EINSTEIN'S UNIVERSE
THE UNIVERSAL CORRECTION
1. When a sailing boat gathers speed under a beam wind (coming from the side) the wind shifts. It seems to come from somewhat ahead of the boat. The flag at the top of the mast, which shows the helmsman the wind direction, on longer trails exactly sideways away from the wind, but points at an angle towards the stern. The faster the boast goes the greater this angle becomes. The motion of the boat is not, of course, altering the true wind, which is set by the great areas of high and low pressure on the Earth's surface; all that changes is the direction of the apparent wind as judged by the people in the boat. Nevertheless the apparent wind is real enough: it is what drives the boat forward.
2. Alber Einstein was a small-boat sailor and so was the eighteenth-century Oxford astronomer James Bradley. Bradley made an important discovery in relativity, two hundred years before Einstein, as a result of reflecting on the apparent wind direction while sailing on the thames. He realised that the apparent positions of the distant 1"fixed" stars must be affected by the Earth's motion chnges as it circles the Sun, so the apparent positions of stars in the sky chould change a little with the seasons. When he checked he found it was so- a shift of about on-ninetieth of a degree from summer to winter, for stars lying 2"abeam" of the Earth's orbit. Bradley was then able to estimate the speed of light as a multiple of the Earth's orbital speed.
3. The astronomer has to tilt his telescope forward a little, in the direction of travel of the Earth, to catch the apparent atream of particles of light coming from a distand star. It is the same affect as the apparent wind alteration of the lie of the boat's flag. (For landlubbers let me offer another analogy: tilting the telescope is like tipping your umbrella forward as you hurry through the rain, in order to keep your knees dry.) For speeds which are small compared with the speed of light, thes aberration, as astronomers call it, is also small. But a fast poverboat can make the apparent wind come from almost dead ahead, regardless of the true wind direction, Similarly very high speeds relative to a source of light can have dramatic effects on its apparent direction and appearance.
4. Imagine, for example, a spaceship passing the Earth from east to west, at a speed close to the speed of light. Point your telescope towards the eastern sky and you will see the spaceship coming towards you-tail first! The aberration is now so great that the light which is to enter your telescope at the correct angel has to be launched almost straight backwards form the spaceship. Boats cease to be a good analogy; think of this way, light can travel no faster than 186,282 miles per second. The speed of light is always the same reguardless of speed of the observer or it's sorce. And in order to see the spaceship it's light ways have to be reflected back to you from the spaceship. The spaceship is moving so fast that the light ways use to see it cant out run it so you want see it until it has passed you. And once it passes you, you will seeing the light waves from behind the ship.
5. Come back to your vantage point on the Earth: as you turn the telescope straight upwards, to try to see the spaceship at its moment of closest approach, you will still se its tail facing you. In other words, instead of facing along its line of travel past the Earth, the spaceship appears to be turned to point away from the Earth. Even at less extreme speeds, a passing shaceship will appear to be swivelled away from the Earth.
6. The apparent rotation of the passing shaceship, as a result of the aberration, also gives a more direct explanation of the apparnt slowing of its clock. If the apparently receding spaceship sends you time pulses from its clock, they will arrive "spaced out" and you will judge the clock to be running slow. Extreme speeds have effect on all matter and time. As our spaceship appoaches the speed of light, time for our intrepid space travelers slows down relative to them. To them time ticks right along at its normal speed, but if you could look inside to spaceship, from the Earth, the spacetravelers would appear to be moving in slow motion. This speed also effects the length and mass of the spaceship and its occupants. The spaceship becomes shorter and shorter and it clock will run slower and slower as its speed increases. The slowing of its clock is easy to calculate using a factor called "gamma" which depends on the speed. And the apparent duration of one second on the spaceship's clock is judged by the onlooker to be one second multiplied by the gamma factor. The shortening of the spaceship is calculated by a simulalar factor.
Speed (as percentage
of speed of light)__________________________________ Gamma factor
00 ________________________________________________1.000
10 ________________________________________________1.005
20 ________________________________________________1.021
30 ________________________________________________1.048
40 ________________________________________________1.091
50 ________________________________________________1.155
60 ________________________________________________1.250
70 ________________________________________________1.400
80 ________________________________________________1.667
90 ________________________________________________2.294
95 ________________________________________________3.202
99 ________________________________________________7.089
99.9______________________________________________22.361
99.999___________________________________________223.607
100 ______________________________________________infinite
7. The mass of a our spaceship also increases by the "gamma" with respect to its speed. To understand how this comes about, remeber that the mass of an object is a measure of its resistance to acceleration. suppose that the astronaut runs his rocket motor to increase his speed. As far as he is concerned, the motor is working according to the maker's specifications and is accelerating him at, say one g, increasing his speed by 32 feet per second in every second. But by the omlooker's reckoning the astronaut's second is a protracted second-gamma seconds in fact-and the spaceship is not gathering speed as rapidly as the astronaut supposes. The motor is also running more slowly, as judged by the onlooker. the effort required to increase the speed of the spacecraft by a given amount, in the onlooker's estimation, has been increased by the gamma factor. The high-speed spaceship is sen to accelerate ever more sluggishly.
8. Picture the spaceship still puffing away. While it fails to gain much in speed, its mass, as judged by the onlooker, goes on increasing formidably. By the time it is going at 99.9 percent the speed of light, what is nominally a 100-ton spaceship by the builder's certificate has an effective mass of 2237 tons by the gamma factor. This is by no means the end of the mass gain or the slowing of time. Our spaceship has a lot more eccelarating to do before it reaching the speed of light because at the speed of light it's mass, becomes infinate. Time also stops for it. And by now our spaceship has shortened so much that it is only 2 dimensional now! The gamma factor decribes the "light barrier", which prevents material objects travelling as fast as light. 9. If you could reach the speed of light, you could reach any point in the universe in an instant. No matter how far it way away for you. The gamma factor is infinate at this speed so no time passes for you!
Much of the text on this page was taken from "Einstein's Universe" by Nigel Calder
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