# Explanation of What Time in Kinematics Is and Dispelling Myths Allegedly Stemming from the Special Theory of Relativity

## Abstract

**:**

## 1. Introduction

- I.
- Coordinate and time transformation “inertial frame of reference—inertial frame of reference” is linear.
- II.
- There is at least one inertial frame of reference (called the universal frame of reference) in which the speed of light in a vacuum is the same in each direction. The constant one-way speed of light is indicated by the symbol c = constants.
- III.
- For each motionless observer in relation to the universal frame of reference, the space has the same properties in each direction, i.e., it is isotropic.
- IV.
- The average speed of light in the vacuum flowing way back and forth is constant for each observer from the inertial frame of reference. This average speed is indicated by the symbol c
_{av}= constants. This average speed does not depend on the observer’s speed in relation to the universal frame of reference nor on the direction of light propagation (these results are from the Michelson–Morley and Kennedy–Thorndike experiments).

## 2. Light Clock

#### 2.1. Principle of Light Clock Operation

_{0}in a homogeneous medium. The universal frame of reference U is connected with the medium in which the signal propagates. The clock can move relative to the medium in which the signal is propagated (at v speed). The clock is connected to the inertial system U′.

#### 2.2. Light Synchronization of Clocks Means Using Light Clocks

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

_{A1}, a light impulse is sent from it to clock B. If the one-way speed of light in this direction is c

^{+}, then when the light impulse reaches the clock B, the following value must be set on it

^{−}, then when the light impulse returns to clock A, it indicates the value

_{av}on the way back and forth. It is worth noting that the time lapse on clock A does not depend on the one-way speed of light c

^{+}and c

^{−}if c

_{av}= c = constants (assumption IV).

^{+}, and therefore synchronization depends on what theory this process is based on (classical kinematics, Special Theory of Relativity, or any of the Special Theory of Ether). However, clock B does not affect the speed at which clock A measures time. Although in the synchronization process the light impulse was sent to clock B, the speed at which clock A measures the time depends only on the total time it takes for the light impulse to go back and forth. This means that clock A measures the time exactly like a light clock. Since the requests received for clock A apply to every clock, all light synchronized clocks measure the time exactly the same as a light clock.

#### 2.3. Time Measurement in Own Clock System (in Inertial Frame of Reference)

_{x}always has the same value because the clock arm is the same as the standard length.

_{x}(v). If v = 0, then the length of the clock arm is the same for observers from U′ and U systems, and therefore D′

_{x}= D

_{x}(0).

^{+}(when the light moves in the mirror direction) and c

^{−}(when the light moves on its way back to the light source) [1]. As one-way speed c

^{+}and c

^{−}may depend on the direction of light propagation or speed v, the one-way light clock, in which the signal flows in only one direction, may not be a good time standard (time etalon). However, if the average speed of light flowing along the way to the mirror and back is constant (assumption IV), then the bi-directional clock is a stable time unit standard. With such a unit, the time will not depend on the direction of light emission, i.e., the way the light clock is set, nor on speed v. Therefore, in this paper, we will use a two-way light clock.

#### 2.4. Time Measurement from Universal Frame of Reference

_{x}(0) = D′

_{x}in U′ and D

_{x}(v) in U.

_{x}(0) = D′

_{x}at time t′

_{1}, at a speed c

_{x}

^{+}. Returning to the source, the light follows a path of the same length D

_{x}(0) = D′

_{x}, at time t′

_{2}, at a speed c

_{x}

^{−}. If the clock follows one cycle, then according to the observer in the same inertial system U′, the time elapse t′ = t′

_{1}+ t′

_{2}with value (5).

_{x}(v).

_{1}length, at time t

_{1}, at a speed c. Returning to the source, the light travels a distance of L

_{2}, at time t

_{2}, at the same speed c. From Figure 4 (part b), we obtain

_{1}and t

_{2}. Then we obtain the time and the path of light flow in the system U in the form of

_{1}+ L

_{2}. Therefore, for the observer from the U system, the time t elapses, which the light needs in this system to cover a distance of L

_{1}+ L

_{2}.

_{x}(v)/D′

_{x}). Time dilation also depends on the speed c with which the signal moves.

#### 2.5. Time Measured by a Moving Clock with a Freely Set Arm

## 3. Time Dilation in Different Kinematics

#### 3.1. Classical Kinematics

#### 3.2. Kinematics of the Special Theory of Ether

_{x}(v) long and the arms inclined at an angle α to speed v is D(v) long. In STE, these clocks measure time identically, but their arms lengths for an ether observer are not equal in general. In order to determine the relationship between the arm lengths of these two clocks, Equation (25) will be divided by (15), and (28) will be considered. Then the following will be obtained

#### 3.3. Kinematics of the Special Theory of Relativity

## 4. There Is No Reason to Claim That the Speed of Light in a Vacuum Is the Maximum Speed

_{s}< c. This could be performed by a civilization that would live in a material medium that slows down light, for which vacuum would be unavailable. In their atmosphere, the speed of light would always be, e.g., c

_{s}= c/2. In their transformations, there would always be the speed c

_{s}, not the speed c. Their transformations would stop functioning for inertial systems moving with the speed of c

_{s}. If they interpreted it in the same way as the value c is interpreted according to contemporary physics, they would claim that c

_{s}is the maximum speed that cannot be exceeded. This is not the case, of course, and their transformations would stop functioning for the speed of c

_{s}or higher, only because for such velocities, the light clock based on the signal propagating with the speed of c

_{s}does not function.

_{s}> c speed, then the transformations based on the signal clock will function, also for velocities higher than the light speed in a vacuum. In the extreme case, when c

_{s}= ∞, the signal clock functions correctly in all inertial systems, regardless of their speed. Therefore, in this case, the transformations act for inertial systems moving at any high speed. This is the way it is in classical kinematics.

## 5. Atomic Clock, Time Dilation, and Absolute Velocity Determination

## 6. Coordinate and Time Transformations

## 7. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**The signal clock is based on the signal propagating in the distinguished reference system.

**Figure 3.**Comparison of time elapse: (

**a**) clock moving in relation to ether; (

**b**) motionless clocks in relation to ether.

**Figure 4.**Light clock: (

**a**) the path of light impulse seen from U′ system in which the clock is located; (

**b**) the path of light impulse seen from U system in which the light propagates.

**Figure 6.**Time dilation for four kinematics of the Special Theory of Ether. The graphs show the ratio of time t′ measured in the inertial system to time t measured in the universal frame of reference.

**Figure 7.**Inertial system moves in relation to the ether with speed v, while the ether moves in relation to the inertial system with speed v′ (v⋅v′≤ 0).

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**MDPI and ACS Style**

Szostek, R. Explanation of What Time in Kinematics Is and Dispelling Myths Allegedly Stemming from the Special Theory of Relativity. *Appl. Sci.* **2022**, *12*, 6272.
https://doi.org/10.3390/app12126272

**AMA Style**

Szostek R. Explanation of What Time in Kinematics Is and Dispelling Myths Allegedly Stemming from the Special Theory of Relativity. *Applied Sciences*. 2022; 12(12):6272.
https://doi.org/10.3390/app12126272

**Chicago/Turabian Style**

Szostek, Roman. 2022. "Explanation of What Time in Kinematics Is and Dispelling Myths Allegedly Stemming from the Special Theory of Relativity" *Applied Sciences* 12, no. 12: 6272.
https://doi.org/10.3390/app12126272