### Relativistic Mass

The mass of an object consists of its internal energy, as discussed on the previous page. This includes its heat energy, for example. If you heat something up, it gets a tiny bit heavier! As you may recall from chapter 3, heat is essentially kinetic energy at the molecular level. But there is also a sense in which the kinetic energy of the object as a whole contributes to its mass. Roughly speaking, an object gains mass as it goes faster.

The reason for this isn’t hard to see, if we think of mass as a measure of an object’s resistance to acceleration (as discussed on this page from chapter 5). When an object is already moving close to the speed of light, we could push on the object with an extremely strong force and its speed still wouldn’t increase much at all, since the speed of light is the maximum speed at which any object can travel. Thus, an object’s resistance to acceleration (its mass) approaches infinity as its speed gets closer and closer to the speed of light.

In fact, we can use equations from classical physics (chapters 2 and 3) to show that if the speed of light is the absolute speed limit, then the energy used to accelerate the object must be equal to its increase in mass times the speed of light squared, just as Einstein’s famous equation predicts. To see how, check out this simple explanation by John Norton. (If you know a little calculus, you may also appreciate his slightly more careful version of the proof.)

Because the kinetic energy of an object depends on its speed, however, kinetic energy is a relative quantity: it varies from one reference frame to another. For this reason, some physicists draw a distinction between rest mass (an object’s mass in its own reference frame) and relativistic mass, which includes the object’s overall kinetic energy in a given frame of reference. The rest mass of an object is determined solely by the energy it contains intrinsically, and does not vary with speed. Relativistic mass, on the other hand, varies from one reference frame to another.

There is some controversy surrounding this distinction between rest mass and relativistic mass. While it is true that resistance to acceleration increases with speed (especially as an object approaches the speed of light), many contemporary physicists prefer to use the term “mass” only in reference to rest mass. For various technical and pragmatic reasons, some argue that mass should be defined strictly in terms of the internal energy an object contains. The increasing resistance to acceleration (which occurs as an object nears the speed of light) can then be characterized as an increase in momentum, not mass. In special relativity, the momentum of an object is described in terms of the object’s velocity and rest mass, so the concept of relativistic mass is not needed.
This consequence of relativity has practical implications for experiments conducted in the Large Hadron Collider. Since the protons whiz around the collider tunnels at 99.999999% the speed of light, they behave as though they have many times more mass than they have at rest.

Einstein’s special theory of relativity yielded surprising discoveries about mass, as discussed on the previous pages. Mass is related to energy in ways no one else ever suspected. But Einstein wasn’t finished thinking about the concept of mass. Ten years after proposing his first theory of relativity, he published an even more astonishing theory. Mass actually alters the structure of space and time! We’ll examine this wild idea in what follows.