XVI
THE QUEST OF THE ABSOLUTE
Modern Developments in Theoretical Physics, and the Climax Supplied by Einstein
BY DR. FRANCIS D. MURNAGHAN,
JOHNS HOPKINS UNIVERSITY
BALTIMORE
We shall discuss the more important aspects of the theory popularly known as the “Einstein Theory of Gravitation” and shall try to show clearly that this theory is a natural outcome of ideas long held by physicists in general. These ideas are:
(a) The impossibility of “action at a distance;” in other words we find an instinctive repugnance to admit that one body can affect another, remote from it, instantaneously and without the existence of an intervening medium.
(b) The independence of natural, i.e., physical, laws of their mathematical mode of expression. Thus, when an equation is written down as the expression of a physical law it must be satisfied, no matter what units we choose in order to measure the quantities occurring in the equation. As our physics teacher used to say “the expression of the law must have in every term the same dimensions.” More than this the choice of the quantities used to express the law—if there be a choice open—must have no effect on its correctness. As we were told—“all physical laws are capable of expression as relations between vectors or else as relations between magnitudes of the same dimensions.” We shall hope to make this clearer in its proper place in the essay, as its obvious generalization is Einstein’s cardinal principle of relativity.
The measurements which an experimental physicist makes are always the expression of a coincidence of two points in space at the same time. If we ask such an experimenter what he means by a point in space he tells us that, for him, the term has no meaning until he has a material body with reference to which he can locate the point by measurements; in general it requires three measurements and he expresses this by saying that space has three dimensions. He measures his distance, as a rule, parallel to three mutually perpendicular lines fixed in the material body—a Cartesian reference-frame so-called. So that a “point in space” is equivalent to a given material reference-frame and three numbers or coordinates. If, for any reason, we prefer to use a new material reference-frame the coordinates or measurements will change and, if we know the relative positions of the two material reference-frames, there is a definite relation between the two sets of three coordinates which is termed a transformation of coordinates. But which particular material reference-frame shall we use? The first choice would, we think, be that attached to the earth. But, even yet, we are in doubt as there are numberless Cartesian frameworks attached to the earth (as to any material body) and it is here that our idea (b) begins to function. We say it must be immaterial which of these Cartesian frames we use. In each frame a vector has three components and when we change from one frame to another the components change in such a way that if two vectors have their three components equal in one framework they will be equal in any other attached to the same material system. So our idea (b), which says that our physical equations must be vector equations, is equivalent to saying that the choice of the framework attached to any given material body can have no effect on the mode of expression of a natural law.
Shall we carry over our idea (b) to answer the next question: “To which material body shall we attach our framework?” To this question Newton gave one answer and Einstein another. We shall first consider Newton’s position and then we may hope to see clearly where the new theory diverges from the classical or Newtonian mechanics. Newton’s answer was that there is a particular material frame with reference to which the laws of mechanics have a remarkably simple form commonly known as “Newton’s laws of motion” and so it is preferable to use this framework which is called an absolute frame.