The A B C of Relativity

view, will think that distant clocks are going slow as compared with those in his neighborhood. They will seem to go slower and slower, until, at a distance of one quarter of the circumference of the universe, they will seem to have stopped altogether. That region will seem to our observer a sort of lotus [Pg 173] land, where nothing is ever done. He will not be able to have any cognizance of things farther off, because no light waves can get across the boundary. Not that there is any real boundary: the people who live in what our observer takes to be lotus land live just as bustling a life as he does, but get the impression that he is eternally standing still. As a matter of fact, you would never become aware of the lotus land, because it would take an infinite time for light to travel from it to you. You could become aware of places just short of it, but it would remain itself always just beyond your ken. There will not be the ghostly suns of Einstein’s world, because light cannot travel so far. One of the oddest things about this state of affairs is that empirical evidence for or against it is possible, and that there is actually some slight evidence in its favor. If all “clocks” are slowed down at a great distance from the observer, this will apply to the periodic motions of atoms, and therefore to the light which they emit. Consequently all rays of light emitted by distant objects ought, when they reach us, to look rather more red or less violet than when they started. This can be tested by the spectroscope. We can compare a [Pg 174] known line, as it appears in the spectrum of a spiral nebula, with the same line as it appears in a terrestrial laboratory. We find, as a matter of fact, that in a large majority of spiral nebulæ there is a considerable displacement of spectral lines towards the red. The spiral nebulæ are the most distant objects we can see: Eddington states that their distances “may perhaps be of the order of a million light-years.” (A light-year is the distance light travels in a year.) The usual interpretation of a shifting of spectral lines towards the red is that it is a “Doppler effect,” due to the fact that the source of light is moving away from us. But one would expect to find the nebulæ just as often moving towards us as moving away from us, if nothing operated but the law of chances. If the world is such as De Sitter says it is, the spectral lines of the spiral nebulæ will be displaced towards the red owing to the slowing down of distant clocks, even if in fact they are not moving away from us. This, for what it is worth, is an argument in favor of De Sitter. The same facts afford another argument in favor of De Sitter, for another reason. If, at a given moment, a body is at rest relatively to [Pg 175] the observer, and at a distance from him, it will (in the absence of counteracting causes) not remain at rest from his point of view, but will begin to move away from him, and will continue to move away faster and faster; the further it is from him, the more its retreat will be accelerated. For bodies which are not too distant from each other, gravitation may overcome this tendency; but as this tendency increases with the distance, while gravitation diminishes, we should expect to find very distant bodies receding from us if De Sitter’s theory is right. Thus we have two reasons for the displacement of spectral lines in spiral nebulæ: one, the slowing down of time; the other, the movement away from us which we should expect at distances too great for gravitation to be sensible. However, it cannot be said that the argument, on either ground, is very strong. Eddington gives a list of forty-one spiral nebulæ, of which five have their spectral lines shifted towards the violet, not towards the red. Thus the material is neither very copious nor quite harmonious. Einstein’s and De Sitter’s hypotheses do not exhaust the possibilities of a finite world: they are merely the two simplest forms of such a [Pg 176] world. There are arguments against each, and it hardly seems probable that either is quite true. But it does seem probable that something more or less analogous is true. If the universe is finite, it is theoretically conceivable that there should be a complete inventory of it. We may be coming to the end of what physics can do in the way of stretching the imagination and systematizing the world. The period since Galileo has been essentially the period of physics, as the age of the Greeks was the period of geometry. It may be that physics will lose its attractions through success: if the fundamental laws of physics come to be fully known, adventurous and inquiring intellects will turn to other fields. This may alter profoundly the whole texture of human life, since our present absorption in machinery and industrialism is the reflection in the practical world of the theorist’s interest in physical laws. But such speculations are even more rash than those of De Sitter, and I do not wish to lay any stress upon them.