26th Jan '16 1:19:23 PM

**FordPrefect** Is there an issue? Send a Message

**Changed line(s) 311,312 (click to see context) from:**

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.

26th Jan '16 1:16:24 PM

**FordPrefect** Is there an issue? Send a Message

**Changed line(s) 289 (click to see context) from:**

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.)

**to:**

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.)

16th Oct '15 11:46:35 PM

**nombretomado** Is there an issue? Send a Message

**Changed line(s) 124,125 (click to see context) from:**

seconds pass. The 14-year travel time mentioned for ''PlanetOfTheApes'' 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).

**to:**

seconds pass. The 14-year travel time mentioned for ~~''PlanetOfTheApes'' ~~''Film/{{Planet of the Apes|1968}}'' 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).

16th Oct '15 11:46:19 PM

**nombretomado** Is there an issue? Send a Message

**Changed line(s) 70,71 (click to see context) from:**

In ''PlanetOfTheApes'', George Taylor travels away from Earth for 2,000 years. Presumably he spent half his time speeding up and half his time slowing down. If you accelerate at 10 meters/second/second for 1,000 years, you get up to 99.999955% of the speed of light. Time dilation does take effect, so George Taylor should have aged rather less than 2,000 years. However, it takes a while to kick in--the astronauts should have experienced a trip of about 14 years, not 18 months.

**to:**

In ~~''PlanetOfTheApes'', ~~''Film/{{Planet of the Apes|1968}}'', George Taylor travels away from Earth for 2,000 years. Presumably he spent half his time speeding up and half his time slowing down. If you accelerate at 10 meters/second/second for 1,000 years, you get up to 99.999955% of the speed of light. Time dilation does take effect, so George Taylor should have aged rather less than 2,000 years. However, it takes a while to kick in--the astronauts should have experienced a trip of about 14 years, not 18 months.

11th Sep '15 5:01:38 PM

**FordPrefect** Is there an issue? Send a Message

**Changed line(s) 29,30 (click to see context) from:**

Second, Mars will get brighter and Earth will get dimmer. Here's one way to think about this. Suppose Boothby stays behind on Earth and flashes one pulse of light at the ''Enterprise'' every second. Since the ''Enterprise'' is moving away, a second after O'Brien sees the first pulse, the ship will have moved away from Earth, so the second pulse won't have caught up--it will take more than a second for him to see the second pulse. If you picture now a strobe light flashing bursts every millisecond, then from O'Brien's viewpoint, this delay will "smear out" until it looks like a steady, dimmer light.[[note]]Relativistic effects (length contraction and time dilation) will change the picture, but not much; O'Brien will still see the the light pulses spaced out, just not as much as Sir Isaac Newton would expect.[[/note]]

**to:**

Second, Mars will get brighter and Earth will get dimmer. Here's one way to think about this. Suppose Boothby stays behind on Earth and flashes one pulse of light at the ''Enterprise'' every second. Since the ''Enterprise'' is moving away, a second after O'Brien sees the first pulse, the ship will have moved away from Earth, so the second pulse won't have caught up--it will take more than a second for him to see the second pulse. If you picture now a strobe light flashing bursts every millisecond, then from O'Brien's viewpoint, this delay will "smear out" until it looks like a steady, dimmer light.[[note]]Relativistic effects (length contraction and time dilation) will change the picture, but not much; O'Brien will still see the ~~the ~~light pulses spaced out, just not as much as Sir Isaac Newton would expect.[[/note]]

1st Jul '15 8:27:11 PM

**nombretomado** Is there an issue? Send a Message

**Changed line(s) 94,95 (click to see context) from:**

Suppose that [[Series/StarTrekTheNextGeneration Captain Picard]] and [[Series/BattlestarGalacticaReimagined William Adama]] fly past each other. They are in deep space, far from any planets, so they have no notion of who is "really" standing still and who is "really" moving. The ''Enterprise'' passes the ''Galactica'', so all they know is that the ''Enterprise'' is going some amount ''v'' faster than the ''Galactica''.

**to:**

Suppose that [[Series/StarTrekTheNextGeneration Captain Picard]] and ~~[[Series/BattlestarGalacticaReimagined ~~[[Series/BattlestarGalactica2003 William Adama]] fly past each other. They are in deep space, far from any planets, so they have no notion of who is "really" standing still and who is "really" moving. The ''Enterprise'' passes the ''Galactica'', so all they know is that the ''Enterprise'' is going some amount ''v'' faster than the ''Galactica''.

19th Aug '14 10:01:43 PM

**Uchuujinsan** Is there an issue? Send a Message

**Changed line(s) 60,62 (click to see context) from:**

** This above equation only applies if velocity can be assumed to be zero. For a mass at nonzero velocity the appropriate equation becomes E[[superscript:2]]=m[[superscript:2]]c[[superscript:4]]+p[[superscript:2]]c[[superscript:2]]

*** And then the reason that it simplifies down to E=mc[[superscript:2]] is that the full equation has E as the hypotenuse of a right-triangle, and applies the Pythagorean theorem. E is the hypotenuse, and the legs are mc[[superscript:2]] and pc, respectively.

*** And then the reason that it simplifies down to E=mc[[superscript:2]] is that the full equation has E as the hypotenuse of a right-triangle, and applies the Pythagorean theorem. E is the hypotenuse, and the legs are mc[[superscript:2]] and pc, respectively.

**to:**

** This ~~above equation only applies if velocity can be assumed ~~is often corrected to ~~be zero. For a mass at nonzero velocity ~~E[[superscript:2]]=m[[superscript:2]]c[[superscript:4]]+p[[superscript:2]]c[[superscript:2]]. In fact, both formulas are correct and apply to moving objects, the ~~appropriate equation becomes E[[superscript:2]]=m[[superscript:2]]c[[superscript:4]]+p[[superscript:2]]c[[superscript:2]]~~

*** And then the reason that it simplifies down to E=mc[[superscript:2]]difference is that in the ~~full equation has E as the hypotenuse of a right-triangle, and applies the Pythagorean theorem. E ~~original formula E=mc[[superscript:2]] m is the ~~hypotenuse, ~~relativistic mass while in the other formula it's the rest mass, often just called mass. Basically both are the same formula, just written differently, and ~~the legs are mc[[superscript:2]] and pc, respectively.~~

can be changed into each other with a little math.

*** And then the reason that it simplifies down to E=mc[[superscript:2]]

12th Jul '14 5:31:08 PM

**StevieC** Is there an issue? Send a Message

**Changed line(s) 9,10 (click to see context) from:**

Starting with the ancient Greeks, and ending around the [[http://en.wikipedia.org/wiki/R%C3%B8mer%27s_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. Galileo tried to measure the speed of light with lanterns and mirrors on mountaintops, but failed. 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. Later scientists created successively more and more precise means of measuring the speed of light, and today we can measure its speed with such great precision that the meter is defined in terms of the speed of light rather than the other way around. The speed of light in a vacuum is exactly 299,792.458 kilometers per second.[[note]]The speed of light through a medium other than a vacuum is slower, because the light is absorbed as it collides with the molecules of the medium, and there's a small delay each time before it is re-emitted out of the other side of the molecule. When particles travel through a non-vacuum at a speed greater than light can travel through the same substance, it induces something called Cherenkov radiation, which is the optical equivalent to a sonic boom.[[/note]]

**to:**

Starting with the ancient Greeks, and ending around the [[http://en.wikipedia.org/wiki/R%C3%B8mer%27s_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. Galileo tried to measure the speed of light with lanterns and mirrors on mountaintops, but failed. 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. Later scientists created successively more and more precise means of measuring the speed of light, and today we can measure its speed with such great precision that the meter is defined in terms of the speed of light rather than the other way around. The speed of light in a vacuum is exactly 299,792.458 kilometers per second.[[note]]The speed of light through a medium other than a vacuum is slower, because the light is absorbed as it collides with the molecules of the medium, and there's a small delay each time before it is re-emitted out of the other side of the molecule. When particles travel through a non-vacuum at a speed greater than light can travel through the same substance, it induces something called ~~Cherenkov ~~Čerenkov radiation, which is the optical equivalent to a sonic boom.[[/note]]

12th Jul '14 5:25:27 PM

**StevieC** Is there an issue? Send a Message

**Changed line(s) 9,10 (click to see context) from:**

Starting with the ancient Greeks, and ending around the [[http://en.wikipedia.org/wiki/R%C3%B8mer%27s_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. Galileo tried to measure the speed of light with lanterns and mirrors on mountaintops, but failed. 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. Later scientists created successively more and more precise means of measuring the speed of light, and today we can measure its speed with such great precision that the meter is defined in terms of the speed of light rather than the other way around. The speed of light in a vacuum is exactly 299,792.458 kilometers per second.[[note]]The speed of light through a medium other than a vacuum is slower, because the light is absorbed as it collides with the molecules of the medium, and there's a small delay each time before it is re-emitted out of the other side of the molecule.[[/note]]

**to:**

Starting with the ancient Greeks, and ending around the [[http://en.wikipedia.org/wiki/R%C3%B8mer%27s_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. Galileo tried to measure the speed of light with lanterns and mirrors on mountaintops, but failed. 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. Later scientists created successively more and more precise means of measuring the speed of light, and today we can measure its speed with such great precision that the meter is defined in terms of the speed of light rather than the other way around. The speed of light in a vacuum is exactly 299,792.458 kilometers per second.[[note]]The speed of light through a medium other than a vacuum is slower, because the light is absorbed as it collides with the molecules of the medium, and there's a small delay each time before it is re-emitted out of the other side of the molecule. When particles travel through a non-vacuum at a speed greater than light can travel through the same substance, it induces something called Cherenkov radiation, which is the optical equivalent to a sonic boom.[[/note]]

12th Jul '14 5:21:47 PM

**StevieC** Is there an issue? Send a Message

**Changed line(s) 60,62 (click to see context) from:**

** This above equation only applies if velocity can be assumed to be zero. For a mass at nonzero velocity the appropriate equation becomes

*** E[[superscript:2]]=m[[superscript:2]]c[[superscript:4]]+p[[superscript:2]]c[[superscript:2]]

*** E[[superscript:2]]=m[[superscript:2]]c[[superscript:4]]+p[[superscript:2]]c[[superscript:2]]

**to:**

** This above equation only applies if velocity can be assumed to be zero. For a mass at nonzero velocity the appropriate equation ~~becomes~~

***becomes E[[superscript:2]]=m[[superscript:2]]c[[superscript:4]]+p[[superscript:2]]c[[superscript:2]]

*** And then the reason that it simplifies down to E=mc[[superscript:2]] is that the full equation has E as the hypotenuse of a right-triangle, and applies the Pythagorean theorem. E is the hypotenuse, and the legs are mc[[superscript:2]] and pc, respectively.

***

*** And then the reason that it simplifies down to E=mc[[superscript:2]] is that the full equation has E as the hypotenuse of a right-triangle, and applies the Pythagorean theorem. E is the hypotenuse, and the legs are mc[[superscript:2]] and pc, respectively.

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