4.11 Light clock and time dilation

Background and actual explanation

Besides transverse Doppler Effect already explained, in special theory of relativity time clock and dying muons are other proofs of time dilation.

Time dilation equation can be derived using the concept of a light clock which is an imaginary device composed by a blip of light and two mirrors facing each other like in fig.

If the two mirrors are a distance d apart, the round trip distance for the blip from one mirror to the other mirror and back is 2d. Since we know the light travels with speed c, we find the round trip time to be 2d/c, so this is the time between clicks.

Let us now consider two observers S and S’, each equipped with a calibrated inertial frame of reference, and a light clock.

Figure 1

One observer (S) look the light clock and sees the light pulse moving backwards and forwards between the same two points. The same observer (S) sees the light pulse moving in a zigzag fashion between the moving mirrors of the S’ light clock. The length of each leg of the zigzag path is greater than the distance between the two mirrors. If both observers are to measure the same universal speed of light, then time must be slowed in one observer's system relative to the other observer's system

From Pythagoras theorem, then,

c²t²=v²t²+d²

so

t²(c²-v²)=d²

or

t²(1-v²/c²) =d²/c²

This means that S sees S’ light clock to be going slow, and reciprocally S’ sees S light clock, due to the longer time between clicks, compared to his own identical clock.

Figure 2

Proposed interpretation

Judging from special relativity point of view the up presented demonstration is inconsistent and absurd.

In terms of special relativity the transfer of information between referential must be less or equal with the light speed. Let’s suppose at t= 0, both referential are at x=0, and in the same moment in both referential the photons are emitted. S’ has a drift velocity so S can’t see from his referential the S’ clock. It is necessary another photon to leave the S’ when a cycle of light clock is finished, to be sent in the direction of S in order to inform him about this fact.

Figure 3

If we make the analyze from S’ referential, for him, S referential is moving with speed v in opposite side, and also this observer need another photon from S, when a cycle of light clock is finished, to be emitted in the direction of S’ in order to inform him about this fact.

Figure 4

For both observers, let’s neglect the time interval necessary for seeing the clocks.

An observer will measure for his own clock (observer O, in referential S) a time of light trip of t = 2d/c. The same observer O, will measure for the clock situated in S’, a time interval equal with the sum of time necessary for light blip to travel between moving mirrors and the supplementary interval of time necessary for information to travel back to the S inertial.

The O’ observer will consider that O observer and his clock as moving with –v speed like in fig 4, so he will see the zigzag of O light blip in opposite direction on the x axe.

For his own clock, O’ observer, will measure a time of light trip of t = 2d/c. When the observer O’ look at the O clock, the time measured by O’ will be the sum of time necessary for light blip to travel between moving mirrors and the supplementary interval of time necessary for information to travel back to the O’ observer.

Due to the symmetry of motion for both observers O and O’ the same interval of time is measured when O looks at O’ clock and the same interval of time is measured when O’ looks at O clock, and of course this interval is different from the interval time of stationary clocks.

In proposed theory there is no real time dilation or space contraction. The difference of time measured for the same clock in stationary and moving referential is due to the characteristic of physical process involved in time measurements and speed of transfer information between referential.

Due to the symmetry of path, both observers measure for moving clock a greater time then calibrated clock from their referential, but also a greater time that predicted by special theory of relativity. Of course the measured time is composed from an intrinsic time of event evolving and an actualizing time.

The relativistic demonstration is absurd because suppose a transfer of information with infinite velocity between two different referential and overlap to Galilean relativity concepts; another possibility needs a strange observer able to be simultaneously in different referential, which is a physical impossibility.

The up presented experiment demonstrates that measured time is affected by physical processes. It is necessary to reinforce the idea that the clock and the process of time measuring is affected by certain specific conditions and not the ,,time” itself. In any case the up presented experiment, does not means a time modification relative to any observer.

More … in the book…..