What you never learned about mass

From time to time, there are very interesting topics in physics that are not appreciated at all. One of those things is

mass

, which could colloquially be called the amount of "material" something is made of. However, there are many interesting facets to this seemingly simple concept. Now, I'm not talking about the origin of

mass

, for which I made a video (watch it by the way, it's one of my favorites) or even the Higgs field and its role in giving mass to point subatomic structures. particles. And of course, I made a couple of videos about that as well.

No, I'm talking about a very interesting idea that only requires the kind of topics one finds in an introductory physics class, whether in high school or freshman year of college. It's not about Einstein's theory of relativity or anything like that. You don't even need calculus for this, just algebra. I'm going to start with some basic equations and then tell you

what

they mean. This is how this goes. We've all been indoctrinated into the idea that there is only one type of dough, but it turns out that, at least conceptually speaking, there are actually two types. One type of mass is mass that resists movement.

Push a marble and it moves very easily, whereas if you try to push a car, it is much more difficult. This is linked to the notion of inertia and that is why it is called inertial mass. Basically, it says that for any force you exert on an object, an object of small mass will accelerate a lot and an object of large mass will accelerate only a little. And, for those of you who have taken a physics class, this is simply Newton's second law, F equals m a. This is where we need to start being careful. If the type of mass we're talking about here is inertial mass, then we actually need to add a subscript to the mass and say F is equal to m-subinertial times a.

It is important to keep a couple of things in mind. The first is that this has nothing to do with weight. It is equally true in deep space, far from any planet. And the second thing is that it doesn't matter

what

the origin of this force is. It could be someone pushing him. The force could come from a rocket. The strength could come from telekinesis. It doesn't matter. By the way, telekinesis isn't real, but if it were, it would apply here. There is a second type of mass and this mass is linked to both gravity and weight.

An object with more mass is simply attracted by gravity more strongly toward other masses. Newton's theory of gravity says that the force of attraction between two objects with masses m-one and m-two is F equal to 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 since we are careful with the types of mass, we should call this type of mass "gravitational mass" and then we would write the equation with the subscripts as we see here. This is the first key point: that there is an inertial mass, which resists movement, and a gravitational mass, which is something like the load 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 too fancy a way of saying that we can drop the ball and see what happens. Since we have a gravitational force, we can equate it with the equation of Newton's second law. F is equal to m a; I mean, F is equal to m, multiplied by inertia a.

So, writing this carefully, we see that the inertial m of the ball, times the acceleration of the ball, is equal to G times the gravitational mass of the ball, times the gravitational mass of the Earth, divided by the Squared distance of the ball from the center of the Earth. And if we want to solve for the acceleration of the ball, we get this equation here. We see that the acceleration of the ball depends on some constants multiplied by the relationship between the gravitational and inertial mass of the ball. Well, let's leave the math for a moment and ask what the experiment tells us;

After all, physics is ultimately an experimental science. If an idea does not agree with the measurement, it is wrong. A long time ago, Aristotle thought that a heavier object would fall faster than a lighter one, which we now know is not true. Legend has it that Galileo dropped two balls, one heavier and one lighter, from 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 moon landings, astronaut David Scott dropped a hammer and a feather at the same time while he was on the moon.

Working with the BBC, physicist Brian Cox repeated the same experiment here on Earth, when he dropped some feathers and a bowling ball into a huge vacuum chamber and the two fell identically. But the bottom line is that objects of different inertial or gravitational mass fall at identical speeds, which means they experience identical acceleration. And, going back to our equation, that can only happen if the inertial and gravitational mass of the object are the same. Then they cancel out in the equation and you get the formula you could have calculated if you had ever studied physics. So you might be thinking “So what?

That Lincoln guy sure took a detour to show me something I already knew." But now this is the part where it gets really interesting. Remember that inertial mass is what resists motion and gravitational mass is effectively the load of gravity Shouldn't we expect them to cancel? Well, no. What if we did the same exercise, but this time instead of using Newton's law of gravity, we could write the force between two. objects with an electric charge. Since F is equal to k multiplied by 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. , then we would equate it to the inertial mass times acceleration. If we were to solve for the acceleration, we would see an equation like the one we saw before, but the relationship would be the electric charge of the ball, divided by its inertial mass. things are not like that. They are not cancelled. After all, charge and any type of mass are different, but they cancel out due to gravity. And this tells us something incredibly profound about the universe. That is to say, the resistance of an object to movement is closely linked to the gravitational influence of an object.

It's not really understood why that is true. However, Einstein took this idea and said that inertial mass and gravitational mass were identical. Of course, this was just a hypothesis, although, as we have 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 curvature of space and time. Gravitational waves, black holes, event horizons and clocks slowing down in high gravitational fields and all of that are a consequence of the equivalence of inertial and gravitational mass. This is really surprising and I bet you didn't really appreciate its importance.

The fact that there is only one type of mass is deeply tied to the very structure of the entire universe. And that has to leave you speechless. I like this video because it shows us how something seemingly simple can have profound and underappreciated implications. Who knows? If you liked learning about this, let us know in the comments and of course we would appreciate it if you like, subscribe and share. We love reaching even broader audiences. See you next time and remember, physics is everything.