Spacetime

“ Travelling thus continually, in twenty-four hours you would leave the last member of the solar system behind you, and begin your plunge into the depths of space. How long would it be before you encountered another object? A month, should you guess? Twenty years you must journey with that prodigious speed before you reach the nearest star, and then another twenty years before you reach another. At these awful distances from one another the stars are scattered in space, and were they not brilliantly self-luminous and glowing like our sun, they would be hopelessly invisible. ”

“ Our mischievous geocentric outlook has cropped out again unsuspected, persuading us to insist on this terrestrial space-time frame which in the general scheme of nature is in no way superior to other frames.
The more closely we examine the processes by which events are assigned to their positions in space and time, the more clearly do we see that our local circumstances play a considerable part in it. We have no more right to expect that the space-time frame on the sun will be identical with our frame on the earth than to expect that the force of gravity will be the same there as here. ”

“ The negation of absolute motion is thus associated with the possibility of choosing the time-direction in any way we please. What determines the separation of space and time for any particular observer can now be seen. Let the observer place himself so that he is, to the best of his knowledge, at rest. If he is a normal human being, he will seat himself in an arm-chair; if he is an astronomer, he will place himself on the sun or at the centre of the stellar universe. ”

“ The plane of the orbit of his planet being supposed to pass through the center of the spherical system, our observer would, during his year, behold the night at one season blazing with the splendors of the clustered suns, and at another emptied of brilliant orbs and faintly lighted with the soft glow of the Milky-Way and the feeble flickering of distant stars, scattered over the dark vault. ”

“ Warp space with a rapidly moving object, move away from the observer with the speed of light—and the whole of human history assumed the firm contours of a landscape in space. Time and space merged and became one. And a man in an intricately-equipped Time Observatory could revisit the past as easily as he could travel across the great curve of the universe to the farthest planet of the farthest star. ”

“ At the distance, then, of more than ninety-five millions of miles, this dim spot which men call earth, this great globe and all its dwellers, this ever-spinning planet, revolves around the sun once every year, that revolution being both the cause and the measure of that space of time. Its orbit is not a circle; it is an ellipse, but not very far removed from the circular path. ”

“ So at our utmost speed we flashed on through the void toward the galaxy, a mighty belt of burning suns across the blackness before us, and toward the close-massed cluster of suns at its edge that shone among the scattered stars around it like a solid ball of light, while there rushed after us through space at the same mighty speed the great swarm of strange craft which we were attempting to lead into that cluster. ”

“ We see it now hanging in space, with no visible support, held in its place by two mighty forces; spinning on year after year, attended by its satellite the moon, while we run, and walk, and cry, and laugh, and play about on its surface—little atoms who, except for the brain that God has given them, would never even have known that they are continually moving on through endless space. ”

“ The astronomer, I assert, can neither from any data at his command postulate nor prove the beginning nor the end of the reverberating motion that exists in his solar system, which is itself the fragment of a system that is circulating and revolving in and about itself, and in which, since the birth of man, the universe he knows has not passed the first milestone in the road that universe is traveling in space immensity. ”

“ The “flying synods of worlds” formed by them must gravitate one towards another as if concentrated at their several centres of gravity. Accordingly, “a star, or sun, such as ours, may have a proper motion within108 its own system of stars, while the whole may have another proper motion totally different in quantity and direction.” We may thus, he continued, “arrive in process of time, at a knowledge of all the real, complicated motions of the planet we inhabit; of the solar system to which it belongs; and even of the sidereal system of which the sun may possibly be a member.” ”

“ There is yet a third character of space-time. Everything which is in space receives a definite limitation of some sort, so that in a sense it has just that shape which it does have and no other, also in some sense it is just in this place and in no other. Analogously for time, a thing endures during a certain period, and through no other period. I will call this the ‘modal’ character of space-time. It is evident that the modal character taken by itself gives rise to the idea of simple location. ”

“ We are, in the first place, to observe that the moment of momentum of any planet may alter. It would alter if the distance of the planet from the sun changed, or if the velocity with which the planet rotates upon its axis changed; so, too, the moment of momentum of the sun may change, and so may those of the satellites. In the beginning a certain total quantity of moment of momentum was communicated to our system, and not one particle of that total can the solar system, as a whole, squander or alienate. ”

“ I quite understand that the orbit of a planet might be perceived all at once or in a very short time, because its successive positions or the results of its movement are the only things that matter, and not the duration of the equal intervals which separate them. ”

“ For example, if a person could leave the earth and travel about for a time and then return, the time between his departure and return would be less by his clocks than by those on the earth: the earth, in its journey round the sun, chooses the route which makes the time of any bit of its course by its clocks longer than the time as judged by clocks which move by a different route. This is what is meant by saying that bodies left to themselves move in geodesics in space-time. ”

“ In addition to the existence of space-time and its invariant intervals, the really novel views which the theory forces upon us consist in the relativity of such primary concepts as length, duration, simultaneity, mass, force, etc., to which temperature should also be added. We also obtain new views on causal connections, and a better understanding of the principle of action and of the principles of conservation. Matter becomes fused with energy and disappears as a substance, and conservation is not rigorous. Furthermore, matter possibly creates space-time, and all motion may be relative. ”

“ Their space-time theory provided, they claimed, a neat device for survival on our high-velocity journey.
The faster a body moves in reference to another, the slower time appears to act on the moving body. If, they said, man could travel at the speed of light, supposedly time would stand still for him. ”

“ But amid that ether motions are transmitted with velocities transcending all but infinitely those which take place among the particles of matter composing the universe in which we "live and move and have our being." The planets, immense aggregates of matter such as we know it, sweep onwards upon their immense orbits, traversing many thousands of miles in an hour; but light and heat sweep along the ether of space, and by virtue of motions taking place within that ether at the rate of many tens of thousands of miles per second. ”

“ In much the same way, quite apart from the disclosures of relativity, were our eyes to be suddenly gifted with microscopic vision, our familiar world would become so terrifying as to baffle description.
Now the essential characteristic of space-time is that it exhibits no absolute separation between space and time which would hold for all observers, regardless of their motion. Each and every observer will split it up in a different way, so that the totality of space at an instant for one becomes a successive spread of points throughout space at a succession of times for another. ”

“ The moon moves among the illuminated figures, traversing the dial quickly, like a second-hand, once a month. The sun, like a minute-hand, goes over the dial once a year. Various planets stand for hour-hands, moving over the dial in various periods reaching up to one hundred and sixty-four years; while the earth, like a ship of exploration, sails the infinite azure, bearing the observers to different points where they may investigate the infinite problems of this mighty machinery. ”

“ But since the motion of the solar system itself will, in the course of so long a period as fifty thousand years, produce a great change in the perspective of the heavens as seen from the earth, by carrying us nearly nineteen trillion miles from our present place, why, it may be asked, seek to represent future appearances of the constellations which we could not hope to see, even if we could survive so long? The answer is: Because these things aid the mind to form a picture of the effects of the mobility of the starry universe. ”

“ If the stars can be considered at relative rest, inasmuch as their world lines constitute geodesics of space-time, it is necessary that these geodesics should not taper together but should lie along parallel time directions through space-time. This is possible only provided the structure of space-time is such that one same time direction endures at every point of space for an observer at rest with respect to the star distribution. We thus obtain one same straight time direction for the universe. ”

“ And what is true of the discrepancies existing between the space and time conceptions of the earth and Arcturus is true of any other two bodies in space moving at different velocities.
But is there no relationship existing between the space and time of one body in the universe as compared to the space and time of another? Can we not find something which holds good for all bodies in the universe? ”

“ But, though, by the eccentricity of the great Sphere, they were thus able, in some measure, to connect together the unequal velocities of the heavenly bodies, and by the revolutions of the little Sphere, the direct, stationary, and retrograde appearances of the Planets, there was another difficulty that still remained. Neither the Moon, nor the three superior Planets, appear always in the same part of the heavens, when at their periods of most retarded motion, or when they are supposed to be at the greatest distance from the Earth. ”

“ Is not the earth rotating on its axis, so that in the course of a few hours the observatory on the equator is carried bodily round for thousands of miles? As the morning approaches the observations are to be repeated. The planet is found to have changed its place very considerably with regard to the stars. This is partly due to its own motion, but it is also largely due to the parallactic displacement arising from the rotation of the earth, which may amount to so much as twenty seconds. ”

“ The aged scientist explained, “Since space is now reversed by the relativity effect, it is the star in front of us rather than the one behind that disappears and then reappears in front of us as we catch up with its light. ”

“ Now the galaxy's flaring suns filled the heavens before us as our mighty armada raced in through the outer void toward them, the Cancer cluster flaming ahead in all the blinding glory of its gathered suns, those suns appearing on the upper part of our space-chart as a mass of glowing little circles, toward which our vast swarm of ship-dots was speeding. ”

“ Thus, if a body were 1,000,000 miles away the light would reach it in from five to six seconds, while over a distance as great as that which separates the earth from the sun the news would be carried in about eight minutes. We can calculate how long a time must elapse ere the light shall travel over a distance so great as that between the star and our earth. You will find that from the nearest of the stars the time required for the journey will be over three years. ”

“ Most of the arguments in favour of this opinion are necessarily based on considerations connected with the phenomena of the heavens, effected in the long course of ages by a slow revolution of the earth’s axis. Astronomers during the last two thousand years have carefully observed the effects and studied the causes of this slow terrestrial movement, and they can now tell us with confidence and exactness that the space of 25,868 years is required for the accomplishment of one such revolution of the earth’s axis. ”

“ We must seek for some magnitude which is commensurate with these immensities of space; and, in the wonderfully rapid motion of light, astronomy furnishes us with a suitable standard. By the eclipses of Jupiter's satellites the astronomers have determined that this mysterious effluence reaches us [Pg 87] from the sun in eight minutes and a half, and therefore must travel through space with the incredible velocity—shall I dare to name it?—of 186,000 miles in a second of time! ”

“ In the beginning, the orb was placed in vacuum, stationary, and with its axis perpendicular to the plane of what is now called its orbit. Its only revolution was the diurnal.”
“And the changes of the seasons?”
“Had not yet taken place. The days and nights were equal; there were no eclipses; the same stars were always visible. This state of the earth is supposed, from certain geological proofs, to have continued about a thousand years, during which time the struggle between mind and matter was solely confined to quadrupeds. ”