7 General Relativity
123
the elevator motor is applying a constant acceleration to the elevator. The
passenger will feel in his legs that he is becoming heavier. It is as though the
force of gravity has increased.
Now imagine that the elevator is allowed to fall freely, as in the second
example in Fig. 7.1. The passenger will drift about inside the elevator, as
if gravity has suddenly been turned off. It hasn’t, of course; it is just that
gravity accelerates the cabin and the passenger downwards by equal amounts.
Another way of looking at this is to say that the elevator and passenger are
both falling at the same rate. This is what is happening in those videos we
have all seen of astronauts floating and tumbling around inside satellite space
laboratories.
These ideas owe their origin to Galileo, who noted that, ignoring air resistance, different objects dropped from a height at the same time would hit
the ground together, irrespective of their mass. He realised that mass appears
in two different guises: gravitational mass, which is responsible for an object’s
weight, and inertial mass, which is a measure of its resistance to changes in
its state of motion. If you weigh an object, you are measuring its gravitational mass; if you push an object to set it in motion, you are resisted by the
object’s inertial mass. The fact that objects fall at the same rate, irrespective
of their gravitational mass, told Galileo that their gravitational masses and
inertial masses have the same value. This property is known as the Principle
of Equivalence.
The genius of Einstein lay in his ability to pursue the consequences of his
hypotheses, wherever they happened to lead him, with no regard to conventional thinking or common sense. His tool was rigorous logic, of the type that
we have discussed in Part 1 of this book. In formulating Special Relativity,
Einstein had asserted that there was no experiment observers could perform
to determine whether they were in motion or not. He now maintained that
there was no experiment observers could perform to determine whether they
were in an accelerating elevator or under the influence of gravitational fields.
This hypothesis became the basis of his theory of General Relativity.
However, in this case we must attach a caveat. Einstein is assuming here
that the elevator and its immediate surrounds are small compared with the
distance to the centre of the external gravitational field. If our elevator had a
size of many kilometres and were located near the surface of the earth, then
clearly the gravitational field experienced by the observer would be greater at
the bottom of the elevator than at the top. This difference could be detected
by the observer, as it results in a stretching force, or tidal force, acting on the
observer.
123
the elevator motor is applying a constant acceleration to the elevator. The
passenger will feel in his legs that he is becoming heavier. It is as though the
force of gravity has increased.
Now imagine that the elevator is allowed to fall freely, as in the second
example in Fig. 7.1. The passenger will drift about inside the elevator, as
if gravity has suddenly been turned off. It hasn’t, of course; it is just that
gravity accelerates the cabin and the passenger downwards by equal amounts.
Another way of looking at this is to say that the elevator and passenger are
both falling at the same rate. This is what is happening in those videos we
have all seen of astronauts floating and tumbling around inside satellite space
laboratories.
These ideas owe their origin to Galileo, who noted that, ignoring air resistance, different objects dropped from a height at the same time would hit
the ground together, irrespective of their mass. He realised that mass appears
in two different guises: gravitational mass, which is responsible for an object’s
weight, and inertial mass, which is a measure of its resistance to changes in
its state of motion. If you weigh an object, you are measuring its gravitational mass; if you push an object to set it in motion, you are resisted by the
object’s inertial mass. The fact that objects fall at the same rate, irrespective
of their gravitational mass, told Galileo that their gravitational masses and
inertial masses have the same value. This property is known as the Principle
of Equivalence.
The genius of Einstein lay in his ability to pursue the consequences of his
hypotheses, wherever they happened to lead him, with no regard to conventional thinking or common sense. His tool was rigorous logic, of the type that
we have discussed in Part 1 of this book. In formulating Special Relativity,
Einstein had asserted that there was no experiment observers could perform
to determine whether they were in motion or not. He now maintained that
there was no experiment observers could perform to determine whether they
were in an accelerating elevator or under the influence of gravitational fields.
This hypothesis became the basis of his theory of General Relativity.
However, in this case we must attach a caveat. Einstein is assuming here
that the elevator and its immediate surrounds are small compared with the
distance to the centre of the external gravitational field. If our elevator had a
size of many kilometres and were located near the surface of the earth, then
clearly the gravitational field experienced by the observer would be greater at
the bottom of the elevator than at the top. This difference could be detected
by the observer, as it results in a stretching force, or tidal force, acting on the
observer.