What is the physical cause behind time dilation?

[David Lewis]

It sounds like you are invoking a mechanical metaphor by using the word rotation, but I can't follow what you are saying (and I am not implying that is your fault). Can you clarify?

"Hermann Minkowski developed the concept of three-dimensional space combined with time to form a four-dimensional space-time. The importance of this concept is that... the effect of relative movement... appears in the same manner as does the effect of a rotation in three-dimensional space." -- Dr. Ron Davis

 

[sweet springs]

appears in the same manner as does the effect of a rotation in three-dimensional space."

Coordinate transformation for rotation is given by, say $\theta$ is rotaion angle,
$$x'=x\ cos\theta + y\sin\theta$$
$$y'=-x\ sin\theta + y\cos\theta$$
which satisfies the relation
$$x'^2+y'^2=x^2+y^2$$Similarly that of boost is given by, say $\theta=\frac{v}{\sqrt{1-v^2}}$ where dimensionless v is $v=V/c$
$$ct'=ct\ cosh\theta + z\sinh\theta$$
$$z'=-ct\ sinh\theta + z\cosh\theta$$
which satisfies the relation
$$c^2t'^2-z'^2=c^2t^2-z^2$$

cosh and sinh are hyperbolic cos and hyperbolic sin.

 

[sweet springs]

EDIT
For boost
$$tanh\theta=v=V/c$$,
$$\theta=tanh^{-1}v$$

 

[FactChecker]

It is just an explanation of how the space-time coordinate system that we perceive and measure things in works. I don't know if you want to call that a physical thing or a mathematical thing.

 

[sweet springs]

EDIT^2 to post#37
$$z'=ct\ sinh\theta+z\ cosh\theta$$

 

[David Lewis]

"It is sometimes said that length contraction occurs because objects rotate into the time axis. This is actually a half truth, there is no actual rotation of a three dimensional rod, instead the observed three dimensional slice of a four dimensional rod is changed which makes it appear as if the rod has rotated into the time axis. In special relativity it is not the rod that rotates into time, it is the observer's slice of the worldtube of the rod that rotates." https://en.wikibooks.org/wiki/Special_Relativity/Simultaneity,_time_dilation_and_length_contraction

 

[pervect]

A bit of a necropost (revival of a old thread, where the OP has most likely moved onto other topics) here , the latest post being on july 25 2019, the previous post on Nov 4 2018.