Does elementary charge exist?

If you listened attentively at your physics classes at school, you may be acquainted with Newton's first principle of dynamics, which runs as follows:

  • There exists a frame of reference with respect to which a body either moves with rectilinear uniform motion or rests, when there is no force acting upon it or the acting forces are counterbalanced.

Such inertial systems may be infinitely many, since any system with uniform rectilinear motion with respect to an inertial system is inertial itself. The principle above defines an inertial system, but says nothing about its nature, providing only a criterion to decide whether a system is inertial or not. In fact, the criterion is not very reliable in view of the fact that no complete balance of forces can be attained in practice. Thus we can only speak of inertiality up to some degree of precision. The situation seems to be rather unpleasant. If we cannot decide whether unbalanced forces act upon a body or not, then how can we write equations for motion to relate acceleration with the forces? But then to establish the existence of forces we have to resort to acceleration! It seems that this difficulty is of conceptual character only. After all, mechanics applied to practice works quite well.

According to Newton, the existence of an inertial system depends on the existence of absolute space, being just one of its properties. Even if velocity is relative, acceleration is not. Unfortunately, this attractive idea brings us no closer to the understanding of the problem. What does "acceleration with respect to absolute space" mean? If there were only one point-like body in the entire universe, then any reference to its motion would seem to be an abuse. For Newton, however, absolute acceleration would still be meaningful. And what if there were two bodies only?

Berkeley's ideas were quite opposed to those of Newton. There is no absolute space, so both acceleration and velocity can only be relative. To understand better the difference, let's perform a mental experiment. First, however, we will refer to our knowledge derived from a real experiment. The non-inertiality of the Earth reference system can be deduced from some simple experiments, the best known being Foucault's pendulum. But one can also observe the motion of celestial bodies with respect to the horizon. It turns out that allowing for possible inexactness of observation, the motion with respect to distant stars (so-called constant stars) and the local deviation from the non-inertiality of the reference system are the same. Let's return now to our mental experiment. If we set a bucket with water spinning, the surface of the liquid will take the shape of a paraboloid. And what if we take the stars instead of the bucket? Newton would say that nothing special would happen. The surface of the water would remain flat, because it remains in rest with respect to the inertial system (i.e. the absolute space). Nevertheless, the opposite opinion (i.e. that the paraboloid would reappear) has its supporters too. The Austrian physicist and philosopher Ernest Mach, the author - with Berkeley - of the idea of relative acceleration, assumed that the coincidence of the reference system established through terrestrial measurements with the system determined by the constant stars cannot be accidental. Hence the inertial system must be determined by the distribution and motion of masses in the universe.

This brings us close to the so-called Mach principle and the generalized Mach principle. They state that there are no "inner" properties of matter, like charges or masses of elementary particles. All the attributes of matter result from its dynamic coupling with the rest of the universe. This idea has not been universally accepted by physicists, although it has not been refuted by any experimental data up to date either. Consequently, we just cannot say whether constant mass and constant charge of the electron exist.

Krzysztof Rejmer