REFLECTIONS ON THE EINSTEIN THEORY 679
toward infinite values, which is another way of saying that it is physically impossible.
In the iV-system we had two kinds of energy; one was called vis viva, or kinetic energy, and was represented by; the other was called potential
energy, or capacity for work, and was denoted by U. The law of conservation of energy in the 2V-system was expressed by the statement that the sum, T +U=E, or the total mechanical energy of a system remains constant (zero variation) during the motion of the body.
We see that as the above formula involves the terms m and v, the older formulae for energy must be altered, especially since they do not survive a Lorentz-Einstein transformation. It is found that
which formula appears rigorous as a definition of kinetic energy even if members of order higher than the second are taken into account. In words, the mass in motion differs from mass at rest by the kinetic energy divided by the square of the velocity of light.
This expression suggests immediately that the static mass, m, is similarly related to the energy content in the body at rest. Generalizing our results we would have m =E/c2, an equation which holds generally between mass and energy. This fact has been called by Einstein the law of the inertia of energy. It has been verified repeatedly by experiments, and is one of the most striking structural results of Einstein's theory. The above statement means that the two fundamental notions of 'mass' and 'energy' are equivalent and thus we have a clearer vision of the structure of 'matter'. The two older structural laws of 'conservation of matter' and of 'conservation of energy' become fused into one. Mass becomes structurally and verbally nothing else than energy concentrated at a point, and it appears as a form of energy manifestation.2
The above considerations have also led to a revision of our structural notions about 'energy' which we do not need to explain here. Suffice it to say that the old 'potential' energy is not associated structurally any longer with any features of this world. It can be made to vanish by a proper selection of co-ordinates, hence it is no longer considered as energy of any kind.3
With the Minkowski world we became acquainted with a new language which represents structurally more nearly the facts of experience (lower order abstractions) and shares the structure of our higher order of abstractions. So we have the language of 'space-time'. How about 'matter'? The bumping against something hard is not to be disregarded. True, we need a language of new structure, but that is all. In the Einstein theory, 'matter' of course is not treated separately as such. It is an offspring of the field, and is connected with the curvature of the world. The reader should not be surprised to find that the Minkowski world, which has accelerations, must be curved in this structurally new form of representation.
We have already defined a most fundamental entity called 'action'. Naturally in a space-time manifold, energy multiplied by 'time' should be a more fundamental entity than energy, and we call it 'action'. When we speak about