Aside from its profound experimental consequences (length contractions and time dilation), special relativity is important because it establishes the fundamental invariance principle that ties together the Newtonian world and that of Maxwell. The key principle is that uniform motion does not change the laws of physics and hence must leave both theories unchanged.

Notice that you cannot make any invariant from space or time variables alone. That's why we call the SR world is 4-D, and call the old world 3-D + time. No true feature of the world itself is representable in the 3 spatial dimensions or the 1 time dimension separately.

The establishment of a coordinate system for measuring position and time is done by distributing a set of clocks on a lattice. Clock synchronization is done by sending a round trip signal between two clocks. The signal is assumed to arrive at the second clock halfway between emission and reception by the first.

The position of each clock is measured similarly. Half of the round trip time, divided by c, gives the distance.

Einstein's operational recipe (make a bunch of identical rods and clocks, build a lattice of the rods to mount the clocks on, check the clock synchrony with light rays) also allows you to check if relativity is correct. It assumes that once the clocks are synchronized by this procedure, they will stay synchronized. (It also makes other assumptions, but we needn't think about them.)

So while you are getting used to the ideas that:

Einstein has at least opened the possibility that his Special Relativity also is wrong, there may be no inertial frames.

Special relativity applies to inertial reference frames, that is frames that are not accelerating. Hence, it does not apply to frames in which gravity is acting. Einstein hunted for the general theory that should apply when gravity was present. The first problem Einstein had to solve was gravity, namely how do we really know that we are being acted on by gravity?

• Where do you feel gravity?

• Do you feel gravity when you're falling?

• Does gravity change when you land?

• If you have a collection of particles in a uniform gravitational field, how are their mutual distances, velocities, etc affected by the field?

What does that mean?

Notice that when you calculate the acceleration of an object using a = F/m the object's own mass, m DROPS OUT,

The result is that gravity makes every different type of object accelerate together: the effect of gravity is completely describable classically by an acceleration field, as has been known since Galileo’s time.

That means that you don't feel gravity in the same way that you feel other forces. Since all your parts are accelerating together, gravity creates no strains, tickles no nerves…

However, as Einstein put it, he was the first to "interpret" this fact.

Consider the famous "elevator" gedanken experiment (E called it a chest). We are somewhere in intergalactic space, with no planets or other junk nearby. Fred is resting at ease in his unaccelerated reference frame. Barney, on the other hand is inside a box and can’t see out.

Suppose there is a rope attached to the box, and some external agent pulls on the rope, accelerating the box at exactly 9.8 m/s².

Who is correct? Einstein insists that in the absence of a reason for preferring one point of view, one must accept both. This is the strong principle of equivalence, namely that all phenomena are equally describable by either picture. The weak principle of equivalence asserts that the gravitational and inertial masses are the same.

Einstein proposed another modest generalization:

If we accept Einstein's generalization we cannot distinguish an accelerated frame from a gravitational field. We said that no sane person would voluntarily accept accelerated frames, because they lead to all sorts of crazy effects.

If gravity were completely uniform, you could get rid of it by transforming to another reference frame. Gravity can always be eliminated in a small region (e.g., inside Barney’s elevator), but not over a large spacetime domain, because there is an uneven distribution of matter.

So no sane person can reject a universe with gravity: you can't get rid of gravity without getting rid of everything. The gravity isn't uniform.

Other strange things happen in uniformly accelerated frames. A light ray travelling at right angles to the acceleration seems to bend, as if it were falling in the direction opposite to the acceleration.

Straight lines are supposed to be the shortest paths between two points. Now the quicker path here IS the path of the uninterrupted light ray (we can see that easily in the LAB frame) but the spatial path length of that light ray seems LONGER than the path of the ray that makes a bounce off the wall. Isn't the speed of light supposed to be constant? If we tried to make our ordinary laws of physics work in such a frame, we couldn't identify light rays' paths with straight lines.

The path of a light ray? (Doesn't seem satisfactory by our usual standards.)

The shortest path between two points?

(We have to be very careful about how distance is measured)

The locus of a stretched string? (WHEN should the two ends be at particular places, since they don't agree on how fast time is elapsing?)

An abstraction without a simple physical realization?

We'll come back to this question after considering even worse reference frames.

As long as we're looking at yucky reference frames, let's see what would happen if you used a NON-uniformly accelerating reference frame, e.g. a merry-go round.