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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.