Relativity: Difference between revisions

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== The speed of light ==

Starting with the ancient Greeks, and ending around the [[wikipedia:Rømer'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.)

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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? ==

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?

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== Special Relativity ==

There are two facts that give rise to most of special relativity:

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== The mathematical formulas for these effects ==

Mathematically, the factor by which time slows down, distances in the direction of travel shrink, and momentum increases, is called "gamma" (γ). The formula for gamma is:

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== 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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== Whose clock runs slower? ==

So if you are moving, then your clock runs slower.

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== How to have ships that aren't time machines ==

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.

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== Shortening of the way ==

Now let's suppose that the ''Enterprise'' NCC-1701-D flies past Deep Space Nine and then past Bajor. Bajor is 1 terameter<ref>A terameter is a trillion meters, or a billion kilometers, or 0.92 light-hours, which is close enough to 1 light-hour for the purposes of this article.</ref> away from Deep Space Nine, so it takes light 1 hour to get to Bajor. So from Sisko's perspective, it will take the ''Enterprise'' two hours to get to Bajor. But remember, Sisko believes that Picard's clock runs slowly. So Sisko thinks that Picard should think that it takes only 1.7 hours to get to Bajor.

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== Momentum ==

Let's suppose that Deep Space Nine and the ''Enterprise'' have identical shuttles. Major Kira takes one shuttle and flies it to Bajor. She accelerates to 8% of the speed of light. (At this speed, [[Time Dilation]] is going to add about three minutes to the trip, so we're not going to worry about it.)

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(At low speeds where γ is about 1, this reduces to "momentum = mv", which is [[Sir Isaac Newton]]'s definition for momentum.)

== Mass is a kind of energy, or E = mc^2 ==

== Mass is a kind of energy, or E = mc<sup>2</sup> ==

The equation E=mc<sup>2</sup> is an equation, and as such, it cannot really be justified without a bunch of other equations. So in this section, we're going to use the γ from the "Formulas" folder above.

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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.

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== General relativity ==

Objects in the universe don't just move with constant velocities; they can accelerate. You can measure this acceleration without any reference to the outside world. If you were in an elevator with no windows, you couldn't tell how fast you were moving relative to other objects in the universe, but you ''could'' tell how fast you were accelerating. If a giant were way way up above your elevator, pulling up on the elevator cable hard enough to accelerate you at 9.8 meters-per-second-per-second, you could measure this acceleration with any number of experiments (including a simple accelerometer you picked up at Radio Shack, or a bathroom scale), even though you couldn't see any objects outside the elevator for reference. You would be pressed down onto the floor of the elevator with a force of 9.8 Newtons for every kilogram of your mass.