Time t' on the ship in motion (the operating speed of the instruments located on this ship in motion) passes more slowly than time t on the ship at rest.


Fig. 1. The ship on the left is at rest on the water surface. A shuttle moves at a velocity of V from a barge to the bottom and back. The ship on the right is moving at a velocity of v along the water body surface. The speed of movement of the shuttle equals V, the shuttle’s horizontal velocity component equals v, and the vertical component equals VZ.

If a ship is proceeding at a speed of v, the clock tick rate and the operating speed of the instruments on the barges are decreased. This occurs due to the fact that when a ship is moving at a speed of v, the ascent and descent rate, VZ, of a shuttle making trips in the water between a ship and the bottom of the water body according to the hypotenuses of right triangles happens to equal . Time t' on the ship in motion passes more slowly than time t on the ship at rest. Thus, the more rapidly a ship proceeds through the water, the less often the pendulum “swings” and the more slowly the operations of the instruments located on this ship are performed, the operating speed of which is proportional to the shuttle pendulum frequency.

We suppose there are no instruments on the ships that make contact with the water, which would make it possible to record an instance of ship motion or rest relative to the water. There are also no optical instruments and radio devices on the ships that are capable of almost instantaneously transmitting information from ship to ship. The transfer of information from ship to ship on physical media is only accomplished directly (when the ships are located in direct proximity to one another) or using speedboats (that ply the water surface at a velocity of V), which carry the physical information media from one ship to another. Only the information contained on the physical media is regarded as documentary (documented) information.

Let us imagine two ships under way one after another at a speed of v. Let’s assume that the first ship moves past a ship at rest at some point in time, then the second ship also moves past the ship at rest at some later point in time. Comparing the clock readings of the ship at rest with those of the previously synchronized clocks of their own ships, the instruments of the ships in motion detect a difference in the rate of their clock and that of the clock on the ship in motion. The result of a comparison of the clock on the ship at rest and the clocks on the ships in motion will depend upon the clock synchronization technique.

If the instruments on the ships in motion have information concerning the fact that their ships are moving at a speed of v, then by synchronizing their clocks using a speedboat moving between the ships, they take into account the disparity of the speed of the speedboat they are using relative to their ships in the direction and opposite the direction of their movement. By synchronizing the clocks in this manner, they obtain a true result, according to which time on the ship at rest passes times more quickly than their own time.

Now answer the following questions:

  1. What is the real relationship between time t on the ship in rest and time t' on the ship in motion?
  2. 2) Can the instruments on the ships, having information concerning the essence of the environment and concerning the fact that time t on the ship at rest passes more quickly than time t' on the ship in motion, using speedboats determine which ship is in motion and which ship is at rest relative to the water?
  3. 3) What result do obtain the instruments on the two ships in motion if comparing their clock rate to that of the ship at rest they have no information concerning the movement of their ships and use the false condition of the equality of the speedboat’s speed relative to their ships in the direction of their movement and opposite it?

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