"Much of the confusion which exists in your scientific concepts today is brought about by your failure to distinguish carefully between matter and mass,"
"Until a comparatively few years ago, it was assumed that mass was a property which was exhibited only by matter. Upon closer examination, however, it appeared that energy also possessed mass, as when energy was added to a body of matter, the mass of the body was increased.
"We should, perhaps, pause at this point to define the terms which we are using lest we add to the confusion instead of resolving it. Mass is defined as resistance to change in the existing state of motion. It is measured by the amount of energy which is required to produce a given change in velocity. All matter has the property of mass, but not all mass has the property of matter. For our purpose now we will postulate that there are two types of mass, inertial mass, which is simply the property of resistance to change in a state of motion, and the mass inherent in matter, which we will call Newtonian mass because it includes all mass which obeys the original laws laid down by Sir Isaac Newton. Since you may be under the impression that all mass obeys the Newtonian laws, let us pause here long enough to examine the facts and to point out he differences in the properties of inertial and Newtonian mass.
"All physicists of today are agreed that the electron has mass. Yet if it were possible for us to hold an electron between two of our fingers and then suddenly release, we would find that there was not the slightest tendency for the electron to fall to the Earth (unless the surface happened to be positively charged at the moment). The electron is not in the least affected by the gravitational field of the Earth, so long as it is at rest with respect to that field (if the electron is moving through the field, however, the direction of the motion will be affected).
"The electron has mass only because it has electric charge. As we know, when an electric charge is accelerated in Space, a magnetic field is produced, and energy is required to produce this field. The energy 'spent' in producing this field is said to be the 'mass' of the electron, since it is the entire cause of its resistance to acceleration. The greater the degree of acceleration, of course, the more intense the field, and the greater the amount of energy required to produce it. So we say that the electron gains 'mass' with every increase in its velocity. If an electron could be accelerated to the velocity C (commonly called the velocity of light), it would have acquired the maximum velocity with which energy can be propagated. It is obvious, therefore, that no amount of energy could further accelerate this electron (with respect to its original reference point), so it would be considered to have acquired 'infinite' mass.
"Let us pause a moment to examine this statement carefully, since it is a point upon which there is much confusion. The electron would have acquired infinite mass only in reference to which its original energy level. If observed from a reference pint which had itself received the same degree of acceleration, the increase of inertial mass with increasing velocity is simply the measure of the kinetic energy differential between the observer and the point which he is observing.
"Let us make a simple analogy, in the hope of making this more readily understood. An observer is stationed in 'free Space' far from any gravitational or other fields which might affect the results of the experiment which he proposes to make. He has in one hand, a sphere of cork or other light material which has a mass of 10 grams. In the other hand he has a pistol which fires bullets also having a mass of 10 grams and a velocity of 1,000 feet per second. The man holds the ball out at arm's length, and fires a bullet from the gun into it. The bullet is not absorbed by the cork, but shares its kinetic energy with it, so that after the impact, the bullet and the cork ball each have a velocity of 500 feet per second. The observer now fires a second bullet at the cork. This bullet also has a velocity of 1,000 feet per second with respect to the observer, but now the target has a velocity of 500 feet per second in the same direction, so that there is a differential of only 500 feet per second which the bullet can share with its target. After this impact, the bullet and the ball each have a velocity of 750 feet per second. When the observer fires the third bullet, he finds that now there is a differential of only 250 feet per second between it and the target, so that the velocity of the target is raised by only 125 feet per second, and so on.
"The observer notes that each succeeding bullet, although it has the same energy with respect to him, produces a smaller and smaller acceleration in the target. He would observe that the 'mass of the target' (its resistance to acceleration) appears to increase with its velocity. It would be necessary to fire an infinite number of bullets. His experiment demonstrates conclusively that as the velocity of the target approaches 1,000 feet per second, his ability to accelerate it further approaches zero. Persons with lesser intelligence o insight than our observer might be convinced that this figure of 1,000 feet per second was an absolute and inescapable limit. The observer, however, as we have said, has greater understanding. After he has accelerated his target to the 'limiting' velocity of 1,000 feet per second (by firing an infinite number of bullets), he steps aboard a small Space Ship (with which he has thoughtfully provided himself), and takes off in the direction of the target. He accelerates his ship off in the direction of the target. He accelerates his ship to a velocity of 1,000 feet per second, with respect to his starting point, and now finds that he is back upon exactly the same energy level as his target, and he can begin his shooting all over again. He observes that his first bullet accelerates the target to a velocity of 500 feet per second with respect to his new reference point, and he notes that the 'infinite mass' of the target returns to its original 10 grams, as soon as he reaches the same energy level. He realises then that the 'increasing mass' of the target is only the measure of the kinetic energy differential which exists between them. The mass approaches infinity only as the energy level approaches that of the accelerating force. (In this case it is 1,000 feet per second.) In the case of the quantity C, usually called the velocity of light, the differential is equal to the total energy inherent in matter (about 3 x 100 to the 10th power centimeters per second or 9 x 10 to the 20th power ergs per gram).
It is, therefore, a maximum of limiting velocity, but only with respect to a given reference point. "When I was telling you about the non-linearity of physical law, I said that the energy inherent in a gram, or any other quantity of matter is precisely the quantity of energy necessary to accelerate its mass to a velocity equal to the quantity C by energy conversion. This statement may be hotly disputed by some of your Earth students \who have not yet learned to distinguish between matter and mass. Their argument is to the effect that no mass can ever be accelerated to the velocity of light since the mass would then be 'infinite' and consequently light since the mass would then be 'infinite' and consequently the energy required to produce the velocity would also be 'infinite.' The incorrectness of this assumption can be demonstrated simply by pressing the button of a pocket flashlight. A beam of light will be produced which any physicist will agree has mass and which but its very definition, moving at the velocity of light. Yet all the energy required is released by a small amount of chemical change taking place within the cells of a battery."
