Two twin clocks are examined to illustrate that time displayed on any clock is an invariant in Lorentz Transformation, which contradicts the time conversion formula in Lorentz Transformation. Therefore, this contradiction has proved that Special Relativity is wrong.

Since Einstein published the theory of Special Relativity in 1905, many people have been struggling in understanding the meaning of time and space and many other people are fascinating on time traveling: imagining traveling back to the past and forward to the future. However, all these now seem just pure imagination and will never happen in the physical world. According to Special Relativity, there is no time dilation that can be observed on any clock. That is, no matter how fast a clock moves, the display of time on the clock will never change after Lorentz Transformation. Here is my reasoning to show the contradiction of Special Relativity.

Assume there are two clocks (clock A and clock B) which were exactly at zero time (t = t’ = 0) and zero position (x_{A}= x’_{A}= x_{B}= x’_{B}= 0) in both reference frames: the inertial reference frame attached to clock A (called frame A) and the inertial reference frame attached to clock B (called frame B) when the two clocks started moving away from each other at a constant speed v in x-direction (note: variables with apostrophe are referred in frame B). Each clock uses two different ways to display its time: one is an analog way in which its time is displayed as the position of a ball moving at a constant speed 1 on a ruler in y-direction and the other is a digital display on which time is shown as a number. The core of such a clock can be any existing clock including the most accurate atomic clock. Using a moving ball on a ruler in y-direction is just an intuitive way to show that the displayed time of a clock will not change after Lorentz Transformation, just the same as the image of the time shown on its digital display.

After the time lapse in frame A equals t, clock B has moved a distance x_{B}= vt and its ball has moved a distance y_{B}= t in frame A while clock A itself remains still (x_{A}= 0) and its ball has moved a distance y_{A}= t. Therefore, the two clocks have the same time shown on their digital display. According to special relativity, the ball of clock A and the ball of clock B in frame B have time lapses and positions:

(1) x’_{A}= γ(x_{A}– vt) = - γvt

(2) t’_{A}= γ(t – vx_{A}/c^{2}) = γt

(3) y’_{A}= y_{A}= t

and

(4) x’_{B}= γ(x_{B}– vt) = 0

(5) t’_{B}= γ(t – vx_{B}/c^{2}) = γ(t – v^{2}t/c^{2}) = γt(1 – v^{2}/c^{2}) = t/γ

(6) y’_{B}= y_{B}= t

where γ = 1/(1 – v^{2}/c^{2})^{1/2}.

Equation (2) and (5) show there is a time dilation of a moving clock in Special Relativity.

From Equation (3) and Equation (6), we have y_{A}= y’_{A}= y_{B}= y’_{B}= t, which has confirmed that time shown on both clocks will not change after Lorentz Transformation as y' is t' according to the definition of the clocks. This matches the images of the time shown on the digital display of the two clocks because the number on an image will not change after Lorentz Transformation. However, Equation (2) states that the time of clock A has been increased by a factor of γ and Equation (5) states that the time of clock B has been decreased by the same factor γ after Lorentz Transformation. Since time in physics is defined by its measurement: time is what a clock reads^{[1]}, therefore, Equation (2) and Equation (5) are wrong, which confirms that Special Relativity is wrong.

People may argue that in the above derivation, y’_{A}= u’_{A}t’_{A}and y’_{B}= u’_{B}t’_{B}which are not the same as the times in the moving reference frame as u’_{A}and u’_{B}are no longer equal to 1 in the moving reference frame (i.e., u’_{A}= 1/γ and u’_{B}= γ). This argument has admitted that what a clock reads is not the time in Special Relativity and all moving clocks will fail to tell the correct time in Special Relativity. Moreover, this argument has also mystified the time in Special Relativity and made it unmeasurable by clocks.

Above derivation has shown that in Special Relativity, a moving reference frame has a time slower than the time on the static reference frame, but every process in the moving frame has a speed or rate faster than that in the static reference frame. Therefore, the observed result of any process which is the result of speed or rate multiplied by time will be the same no matter at what speed the reference frame moves because the increase of the speed or rate and the decrease of the time have canceled their effects by each other in the multiplication. Therefore, time dilation will never be noticed in the physical measurement as predicted by Special Relativity. Therefore, the introduction of the mixed space-time in Special Relativity becomes an unnecessary manipulation of physics. All experiments with time measured by physical clocks do not verify the predictions of Special Relativity.

Many people believe that according to Special Relativity, space traveling will make the twin brother younger than his twin brother remaining on the earth. Actually this will never happen even in Special Relativity. Though the time in the fast moving rocket is expanding, the aging speed of the traveling brother is also increasing. The result of the age of the traveling brother remain the same as his twin brother on the earth because the faster aging speed has canceled the effects of the time dilation caused by motion. Similarly, the times displayed on clocks moving at different speeds will never show any differences or time dilation because the clock tick rate has increased by motion which will cancel the effects of time dilation in the final display of the time.

Though Special Relativity is beautiful in mathematical formulation, it contradicts itself in the prediction of time dilation in the physical world. There is no such thing called time dilation in the physical world. People will never be able to travel to the past or future.

References

1. Considine, Douglas M.; Considine, Glenn D. (1985). Process instruments and controls handbook (3 ed.). McGraw-Hill. pp. 18–61. ISBN 0-07-012436-1.