Let’s imagine the surface of a flat-bottomed water body with a depth of h, filled with still water. A ship equipped with a pendulum clock and with instruments that operate based on signals generated by this clock (in time with this clock) is located on the water body surface. A high-speed shuttle that is in continuous motion along a plumb line (relative to a given barge) between the barge and the bottom performs the function of the clock’s pendulum. Each shuttle trip to the bottom and back requires a time of Δt = 2h/VZ , where VZ – rate of descent and ascent of the underwater shuttle, and is accompanied by a change in the clock reading. The shuttle moves at a constant speed of V relative to the water, and if the ship is at rest, the shuttle moves perpendicular to the bottom, and the rate of the shuttle’s descent and ascent, VZ, equals V. The time, Δt, of a shuttle trip to the bottom and back equals 2h/V. The V velocity value exceeds the ship’s speed of v; i.e., the condition v < V is satisfied.

If a ship is proceeding at 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 on the ship in motion, which can be called simulated time, t', passes more slowly than time, t, on the ship at rest also by times. 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.>

It is easy to simulate time dilation using ships of this type.

Let us assume that two ships at rest are located on a water surface at some distance from one another. Let’s imagine that the ships are equipped with speedboats that, like the shuttles, run at a speed of V, but only on the water surface. Let us assume that the ship instruments synchronize the clocks using a speedboat to transmit the information, which runs from one ship to the other and back. If the instruments have information that the speed of the boat relative to ships in opposite directions are equal, then using the boat, the instruments synchronize the clocks, as is done using a light signal in the special theory of relativity.

Having synchronized the clocks, the instruments on the ships at rest can compare their clock rate to that of a ship that is moving past them along the line that connects them. Taking the clock readings of the ship in motion at the locations of the ships at rest and comparing them to the readings of the synchronized clocks on their own ships, the instruments record time dilation of the moving ship times.

Now 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 are able to measure the speed, v, of their ships, or if they have information concerning the fact that their ships are moving at a speed of v, then by synchronizing their clocks using a boat 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. However, this result can be just the opposite if the instruments on the ships in motion have no information concerning the movement of their ships and no other means of communication between the ships other than a speedboat. The truth of the matter is that by sending a boat that carries the requisite information from barge to barge, the instruments can only record the fact of the movement of the barges relative to one another. Basic calculations reveal that the instruments have no way of determining which ship is in motion and which ship is at rest relative to the water. If the instruments use false information concerning the repose of their ships, then mistaking their ships in motion relative to the water for ships at rest, they mistake the ship at rest in the water for a ship in motion relative to them. Here, they use the false condition of the equality of the boat’s speed relative to their ships in the direction of their movement and opposite it. In this instance, by synchronizing the clocks using the Einstein technique, the instruments on the ships in motion, strange as it may seem, record a false time dilation on the ship at rest in the water, which in their estimation is moving relative to them.

Over the course of the simulation work, the book’s authors detected a regularity that served as the basis of the work, the results of which are presented in an article entitled “Why the Velocities of Material Bodies Cannot Achieve the Speed of Light in a Vacuum”. The reason for the finiteness of the speed of light and the limitation of the speed of material objects to the speed of light is demonstrated in the article. The reason consists of the presence, both in space and inside materials bodies, of massless signals that, when present in material bodies, initiate the occurrence of microprocesses (events) therein that are responsible for the physical alteration of these bodies.The hypothesis at the mathematical level is that an increase in the velocity of massless signals leads to a proportional increase in the rate of change of material bodies, which is fundamentally the rate of the passage of time. The hypothetical increase in signal velocity inside material bodies and the proportional increase in the rate of the passage of time that it causes lead to the inalterability of the finite physical velocity of massless signals. Read the full article at http://www.theoryrelativity.com/EN/all-articles/8-why-the-velocities-of-material-bodies-cannot-achieve-the-speed-of-light-in-a-vacuum.html.