; the time components give the electric force, while the space components yield the magnetic force. The advantage of the new point of view is chiefly to show us that what we once considered different entities now reveal themselves as the different components of the same space-time existent. The reason for the observed connections between these different entities then becomes apparent.
In particular, let us examine the case of the equations of electrodynamics. In the study of electricity and magnetism we may consider phenomena in which conditions do not vary as time passes by; the electric charges and the magnets remain at rest, and currents flowing in fixed wires do not vary in intensity. Conditions are then termed stationary; it is as though time played no part. The laws which govern this type of phenomena were discovered empirically over a century ago, and were expressed mathematically in terms of spatial vectors. The problem of ascertaining how electric and magnetic phenomena would behave when conditions ceased to be stationary was one that could not be predicted; further experimental research work was necessary before the general laws could be obtained. Even so, the difficulties were considerable, and it needed Maxwell’s genius to establish the laws from the incomplete array of experimental evidence then at hand. All this work extended over nearly a century; it was slow and laborious.
Yet, had men realised that our world was one of four-dimensional Minkowskian space-time, and not one of separate space and time, things would have been very different. By extending the well-known stationary laws to four-dimensional space-time, through the mere addition of time components to the various trios of space ones, we should have written out inadvertently the laws governing varying fields, or, in other words, we should have constructed Maxwell’s celebrated equations. Electromagnetic induction, discovered experimentally by Faraday, the additional electrical term introduced tentatively by Maxwell, radio waves, everything in the electromagnetics of the field, could have been foreseen at one stroke of the pen. A century of painstaking effort would have been saved.[121]
It is also interesting to note that the four separate relations which constitute Maxwell’s equations of electromagnetics are now merged into two; and the cumbersome aspect of the equations gives place to forms of great simplicity.
Still another simplification which the discovery of space-time has conferred upon us is to be seen when we study the principles of the conservation of energy and of momentum. We find that these two distinct principles constitute in reality but one. Conservation of energy is given by the time component, while conservation of momentum is given by the three space components, of one same space-time tensor law of conservation.
In a general way, all problems of dynamics or kinematics in three-dimensional space can be treated as problems of statics in four-dimensional space-time. All these advantages of space-time appeal very strongly to the theoretical investigator who deals with mathematical equations; but they all go to show how much simpler it is to understand the workings of the universe when we realise that the fundamental continuum of the world is space-time, and not separate space and time.
We must now mention another most important conception of classical science, namely, Action; and we shall see that this important mathematical entity finds its place in a perfectly natural way in the world of space-time. In order to understand the significance of Action, let us consider any mechanical system passing from an initial configuration
to a final configuration
