Whoo, okay here goes. The concept of ‘relativity’ in physics means that it is meaningless to talk about an object’s velocity in ‘absolute’ terms, only talk about velocity relative to another object. This was first elucidated by Galileo and is just as much a part of Newtonian physics as of Einsteinian physics. But when people talk about the ToR they usually mean one or both of Einstein’s theories. This is 'cos Einstein took the relativity ball and ran with it (relative to the Earth), so to speak.

In the mid-late 19th c, Maxwell worked out the laws of electromagnetism, including the discovery that light was a form of electromagnetic wave. This posed problems for the “Galilean” version of relativity as it was understood at the time. Firstly, you derive the speed of e-m radiation from Maxwell’s equations, without at any time talking about a frame of reference (i.e. what the speed is relative to). This implies that the speed of light (in a vacuum btw) is a constant regardless of the motion of the observer, which seems nonsensical. If a car is trundling along at 60mph down a motorway, and another car is going 50mph in the other direction, we would say the first is going at 60mph relative to the earth, 110mph relative to the second car, or 0mph relative to the driver of the first car. It seems impossible that there could be another object which all three observers simultaneously measure going at, say, 70mph. But light seems to do just this (except at 300,000kps).

[this next bit I’m shaky on]Another problem, which is the one that Einstein used to introduce his theory of Special Relativity, is what happens when a moving magnet induces an electrical current in another wire. This should occur regardless of whether the magnet or the wire is ‘really moving’, but Einstein showed that, as the principle of relativity was understood at the time, one situation would produce a current and the other would not. Experimentally, it made no difference, as we would expect.

Einstein solved this problem in his 1905 paper. He takes two postulates as unshakeable. Firstly, the principle of relativity. Secondly, the constancy of the speed of light (i.e. its independence of the motion of the observer). By insisting these two apparently contradictory notions must both always hold, he showed the real problem was in the way we were changing co-ordinates in switching between observers. Basically we had the wrong ideas about space and time. Einstein showed how to transform them correctly. (The math form of the transformations had been found earlier by Lorentz, but for him they were only an ‘interesting fudge’, Einstein showed the physical basis for them)

The consequences of this constitute Einstein’s “Special Theory of Relativity” of 1905. Standard results include things like

- moving objects are ‘squashed’ in the direction of their motion relative to the observer
- moving clocks run more slowly than their stationary counterparts
- two events that are simultaneous to one observer will not be to other observers (ie time does not flow at the same rate for everyone)
- relative velocities don’t add in the simple way we thought they did. With those two cars, the velocity of the first relative to the second is a teensy bit less than 110mph. For such low speeds the difference is negligible, but for speeds near that of light, the diff is important
- the momentum of a moving massive object is larger than just the ‘mv’ of Newtonian physics. This was originally thought of as saying that moving objects are heavier, but that point of view is deprecated these days.
- nothing with mass can travel faster than (or even at) the speed of light.
- E=mc^2, i.e. mass and energy are equivalent in a certain sense.

After his 1905 breakthrough, Einstein pondered the consequences to the existing theory of gravity. He came up with the ‘equivalence principle’ which basically says that for sufficiently small volumes of space, a gravitational field is equivalent to an accelerating frame of reference. This led in 1915 to his ‘General Theory of Relativity’, in which gravity is no longer thought of as a ‘force’, but rather is a twisting of space (or rather ‘spacetime’, as it had become more useful to think of space and time together as a four-dimensional entity at this point). This is much more complicated mathematically and it hurts my brane. Note it’s not just a ‘new way of looking at gravity’ but gives very different predictions when the grav fields are strong enough.

GR got experimental verification when it was predicted that grav fields bend light, and this was observed during an eclipse when the stars near it wobbled. Also it resolved a long-standing mystery about the precession of Mercury’s orbit, which I believe was about twice what Newton said it was supposed to be. It also predicts that grav fields mess time up. There was a cool experiment (Hafele-Keating?) where an atomic clock kept on a very fast aircraft for a while ran slow. And apparently it is crucial to take GR time corrections into account for GPS systems to work accurately.

You can also apply the equations of GR to the mass distribution of the universe as a whole, and so talk about cosmology. First time Einstein tried this, he got an expanding universe which appeared ridiculous. The equations permitted him to insert a ‘fudge factor’ called the cosmological constant, which would make the universe nice and static like it ‘obviously was’. Then Hubble realised the universe really WAS expanding so Einstein dropped the CC, calling it his ‘greatest blunder’. Weirdly, in the last ten years or so, cosmologists have discovered that the expansion of the universe appears to be *accelerating*. This appears to require bringing back the CC after all. Except in the age of Star Trek we call it ‘dark energy’.

A proper understanding of GR requires using mathematical objects called “tensors”. Nobody in the world knows what these are, and if they say they do, they are lying. [/ego-protecting projection of my final-year physics degree difficulties]