## The Twin Paradox Analogy in Classical Physics

*Imagine an h-deep flat bottom still water pond. On its water surface, there is a boat fitted with a pendulum clock and instruments activated by signals generated by this clock (in time with this clock). The function of the clock pendulum is performed by a high-speed shuttle continuously moving along a vertical (relative to the boat) line between the boat and the bottom. Each run of the shuttle to the bottom and back takes the time Δt=2h/Vz, where Vz is the rate of dive and emergence of the underwater shuttle, and the process is accompanied by a change in the clock readings. The shuttle moves at a constant speed V relative to water, and when the boat is at rest, the shuttle moves perpendicular to the bottom. The speed Vz of dive and emergence of the shuttle is equal to V. The time Δt of the shuttle run to the bottom and back is equal to 2h/V. The speed V of the shuttle exceeds that of the boat (v), i.e. the condition v<V is satisfied.*

## Simulation of Time Dilation and Other Relativistic Effects Based on the Example of Floating Ships

*Let us consider the behavior of objects that, although slow-moving, nonetheless act in accordance with the laws of the special theory of relativity.*

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 ,i>v, and the vertical component, *V _{Z}*, equals .

## The Relativistic Trolley Paradox

*Imagine that an observer being on a hypothetical trolley is spinning the drive wheel to a certain angular velocity ω, and this wheel is rolling along the rail without slipping, thus driving the trolley. Upon reaching the angular velocity ω, the linear velocity v of the rotating rim of the drive wheel becomes constant and equal to ωR, where R is the radius of the wheel rim.*

## The Pulsed Nature of Inertia?

A long lightweight pipe lies on the Earth’s surface. A “filler” is located inside the pipe. The “filler” in evenly distributed along the pipe’s length. The weight of the “filler” per kilometer of pipe equals m. The weight of the pipe itself is negligible as compared to the weight of the “filler”.

What does the weight of one kilometer of pipe equal; i.e., what force does one kilometer of pipe exert on the ground?

## How to Measure the One-Way Speed of Light

*The paper discusses a method of measuring the one-way speed of light based on the use of a rigid rod freely rotating around its axis. The authors analyze the conditions related to phase correlation and synchronism of rotation of the rod ends in the reference frame wherein its axial velocity is zero and in the reference frames wherein it moves at a high axial velocity. The anticipated results of the experiment within special relativity and Lorentz ether theory are also considered.*

## Specific Features of Time Dilation During Circular Movement

Imagine that all the processes in your body, and the objects that you hold in your hands, have slowed. For those around you, you would become a dawdler, while a lamp in your hands, which you think is giving off a green light, during a certain degree of slowing would be perceived by the people around you as yellow due to a decrease in the light wave frequency. In turn, you would notice accelerated life and the rapid movement of each person in the world around you, while a lamp just like yours in the hands of one of these individuals would emit a blue light from your point of view. These disparate, diametrically opposed perceptions by you and the people around you can be called asymmetric. There is no similar asymmetric and what would appear to be such a natural result of mutual observation in Einstein’s special theory of relativity. __Therein, each observer in motion relative to another observer notices a slowing of the other observer’s processes that is strange from the standpoint of “common” sense; i.e., the results prove to be symmetric. But can a disturbance of this symmetry be observed in the physics of moving bodies?__

Read more: Specific Features of Time Dilation During Circular Movement

## The Non-Relativistic Models of the Relativistic Bell’s Paradox

*Here the so-called Bell’s accelerating rockets paradox is examined. The non-relativistic models of Bell's effect are presented, where likewise the theory of special relativity the proper distance between two rockets following one another is increased them being accelerated on identical programmes. It becomes clear that the proper distance increase is determined by Einstein’s simultaneity of the moments of the start of the programmes execution on the rockets. It is also shown that Einstein’s relative simultaneity does not ensure reversibility of the proper distance between the rockets upon their joint return to their initial state. The reversibility is only achieved by the introduction of the preferred reference frame (not necessarily absolute!) and of the universal time in all inertial reference frames.*

Read more: The Non-Relativistic Models of the Relativistic Bell’s Paradox

## Why the velocities of material bodies cannot achieve the speed of light In a vacuum

*V. N. Matveev and O. V. Matvejev*

*A possible cause of the finiteness of the velocity of tangible objects is demonstrated without reference to the provisions of the special theory of relativity. A condition is formulated on the basis of which the assumption of the movement of tangible objects at any prescribed velocities proves to be self-contradictory in instances when the prescribed velocities of the objects exceed a certain value. This condition consists of the presence of interaction signals and carrier particles in material bodies that are propagated at a velocity greater than any prescribed velocity of the material bodies.*

Read more: Why the velocities of material bodies cannot achieve the speed of light In a vacuum

## An Entertaining Exercise- which clock is ticking slower?

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/V_{Z} , where V_{Z} – 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, V_{Z}, 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.

Read more: An Entertaining Exercise- which clock is ticking slower?

## Full simulation of the special theory of relativity by means of classical mechanics

*V. N. Matveev and O. V. Matvejev*

Based on pre-Einstein classical mechanics, a theoretical model is constructed that describes the behavior of objects in a liquid environment that conduct themselves in accordance with the formal laws of the special theory of relativity. This model reproduces Lorentz contraction, time dilation, the relativity of simultaneity, the Doppler effect in its symmetrical relativistic form, and the twin paradox effects. The model makes it possible to obtain Lorentz transforms and to simulate Minkowski four-dimensional space-time.

#### Quote

**In the work at hand, we demonstrate that a significant number of relativistic effects can be simulated in an environment without manipulations and machinations, the fundamental means for which consist of classical mechanics**

All the effects that simulate the effects of the special theory of relativity appear to be absolute in content, but relativistic in form. The relativistic nature of the model and the relativity of the physical effects within the framework of the proposed model are achieved by means of refusing to take the presence of an environment into account and introducing additional conditions. Once such condition consists of replacing the fact of the inequality of the speeds of information dissemination in opposite directions within a moving environment with the assumption of the equality of these speeds.

Read more: Full simulation of the special theory of relativity by means of classical mechanics