History UsefulNotes / Relativity

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.) (Or even [[http://gamelab.mit.edu/games/a-slower-speed-of-light/ this prototype game]] to experience it first hand.)

Jack's view out the sides of the ship is even more bizarre. Let's suppose that he wants to look at Jupiter. And let's suppose that Jupiter happens to be on the right--if the ''Enterprise'' stopped, Jack could point his telescope straight out the window and be aimed at Jupiter.

From Adama's point of view (in Adama's "rest frame"), every event that happens on the ''Galactica'' happens at coordinates (0,0,0,''t''), for some number ''t'' equal to whatever the ''Galactica'''s clock says when the event happens. And from Adama's point of view, every event that happens on the ''Enterprise'' happens at coordinates (''vt'',0,0,''t'') for some number ''t''.

When the TARDIS appears on Deep Space 9, Sisko's clock says that it is 6:00. Picard isn't surprised--he knows that Sisko's clock runs slowly, so if the TARDIS traveled instantaneously, then that's exactly what he'd expect to see. Sisko, on the other hand, knows that Picard's clock runs slowly. And he's perfectly entitled to point out that the TARDIS is a time machine, so Picard could easily have traveled backwards in time.

If you accept special relativity, ''all'' faster-than-light travel is like this. If you have a faster-than-light spaceship, then from someone's viewpoint, what you really have is a time machine. Even if you only have a SubspaceAnsible, so you can ''talk'' faster than light but not ''move'' faster than light, from someone's viewpoint, you're talking backwards through time. And of course, since all viewpoints are equally valid, you should also be able to travel through time in the ship's own reference frame.

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.

Remember, by length contraction, one of the ''Enterprise''[==]'s kilometers is only half of one of Deep Space Nine's kilometers. And by time dilation, one of the ''Enterprise''[==]'s seconds lasts for two of Deep Space Nine's seconds. So Sisko and O'Brien see Riker as traveling only 6,000 kilometers per second faster than the ''Enterprise''. They do not think that Riker is traveling at 94.6% of the speed of light (86.6% + 8%). They think that Riker is traveling much slower, only 88.6% of the speed of light.

From Picard's point of view, Riker is now holding still. Deep Space Nine is still traveling with velocity -''v''. And Kira is now traveling with velocity not quite -2''v''. Kira's γ is also different from Deep Space Nine's γ.

That means that the two shuttles carry kinetic energy 2''m''(γ-1)''c''[[superscript:2]]. And we lost 2''m''(γ-1) kilograms. That means that every joule of stored energy had a mass of 1/''c''[[superscript:2]] kilograms. Put another way, every kilogram of stored energy gave rise to ''c''[[superscript:2]] joules of kinetic energy.

UsefulNotes/AlbertEinstein's Theory of General Relativity is perhaps the second-most confusing subject in all of modern physics, beaten only by Quantum Mechanics. EEqualsMCHammer applies to this in full force, meaning very few people understand all the [[MindScrew incredibly weird]] results that Einstein's very, very simple ideas imply. (WritersCannotDoMath means that most of the media isn't helping.)

(At low speeds where γ is about 1, this reduces to "momentum = mv", which is Creator/IsaacNewton's definition for momentum.)

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[[folder: Mass is a kind of energy, or E = mc^2]]

Now let's suppose that the ''Enterprise'' NCC-1701-D flies past Deep Space Nine and then past Bajor. Bajor is 1 terameter[[note]]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.[[/note]] 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.

Relativity was worked out by Albert Einstein in two pieces, special relativity and general relativity. Bright high schoolers can handle the math of special relativity with ease. The math of general relativity makes [=PhD=] candidates cry black blood, so we'll leave it to [[http://en.wikipedia.org/wiki/Mathematics_of_general_relativity the other wiki]].

Relativity was worked out by Albert Einstein in two pieces, special relativity and general relativity. Bright high schoolers can handle the math of special relativity with ease. The math of general relativity makes PhD candidates cry black blood, so we'll leave it to [[http://en.wikipedia.org/wiki/Mathematics_of_general_relativity the other wiki]].