If time time dilation is infinite at v=c, then time stands still only

[jmonlive]

How can speed of light be absolute yet that fact and relativity of sublight speed implies relativity of space and time intervals; if time time dilation is infinite at v=c, then time stands still only from that reference frame, but light takes a longer time relative to any other reference frame (thought it isn't at rest relative to our reference like any sublight speeds-to-rest reference-frame transform)?

 

[ghwellsjr]

How can speed of light be absolute yet that fact and relativity of sublight speed implies relativity of space and time intervals; if time time dilation is infinite at v=c, then time stands still only from that reference frame, but light takes a longer time relative to any other reference frame (thought it isn't at rest relative to our reference like any sublight speeds-to-rest reference-frame transform)?

Part of the definition of an Inertial Reference Frame (IRF) is that light travels at c so how can you transform an IRF to v=c? If you try to do it, you will see that you have to divide by zero which isn't allowed. So there is no such thing as an IRF where time stands still. There's no such thing as time dilation being infinite. There's no such thing as light taking a longer time (traveling slower than c, if that's what you mean).

By the way, what is sublight speed?

 

[Nugatory]

How can speed of light be absolute yet that fact and relativity of sublight speed implies relativity of space and time intervals; if time time dilation is infinite at v=c, then time stands still only from that reference frame, but light takes a longer time relative to any other reference frame (thought it isn't at rest relative to our reference like any sublight speeds-to-rest reference-frame transform)?

The Lorentz transformations which lead to the time dilation and length contraction formulas are derived from the assumption that the speed of light is the same for all observers. Google will find you many good derivations.

Time dilation is not infinite at $v=c$; it's not defined at all because there can be no reference frame whose origin is moving at $c$ relative to the origin of some other reference frame, and therefore no situation physical situation in which the $v$ that you might plug into the time dilation and length contraction formulas could be equal to $c$. We have a FAQ that you might want to take a look at: https://www.physicsforums.com/showthread.php?t=511170