We Relativists find this distinction no longer necessary. Material
masses, like light, travel in a straight line when they are far
from a gravitational field, and in a curved line when they are near
gravitational masses. In virtue of symmetry a free material point can
only follow a geodetic in the universe.
If we now reflect that the force of gravitation introduced by Newton
does not exist—such action at a distance is very problematical—and
that in empty space there are only objects freely left to themselves,
we are driven to the following conclusion, which unites in a simple way
the previously separated sisters, inertia and weight: _Every moving
body freely left to itself in the universe describes a geodetic._
Far from the massive stars this geodetic is a straight line, because
there the universe is almost Euclidean. Near the stars it is a curved
line, because there the universe is not Euclidean. A fine conception,
combining in a single rule the principle of inertia and the law of
gravitation! A brilliant synthesis of mechanics and gravitation,
putting an end to the schism which so long kept them separate and
non-corresponding sciences!
In this bold and simple theory gravitation is not a force. The planets
have curved paths because near the sun, just as in the neighbourhood
of every concentration of matter the universe is curved or warped.
The shortest path from one point to another is a line that only seems
straight to us—poor pygmies that we are—because we measure it with
very small rods and over small distances. If we could follow the line
over millions of miles, and during a sufficient period, we should find
it curved.
In a word—to use an illustration that must be regarded only as an
analogy—the planets describe curved paths because they follow the
shortest path in a curved universe, just as at a sports ground cyclists
have no need to turn the handles when they reach the corner, but pedal
straight on, because the slope of the ground compels them of itself to
turn. In the sports ground, as in the solar system, the curvature is
greater in proportion as the machine is nearer to the inner edge of the
track.
All that now remains is to assign to the universe, to space-time, such
a curvature at its various points that the geodetics will exactly
represent the paths of the planets and of falling bodies, admitting
that the curvature of the universe is caused at each point by the
presence or vicinity of material masses.
In this calculation we have to take into account the fact that the
“Interval”—that is to say, the part of the geodetic between two points
that are very near each other—must be an invariant whoever may be
the observer. In this way the same geodetic will be a curved or even
wavy line for the drunken man we introduced and a straight line for a
stationary observer. The length of the line is the same, whether it
appears straight or curved.
Public-domain text, read in full here on John Shaqi.
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