Because this is me, I must start with a lot of disclaimers. First, the title is catchy, but many would disagree with the mystery I’ve identified. Even I might. So, please try to avoid flaming me for my choice. Second, very shortly I will post “The Most Elegant Solution In All Of Physics,” a post that might allow one to argue that what I’m about to identify as the greatest mystery isn’t a mystery at all! Groundwork laid, here we go….
In physics, there is this quantity “mass” that we use to describe how much “stuff” there is in a particle. Technically speaking, “mass” is the energy content of an object measured by an observer when that object is at rest with respect to the observer, and when the observer is viewing that object as a closed system from the outside. (In other words, we don’t know anything about “internal energy,” because the object is just a thing.)
The thing is, there really are two different kinds of mass. First, there is inertial mass, which describes how much an object resists being pushed around by any kind of force. Second, there is gravitational mass, which describes how strongly an object couples to the gravitational field. And, yet, to the best precision we’ve been able to measure, these two kinds of mass are exactly the same. So much so that in introductory physics classes we just call it “mass”, and students may not even realize that there’s anything surprising about the fact that the two are the same!
If you’ve taken freshman Physics, you’ve seen a couple of equations. (Yes, I’m about to post equations; they’re very simple, and even people who are “not math people” can understand what I want you to understand about them; please bear with me!)
First, we have the second-most famous equation in all of Physics:
In this equation, a is acceleration. If something is at rest, you must accelerate it to get it moving. F is the force it takes to move an object with acceleration a, and m is that object’s mass, or how much inertia the object has. It takes more force to get a heavier object moving; this is intuitive, and matches our everyday experience.
The second equation I write in a slightly non-standard form:
Here, F is the gravitational force between two objects, one of mass big-M, and one of mass little-m. G is the universal gravitational constant (basically, a parameter of our Universe that describes how strong gravity is in general), and r is the distance between the two objects.
For present purposes, think of this slightly differently. Assume that M is a really big mass– say, the Earth– and that m is a much smaller mass&ndash: say, you. Then, the quantity in parentheses, (GM/r^2), describes how strong the gravitational field of the Earth is. Put in the radius of the Earth for r. Multiply that by your mass, and you get how much the Earth is pulling on you due to its gravity.
In freshman physics, we get so used to using these two equations that we never stop to think… why should the little-m in those two equations be the same? Indeed, perhaps we should be writing the equations as follows:
The two concepts are very different. Inertial mass says how much an object resists being pushed around by any force whatsoever. Gravitational mass says how much an object couples to the very specific force of gravity. Why are they the same? To try to put this in higher relief, consider another formula that many see in freshman physics:
This is the electric force between two objects, one of charge big-Q, the other of charge little-q. (It’s conventional to use the variable q for charge; don’t ask me why, I have no clue.) Or, to put it another way, the quantity in parentheses is the electric field strength created by a particle of charge big-Q a distance r away (where the 1/4πε_0 represents the strength of electric forces in general, and is just a constant). Then, little-q tells you how strongly the particle with charge little-q couples to that electric field. If you then wanted to figure out how much the particle moved around, you’d need its inertial mass. Notice, however, that the electrical charge is completely different from the inertial mass. One says how strong something couples to a field, the other says how much you need to push something around to get it moving.
Yet, with gravity, how much an object couples to the field is exactly the same as how much the object resists moving around. This isn’t true with any other force. There’s clearly something special about gravity.
So here’s my candidate for the greatest mystery in all of physics: why are inertial mass and gravitational mass the same?
Coming soon to this blog: the solution, in the form of Einstein’s General Relativity.