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Reference: Essays on Substance

Light has no mass, but it has momentum. This indicates that, according to Einstein’s famous equation E = mc², light could have a “mass” of the order of 1/c² in mass units. This amount is so small that it is ignored as mass. But it is still significant as momentum; and we can call it consistency.

CONSISTENCY means “a degree of density, firmness, viscosity, etc.” The use of ‘consistency’ in place of ‘mass’ establishes an equivalence between radiation and matter as two different categories of substance.

The terms SUBSTANCE and CONSISTENCY have not been used in the vocabulary of science because they have not had precise definitions in the past. The Theory of Substance now assigns them precise definitions as follows:

SUBSTANCE
“Substance is anything that is substantial enough to be sensed. We can sense matter, radiation and thought; and, therefore, they are three different categories of substance.”

CONSISTENCY
“Consistency is the measure of the substantiality of substance. Matter has very high consistency called MASS. Radiation has no mass but it has consistency of the order of 1/c² in mass units. Thought has a consistency so small that it can be sensed only mentally.” 

To be part of scientific vocabulary, a term must have precise definition. Newton introduced the terms FORCE, INERTIA, MASS and GRAVITY to science by assigning them precise definitions. We now introduce the terms SUBSTANCE and CONSISTENCY to the scientific vocabulary.

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Reference: The Book of Physics

Note: The original text is provided below.
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Summary

We are confronted by the fact that we do not know the absolute motion of bodies in space by comparing it to a body at complete rest. We only know their relative motions. Each body has its own frame of space within which perception occurs and measurements are made. The measurements are consistent within each frame of reference, but they do not have an absolute basis just like the motion of the body has no absolute basis.

We may accept all measurements to be relative. But then we do not have an absolute view of the universe. We run into mystery about cosmic phenomenon, such as, gravity.

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Comments

The solution to the problem of relativity requires a universal invariant such as a body at complete rest. Einstein used the velocity of light to be invariant. But, this is not fully verified. The velocity of light appears as an invariant only because it is so large compared to the motion in material realm, and for no other reason. It does fully resolve the problem of gravity.

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Original Text

Let us take a last glance back before we plunge into four dimensions. We have been confronted with something not contemplated in classical physics—a multiplicity of frames of space, each one as good as any other. And in place of a distance, magnetic force, acceleration, etc., which according to classical ideas must necessarily be definite and unique, we are confronted with different distances, etc., corresponding to the different frames, with no ground for making a choice between them. Our simple solution has been to give up the idea that one of these is right and that the others are spurious imitations, and to accept them en bloc; so that distance, magnetic force, acceleration, etc., are relative quantities, comparable with other relative quantities already known to us such as direction or velocity. In the main this leaves the structure of our physical knowledge unaltered; only we must give up certain expectations as to the behaviour of these quantities, and certain tacit assumptions which were based on the belief that they are absolute. In particular a law of Nature which seemed simple and appropriate for absolute quantities may be quite inapplicable to relative quantities and therefore require some tinkering. Whilst the structure of our physical knowledge is not much affected, the change in the underlying conceptions is radical. We have travelled far from the old standpoint which demanded mechanical models of everything in Nature, seeing that we do not now admit even a definite unique distance between two points. The relativity of the current scheme of physics invites us to search deeper and find the absolute scheme underlying it, so that we may see the world in a truer perspective.

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Reference: The Book of Physics

Note: The original text is provided below.
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Summary

This chapter by Eddington does not provide a clear understanding of relative and absolute quantities. A relative quantity is measured from a relative reference point. An absolute quantity is measured from an absolute reference point.

Relative motion occurs between two objects. Their relative motion is the same with respect to each other. This works for two material objects; but it does not work for light and a material object. We can say that the speed of light is 186,000 miles per second relative to earth; but we cannot say that the speed of earth is 186,000 miles per second relative to light. Common sense tells us that earth has inertia and it cannot move that fast. So, the concept of relative motion breaks down for light.

The theory of relativity uses “inertial frame of reference.” That means it restricts itself to the domain of matter.

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Comments

Common sense tells us that the greater is the inertia, the more difficult it is to move something. We may, therefore, postulate that a body of infinite inertia will have no motion, and a body of zero inertia will have infinite motion. This gives a sense of absolute motion in terms of inertia. Here we are looking at a deeper truth.

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Original Text

I will try to make clear the distinction between absolute and relative quantities. Number (of discrete individuals) is absolute. It is the result of counting, and counting is an absolute operation. If two men count the number of people in this room and reach different results, one of them must be wrong.

The measurement of distance is not an absolute operation. It is possible for two men to measure the same distance and reach different results, and yet neither of them be wrong.

I mark two dots on the blackboard and ask two students to measure very accurately the distance between them. In order that there may be no possible doubt as to what I mean by distance I give them elaborate instructions as to the standard to be used and the precautions necessary to obtain an accurate measurement of distance. They bring me results which differ. I ask them to compare notes to find out which of them is wrong, and why? Presently they return and say: “It was your fault because in one respect your instructions were not explicit. You did not mention what motion the scale should have when it was being used.” One of them without thinking much about the matter had kept the scale at rest on the earth. The other had reflected that the earth was a very insignificant planet of which the Professor had a low opinion. He thought it would be only reasonable to choose some more important body to regulate the motion of the scale, and so he had given it a motion agreeing with that of the enormous star Betelgeuse. Naturally the FitzGerald contraction of the scale accounted for the difference of results.

I am disinclined to accept this excuse. I say severely, “It is all nonsense dragging in the earth or Betelgeuse or any other body. You do not require any standard external to the problem. I told you to measure the distance of two points on the blackboard; you should have made the motion of the scale agree with that of the blackboard. Surely it is common sense to make your measuring scale move with what you are measuring. Remember that next time.”

A few days later I ask them to measure the wavelength of sodium light—the distance from crest to crest of the light waves. They do so and return in triumphal agreement: ”The wave-length is infinite”. I point out to them that this does not agree with the result given in the book (.000059 cm.). “Yes”, they reply, “we noticed that; but the man in the book did not do it right. You told us always to make the measuring scale move with the thing to be measured. So at great trouble and expense we sent our scales hurtling through the laboratory at the same speed as the light.” At this speed the FitzGerald contraction is infinite, the metre rods contract to nothing, and so it takes an infinite number of them to fill up the interval from crest to crest of the waves.

My supplementary rule was in a way quite a good rule; it would always give something absolute—something on which they would necessarily agree. Only unfortunately it would not give the length or distance. When we ask whether distance is absolute or relative, we must not first make up our minds that it ought to be absolute and then change the current significance of the term to make it so.

Nor can we altogether blame our predecessors for having stupidly made the word “distance” mean something relative when they might have applied it to a result of spatial measurement which was absolute and unambiguous. The suggested supplementary rule has one drawback. We often have to consider a system containing a number of bodies with different motions; it would be inconvenient to have to measure each body with apparatus in a different state of motion, and we should get into a terrible muddle in trying to fit the different measures together. Our predecessors were wise in referring all distances to a single frame of space, even though their expectation that such distances would be absolute has not been fulfilled.

As for the absolute quantity given by the proposed supplementary rule, we may set it alongside distances relative to the earth and distances relative to Betelgeuse, etc., as a quantity of some interest to study. It is called “proper-distance”. Perhaps you feel a relief at getting hold of something absolute and would wish to follow it up. Excellent. But remember this will lead you away from the classical scheme of physics which has chosen the relative distances to build on. The quest of the absolute leads into the four-dimensional world.

A more familiar example of a relative quantity is “direction” of an object. There is a direction of Cambridge relative to Edinburgh and another direction relative to London, and so on. It never occurs to us to think of this as a discrepancy, or to suppose that there must be some direction of Cambridge (at present undiscoverable) which is absolute. The idea that there ought to be an absolute distance between two points contains the same kind of fallacy. There is, of course, a difference of detail; the relative direction above mentioned is relative to a particular position of the observer, whereas the relative distance is relative to a particular velocity of the observer. We can change position freely and so introduce large changes of relative direction; but we cannot change velocity appreciably—the 300 miles an hour attainable by our fastest devices being too insignificant to count. Consequently the relativity of distance is not a matter of common experience as the relativity of direction is. That is why we have unfortunately a rooted impression in our minds that distance ought to be absolute.

A very homely illustration of a relative quantity is afforded by the pound sterling. Whatever may have been the correct theoretical view, the man in the street until very recently regarded a pound as an absolute amount of wealth. But dire experience has now convinced us all of its relativity. At first we used to cling to the idea that there ought to be an absolute pound and struggle to express the situation in paradoxical statements —the pound had really become seven-and-sixpence. But we have grown accustomed to the situation and continue to reckon wealth in pounds as before, merely recognizing that the pound is relative and therefore must not be expected to have those properties that we had attributed to it in the belief that it was absolute.

You can form some idea of the essential difference in the outlook of physics before and after Einstein’s principle of relativity by comparing it with the difference in economic theory which comes from recognizing the relativity of value of money. I suppose that in stable times the practical consequences of this relativity are manifested chiefly in the minute fluctuations of foreign exchanges, which may be compared with the minute changes of length affecting delicate experiments like the Michelson-Morley experiment. Occasionally the consequences may be more sensational—a mark-exchange soaring to billions, a high-speed β particle contracting to a third of its radius. But it is not these casual manifestations which are the main outcome. Clearly an economist who believes in the absoluteness of the pound has not grasped the rudiments of his subject. Similarly if we have conceived the physical world as intrinsically constituted out of those distances, forces and masses which are now seen to have reference only to our own special reference frame, we are far from a proper understanding of the nature of things.

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