"Greg Egan - Foundations 3 - Black Holes" - читать интересную книгу автора (Egan Greg)

although they'll experience the same electrostatic force — the same push — if placed in
the same electric field, they won't accelerate identically like the truck and the pebble.
What's so special about the gravitational force that it's always perfectly matched to an
object's inertial mass?
Einstein's answer is that gravity isn't a force at all. Rather, in the absence of
forces, any object — whatever its mass and composition — simply follows a geodesic in
spacetime: it takes the straightest possible world line in the direction it happens to be
heading. In the curved spacetime near the Earth, the geodesic of an object that started out
stationary would carry it straight to the centre of the planet if nothing got in its way. The
only reason a pebble and a truck sitting motionless on the edge of a cliff aren't following
such paths is because the cliff pushes up on them, with an electrostatic force between the
electrons of the atoms at the surfaces making contact. The different forces required by
the pebble and the truck to keep them from falling aren't really opposing two different
“gravitational forces.” If you define an object's acceleration in curved spacetime as the
degree to which its world line fails to be a geodesic — by analogy with the case in flat
spacetime, where having a constant velocity means having a perfectly straight world line
— the cliff is simply applying different forces to produce the same acceleration in two
different masses.
If the idea that a motionless object can be accelerating strikes you as bizarre,
imagine swinging a weight on the end of a rope: once it's swinging in a fixed circle, you
still need to apply a constant force to accelerate it towards you, just to keep it from getting
further away. What you're doing is curving a path that would otherwise be straight: cut
the rope and the weight will fly off in a straight line. Letting the rope hang vertically is
similar: the force you're applying to keep the weight motionless is still keeping its world
line from being the straightest possible path through spacetime, a path that would carry it
towards the Earth. Being “motionless in space” (relative to some massive object like the
Earth) generally doesn't produce the straightest possible world line in curved spacetime.
Compare this to a ship travelling east at a fixed latitude, say 45° S. The ship is
“motionless” in the dimension of latitude — it's not drawing closer to either the south
pole or the equator — but it can only do this if its engines are constantly applying a
south-directed force to keep it from heading north along a great circle, the geodesic it
would otherwise naturally follow if merely propelled forward.
So, your inertial mass tells you how much force must be provided (by the
ground, or the floor, or the chair you're sitting in) to accelerate you sufficiently to keep
you motionless with respect to the surface of the Earth, in exactly the same way as it tells
 Egan: "Foundations 3"/p.3


you how much force must be provided to accelerate you into motion. The idea of a
“gravitational mass” that determines your response to a gravitational field is illusory.
There is only one kind of mass: inertial mass.
However, as we'll see shortly, matter isn't the only thing with inertia.


Velocity and Acceleration

To provide a full description of matter and energy as the source of spacetime curvature,
we need to introduce the relativistic versions of some simple ideas from classical physics.
The ordinary velocity vector, v, of an object in three dimensions tells you how fast the
object is travelling in each of three directions — the velocity's coordinates vx, vy and vz