Hi everybody. I was sick last week and lost like 10 pounds
in 3 days, which brings up the question, what is weight? Weight is actually the force that acts on
your body due to the pull of gravity. Now, the gravitational force depends on the
mass of the object that is generating the force, in this case, planet Earth. So you can lose weight by simply moving to the moon. Technically, therefore, I should have said
I lost mass, not weight. Why do we normally not make this distinction? That’s because in practice it doesn’t
matter. Mass just a number – a “scalar” – as
physicists say, but weight, since it is a force, has a direction. So if you wanted to be very annoying, I mean
very accurate, then whenever you’d refer to weight you’d have to say which direction
you are talking about. The weight in East direction? The weight in North direction? Why doesn’t anyone ever mention this? We don’t usually mention this because we
all agree that we mean the force pulling down, and since we all know what we are talking
about, we treat weight as if it was a scalar, omitting the direction. Moreover, the gravitational attraction downwards
is pretty much the same everywhere on our planet, which means it is unnecessary to distinguishing
between weight and mass in everyday life. Technically, it’s correct: mass and weight
are not the same thing. Practically, the difference doesn’t matter. But wait. Didn’t Einstein say that gravity is not
a force to begin with? Ah, yes, there’s that. Einstein’s theory of general relativity
tells us that the effect we call gravity is different from normal forces. In General Relativity, space and time are
not flat, like a sheet of paper, but curved, like the often-named rubber sheet. This curvature is caused by all types of mass
and energy, and the motion of mass and energy is in return affected by the curvature. This gives you a self-consistent, closed,
set of equations know as Einstein’s Field Equations In Einstein’s theory, then, there is no
force acting on masses. The masses are just navigating the curved
space-time. We cannot see the curvature directly. We only see its effects. And those effects are what we call gravity. Now, Einstein’s theory of General Relativity
rests on the equivalence principle. The equivalence principle says that locally
the effects of gravity are the same as the effects of acceleration in flat space. “Locally” here roughly means “nearby”. And acceleration in flat space is described
by Einstein’s theory of Special Relativity, so with the equivalence principle, you can
generalize special relativity to general relativity. Special relativity is the special case in
which space-time is flat, and there is no gravity. The equivalence principle was well illustrated
by Einstein himself. He said, let us consider you are in an elevator
that is being pulled up at constant acceleration. There is one force acting on you, which is
the floor pushing up. Now Einstein says, gravity has the very same
effect without something pulling up the elevator. And again, there is only one force acting
on you, which is the floor pushing up. If there was nothing pulling the elevator,
so if there was no acceleration, you would feel no force at all. In General Relativity, this corresponds to
freely falling in a gravitational field. That’s the key point of Einstein’s insight:
If you freely fall, there is no force acting on you. And in that Einstein and Newton differ. Newton would say, if you jump off a roof,
the force of gravity is pulling you down. Einstein says, nope, if you jump off a roof,
you take away the force that was pushing you up. Again, however, the distinction between the
two cases is rather technical and one we do not have to bother with in daily life. That is because in daily life we do not need
to use the full blown apparatus of General Relativity. Newton's theory works just fine, for all practical
purposes, unless possibly, you plan to visit a black hole. Thanks for watching, see you next week.
