The symbol, c, represents both the speed of light and the speed of sound in most scientific reference texts. Can the speed of sound be substituted for the speed of light in the Michelson-Morley (MM) formula: T = [L / (c - v)] + [L / (c + v)]?
Consider an observer on a train of length, L. It is moving with a constant velocity, v. Can this observer find the train’s velocity relative to the embankment (Earth), with a single clock? That is, if there is an inertial reference frame attached to the moving train, and another inertial reference frame, with another observer, attached to the Earth (which is considered at rest), can the caboose observer find the train’s relative velocity? Will this value be in the form of the simplest law of motion: v = d / t, or in a form that violates the classical principle of relativity? Alternatively speaking, will the two observers, one in motion and one at rest, measure two different values (via Galilean transformation) for the velocity, v of the train. Or, is it possible for them to measure the same value, v?
It is a windless day (air, medium at rest). The observer is in the caboose with a lantern to signal the engineer in the locomotive. When he sees the flash of light (effectively instantaneous at this distance), he blows the whistle. She starts her clock at the same moment she sends the light flash, and thusly she can measure the time, t, for the sound wave of the whistle to travel the length, L. When the sound wave reaches her, she flashes the lantern once more. An observer at rest on the platform sees the first flash and the second flash, and with his clock measures the time between these flashes. Will each observer measure the same time, t, between the two flashes?
If the platform observer has a means to establish the distance between the flashes (by some landmarks running parallel to the track, for example). The length of the train is obtained from the specifications; the constant velocity of sound in still air is agreed upon amongst the observers; their clocks are mechanically similar. Will he then be able to determine the same velocity for the train? Will these two observers use the same formula: L = ct + vt? This formula describes the idea that as the sound wave (velocity, c) travels rearward, it meets the caboose (velocity, v) traveling forward. Each begins at the endpoints of the distance, L. This formula can be rearranged to the MM form: L / (c + v) = t; v = [L / t] - c, to find the velocity of the train relative to the earth.
Consider an observer on a train of length, L. It is moving with a constant velocity, v. Can this observer find the train’s velocity relative to the embankment (Earth), with a single clock? That is, if there is an inertial reference frame attached to the moving train, and another inertial reference frame, with another observer, attached to the Earth (which is considered at rest), can the caboose observer find the train’s relative velocity? Will this value be in the form of the simplest law of motion: v = d / t, or in a form that violates the classical principle of relativity? Alternatively speaking, will the two observers, one in motion and one at rest, measure two different values (via Galilean transformation) for the velocity, v of the train. Or, is it possible for them to measure the same value, v?
It is a windless day (air, medium at rest). The observer is in the caboose with a lantern to signal the engineer in the locomotive. When he sees the flash of light (effectively instantaneous at this distance), he blows the whistle. She starts her clock at the same moment she sends the light flash, and thusly she can measure the time, t, for the sound wave of the whistle to travel the length, L. When the sound wave reaches her, she flashes the lantern once more. An observer at rest on the platform sees the first flash and the second flash, and with his clock measures the time between these flashes. Will each observer measure the same time, t, between the two flashes?
If the platform observer has a means to establish the distance between the flashes (by some landmarks running parallel to the track, for example). The length of the train is obtained from the specifications; the constant velocity of sound in still air is agreed upon amongst the observers; their clocks are mechanically similar. Will he then be able to determine the same velocity for the train? Will these two observers use the same formula: L = ct + vt? This formula describes the idea that as the sound wave (velocity, c) travels rearward, it meets the caboose (velocity, v) traveling forward. Each begins at the endpoints of the distance, L. This formula can be rearranged to the MM form: L / (c + v) = t; v = [L / t] - c, to find the velocity of the train relative to the earth.
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