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Relativity: Difference between revisions
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{{Useful Notes}}
This article needs [[Wiki Magic]].
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Starting with the ancient Greeks, and ending around the [[wikipedia:R%C3%B8merchr(27)s determination of the speed of light|seventeenth century]], scientists and philosophers argued extensively about whether light had a speed, or whether it moved infinitely fast. In 1676, a Danish astronomer named Ole Rømer discovered, by observing a solar flare and timing how long it took for the brighter light to be reflected off Jupiter's moons, that light did indeed have a finite speed. That means that you ''can'' move nearly as fast as light. And when you do, things start to look strange. (Check out [http://apod.nasa.gov/apod/ap111018.html this movie] to see just how strange.)
These effects are only visible if you move near the speed of light, so they're often viewed as being part of relativity. However, a lot of them are really due just to the fact that light has a finite speed. A bat flying at near the speed of sound would notice the same sort of effects, and sound travels far too slowly for relativity to have an effect.
== What does it look like to travel near the speed of light? ==
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Let's suppose that the ''Enterprise'' flies straight from Earth to Mars, speeding up the whole way.<ref>For purposes of this article, we'll assume that the Enterprise does ''not'' use its warp drive, and flies slower than the speed of light.</ref> Guinan looks out a window at the front. Chief O'Brien looks out of a window at the back. [[Stargate SG-1|Jack O'Neill]] brings his telescope along and looks out the side window. What do they see?
Their view will be drastically different than the view from a slower ship.
First, the Doppler shift will change the colors of everything involved. Everything ahead of the ship will be blue-shifted, and everything behind the ship will be red-shifted.
As seen from Earth, Mars is red. As the ship speeds up, the Mars Guinan sees will change color: it will first appear orange, then yellow, then green, then blue, then violet, then (if Picard decides to go very ''very'' fast) Mars will disappear entirely into the ultraviolet. Meanwhile, the same thing is happening in reverse to O'Brien: Earth will go from blue to green to yellow and on up.
If the ship accelerates while O'Brien is close enough to Earth to see the ocean and the forest, then the forest will change color "ahead" of the ocean. That is, if Earth is redshifted enough that the oceans look yellow, the forests will all look orange.
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Some of them (simultaneity and the finite-speed effects above) ''should'' show up, but often don't. You can [[Hand Wave]] them away, but usually, it's just because the writer [[Did Not Do the Research]].
And some of these consequences ([[Time Dilation]] and increased mass) do show up, and have much bigger effects than they really should.
If you speed up in a car, you get pushed back in your seat; acceleration, or speeding up, feels a lot like being pulled down by the force of gravity.<ref>Actually, it feels ''exactly'' like being pulled down by the force of gravity, but that's general relativity and we won't get to it here.</ref> Avoiding this effect is the entire point of [[Inertial Dampening]]. Since the force of gravity accelerates you downwards at 10 meters/second/second, if you speed up faster than that, you feel very heavy.
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... where "sqrt" means "square root", v is the velocity of travel, and ''c'' is the speed of light (300,000 km/sec).
At half the speed of light, γ works out to 1.1547. At 86.60254% of the speed of light, γ is 2. At 99% of the speed of light, γ is 7.0888.
Here's how you use the number γ. If you travel at 99% of the speed of light, then γ is pretty close to 7.
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If you travel at 99% of the speed of light in a spaceship that's 700 meters long, to everyone on Earth, it will look like your ship is only 100 meters long.
Remember that if a 1-gram pebble traveling at 99 meters per second crashes into a 98-gram rock, the 99-gram accumulation will move at 1 meter per second. This is known as conservation of momentum, and is pretty simple in Newtonian physics.
If a 1-gram pebble traveling at 99% of the speed of light crashes into a 98-gram rock, the 99-gram accumulation will not move off at 1% of the speed of light. It will move off at 7% of the speed of light, because the 1-gram pebble hits harder than you'd expect.
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There is one important thing Adama and Picard agree on. If two events happen at coordinates (''X'',''Y'',''Z'',''T'') and (''X''+''x'',''Y''+''y'',''Z''+''z'',''T''+''t''), the "interval" between the two events is given by the square root of ''x''<sup>2</sup>+''y''<sup>2</sup>+''z''<sup>2</sup>-(''ct'')<sup>2</sup>.
If the squared interval between two events is positive, then the two events are too far away for light to get from one to the other. If you are present at both events, then you had to travel faster than light.
It turns out that if you make the change of reference frame, the interval between two events may change...but the squared interval will always stay positive or stay negative. That is, if Adama thinks that you had to travel faster than light to get from one event to another, Picard will always agree with him.
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seconds pass. The 14-year travel time mentioned for ''[[Planet of the Apes]]'' above was obtained by plugging in ''t''=1000 years (to speed up) and ''g''=10 meters/second/second, and doubling (to slow back down so you don't crash into your destination).
== Why light always travels at the same speed ==
...and why that is ''weird''.
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== Why moving clocks run slower ==
Let's have an example. The ''[[Star Trek: The Next Generation|Enterprise D]]'' is on impulse drive, flying at half the speed of light towards galactic north. It's about to fly past [[Star Trek: Deep Space Nine|Deep Space Nine]] and will pass it 300,000 kilometers away due east of the station. Captain Picard decides to greet Benjamin Sisko by flashing a light, carefully timed to strike the space station at the moment of closest approach. The second Sisko sees the beam, he shines another light back at the ''Enterprise''--or, rather, where the ''Enterprise'' will be when the beam arrives.
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From Sisko's perspective, the light had to travel along a diagonal path: Picard set off the first light before the moment of closest approach, when the ship was 300,000 kilometers east and some distance south of the station. The second pulse will strike the ship when it is 300,000 kilometers east and some distance north of the station. So the light travels a distance of more than 600,000 kilometers. Since light travels at 300,000 kilometers per second, from Sisko's perspective, more than 2 seconds pass between when when Picard sends off his own greeting and when Picard receives Sisko's greeting. (If you do the math--it's not particularly hard math--it comes out to about 2.3 seconds.)
However, from Picard's perspective, the light pulses travel in straight lines: his goes 300,000 kilometers due west, and Sisko's goes 300,000 kilometers due east. The round trip distance is 600,000 kilometers and takes exactly 2 seconds.
So Captain Picard's clock is running slower than Captain Sisko's clock. This is the [[Time Dilation]] effect, and is probably the most well-known effect of special relativity--although, as explained above, it tends to be exaggerated in fiction pretty severely.
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It's possible in fiction to have faster-than-light travel without [[Time Travel]] and its attendant [[Time Travel Tropes|problems]]. You just have to designate one viewpoint as the "right" one: things can move faster than light, as long as they don't travel backwards in time from ''that'' viewpoint. This is enough to keep anyone from [[My Own Grampa|becoming their own grandparent]], since that involves traveling backwards in time from ''everyone'''s viewpoint.
This can be [[Justified Trope|justified]] if you travel via [[Subspace or Hyperspace]]. Subspace always has different physics than the real world, so you can decide that subspace ''does'' have a correct viewpoint, and so the real world has a correct viewpoint, the one that matches the subspace viewpoint.
It can also be justified if you travel by [[Our Wormholes Are Different|wormholes]]: if the wormholes in your universe agree about space and time, you can pick their viewpoint as the "correct" viewpoint.
However, usually FTL with no time travel is simply a case of the writer [[Did Not Do the Research|not doing the research]]. This tends to be especially jarring in series with both [[Time Dilation]] and [[Subspace Ansible|instantaneous communication]], since the logic that leads to [[Time Dilation]] and the logic that proves that "instantaneous" means "time travel" are exactly the same.
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Similarly, from Picard's perspective, the ''Enterprise'' is holding still, and Bajor is rushing towards it at half the speed of light. It takes 1.7 hours for Bajor to get to the ''Enterprise'', and so from Picard's perspective, Bajor must be only 0.85 terameters away from Deep Space Nine.
This is referred to as "length contraction," or "Lorentz contraction" (after the pre-Einstein theorist who first proposed it), or "shortening of the way". If you think something is moving, then you see it squished relative to the direction of travel. Data and LaForge can measure the ''Enterprise'' and conclude that it is 642 meters long, but when the ''Enterprise'' flies past Deep Space Nine, Sisko can look out the window and see a ship that seems to be only 550 meters long. And when the Bajoran solar system comes rushing at Picard at half the speed of light, Bajor seems to be only 0.85 terameters from Deep Space Nine.
From Picard's perspective, this is why time dilation happens. Suppose that Picard flies from Deep Space Nine to Bajor and back. From Sisko's perspective, Picard travels 2 terameters at half the speed of light, so it takes 4 hours according to Sisko's clock; since Picard's clock runs slowly, the whole round trip takes 3.4 hours according to Picard's clock. From Picard's perspective, Bajor and Deep Space Nine each travel 1.7 terameters at half the speed of light, so the entire round trip takes only 3.4 hours.
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This means that it takes, in some sense, the same amount of effort to go from 0% to 8% of the speed of light and to go from 86% to 88% of the speed of light. Put another way, the faster you go, the harder it is to speed up.
One way to think about this is that Riker's shuttle weighs more than Kira's--that it gets more massive as you accelerate. This isn't really the best way to think about this, though. Riker doesn't feel any heavier on the shuttle than he did on the ''Enterprise'' or back at Deep Space Nine.
A better way to think about it is to simply say that Riker's shuttle, which is going eleven times as fast as Kira's, has 22 times as much momentum, and that increasing its speed by a little bit requires a big change in momentum, and so a lot of fuel.
It turns out that as your velocity gets closer and closer to the speed of light, your momentum grows without bound: if Riker could get his shuttle ''to'' the speed of light, then he would have infinite momentum.
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== History ==
In the late 19th century, [[wikipedia:James Clerk Maxwell|James Clerk Maxwell]] published his theory<ref>in this case, a mathematical description</ref> of electromagnetism, which described how electric and magnetic fields interacted. However, as he studied his theory more thoroughly, he found a peculiar result: the equations said that there could exist an electromagnetic field that could "leapfrog" its way through space; an electric field would generate a magnetic field as it disappeared, and this magnetic field would then disappear, and generate the original electric field, which would continue until the continually generating and shrinking fields hit something. The equations also allowed him to calculate exactly how fast the leapfrogging traveled through space, and he was amazed by the result: 299,792,458 metres per second, precisely the speed of light.
However, the physicists were left with a problem, because Maxwell's calculations of the speed of light didn't depend on how fast the measurer was moving; it depended only on the properties of space itself. Did this mean that if Alice was moving when compared to Bob, she would see light moving at the same speed as he did? And if not, why not? Did space change in some way to make it possible?
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{{reflist}}
[[Category:Relativity]]
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