Under the Special Theory of Relativity, the units of time are to be measured in terms of a triangle formed by a reflected light bean. This gives rise to the effect of time dilation appearing between an observer in motion and an observer at relative rest. The phenomenon of time dilation is, however, indiscernible for the observer who shares in the motion.
If a sound wave is used to measure the unit of time, the time dilation assumes a cloak of invisibility. The dilation appears only slightly when the sound source is in motion (v << c). So, while measuring a unit of time on a clock, across reference frames, is impossible for a light beam, it is well within the grasp of a sound wave. An observer in motion will totally agree with an observer at relative rest.
The formulae of c = L / t or t = L / c, is the simplest form of the Newtonian law, or equation of motion in an inertial reference frame attached to the train, by the principle of relativity. A comparison with the result of my thought experiment yields an unmasking of length contraction. The time of travel of the sound wave down the length of the train car, L, if it were at rest, can be read from the length specifications, and the known speed of sound waves c.
The observer on board the train would anticipate the measured time can be solved for by using algebra. But, if the train is in motion (forward), then the time measured will be different from this time: t = L - vt / c, (with t = t), or t = L / (c + v), due to the forward motion of the train car at the velocity, v. And thus the time that the sound wave has taken while traveling, as interpreted by the observer, will be shorter than the time of travel for the sound wave down the train car, if it were at rest.
The setup of my thought experiment uses a single clock so that no synchronization is necessary. This has been put forward as a proof for supporting STR. In most examples to illustrate STR, it is put forward that the observer at rest has to use two clocks for two events that occur at different locations in space.
However in my hypothesis, there is only one clock, and only one observer within the train reference frame; thus doing an end run around synchronization; it is not a limitation for my hypothesis. I propose that the answer the train car observer measures is identical to that of an observer on the platform, without any sort of communication going on between the two.
This shakes the appearance and reality of Relativity. An axiomatic statement that these two observers, one at rest one in motion, will measure two different times and velocities for the same event, is at the heart of Relativity. But my setup has done precisely that.
Both the train observer and the platform observer will claim the same, identical formula for the motion of the train car. This is the same formula found by the platform observer by the Galilean transformation. Units of time cannot be measured by light waves across reference frames, to get a single common value; but it can be measured thusly by sound waves, under easily met conditions.
https://en.wikipedia.org/wiki/Time_dilation
If a sound wave is used to measure the unit of time, the time dilation assumes a cloak of invisibility. The dilation appears only slightly when the sound source is in motion (v << c). So, while measuring a unit of time on a clock, across reference frames, is impossible for a light beam, it is well within the grasp of a sound wave. An observer in motion will totally agree with an observer at relative rest.
The formulae of c = L / t or t = L / c, is the simplest form of the Newtonian law, or equation of motion in an inertial reference frame attached to the train, by the principle of relativity. A comparison with the result of my thought experiment yields an unmasking of length contraction. The time of travel of the sound wave down the length of the train car, L, if it were at rest, can be read from the length specifications, and the known speed of sound waves c.
The observer on board the train would anticipate the measured time can be solved for by using algebra. But, if the train is in motion (forward), then the time measured will be different from this time: t = L - vt / c, (with t = t), or t = L / (c + v), due to the forward motion of the train car at the velocity, v. And thus the time that the sound wave has taken while traveling, as interpreted by the observer, will be shorter than the time of travel for the sound wave down the train car, if it were at rest.
The setup of my thought experiment uses a single clock so that no synchronization is necessary. This has been put forward as a proof for supporting STR. In most examples to illustrate STR, it is put forward that the observer at rest has to use two clocks for two events that occur at different locations in space.
However in my hypothesis, there is only one clock, and only one observer within the train reference frame; thus doing an end run around synchronization; it is not a limitation for my hypothesis. I propose that the answer the train car observer measures is identical to that of an observer on the platform, without any sort of communication going on between the two.
This shakes the appearance and reality of Relativity. An axiomatic statement that these two observers, one at rest one in motion, will measure two different times and velocities for the same event, is at the heart of Relativity. But my setup has done precisely that.
Both the train observer and the platform observer will claim the same, identical formula for the motion of the train car. This is the same formula found by the platform observer by the Galilean transformation. Units of time cannot be measured by light waves across reference frames, to get a single common value; but it can be measured thusly by sound waves, under easily met conditions.
https://en.wikipedia.org/wiki/Time_dilation
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