Editing 1366: Train
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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 β though in practice different trains often move in mutually-exclusive directions, thus each train would have to define its own frame of reference. It is said that Einstein once asked a ticket collector, "What time does Oxford stop at this train?" | 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 β though in practice different trains often move in mutually-exclusive directions, thus each train would have to define its own frame of reference. It is said that Einstein once asked a ticket collector, "What time does Oxford stop at this train?" | ||
| β | Changing the reference frame into the inside of the train only means that you see the outside world in a different reference, since the train doesn't really move the Earth | + | Changing the reference frame into the inside of the train only means that you see the outside world in a different reference, since the train doesn't really move the Earth (the train's engine and the friction of the wheels aren't even remotely powerful enough) it simply appears that way from the inside. |
From the Newtonian perspective this choice of frame is valid, but results in unnecessarily complicated math; the equation of motion would include terms for centrifugal, Coriolis and other so-called {{w|Inertial force|"fictional forces"}} (see [[123: Centrifugal Force]]). {{w|Isaac Newton|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. | From the Newtonian perspective this choice of frame is valid, but results in unnecessarily complicated math; the equation of motion would include terms for centrifugal, Coriolis and other so-called {{w|Inertial force|"fictional forces"}} (see [[123: Centrifugal Force]]). {{w|Isaac Newton|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. | ||
