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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.)

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UsefulNotes/AlbertEinstein's Theory of General Relativity is perhaps the second-most confusing subject in all of modern physics, beaten only by Quantum Mechanics. It overhauls many previously-established studies on space, time, matter and [[UsefulNotes/{{Energy}} energy]], so the dificulty on understanding the theory is caused by our need of re-examining our grasp on those concepts. 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.)

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

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

]]

]]

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[[folder: Mass is a kind of energy, or E = ~~mc~~

]]

mc[[superscript:2]]]]

]]

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

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

mc

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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.

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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 ~~hour[[note]]really 55 light–minutes and [[LudicrousPrecision 35.640951985205 light–seconds]][[/note]] 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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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]].

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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=] ~~[=Ph. D=] candidates cry black blood, so we'll leave it to [[http://en.wikipedia.org/wiki/Mathematics_of_general_relativity the other wiki]].

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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]].

**to:**

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 ~~[=PhD=] candidates cry black blood, so we'll leave it to [[http://en.wikipedia.org/wiki/Mathematics_of_general_relativity the other wiki]].

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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. The math of general relativity makes graduate students cry, so we'll leave it to [[http://en.wikipedia.org/wiki/Mathematics_of_general_relativity the other wiki]].

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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. ~~relativity with ease. The math of general relativity makes ~~graduate students cry, ~~PhD candidates cry black blood, so we'll leave it to [[http://en.wikipedia.org/wiki/Mathematics_of_general_relativity the other wiki]].

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Let's suppose that the [[Series/StarTrekTheNextGeneration ''Enterprise'']] flies straight from Earth to Mars, speeding up the whole way.[[note]]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.[[/note]] Guinan looks out a window at the front. Chief O'Brien looks out of a window at the back. [[Series/StargateSG1 Jack O'Neill]] brings his telescope along and looks out the side window. What do they see?

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Let's suppose that the ~~[[Series/StarTrekTheNextGeneration ''Enterprise'']] ~~''[[Series/StarTrekTheNextGeneration Enterprise]]'' flies straight from Earth to Mars, speeding up the whole way.[[note]]For purposes of this article, we'll assume that the ~~Enterprise ~~''Enterprise'' does ''not'' use its warp drive, and flies slower than the speed of light.[[/note]] Guinan looks out a window at the front. Chief O'Brien looks out of a window at the back. [[Series/StargateSG1 Jack O'Neill]] brings his telescope along and looks out the side window. What do they see?

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So, to recapitulate, Picard and Sisko will forever disagree about whose clock slowed down. The only way to settle the argument is for Picard to turn around and come back so they can compare notes. The only way to do this is for him to accelerate, and that will pick his viewpoint out as the "wrong" one.

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So, to recapitulate, Picard and Sisko will forever disagree about whose clock slowed down. The only way to settle the argument is for Picard to turn around and come back so they can compare notes. The only way to do this is for him to accelerate, and that will pick his viewpoint out as the "wrong" ~~one.~~

one. [[note]]To be fair, if the universe is [[https://en.wikipedia.org/wiki/Three-torus_model_of_the_universe torus-shaped]] ([[Recap/TheSimpsonsS10E22TheySavedLisasBrain "doughnut-shaped"]], so that after traveling a certain distance, you'll find yourself back where you started), Picard could "catch up" with Sisko without slowing down. That being true wouldn't completely break down relativity (after all, this is a serious proposal for the shape of the universe), but it ''would'' establish an absolute frame of reference, so there ''would'' be a "standing still".[[/note]]

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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.)

Relativity was worked out by AlbertEinstein in two pieces, special relativity and general relativity. Bright high schoolers can handle the math of special relativity. The math of general relativity makes graduate students cry, so we'll leave it to [[http://en.wikipedia.org/wiki/Mathematics_of_general_relativity the other wiki]].

Relativity was worked out by AlbertEinstein in two pieces, special relativity and general relativity. Bright high schoolers can handle the math of special relativity. The math of general relativity makes graduate students cry, so we'll leave it to [[http://en.wikipedia.org/wiki/Mathematics_of_general_relativity the other wiki]].

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Relativity was worked out by

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It actually bothered AlbertEinstein quite a bit that non-accelerating viewpoints are better. So much, in fact, that he came up with general relativity to explain the physics of acceleration. But that we'll have to save for later.

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It actually bothered ~~AlbertEinstein ~~Albert Einstein quite a bit that non-accelerating viewpoints are better. So much, in fact, that he came up with general relativity to explain the physics of acceleration. But that we'll have to save for later.

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

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

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The effect would become more significant near an extremely dense object, such as a neutron star or a [[UsefulNotes/BlackHoles black hole]]. Say we have a 5 solar mass black hole, which would have a Schwarzchild radius of 15 kilometers. (Incidentally, the Schwarzchild radius for a black hole corresponds to where its ''event horizon'' is. Objects that are bigger than their own Schwarzchild radius aren't black holes and don't have event horizons.) Now say you're standing 30 kilometers from the center of the black hole, which is only 15 km above its event horizon. The gravitational time dilation factor here works out to 0.707, which is ''significant'' but not ''huge''. For every 7 seconds that elapse for you, 10 seconds elapse for us folks who are a nice safe distance away from the black hole. You'll have to re-synch your clock when you rejoin us -- assuming the tidal forces from the black hole don't turn you into molecular spaghetti first -- but you're not going to find yourself flung years into the future just by dawdling there for a few hours. If, however, you got closer, such that you were hovering only 1 kilometer above the event horizon, the gravitational time dilation factor would be 0.25, meaning 4 seconds would pass for the outside world for every 1 second you experienced. The effect would get more and more pronounced the closer you got to the event horizon, and when you actually ''reached'' the event horizion the gravitational time dilation factor would be exactly zero. You would be frozen in time right at the event horizon for all eternity, as far as the outside world was concerned.

**to:**

The effect would become more significant near an extremely dense object, such as a neutron star or a [[UsefulNotes/BlackHoles black hole]]. Say we have a 5 solar mass black hole, which would have a Schwarzchild radius of 15 kilometers. (Incidentally, the Schwarzchild radius for a black hole corresponds to where its ''event horizon'' is. Objects that are bigger than their own Schwarzchild radius aren't black holes and don't have event horizons.) Now say you're standing 30 kilometers from the center of the black hole, which is only 15 km above its event horizon. The gravitational time dilation factor here works out to 0.707, which is ''significant'' but not ''huge''. For every 7 seconds that elapse for you, 10 seconds elapse for us folks who are a nice safe distance away from the black hole. You'll have to re-synch your clock when you rejoin us -- assuming the tidal forces from the black hole don't turn you into molecular spaghetti first -- but you're not going to find yourself flung years into the future just by dawdling there for a few hours. If, however, you got closer, such that you were hovering only 1 kilometer above the event horizon, the gravitational time dilation factor would be 0.25, meaning 4 seconds would pass for the outside world for every 1 second you experienced. The effect would get more and more pronounced the closer you got to the event horizon, and when you actually ''reached'' the event ~~horizion ~~horizon the gravitational time dilation factor would be exactly zero. You would be frozen in time right at the event horizon for all eternity, as far as the outside world was concerned.

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Einstein's second brainwave it just as important as the first, and arguably more intuitive: ''Velocity is relative''. There is an UrbanLegend that he came up with this while sitting on a stationary train, looking out of the window. The train beside his began to pull away, and he realized that his train pulling away would appear exactly the same from the other train, as the other train pulling away appeared to him. (Apart from the acceleration, which will be discussed later.)

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Einstein's second brainwave ~~it ~~is just as important as the first, and arguably more intuitive: ''Velocity is relative''. There is an UrbanLegend that he came up with this while sitting on a stationary train, looking out of the window. The train beside his began to pull away, and he realized that his train pulling away would appear exactly the same from the other ~~train, ~~train as the other train pulling away appeared to him. (Apart from the acceleration, which will be discussed later.)

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