Editing 1366: Train
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This comic, which appeared the day before {{w|National Train Day}}, plays on the fact that a choice of a {{w|Inertial frame of reference|reference frame}} is arbitrary, leading to the {{w|Principle of relativity|"Principle of relativity"}} in {{w|Albert Einstein}}'s theories of {{w|special relativity}} and {{w|general relativity}}. But at speeds much lower than the speed of light it also applies to the {{w|Classical mechanics|newtonian mechanics}}. | This comic, which appeared the day before {{w|National Train Day}}, plays on the fact that a choice of a {{w|Inertial frame of reference|reference frame}} is arbitrary, leading to the {{w|Principle of relativity|"Principle of relativity"}} in {{w|Albert Einstein}}'s theories of {{w|special relativity}} and {{w|general relativity}}. But at speeds much lower than the speed of light it also applies to the {{w|Classical mechanics|newtonian mechanics}}. | ||
| − | Rather than viewing this situation as a train causing itself to move relative to an immobile Earth, [[Randall]] provides the unconventional perspective of a train remaining fixed in space while causing the Earth itself and all the stars in the sky to rotate instead. In principle either perspective is equally valid | + | Rather than viewing this situation as a train causing itself to move relative to an immobile Earth, [[Randall]] provides the unconventional perspective of a train remaining fixed in space while causing the Earth itself and all the stars in the sky to rotate instead. In principle either perspective is equally valid (though in practice different trains often move in mutually-exclusive directions, thus each train would have to define its own frame of reference). There is a quotation, attributed to Einstein, that he once asked a ticket collector, "What time does Oxford stop at this train?" |
| − | + | From the Newtonian perspective this choice of frame is valid, but results in unnecessarily complicated maths; the equation of motion would include terms for centrifugal, Coriolis and other so-called "fictional forces" see [[123: Centrifugal Force]]. Newton supposes the existence of "inertial frames", in which these forces are zero, and the surface of the Earth approximates an inertial frame well. In General Relativity, the presence of mass in a system curves the {{w|spacetime}} around of it. The train-earth system could be modeled in general relativity, taking the train as fixed. However the resulting equations would be complex, and not amenable to an exact solution | |
| − | + | The title text takes this further by saying that elevators do the same thing by pulling the Earth up and down, rather than moving up and down in a fixed space via cables and weights affixed to pulleys that are themselves moored to fixed points. | |
| − | The | + | These examples use the train and the elevator as fixed points to define relative travel. The more common method to define movement is to use the Earth's surface as fixed point, but other reference points could be the {{w|Earth's_rotation|Earth's center}}, the {{w|Earth's_orbit|Sun}}, predefined {{w|Fixed_star|"fixed" stars}} or the {{w|Galactic_year|center of our galaxy}}. Each of these would result in a completely different movement speed: |
| + | * The speed of the train (stationary on the equator) relative to the earth's center: 465 m/s (1,674 km/h or 1,040 mph) | ||
| + | * The speed of the train (on earth) relative to the sun: 30 km/s (108,000 km/h or 67,000 mph) | ||
| + | * The speed of the train (on earth) relative the center of our galaxy: 220 km/s (828,000 km/h or 514,000 mph) | ||
| − | + | The train, as seen from the earth's surface, doesn't seem to rotate the earth, but it does in fact have a minute, immeasurable effect on the Earth's rotation (see [http://what-if.xkcd.com/41/ what-if? 41: Go West] and [[162: Angular Momentum|comic 162: Angular Momentum]]). | |
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==Transcript== | ==Transcript== | ||
| − | :''' | + | :'''TRAIN:''' |
| − | :[On the upper edge of a circle representing the Earth, Cueball is in a train car looking to his left.] | + | :[On the upper edge of a circle representing the Earth in a wrong scale, Cueball is in a train car, looking to his left.] |
:Cueball:...almost... | :Cueball:...almost... | ||
:[The train tracks run between another person standing at the 2:00 position, and Hairy standing at the 9:30 position. There's yet another person standing at the 6:00 position, between some snow-capped mountains and some low hills.] | :[The train tracks run between another person standing at the 2:00 position, and Hairy standing at the 9:30 position. There's yet another person standing at the 6:00 position, between some snow-capped mountains and some low hills.] | ||
:[There's a counterclockwise arrow in the middle of the circle, and motion lines indicate that everyone and everything on the planet is moving counterclockwise, except for the train, which is motionless.] | :[There's a counterclockwise arrow in the middle of the circle, and motion lines indicate that everyone and everything on the planet is moving counterclockwise, except for the train, which is motionless.] | ||
| − | :A machine that grabs the Earth by metal rails and rotates it until the part you want is near you | + | :A machine that grabs the Earth by metal rails and rotates it until the part you want is near you |
{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Comics featuring Cueball]] | [[Category:Comics featuring Cueball]] | ||
[[Category:Physics]] | [[Category:Physics]] | ||
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