet is at rest, the effect is easily explained via the Lorentz force. Which requires moving charges. But induction will also work when the magnet moves, and the coil is at rest. This can not be explained by Galilei transformation. It is, however, explained by Lorentz transformation, which predicts that, if a magnetic field is transformed into motion, there will be an extra electric field. You can demonstrate this very easily in class, where the velocities involved are only some cm/s. I think this is where the conflict originated: the strange transformation behavior of e.m. fields.
I think some people introduced ether theory to save the Galilei transformation. So an experimentum crucis was needed to judge over ether theory. That's where Michelson-Morley comes in. I know, up to today, there are some people who doubt the standard interpretation of MM. But I believe the interpretation is correct, there is a null result, and ether theory must be abandoned in favour of Special Relativity.

 

[quartodeciman]

Interesting.

Both the lorentz force equation and the E-B transformation equations depend on v/c factors. That means whenever the magnitude v is tiny compared to c (galilean reduction), then the lorentz force equation just ought to reduce to straight electrostatic force (with no electromotive term) and the transformations reduce to separated, unchanged electrical/magnetic components. So, common induction phenomena must depend always on having large enough v/c, or else the magnetic component normal to the velocity v must be huge enough to compensate for tiny v/c. How else can an ordinary lab experiment demonstrate EM induction?