Free fall

Most of us will never get the chance of being in the above situation
in the first place, so here is another example to get this point across.
If you were ever brave (foolish?) enough to bungy jump,
you would be forgiven if you felt, as you plummeted towards
the surface of the planet accelerating all the time, that the pull
of gravity had never been so manifest or more dramatically
experienced. In fact, quite the opposite is happening. This may
well be the one time in your life that the action of gravity is
completely switched off and you are said to be in ‘free fall’. For
those few exhilarating seconds you are experiencing zero gravity.
It is as though gravity has finally got its way and you are doing
what it has been trying to make you do all your life. It is just
that there is usually solid ground under your feet that ruins things
for it. And so, its job accomplished, gravity has temporarily gone
AWOL. More correctly, rather than saying that gravity is absent we
say that it has been completely cancelled out by your acceleration.
The sensation of free fall is what astronauts feel all the time they
are floating in space away from Earth’s gravity (or in orbit around
the Earth) No wonder they have to undergo rigorous training to
overcome space sickness. It is a sobering thought to think that
space travel is one long bungy jump!
So what does it mean to experience zero gravity? Let’s say
that, as you fall, you ‘drop’ a stone that you have been holding in
your hand. Since it is falling at the same rate as you it will move
alongside you3. A physicist’s way of viewing this, if she has the
presence of mind to stop screaming about how alive she feels and
ignores the ground coming up to greet her, is to shut out all her
surroundings and imagine that only she and the stone exist. Now
the stone appears to be floating in mid-air next to her, in the same
way that objects float in zero gravity out in space. This is why,
in the rocket example, you would not be able to decide, without looking outside, whether the rocket was moving through Earth’s
atmosphere in free fall or floating out in space.
Examples such as the ones I have just described are called
thought experiments since we do not need to physically experience
them in order to glean some insights into the workings of nature.
Einstein was very fond of such an approach since he spent his time
sitting and thinking, rather than working in a laboratory carrying
out real experiments. He called these his gedanken experiments
(‘gedanken’ is just German for ‘thought’). Of course, bungy
jumping and fairground simulator rides showing clips from Star
Wars were not examples he could call upon.
What has all this acceleration stuff to do with Einstein’s ideas
about curving space? I am afraid I have a bit more explaining
to do yet. We must now go back to the example of the rocket.
Remember the bit when you wake up and cannot decide, without
cheating and looking outside, whether the rocket has yet to take
off or is accelerating at one ‘g’ out in space? There is a particular
gedanken experiment you must carry out now. Stand on one side
of the rocket and throw a ball horizontally across the rocket, as
in figure 2.1(a). The ball will follow a curved trajectory and hit
the other side at a point below the one it should have hit if it had
travelled in a straight line. This is just what we would expect to
happen if the rocket were still standing on the launch pad, with
the ball obeying the law of gravity.
If the rocket is now accelerating you should, according to the
principle of equivalence, see the ball follow a similarly curved trajectory.
Hadthe rocket been floating freely in space with its engines
off (i.e. coasting at a constant speed) it would have carried the ball
along with it and you would see the ball move across in a straight
line. This is because the ball and the rocket both have the same
‘upward’ speed. But if the rocket is accelerating, as in figure 2.1(b)
(note that the right hand figure is a fraction of a second later than
the left hand one), then the ball will not feel this acceleration while
it is in flight across the rocket. So by the time it reaches the other
side the rocket will be travelling slightly faster than it was when the
ball left your hand. The point on the opposite wall where the ball
should have hit would have moved up slightly and its trajectory will look curved to you. The principle of equivalence is correct.
Although the explanation of the curved trajectory is different in
the two cases, the effect you observe is the same.
Next, instead of throwing a ball across the rocket, shine a torch
at the other wall so that the light beam is aimed horizontally. If you
had sensitive enough equipment you would find that the beam of
light bends ever so slightly down towards the back/bottom of the
rocket. This is an effect which we can understand quite easily if
the rocket is accelerating in space since we would use the same
reasoning as in the case of the ball. Although the light from the
torch travels across the rocket extremely fast, it still takes a finite
time during which the rocket has gained a little extra speed and
will have moved forward very slightly.
The problem you might have is believing that the light beam
would follow the same curved path when the rocket is standing
on the surface of the Earth. But the principle of equivalence is all
conquering, and light turns out to be no different to the ball. Even
on Earth the light path is slightly curved down by an amount the
same as the curvature it has in the accelerating rocket.
Light does not weigh anything4 so how can it be bent by
gravity? However, mass can be thought of as frozen energy, and
light certainly has energy, so maybe we can think of it as having
weight and should not be surprised if it behaves like material
objects and is pulled down by Earth’s gravity. In fact, Newton
himself had suggested that light is composed of a stream of tiny
particles which would be influenced by gravity in the same way
as the ball. But I amafraid we would get the wrong answer for the
amount of curvature we see if we use Newton’s approach. If we
were to calculate, based on Newton’s argument that light has mass
and is pulled down by gravity, the amount of bending we should
see in the path of the light beam, we would arrive at an answer
that is only half the one we actually measure with our sensitive
equipment. Something therefore had to be wrong with Newton’s
law of gravity, at least when it came to describing the effect of
gravity on light. Einstein’s reasoning was radically different. His explanation
did away completely with the force of gravity. Instead, he said that
all material objects in the Universe will affect the space and time
in their vicinity causing them to warp. So rather than thinking
in terms of the Earth exerting a ‘force’ on us, apples, the Moon,
balls and light beams, which pulls everything towards it, Einstein
claimed that the Earth causes the space around it to be curved.
Now all objects that move in this region of space are simply
following lines of curvature. There is no force that keeps the Moon
in orbit and no force that pulls the light beam in the stationary
rocket down towards the Earth. Everything moves freely, but
along a path that is always the shortest route available. If the
space is flat this path would be a straight line, but since the space
it moves in is curved so is the path it takes. Such paths in curved
space5 are called geodesics.
Einstein developed these ideas during the period leading up
to the First World War. He completed this, his general theory of
relativity, in 1915. But the world had to wait till 1919 before the
theory was verified experimentally.
Einstein had suggested that the Sun’s gravity would bend the
path of light reaching us from distant stars if the light had to pass
close enough to the Sun on its way to Earth. The problem was,
however, that when the star is in the same patch of sky as the
Sun the bright sunlight makes it impossible for us to see the star.
Astronomers had to wait for a total solar eclipse, when the Moon
moves between the Sun and the Earth and blocks out the sunlight,
to test Einstein’s theory. In 1919, the English astrophysicist Sir
Arthur Eddington led an expedition to the Amazonian jungle that
successfully photographed a solar eclipse and measured the small
angle at which the light of a particular star was deflected due
to the Sun’s gravitational field. It was a difficult and delicate
measurement, but it proved that Einstein was right. It made headlines
around the world and Einstein became a household name.