Eddington 1927: Frames of Space


Reference: The Nature of the Physical World

This paper presents Chapter 1 (section 4) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.

The paragraphs of original material are accompanied by brief comments in color, based on the present understanding.  Feedback on these comments is appreciated.

The heading below links to the original materials.


Frames of Space

We can now return to the quarrel between the nebular physicists and ourselves. One of us has a large velocity and his scientific measurements are seriously affected by the contraction of his scales. Each has hitherto taken it for granted that it is the other fellow who is making the mistake. We cannot settle the dispute by appeal to experiment because in every experiment the mistake introduces two errors which just compensate one another.

Two errors, which just compensate one another in every experiment, is a speculation only.

It is a curious sort of mistake which always carries with it its own compensation. But remember that the compensation only applies to phenomena actually observed or capable of observation. The compensation does not apply to the intermediate part of our deduction—that system of inference from observation which forms the classical physical theory of the universe.

Suppose that we and the nebular physicists survey the world, that is to say we allocate the surrounding objects to their respective positions in space. One party, say the nebular physicists, has a large velocity; their yard-measures will contract and become less than a yard when they measure distances in a certain direction; consequently they will reckon distances in that direction too great. It does not matter whether they use a yard-measure, or a theodolite, or merely judge distances with the eye; all methods of measurement must agree. If motion caused a disagreement of any kind, we should be able to determine the motion by observing the amount of disagreement; but, as we have already seen, both theory and observation indicate that there is complete compensation. If the nebular physicists try to construct a square they will construct an oblong. No test can ever reveal to them that it is not a square; the greatest advance they can make is to recognise that there are people in another world who have got it into their heads that it is an oblong, and they may be broadminded enough to admit that this point of view, absurd as it seems, is really as defensible as their own. It is clear that their whole conception of space is distorted as compared with ours, and ours is distorted as compared with theirs. We are regarding the same universe, but we have arranged it in different spaces. The original quarrel as to whether they or we are moving with the speed of 1000 miles a second has made so deep a cleavage between us that we cannot even use the same space.

The natural speed of substance depends on its quantization. Therefore, the natural speed of a material body in the cosmos shall depend on its inertia. Because of the high inertia of matter, the natural speeds of material bodies are not that high as claimed currently by cosmologists. Therefore, the cosmic space does not get distorted to any appreciable extent.

Space and time are words conveying more than one meaning. Space is an empty void; or it is such and such a number of inches, acres, pints. Time is an ever-rolling stream; or it is something signaled to us by wireless. The physicist has no use for vague conceptions; he often has them, alas! But he cannot make real use of them. So when he speaks of space it is always the inches or pints that he should have in mind. It is from this point of view that our space and the space of the nebular physicists are different spaces; the reckoning of inches and pints is different. To avoid possible misunderstanding it is perhaps better to say that we have different frames of space—different frames to which we refer the location of objects. Do not, however, think of a frame of space as something consciously artificial; the frame of space comes into our minds with our first perception of space. Consider, for example, the more extreme case when the FitzGerald contraction is one-half. If a man takes a rectangle 2” x 1” to be a square it is clear that space must have dawned on his intelligence in a way very different from that in which we have apprehended it.

The consideration that space is an “empty void” comes from the unproven “particles in void” perspective. From “continuum of substance” perspective, space is extension of substance. Space empty of material-substance actually consists of field-substance. Therefore, space empty of material-substance cannot be arbitrarily measured in material units of meters and feet.  Such space needs to be measured in units that apply to the field-substance.

The frame of space used by an observer depends only on his motion. Observers on different planets with the same velocity (i.e. having zero relative velocity) will agree as to the location of the objects of the universe; but observers on planets with different velocities have different frames of location. You may ask, “How can I be so confident as to the way in which these imaginary beings will interpret their observations?” If that objection is pressed I shall not defend myself; but those who dislike my imaginary beings must face the alternative of following the argument with mathematical symbols. Our purpose has been to express in a conveniently apprehensible form certain results which follow from terrestrial experiments and calculations as to the effect of motion on electrical, optical and metrical phenomena. So much careful work has been done on this subject that science is in a position to state what will be the consequence of making measurements with instruments travelling at high speed—whether instruments of a technical kind or, for example, a human retina. In only one respect do I treat my nebular observer as more than a piece of registering apparatus; I assume that he is subject to a common failing of human nature, viz. he takes it for granted that it was his planet that God chiefly had in mind when the universe was created. Hence he is (like my reader perhaps?) disinclined to take seriously the views of location of those people who are so misguided as to move at 1000 miles a second relatively to his parish pump.

A scientific measurement requires a well-defined reference point. The frame of space, which depends on the “motion of observer,” reduces to a “human viewpoint” when there is no well-defined reference point. Currently, science has no well-defined reference-point to measure cosmic motion. Mathematics based on arbitrarily assumed reference points cannot be trusted as scientific.

An exceptionally modest observer might take some other planet than his own as the standard of rest. Then he would have to correct all his measurements for the FitzGerald contraction due to his own motion with respect to the standard, and the corrected measures would give the space-frame belonging to the standard planet as the original measures gave the space-frame of his own planet. For him the dilemma is even more pressing, for there is nothing to guide him as to the planet to be selected for the standard of rest. Once he gives up the naive assumption that his own frame is the one and only right frame the question arises, “Which then of the innumerable other frames is right?” There is no answer, and so far as we can see no possibility of an answer. Meanwhile all his experimental measurements are waiting unreduced, because the corrections to be applied to them depend on the answer. I am afraid our modest observer will get rather left behind by his less humble colleagues.

The trouble that arises is not that we have found anything necessarily wrong with the frame of location that has been employed in our system of physics; it has not led to experimental contradictions. The only thing known to be “wrong” with it is that it is not unique. If we had found that our frame was unsatisfactory and another frame was preferable, that would not have caused a great revolution of thought; but to discover that ours is one of many frames, all of which are equally satisfactory, leads to a change of interpretation of the significance of a frame of location.

The frame of space (location) employed in our system of physics is good only for the earth and for the measurement of cosmic bodies out there. Application of this system to cosmic spaces is likely to result in huge errors.


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