7 General Relativity
125
An external observer will see the light traversing from left to right, as the
elevator accelerates upwards. This is shown in the left half of Fig. 7.2, where
each drawing shows the elevator at equally spaced intervals of time. However,
a passenger in the cabin will see the ray falling down, following a parabola,
as shown in the right half of Fig. 7.2.
This all seems fairly straightforward. However, suppose now that we
remove the accelerating drive from the elevator, and replace it by an equivalent downwards gravitational force. An external observer will see that
the elevator is now no longer accelerating, but what about the elevator’s
passenger? According to Einstein, since there is no difference between the effects
of acceleration and gravity, the ray of light will travel on the same parabolic
path as before.
Of course, because of the enormous speed of light compared with the
velocity of the elevator, the distance that the ray is deflected by the gravitational field in this instance would be infinitesimally small. However, in
astronomical examples—e.g., a ray of light from a distant star passing close
by the sun—the effect should be observable. This argument was seized upon
as a possible check on the validity of General Relativity.
Before discussing astronomical observations, let us recall what Newton’s
law of gravity states on the same subject. As we saw in the last Chapter,
the debate about the particle versus wave theory of light had been going on
for centuries when Einstein began working on General Relativity. Maxwell’s
equations (see Chap. 5) represent the zenith of the wave theory’s popularity,
before the advent of Quantum Mechanics. There is no place for gravity in
Maxwell’s theory, a failing it shares with QM. There is therefore no mechanism within it for calculating any deflection of a ray of light by a massive
object.
However, Newton was a believer in the corpuscular theory of light: “Are
not the Rays of Light very small Bodies emitted from shining Substances?” [2].
The corpuscles of light (now called photons) have zero rest mass. As, since
Galileo, it has been known that the path of objects in a gravitational field is
independent of their mass, we would expect all particles, even those with zero
mass, to fall along the same trajectory.
Indeed, Einstein in his first calculation of this effect in 1911 followed
precisely this argument. However, by the time of his 1916 paper, he had
realised that he needed to include the effect of space–time curvature (see
Sect. 7.4), induced by the presence of the gravitational mass, and corrected
his earlier calculation [2] The amended value for the deflection was twice as
large as that of his first (and Newtonian) result.
125
An external observer will see the light traversing from left to right, as the
elevator accelerates upwards. This is shown in the left half of Fig. 7.2, where
each drawing shows the elevator at equally spaced intervals of time. However,
a passenger in the cabin will see the ray falling down, following a parabola,
as shown in the right half of Fig. 7.2.
This all seems fairly straightforward. However, suppose now that we
remove the accelerating drive from the elevator, and replace it by an equivalent downwards gravitational force. An external observer will see that
the elevator is now no longer accelerating, but what about the elevator’s
passenger? According to Einstein, since there is no difference between the effects
of acceleration and gravity, the ray of light will travel on the same parabolic
path as before.
Of course, because of the enormous speed of light compared with the
velocity of the elevator, the distance that the ray is deflected by the gravitational field in this instance would be infinitesimally small. However, in
astronomical examples—e.g., a ray of light from a distant star passing close
by the sun—the effect should be observable. This argument was seized upon
as a possible check on the validity of General Relativity.
Before discussing astronomical observations, let us recall what Newton’s
law of gravity states on the same subject. As we saw in the last Chapter,
the debate about the particle versus wave theory of light had been going on
for centuries when Einstein began working on General Relativity. Maxwell’s
equations (see Chap. 5) represent the zenith of the wave theory’s popularity,
before the advent of Quantum Mechanics. There is no place for gravity in
Maxwell’s theory, a failing it shares with QM. There is therefore no mechanism within it for calculating any deflection of a ray of light by a massive
object.
However, Newton was a believer in the corpuscular theory of light: “Are
not the Rays of Light very small Bodies emitted from shining Substances?” [2].
The corpuscles of light (now called photons) have zero rest mass. As, since
Galileo, it has been known that the path of objects in a gravitational field is
independent of their mass, we would expect all particles, even those with zero
mass, to fall along the same trajectory.
Indeed, Einstein in his first calculation of this effect in 1911 followed
precisely this argument. However, by the time of his 1916 paper, he had
realised that he needed to include the effect of space–time curvature (see
Sect. 7.4), induced by the presence of the gravitational mass, and corrected
his earlier calculation [2] The amended value for the deflection was twice as
large as that of his first (and Newtonian) result.