On time dilation and length contraction

[jbriggs444]

Another question is could we have change of mass in the measurements while length contraction happens?I think it stays the same according to the math.But could it only in the measurements show this?

By mass we conventionally mean the invariant mass. The term "invariant" means that it does not change depending on one's choice of reference frame. Length contraction, on the other hand, depends on reference frame.

So no, length contraction has no effect on mass. Nor do measurements referenced against any particular reference frame show any effect on mass.

 

[Dale]

Could time be a generalisation of a spatial coordinate?Spatial coordinates show the position but time coordinate changes and moves only as a fourth dimension to the future naturally.

See $dt$ in the first equation in post 12.

 

[jbriggs444]

Could time be a generalisation of a spatial coordinate?Spatial coordinates show the position but time coordinate changes and moves only as a fourth dimension to the future naturally.

If we draw a "timelike" curve or follow the path of a massive particle and if we parameterize that curve (say with parameter $\tau$) and if we use a reasonably ordinary coordinate system then the time coordinate t will always increase along with the $\tau$ parameter, yes.

Technically, it is possible to reverse the direction of the curve so that the time coordinate always decreases with increases in the $\tau$ parameter, but that changes nothing physical.

 

[Marcus Parker-Rhodes]

As a total amateur, my guess is that Universe Function is asking for a way of calculating the "Speed Of Time" (can I say that?) in locations where the average gravity is different from where we are standing. For example, something that has been been puzzling me is that the edges of our galaxy appear to move faster than they should. The centre is deep in a gravity well where passes more slowly than at the edges, which could explain why the galaxy appears a more rigid structure than it really is.

 

[jbriggs444]

As a total amateur, my guess is that Universe Function is asking for a way of calculating the "Speed Of Time" (can I say that?) in locations where the average gravity is different from where we are standing.

Gravitational time dilation scales with gravitational potential (how deep you are in a gravitational well) rather than with gravitational acceleration (how hard gravity is "pulling" on you where you are).

In the case of galaxies, clocks in the core run only a fractional percentage point slow when compared to clocks on the rim.