"Greg Egan - Foundations 1 - Special Relativity" - читать интересную книгу автора (Egan Greg)

everyone can agree on? Is there an invariant in spacetime geometry equivalent to the
Euclidean concept of distance?
In the 1880s, Michelson and Morley carried out a series of experiments which
established that the speed of light in a vacuum is always the same, regardless of any
motion of either the source of the light or the observer making the measurement. Light
travels along paths that cut across spacetime in such a way that everyone agrees on its
speed. This is the fact that Einstein used to uncover the geometry of spacetime.




Imagine the set of world lines traced out in spacetime by all the pulses of light,
travelling in every possible direction, that could pass through a given event. This is
known as the light cone for that event. If we're only dealing with one dimension of
space, тАЬevery possible directionтАЭ means either left-to-right or right-to-left, as illustrated
by the two dashed 45┬░ lines in Figure 6, but if you imagine spinning this diagram around
the t-axis, you'll see what the case for two spatial dimensions looks like, and why the
term тАЬlight coneтАЭ is used.
In this diagram, as in Figure 1, we've chosen units where the speed of light
(normally referred to as c) is one. In everyday units, c = 300,000 km/sec, but using light
years and years (or any similar choice, like light minutes and minutes) conveniently
makes c = 1. Be warned, though: if you plug distances and times in metres and seconds
into any of the formulas we're about to derive, they won't work.
Given a velocity of one, the equations for a pulse of light travelling left-to-right or
right-to-left through the event (0,0) are:


x = t
 Egan: "Foundations 1"/p.12


x = тАУt

These two cases can be encompassed by a single equation for the whole light
cone:


x2 тАУ t2 = 0 (12)


The Michelson-Morley experiments showed that, no matter what your own
velocity is, you will agree that this is the equation for the light cone. So for any two
events whose separation in spacetime is such that a pulse of light can travel between
them, such as O and P in Figure 6, the quantity x2тАУt2 must be zero тАФ whoever calculates
it, and no matter what individual x and t values they measure.
That makes x2тАУt2 a good candidate to take the place in spacetime of x2+y2 in
space. A small change to Eqns (1) and (3) can accommodate this:


g[(x,t),(u,w)] = xu тАУ tw (13)