F1 The Credo of Physics
The four most important quantities of physics are:
- electric charge, a scalar with symbol q and unit Coulomb
- mass, a scalar with symbol m and unit kilogram
- momentum, a vector with symbol p and unit kg • m/s or N • s
- energy, a scalar with symbol E and unit Joule.
Why these four and no others? The answer to this question is the central credo of classical physics: In a closed system the total amount of these four quantities remains constant, no matter what else happens! One can neither produce nor destroy electrical charges, one may dissociate or transfer them, but the sum of all positive and negative charges always remains constant. Also the total mass of the scrap heap after a mass collision is equally large as the sum of the masses of the individual cars involved in the collision. But the momentum, will it not be destroyed when I crash to the ground? No, not if one includes everything involved in the impact (all of these conservation laws apply only to closed systems!). The conservation of total energy is an insight of the second half of the 19th century. Energy can be neither produced nor destroyed, but only converted into different manifestations.
On a pedestal next to these core quantities stand Newton’s laws of motion:
- The law ‘actio = reactio’: There are no individual forces, but only reciprocal reactions.
- The law of inertia: In the absence of a force, the velocity v remains constant (including the case v = 0).
- The force law: The change in momentum equals the acting force: F = dp/dt.
The first law (together with the third) is equivalent to the conservation of total momentum. We nevertheless do not want to omit it, because it brings, with its Latin conciseness, a very deep insight. The second law is a special case of the third; it only stands still in order to annoy Aristotle a little. The third law is however indispensable: It tells us how the future motion of a particle is influenced by the forces acting on it.
Thus we must clarify which forces truly exist. The answer is again easily overlooked. There are only three forces, which originate from three different vector fields:
- The gravitational or Newton force, which acts on mass: FN = m • g
- The Coulomb force, which acts on electrical charge: FC = q • E
- The Lorentz force, which acts on fast electrical charges: FL = q • (v x B)
Where, however, do the appropriate fields, i.e., the gravitational field g, the electrical field E and the magnetic field B come from? Newton had already provided the answer for the gravitational field: It not only acts on masses, but it is also produced by the masses. The exact specification gives his gravitation law. Electric and magnetic fields are however produced by electrical charges at rest and in motion. Here the specification is given by the often mentioned four equations of Maxwell. We can only mention and not present in detail these equations, which describe the emergence of the fields.
Thus 5 equations completely describe the origin of the fields, 3 equations describe on what the fields act and the direction of this action and a further equation describes the path of the particle. Together with the 4 conservation laws we have presented the essence of classical physics – all on one page!
It is an enormous mental achievement to ascribe to such a small kernel of basic tenets the richness of the phenomena, which reveals the outside world (its existence is here simply postulated) to an observer. What economics of terminology, what thriftiness of axioms! The geometrical details and the material composition of a gadget may be extremely complicated – yet everything that takes place within it, is completely described by our handful of equations.
Mechanics, thermodynamics and electromagnetism thus cover all phenomena which in the 19th century were considered belonging to physics. It was clear to only a few physicists around 1900, such as Lorentz, Planck and Poincaré that this picture was not as harmonious, complete and self-contained as most thought at the time. The threat did not come from the ‘atomists’. The fact that mass is granular and not continuous did not actually disturb anyone. But there was the problem of the movement of the earth through the ether and the thereby expected fluctuations of the speed of light (see A3). Max Planck opened a further problem area in 1900: He succeeded in theoretically deriving the experimentally well investigated frequency distribution of radiation from a ‘black body’ at a given temperature. He had to use however rather adventurous hypotheses concerning the ‘granularity’ of the radiation energy and also his own unique statistical counting method. Then followed x-rays, the radioactive radium of the Curies, the alpha, beta and gamma radiation of Rutherford and others - nearly every year completely new areas of research were opened. The great building of classical physics was hardly finished and already structural cracks began showing. Various renovations and annexes became necessary.
In the next section we will see an overview of the corrections the STR makes to the core of classical physics, in order to successfully patch one large crack: The incompatibility of Newtonian mechanics, the relativity principle of Galileo and Maxwell's equations.
Also the other large crack, which was opened by Planck's work on radiation, was successfully worked on in 1905 by Einstein. As already mentioned in A4 he himself called this work “On a Heuristic Point of View Concerning the Production and Transformation of Light” [09-177ff] in a letter to Conrad Habicht ‘very revolutionary’. Further work that same spring concerned statistics and provided strong new arguments for the side of the ‘atomists’.