Wikipedia informs us

In the theory of relativity, time dilation is an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at a different rate when compared to a second observer’s own equally accurate clocks. This effect arises neither from technical aspects of the clocks nor from the fact that signals need time to propagate, but from the nature of space-time itself.

According to Einstein’s special theory of relativity space-time event observations in two space-time coordinate systems $S:(x,t)$ and $S^\prime :(x^\prime ,t^\prime )$ moving with constant velocity $v$ with respect to each other, are to be connected by the Lorentz transformation (normalizing the speed of light to 1):

$x^\prime = \gamma (x -vt)$ , $t^\prime = \gamma (t -vx)$ , $\gamma =\frac{1}{\sqrt{1-v^2}}$ .

The Lorentz transformation imposes time dilation with the apparent effect of slowing down the rate of time with the factor $\gamma$ in a moving system from the point of view of a stationary system, as illustrated in the above picture (no acceleration despite the jet engine). This effect is mutual and perceived the same way in both systems.

The question of the physical reality of time dilation including the related twin paradox has never been answered by physicists, but was defined to be a non-question after Herbert Dingle was muted in 1960s.

But the question remains: Is it true that moving clocks really slow down, or is it just an illusion? Is it like two people viewing each other at distance, both having the impression that the other is smaller, while they are equally tall in reality?

They answer can only be: Yes, it is an illusion. A Stubbornly Persistent Illusion in the words of Einstein.

Why? Because the rate of time is measured by clocks and clocks are mechanical devices, classical or quantum mechanical, and it is unthinkable that the rate of a clock can be affected by motion with constant velocity because mechanics is invariant under translation with constant velocity.

According to Leibniz Principle of Sufficient Reason, no physical event can happen without a sufficient reason. But there is no reason whatsoever for the mechanics of a clock to be affected by translation with constant velocity. And so, without reason there can be no physical time dilation, only apparent fictitious illusion.

For a more precise argumentation see Many-Minds Relativity. Recall that Lorentz and Poincare who introduced the Lorentz transformation before Einstein, did not consider the transformed time $t^\prime$ to be real physical time, only a an apparent time. It was Einstein who took the “bold step” to view the transformed time $t^\prime$ as real time, against the view of Lorentz in particular.

Boldness is often presented as Einstein’s strongest virtue, but boldness may border to temerity.

4 Comments

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Michael
January 25, 2012

Please, I am not very expert on this topic but, as far as I know, the speed prolongs the life of particles: when they are accelerated, their life grows many times, even thousands of times.
Is it a physical or mathematical effect?

Reply
- Richard T. Fowler
  January 25, 2012
  
  Michael,
  
  Claes’ answer can be found in this article:
  
  http://claesjohnsonmathscience.wordpress.com/article/many-minds-relativity-yvfu3xg7d7wt-5/
  
  which I quote here:
  
  ——–
  The big problem with Einstein´s special theory of relativity is that it is non-physical, which can be seen from the fact that the x’ – axis is not parallel to the x – axis, in contradiction to physical situtation considered, where X is an observer with an x-axis and X’ and observer with an x’ -axis moving along the x-axis with speed v.
  
  Einstein picked up the Lorentz transformation form the physicist H. A. Lorentz, who when introducing it carefully explained that the transformed time t´ – coordinate should not be interpreted as physical time .
  
  What Einstein did was precisely to do that! And to remove the aether completely.
  
  The Lorentz transformation contain effects of length contraction and time dilation, and the question from start was if these effects are real physical effects or just mathematical conventions/definitions/agreements.
  
  This was not made clear by Einstein, and nobody else, and has caused the confusion surrounding relativity theory still today, with clocks slowing down and space ships being compressed by motion with constant velocity contrary to all logic.
  ——–
  
  (Author’s emphases.)
  
  And I single out Claes’ next sentence with my own boldface emphasis:
  
  “It has gone so far that the lack of logic is used as an argument that the theory is correct.”
  
  I would have inserted the word “now” as in, “is now used”.
  
  Either way, the meaning is clear.
  
  RTF
  
  Reply
- Rickard Norlander
  January 28, 2012
  
  Michael, if you are not an expert on this topic, I advise you to first learn the mainstream theory. Only then are you ready to read about alternative theories.
  
  Reply
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