We will not go into a detailed explanation of N.D. Mermin’s light clock experiment here; since, we assume that the reader is already familiar with this experiment. We will quickly re-construct it in order to present the relation between the clock-ticks and the intrinsic circulations in the confinement volume. Please note that we consider this experiment as a thought experiment.

Suppose that there are two observers (A and R) in front of a lengthy mirror. The distance between the stationary observer A and the mirror is 30 times longer than the size of A’s confinement volume (r_A) (such as electron Compton wavelength) in its frame (L_A=30 r_A). Observer R is accelerated and moves away from A with the speed 0.8c in a parallel direction to the mirror.

Figure 6.15 Observer A is stationary, and observer B moves with 0.8c, L_A=30 r_A

Size of R’s confinement volume (r_R) reduces to 0.6r_A with the acceleration as a function of the gamma factor. (We will present how we derive gamma factor at the end of this chapter.)

E 6.12 β is the dimensionless ratio of v/c, and in our case it is 0.8 (0.8c/c)

Simply according to our definitions, observer A assumes that the distance spatial metric and timeas clock-ticks contract in R’s frame relatively (with gamma factor=1.66).

However, Geometric Generalization suggests another relation beyond Mermin’s original experiment. According to this paper, while light pulse travels back and forth in front of a mirror, the exact same distance is circulated in the confinement volumes. Actually, this conclusion is the basis of this paper’s hypothesis.

Hence, in practical terms, observer A makes 60 circulations (Nrotations) (30x2), while light pulse bounces from the mirror where as the situation is rather different for observer R. Light needs to travel a longer distance in space-time in order to meet observer R again. As a result, observer R makes more intrinsic circulations (Nrotations) for a single bounce.

Mathematically, it is easy to calculate the new increased amount of circulations (Nrotations). We simply equalize the distance light pulse travels to the helical path of the intrinsic circulations. Please note that the radius of the helical path is equal to 0.6r_A, and the height of the helix is equal to the distance observer R travels with the speed of 0.8c in a single bouncing of light pulse from the mirror. Let us call the extended distance that light pulse travels as L_R.

Figure 6.16 Note that the distance light pulse travels is equal to the length of the helical path

E 6.13

According to above equation, we find that L_R is increased to 50 r_A, and observer R makes 100 circulations (Nrotations) (50x2) instead of 60.

We can accept a single bounce of light pulse from the mirror as a single physical event, which is in accordance with N.D. Mermin point of view. However, we surprisingly see that while observer A makes 60 circulations (Nrotations) for a single bounce, observer R makes 100. In other words, for each 100 circulations, observer R lives only one (1) event, while observer A lives 1.66 events, which means that the physical occurrence of events decreases in R’s case within an equal amount of intrinsic circulations (Nrotations).

In fact, the contraction in our metric (timeas clock-ticks) also describes this relativistic consequence. However, this conclusion is important as it gives the exact description of the mechanism of time dilation at the smallest scale.

Please note that although the quantity of clock-ticks decreases in observer R’s frame, distancespatial metric also decreases with the same ratio. As a result, the speed of light is kept constant for both observers.

Careful readers may have realized that if observer R does not know its history of acceleration and assumes its own inertial frame as motionless, then observer R will not be able to realize that the metrics in its frame are relatively contracted to observer A. Einsteinian relativity is also based on the postulate that the state of motion cannot be determined by local mechanical experiments, and observers can only measure their velocity relative to another body. Interestingly, our definition of timeas clock-ticks has interesting results. The mechanism that we discussed here describes the synchronized mechanism at the particle scale between relative observers. According to our definition of simultaneity, intrinsic circulations in confinement volumes of relative observers are synchronized; however, the occurrence of the events varies relatively in this synchronized mechanism. We detail the “Exact Meaning of Relativity” in Section 9.3.