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

out one-dimensional world lines, rather than worrying about the fact that they're really
solid objects whose histories in spacetime are four-dimensional тАЬworld hypercylindersтАЭ.
When you draw a map, you have to choose a compass direction to point тАЬupтАЭ on
the page. North is often convenient, but it's a completely arbitrary choice, and on a
house plan, say, it might be more useful to align the map so that the street frontage is
horizontal. Similarly, to draw a spacetime diagram you have to choose a reference
frame: you have to pick some object, such as the Sun, and treat it as fixed. The chosen
object's world line will then be vertical тАФ it will be тАЬmovingтАЭ only in time, not space тАФ
as will the world line of any other object at a constant distance from it. So the world lines
for the Sun and Sirius are vertical here because the diagram was drawn that way; it's a
matter of convenience, not a statement that the Sun is тАЬtruly motionlessтАЭ, any more than
north is тАЬtruly upтАЭ.
However, some reference frames are different from others. Orienting a map so
that a given straight road runs vertically is one thing; arranging for a meandering river to
appear as a straight line is a much harder task. If we chose the spacecraft to be the fixed
point, everything we did would be complicated by the need to straighten out the curved
 Egan: "Foundations 1"/p.3


sections of its world line when it accelerates and decelerates. To avoid this kind of
complication, special relativity deals only with inertial reference frames, which take
as their fixed point an object that is not accelerating. Unlike the idea of being motionless
(motionless compared to what?) this condition is easily defined in the middle of
interstellar space: if you're not firing your engines, and everything in the ship is
weightless, then you're not accelerating.
Of course, we can imagine a hypothetical second spacecraft which never
accelerates, but conveniently happens to match the first spacecraft's velocity for some
part of the journey тАФ such as the entire middle stage, when the engines are shut off, or
even just for an instant during the acceleration or deceleration stages. That way, we can
analyse the first spacecraft's viewpoint at any given moment, without adopting a
reference frame in which it appears motionless from start to finish.
In a reference frame fixed to the Sun, the world line for the spacecraft starts out
being vertical, tips over as it accelerates, has a constant slope in the cruising stage, then
comes back towards vertical again as it decelerates. The world line for a pulse of light
that leaves the solar system at the same time as the spacecraft is shown for comparison; it
has a constant angle (45┬░ in this diagram), because it travels at a constant velocity all the
way.
To be in motion relative to the Sun means tracing out a world line at an angle to
the Sun's world line. That might sound like nothing but a novel way to describe the
situation, but it's the key to all the relativistic effects of space travel. Two people facing
different directions in ordinary space see the same objects differently. Two people
driving between the same two towns will travel different distances, if one takes the most
direct route while the other takes a detour. In spacetime, the effects are analogous, but
not quite identical, because the geometry of spacetime is not quite the same as the
geometry of space.


Rotations in Space

Despite the differences, analysing the effects of rotating your angle of view in ordinary