How Relativity Connects Electric and Magnetic Fields

Michael Fowler, University of Virginia

A Magnetic Puzzle…

Suppose we have an infinitely long straight wire, having a charge density of electrons of –λ coulombs per meter, all moving at speed v to the right (recall typical speeds are centimeters per minute) and a neutralizing fixed background of positive charge, also of course λ coulombs per meter.  The current in the wire has magnitude I = λv (and actually is flowing to the left, since the moving electrons carry negative charge). 

Suppose also that a positive charge q is outside the wire, a distance r from the axis, and this outside charge is moving at the sam ... Read more »

Relativistic Dynamics

Michael Fowler, UVa Physics,  3/1/2008

The Story So Far: A Brief Review

The first coherent statement of what physicists now call relativity was Galileo’s observation almost four hundred years ago that if you were in a large closed room, you could not tell by observing how things move-living things, thrown things, dripping liquids-whether the room was at rest in a building, say, or below decks in a large ship moving with a steady velocity.  More technically (but really saying the same thing!) we would put it that the laws of motion are the same in any inertial frame.  That is, these laws really only describe relative positions and velocities.  In particular, they do not single out a special inertial frame as the one that’s “really at rest”.  This was later all written down more formally, in ... Read more »

Mass and Energy

Michael Fowler, University of Virginia   3/1/2008

Rest Energy

The fact that feeding energy into a body increases its mass suggests that the mass m₀ of a body at rest, multiplied by c², can be considered as a quantity of energy.  The truth of this is best seen in interactions between elementary particles.  For example, there is a particle called a positron which is exactly like an electron except that it has positive charge.  If a positron and an electron collide at low speed (so there is very little kinetic energy) they both disappear in a flash of electromagnetic radiation.  This can be detected and its energy measured.  It turns out to be ... Read more »

More Relativity: The Train and the Twins

Michael Fowler, UVa Physics  2/27/08

Einstein’s Definition of Common Sense

As you can see from the lectures so far, although Einstein’s theory of special relativity solves the problem posed by the Michelson-Morley experiment—the nonexistence of an ether—it is at a price.  The simple assertion that the speed of a flash of light is always c in any inertial frame leads to consequences that defy common sense.  When this was pointed out somewhat forcefully to Einstein, his response was that common sense is the layer of prejudices put down before the age of eighteen.  All our intuition about space, time and motion is based on childhood observation of a world in which no objects move at speeds comparable to that of light.  Perhaps if we had been raised in a civilization zipping around the universe in spaceships ... Read more »

Adding Velocities: A Walk on the Train

Michael Fowler, UVa Physics, 12/1/07

The Formula

If I walk from the back to the front of a train at 3 m.p.h., and the train is traveling at 60 m.p.h., then common sense tells me that my speed relative to the ground is 63 m.p.h. As we have seen, this obvious truth, the simple addition of velocities, follows from the Galilean transformations.  Unfortunately, it can’t be quite right for high speeds!  We know that for a flash of light going from the back of the train to the front, the speed of the light relative to the ground is exactly the same as its speed relative to the train, not 60 m.p.h. different.  Hence it is necessary to do a careful analysis of a fairly speedy person moving from the back of the train to the front as viewed from the ground, to see how velocities reallyadd.

... Read more »