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 and moving with constant velocity with respect to each other, are to be connected by the Lorentz transformation (normalizing the speed of light to 1):
- , , .
The Lorentz transformation imposes time dilation with the apparent effect of slowing down the rate of time with the factor 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 to be real physical time, only a an apparent time. It was Einstein who took the “bold step” to view the transformed time 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.