Mass in Quantum Field Theory

Mass in Quantum Field Theory

Many people confuse mass with weight – among them my favorite cynic Ambrose Bierce, author of The Devil’s Dictionary:

Gravitation. The tendency of all bodies to approach one another with a strength proportional to the quantity of matter they contain – the quantity of matter they contain being ascertained by the strength of their tendency to approach one another. This is a lovely and edifying illustration of how science, having made A the proof of B, makes B the proof of A. – A. Bierce (B1958, p. 51)

massMass is inertia.  Bierce’s statement, although funny, is wrong and quantum field theory has a different take. The quantity of matter they contain, i.e., their mass, is not ascertained by the strength of attraction between the bodies. In physics, mass means the tendency of an object to resist changes in course or speed. It is what physicists call inertia. Inertia is a kind of “I don’t like to be pushed” feeling. It represents the difficulty in getting something going and the difficulty in stopping it once it is moving, or even the difficulty in deflecting it from its path. If you don’t believe in inertia, try pushing a grand piano and a toy car and see which is easier. Even when we learn that “objects” are really fields (Chapter 6), the role of mass will remain essentially the same. Some fields are harder to change than other fields, and the difference is caused by a mass term in the field equations.

Mass is not weight. It is weight that corresponds to Bierce’s “tendency of all bodies to approach one another”.  Weight is the pull of gravity – the downward force exerted by the earth. If there is no gravity there is no weight, but there is still inertia. In ordinary speech, the two concepts are often blurred, as in “a heavy object is harder to push”. Nevertheless, weight is the pull of gravity and mass is inertia, and they are different concepts.

Ashton-EatonConsider, for example, a shot putter: When John Godina picks up the 16 pound (7.2 kg) shot, he is working against gravity, which is not much of a problem for him. But then he must propel the ball forward, and that’s where the real effort comes in, because he is then working against the inertia of the shot that “wants to stay at rest”. Because its inertia is much greater than a baseball’s, he is not able to make it go nearly as fast. Of course after he releases it gravity comes into play again and pulls it back to earth (after traveling, in the case of Godina, some 21.8 meters). In short, gravity and weight are involved during the lifting and trajectory phases, but it is mass or inertia that is the important factor in the throwing or putting phase.

To illustrate the difference, consider the same thing happening on the moon, where the force of gravity is 1/6 that on earth. When Godina picks up the shot he will find that it only weighs about 2½ pounds! “Oh,” he might think, “this shot put will be a piece of cake.” However when he starts to propel the ball forward, he will be in for a surprise; he will find himself pushing against the same mass as on earth and he will only be able to impart to it the same velocity that he did on earth! Of course the weaker gravity again becomes a factor during the trajectory phase, and Godina will be pleased to see that the shot travels much farther. Nevertheless, the resistance he feels during the “putting” process, and therefore the imparted velocity, are the same as on earth, despite the lighter weight. If you can grasp this, you have under­stood the important difference between gravitational attraction (weight) and mass (inertia). Saying that gravity depends on something so basic and universal as mass is not a mere tautology; it is an experimental fact that makes gravity a very special and unique field – a fact that later became the basis for Einstein’s theory of gravity.

The story of how the gravitational field entered into physics and quantum field theory is a strange one, involving apples and moons, predictions and confirmations, problem-plagued expeditions, and the two greatest scientific geniuses of all time. And it might not have happened if not for the Great Plague.

Posted By: Rodney Brooks

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