Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

[Phys-l] EM fields in spacetime



On 03/24/2012 02:36 PM, I wrote:
It might be easier to analyze things in the frame instantaneously
comoving with the bob. In this frame, there is an electric field
plus the (now irrelevant) magnetic field.

This is another advertisement for the modern (post-1908) _spacetime_
approach to physics.

Given an electromagnetic field specified in the lab frame, it is
trivial to understand what it looks like in some other frame ...
provided you think about it in spacetime, and think of the EM
fields as bivectors rather than plain old vectors.

The picture is well-nigh unforgettable:
http://www.av8n.com/physics/magnet-relativity.htm#fig-wire-bivector

You start with a magnetic field bivector. When you rotate it, a
little bit, it picks up a component in the perpendicular direction,
which is the direction we call an electric field bivector. The
amount is first order in the rotation angle, i.e. the boost angle,
i.e. the velocity.

To say the same thing the other way, this would be very mysterious
if you tried to think about it using the pre-1908 approach, using
clocks that can't be trusted, rulers that can't be trusted, mass
that depends on velocity in various different ways, et cetera.

There's a formula for it, but I can never remember formulas like
that. I can however remember the picture, which means I can
rederive the formula in less time than it takes to ask the question.

See also
http://www.av8n.com/physics/pierre-puzzle.htm
http://www.av8n.com/physics/maxwell-ga.htm

It seems to me that doing anything serious with EM fields without
using spacetime bivectors is like hiking through cactus country
barefoot and blindfolded. You're likely to regret it.