But there is a more curious fact, and that is, that after we have
made this correction we still have not obtained a quantity which is
at all times exactly the same for the same body. When a body absorbs
energy—for example, by growing hotter—its “proper mass” increases
slightly. The increase is very slight, since it is measured by
dividing the increase of energy by the square of the velocity of
light. On the other hand, when a body parts with energy it loses mass.
The most notable case of this is that four hydrogen atoms can come
together to make one helium atom, but a helium atom has rather less
than four times the mass of one hydrogen atom.
We have thus two kinds of mass, neither of which quite fulfils the old
ideal. The mass as measured by an observer who is in motion relative
to the body in question is a relative quantity, and has no physical
significance as a property of the body. The “proper mass” is a genuine
property of the body, not dependent upon the observer; but it, also,
is not strictly constant. As we shall see shortly, the notion of mass
becomes absorbed into the notion of energy; it represents, so to speak,
the energy which the body expends internally, as opposed to that which
it displays to the outer world.
Conservation of mass, conservation of momentum, and conservation of
energy were the great principles of classical mechanics. Let us next
consider conservation of momentum.
The momentum of a body in a given direction is its velocity in that
direction multiplied by its mass. Thus a heavy body moving slowly may
have the same momentum as a light body moving fast. When a number of
bodies interact in any way, for instance by collisions, or by mutual
gravitation, so long as no outside influences come in, the total
momentum of all the bodies in any direction remains unchanged. This law
remains true in the theory of relativity. For different observers, the
mass will be different, but so will the velocity; these two differences
neutralize each other, and it turns out that the principle still
remains true.
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