Occasionally, there are very interesting topics
in physics that are totally unappreciated. One such thing is mass, which could be colloquially
called the amount of “stuff” something is made of. However, there are lots of interesting facets
of this seemingly simple concept. Now I’m not talking about the origin of
mass, for which I’ve made a video- watch it by the way, it’s one of my favorites-
or even about the Higgs field and its role in giving mass to point-like subatomic particles. And, of course, I’ve made a couple of videos
about that too. No, I’m talking about a very interesting
idea that only requires the types of topics one encounters in an introductory physics
class in either high school or the first year of university. This isn’t about Einstein’s theory of
relativity or anything like that. You don’t even need calculus for this one-
just straight algebra. I’m going to start with some basic equations
and then tell you what it all means. So this is how this goes. We’ve all been indoctrinated in the idea
that there is only one kind of mass, but it turns out that, conceptually speaking at least,
there are really two kinds. One type of mass is the mass that resists
motion. Push a marble, and it moves extremely easily,
whereas if you try to push a car, it’s a lot harder. This is tied to the notion of inertia and
therefore it’s called inertial mass. Basically, it says that for any force you
put on an object, an object of small mass will accelerate a lot and an object of large
mass will accelerate just a little. And, for those of you who have taken a physics
class, this is just Newton’s second law, F equals m a. Now this is where we need to begin to be careful. If the kind of mass we’re talking about
here is inertial mass, then we actually need add a subscript to the mass and say F equals
m-sub-inertial times a. It’s important to note a couple of things. The first is that this has nothing to do with
weight. It’s equally true in deep space, far from
any planet. And the second thing is that it doesn’t
matter what is the origin of this force. It could be someone pushing it. The force could come from a rocket. The force could from telekinesis. It doesn’t matter. Telekinesis isn’t real by the way, but-
if it did- it would apply here. There is a second kind of mass and this mass
is tied to both gravity and weight. An object with more mass is simply attracted
by gravity more strongly to other masses. Newton’s theory of gravity says that the
attractive force between two objects with masses m-one and m-two is F equals G M-one
m-two divided by r-squared, where G is just a constant and r is the distance between the
two objects. But because we’re being careful about types
of mass, we must call this kind of mass “gravitational mass” and we would then write the equation
with the subscripts like we see here. So this is the first key point- that there
is inertial mass, which resists motion, and there is gravitational mass, which is kind
of like the charge of gravity. This seems like a cautious point, but bear
with me. So what happens if we try to combine these
two ideas? What does it do for us? Well, we could put an object in a gravitational
field and see how the object resists changes in motion. That, by the way, is an overly fancy way to
say that we could drop a ball and see what happens. Since we have a gravitational force, we can
equate that to the equation of Newton’s second law F equals m a- I mean F equals m-inertial
times a. So writing that out carefully, we see that
m inertial of the ball, times the ball’s acceleration equals G times the gravitational
mass of the ball, times the earth’s gravitational mass, divided by the distance squared the
ball is from the center of the Earth. And if we want to solve for the ball’s acceleration,
we get this equation here. We see that the ball’s acceleration depends
on some constants times the ratio of the ball’s gravitational to inertial mass. Okay- let’s leave the math for a moment
and ask what experiment tells us- after all, physics is ultimately an experimental science. If an idea disagrees with measurement, it’s
wrong. Way back in the day, Aristotle thought that
a heavier object would fall more quickly than a lighter one, which we now know isn’t true. Legend has it that Galileo dropped two balls,
one heavier and one lighter, off the Leaning Tower of Pisa and saw that they fell identically. By the way, that probably didn’t happen-
he actually experimented with objects rolling down an inclined plane. But his conclusion was valid. In the era of the Apollo lunar landings, astronaut
David Scott dropped a hammer and feather at the same time while he was on the moon. Working with BBC, physicist Brian Cox repeated
the same experiment here on Earth, when he had some feathers and a bowling ball dropped
in an enormous vacuum chamber and the two fell identically. But the bottom line is that the objects of
different inertial or gravitational mass fall at identical rates, which means that they
experience identical acceleration. And, getting back to our equation, that can
only happen if the object’s inertial and gravitational mass is the same. Then they cancel out in the equation and you
get the formula that you might have calculated if you ever took physics. So, you might be thinking “So what? That Lincoln guy sure took a roundabout way
to show me something I already knew." But now this is the part where it gets very
interesting. Remember that inertial mass is what resists
motion and gravitational mass is effectively the charge of gravity. Shouldn’t we expect that they cancel? Well, no. What if we did the same exercise, but this
time instead of using Newton’s law of gravity, we used Coulomb’s law? Coulomb’s law describes the force between
two objects with electric charge. It can be written as F equals k times Q-one
Q-two, divided by r-squared. In this case, k is a constant and Q means
charge. If we ask how an object moves under that force,
we would then equate it to the inertial mass times acceleration. If we solved for acceleration, we’d see
an equation like we’ve seen before, but the ratio would be the electric charge of
the ball, divided by its inertial mass. And we know that those two things don’t
cancel. After all, charge and any kind of mass are
different. But they do cancel for gravity. And this is telling us something incredibly
profound about the universe. It is saying that an object’s resistance
to motion is tied very intimately to an object’s gravitational influence. Just why that’s true is not really understood. However, Einstein took this idea and said
that inertial mass and gravitational mass were identical. Mind you, this was just a hypothesis, although,
as we’ve seen- a reasonable one. Using this hypothesis, one of the consequences
is that he could derive his theory of general relativity, and in general relativity, gravity
is understood as the bending of space and time. Gravitational waves and black holes and event
horizons and clocks slowing down in high gravitational fields and all that are a consequence of the
equivalence of inertial and gravitational mass. So this is really pretty amazing and I’ll
bet you really didn’t appreciate its significance. The fact that there is only one kind of mass
is deeply tied into the very fabric of the entire universe. And that has just gotta blow your mind. I like this video because it shows us how
something that is seemingly simple can have deep and unappreciated implications. Who knew? If you liked learning about this, let us know
in the comments and, of course, we’d appreciate it if you’d like, subscribe and share. We love reaching even wider audiences. I’ll see you next time and remember, physics
is everything.
