Reference: The Nature of the Physical World
This paper presents Chapter III (section 6) 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.
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The Velocity of Light
A feature of the relativity theory which seems to have aroused special interest among philosophers is the absoluteness of the velocity of light. In general velocity is relative. If I speak of a velocity of 40 kilometres a second I must add “relative to the earth”, “relative to Arcturus”, or whatever reference body I have in mind. No one will understand anything from my statement unless this is added or implied. But it is a curious fact that if I speak of a velocity of 299,796 kilometres a second it is unnecessary to add the explanatory phrase. Relative to what? Relative to any and every star or particle of matter in the universe.
For practical purposes, the speed of light is relative to any and every star or particle of matter in the universe. The speed of light has the same value relative to earth. This is because the maximum speed possible for a particle of matter is insignificant compared to this number 299,796 kilometres (186,000 miles) a second. The speed of a material particle is limited because of its inertia.
It is no use trying to overtake a flash of light; however fast you go it is always travelling away from you at 186,000 miles a second. Now from one point of view this is a rather unworthy deception that Nature has practiced upon us. Let us take our favourite observer who travels at 161,000 miles a second and send him in pursuit of the flash of light. It is going 25,000 miles a second faster than he is; but that is not what he will report. Owing to the contraction of his standard scale his miles are only half-miles; owing to the slowing down of his clocks his seconds are double-seconds. His measurements would therefore make the speed 100,000 miles a second (really half-miles per double-second). He makes a further mistake in synchronizing the clocks with which he records the velocity. (You will remember that he uses a different Now line from ours.). This brings the speed up to 186,000 miles a second. From his own point of view the traveler is lagging hopelessly behind the light; he does not realise what a close race he is making of it, because his measuring appliances have been upset. You will note that the evasiveness of the light-flash is not in the least analogous to the evasiveness of the rainbow.
A material observer can never travel at the speed of 161,000 miles a second. Anything traveling at that speed shall require a value of inertia that is less than the inertia of an atom. So, the observer has to be reduced to a field-particle like an electron to be able to travel at 161,000 miles a second. There is no scientific confirmation that the speed of light is seen to be 186,000 miles per second by the electron. The argument given by Eddington makes no sense because it does not take inertia into account.
But although this explanation may help to reconcile us to what at first seems a blank impossibility, it is not really the most penetrating. You will remember that a Seen-Now line, or track of a flash of light, represents the grain of the world-structure. Thus the peculiarity of a velocity of 299,796 kilometres a second is that it coincides with the grain of the world. The four-dimensional worms representing material bodies must necessarily run across the grain into the future cone, and we have to introduce some kind of reference frame to describe their course. But the flash of light is exactly along the grain, and there is no need of any artificial system of partitions to describe this fact.
The number 299,796 (kilometres per second) is, so to speak, a code-number for the grain of the wood. Other code-numbers correspond to the various wormholes which may casually cross the grain. We have different codes corresponding to different frames of space and time; the code-number of the grain of the wood is the only one which is the same in all codes. This is no accident; but I do not know that any deep inference is to be drawn from it, other than that our measure-codes have been planned rationally so as to turn on the essential and not on the casual features of world-structure.
The theory of relativity works only when light can serve as a reference point of “zero inertia”. Light has extremely small but finite amount of inertia or quantization. This requires that the inertia of the particle under consideration be very large compared to that of light. This is the case for material-particles, but not for field-particles. Therefore, the theory of relativity works for material-particles as in cosmology; but it does not work in the quantum range.
The speed of 299,796 kilometres per second which occupies a unique position in every measure-system is commonly referred to as the speed of light. But it is much more than that; it is the speed at which the mass of matter becomes infinite, lengths contract to zero, clocks stand still. Therefore it crops up in all kinds of problems whether light is concerned or not.
The speed associated with “zero inertia” will be infinitely large in value. But it must be finite to be used mathematically in the theory of relativity. The speed of 299,796 kilometres per second occupies a unique position because it is extremely large compared to material speeds, and yet it is a finite value representative of field-substance. Material speeds can never approach this value.
A statement, such as, “Speed of light is the speed at which the mass of matter becomes infinite, lengths contract to zero, and clocks stand still,” are unverified and purely speculative. A material-particle can never have low enough inertia to approach this speed. Conclusions from the theory of relativity cannot be taken to extreme because light does have some inertia or quantization, even though it is extremely small.
The scientist’s interest in the absoluteness of this velocity is very great; the philosopher’s interest has been, I think, largely a mistaken interest. In asserting its absoluteness scientists mean that they have assigned the same number to it in every measure-system; but that is a private arrangement of their own—an unwitting compliment to its universal importance. (In the general relativity theory, chapter VI, measure-systems are employed in which the velocity of light is no longer assigned the same constant value, but it continues to correspond to the grain of absolute world-structure.) Turning from the measure-numbers to the thing described by them, the “grain” is certainly an absolute feature of the wood, but so also are the “worm-holes” (material particles). The difference is that the grain is essential and universal, the worm-holes casual. Science and philosophy have often been at cross-purposes in discussing the Absolute—a misunderstanding which is I am afraid chiefly the fault of the scientists. In science we are chiefly concerned with the absoluteness or relativity of the descriptive terms we employ; but when the term absolute is used with reference to that which is being described it has generally the loose meaning of “universal” as opposed to “casual”.
There is nothing absolute about the speed of light other than what is commented above. Its absoluteness is limited to the material domain.
Another point on which there has sometimes been a misunderstanding is the existence of a superior limit to velocity. It is not permissible to say that no velocity can exceed 299,796 kilometres per second. For example, imagine a search-light capable of sending an accurately parallel beam as far as Neptune. If the search-light is made to revolve once a minute, Neptune’s end of the beam will move round a circle with velocity far greater than the above limit. This is an example of our habit of creating velocities by a mental association of states which are not themselves in direct causal connection. The assertion made by the relativity theory is more restricted, viz.—
Neither matter, nor energy, nor anything capable of being used as a signal can travel faster than 299,796 kilometres per second, provided that the velocity is referred to one of the frames of space and time considered in this chapter. (Some proviso of this kind is clearly necessary. We often employ for special purposes a frame of reference rotating with the earth; in this frame the stars describe circles once a day, and are therefore ascribed enormous velocities.)
The velocity of light in matter can under certain circumstances (in the phenomenon of anomalous dispersion) exceed this value. But the higher velocity is only attained after the light has been passing through the matter for some moments so as to set the molecules in sympathetic vibration. An unheralded light-flash travels more slowly. The speed, exceeding 299,796 kilometres a second, is, so to speak, achieved by prearrangement, and has no application in signaling.
The speed of light is more or less an average of the speeds in the field domain.
We are bound to insist on this limitation of the speed of signaling. It has the effect that it is only possible to signal into the Absolute Future. The consequences of being able to transmit messages concerning events Here-Now into the neutral wedge are too bizarre to contemplate. Either the part of the neutral wedge that can be reached by the signals must be restricted in a way which violates the principle of relativity; or it will be possible to arrange for a confederate to receive the messages which we shall send him to-morrow, and to retransmit them to us so that we receive them to-day. The limit to the velocity of signals is our bulwark against that topsy-turvydom of past and future, of which Einstein’s theory is sometimes wrongfully accused.
It is possible to have speeds greater than the speed of light, but that is possible only for a field-particle of extremely low quantization. The bizarre speculations about past and future being reversed come from localized, subjective viewpoints. Such considerations have no objective, scientific value.
Expressed in the conventional way this limitation of the speed of signaling to 299,796 kilometres a second seems a rather arbitrary decree of Nature. We almost feel it as a challenge to find something that goes faster. But if we state it in the absolute form that signaling is only possible along a track of temporal relation and not along a track of spatial relation the restriction seems rational. To violate it we have not merely to find something which goes just 1 kilometer per second better, but something which overleaps that distinction of time and space—which, we are all convinced, ought to be maintained in any sensible theory.
Once we work out the universal law of quantization it would be possible to have signaling speeds greater than the speed of light.
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