A speculation (edited 15 December 2014):

The Geometry Of Space & The Aging Twins Paradox

Each bit of matter has it’s own time. This was proven mathematically by Einstein and experimentally by researchers. The fact that each bit of matter has it’s own time dilation which is independent from any other bit of matter means that a universal time constant is impossible. I do not accept that “time” is a fourth dimension. I accept that “time” is a dimension but I postulate that “time” is one of the three dimensions. The dimension of length contracts as 3D matter approaches the speed of light and “time” slows. What we perceive to be “time” is actually the dimension of length. Having postulated and accepted that “time” is the dimension of length then a universal “time” constant does not exist because the dimension of length changes with changes of acceleration especially when approaching the speed of light. The three dimensions which we experience comprise a bandwidth of dimensions which involve movement. The lower limit of the bandwidth is zero movement which is found at a temperature of absolute zero where all movement ceases. The upper limit of the bandwidth is 3D matter moving at the speed of light where the dimension of length (“time”) contracts, reaches zero, and is no longer three dimensional. Outside of this bandwidth (3D existence) the effects we perceive as “time” do not exist.
What determines which of the three dimensions is the dimension of length? The concept of three dimensions is a stick figure representation of existence which is convenient for human speech and interpersonal communication. Every point in space is at the center of it’s own universe in isotropy. Imagine a stick figure representation of space using ray lines in space emanating from a point in every direction spherically. Now imagine ray lines emanating in every direction spherically from another nearby point in space . The ray lines which are between the two points will crisscross. Now imagine this happening at every point in space with ray lines emanating spherically from every point in space. Now we have an unimaginably complex fabric of space. Space is expanding from every point in space so that there is a dynamic delta in the fabric of space. As a 3D object moves through this geometry (space) the effect in the direction of travel has the object both increase and decrease in size relative to the surrounding space as it moves from point to point (the diverging and converging lines emanating from every point in space). As the object moves through space it is moving from one universe to the next as it passes each point in space with each point being at the center of it’s own universe. This could be referred to as the multiverse. The dimension of length is given priority amongst all other dimensions by the special property of movement. Moving matter has, as a property, the dimension of length in the direction of travel. As matter moves it is constantly being renewed at the quantum level so that in a curved path the dimension of length constantly reorients itself to the direction of travel. I stated in previous writings that “time” is the velocity/distance of 3D matter relative to the velocity/distance of other 3D matter. For example when two bits of matter are traveling together, the relative time dilation between the two is 1:1. As soon as there is a divergence in the direction and/or the velocity of the two bits of matter relative to each other the relative time dilation between the two changes to some ratio which is not 1:1.
The relative difference in aging of twins in the “twins paradox” thought experiment where one twin travels at a significant percentage of the speed of light and the other twin stays at rest has been proven to be real. This means that “time” is a physical manifestation within three dimensional existence. What happens to the twins when one is at rest and the other accelerates to a significant percentage of the speed of light? Nothing happens to them! They each happily experience their own “time” dilation without any problem. The relative difference in aging is the result of the relative movement through space between the two twins.
An hour is one twenty-fourth of one rotation of the Earth on it’s axis. At the equator the velocity/distance of the surface of the Earth, during one hour, is faster/longer than the velocity/distance of the surface of the Earth, during one hour, at the 45th parallel which is slower/shorter . The velocity/distance of the hour hand, during one hour, on a watch or clock is also slower/shorter than the previous two velocity/distance instances. Considering two clocks one physically larger than the other with both having hour hands, the hour hands will move at different rates (faster for the large clock and slower for the small clock) All above examples exist in the same relative space, are synchronized, and originate and destinate for the same arbitrary period of “time”, namely, one twenty-fourth of one rotation of the Earth on it’s axis or what human beings decided to name an “hour”.
I stated above that ” As a 3D object moves through this geometry of space the effect in the direction of travel has the object both increase and decrease in size relative to the surrounding space as it moves from point to point (the diverging and converging lines emanating from every point in space).” As fantastic as this may seem there is some logic to it. The above example of the two clocks of different sizes which have hour hands moving at different rates is given in the context of being in the same relative space. The differently aging twins in the twins paradox are not in the same relative space. They actually have different sizes relative to each other due to the movement through space of one of the twins. The moving, “smaller” twin experiences a slower rate of “time” than the “resting” “larger” twin.

(credit: Pierre J. Hébert/Blogger)