The Lorentz Transformations

Michael Fowler, UVa Physics.  2/26/08

Problems with the Galilean Transformations

We have already seen that Newtonian mechanics is invariant under the Galilean transformations relating two inertial frames moving with relative speed v in the x-direction,

However, these transformations presuppose that time is a well-defined universal concept, that is to say, it’s the same time everywhere, and all o ... Read more »

Time Dilation: A Worked Example

Michael Fowler, UVa Physics, 12/1/07

“Moving Clocks Run Slow” plus “Moving Clocks Lose Synchronization” plus “Length Contraction” leads to consistency!

The object of this exercise is to show explicitly how it is possible for two observers in inertial frames moving relative to each other at a relativistic speed to each see the other’s clocks as running slow and as being unsynchronized, and yet if they both look at the same clock at the same time from the same place (which may be far from the clock), they willagree on what time it shows!

Suppose that in Jack’s frame we have two synchronized clocks C₁ and C₂ set 18 x 10⁸ mete ... Read more »

Special Relativity: Synchronizing Clocks

Michael Fowler, UVa Physics  2/29/08

Suppose we want to synchronize two clocks that are some distance apart.

We could stand beside one of them and look at the other through a telescope, but we’d have to remember in that case that we are seeing the clock as it was when the light left it, and correct accordingly.

Another way to be sure the clocks are synchronized, assuming they are both accurate, is to start them together. How can we do that? We could, for example, attach a photocell to each clock, so when a flash of light reaches the clock, it begins running.

... Read more »

Special Relativity

Michael Fowler, UVa Physics  3/3/08

Galilean Relativity again

At this point in the course, we finally enter the twentieth century—Albert Einstein wrote his first paper on relativity in 1905.  To put his work in context, let us first review just what is meant by “relativity” in physics.  The first example, mentioned in a previous lecture, is what is called “Galilean relativity” and is nothing but Galileo’s perception that by observing the motion of objects, alive or dead, in a closed room there is no way to tell if the room is at rest or is in fact in a boat moving at a steady speed in a fixed direction.  (You can tell if the room is accelerating or turning around.)  Everything looks the same in a room in steady motion as it does in a room at rest.  After Newton formulated his Laws of Motion, desc ... Read more »

Special Relativity: What Time is it?

Michael Fowler, Physics Department, UVa.

Special Relativity in a Nutshell

Einstein’s Theory of Special Relativity, discussed in the last lecture, may be summarized as follows:

The Laws of Physics are the same in any Inertial Frame of Reference.  (Such frames move at steady velocities with respect to each other.) 

These Laws include in particular Maxwell’s Equations describing electric and magnetic fields, which predict that light always travels at a particular speed c, equal to about 3×10⁸ meters per ... Read more »