Regarding the relative time difference of an object at a higher speed, I will explain the following. It is actually the quantity [integral] m dt, or simply m*t, that is conserved in all reference frames. Thus, when mass increases, the apparent time appears to decrease:
m0*t0 = m1*t1
m0 = rest mass
m1 = m0 / sqr(1 - (v/c)^2)
t1 = (m0 / m1)*t0 = sqr(1 - (v/c)^2) * t0
t1 <= t0
Remember that this is t and not dt. t0 & t1 represent the actual position in time of an object relative to the other object or reference frame. This isn't very useful.
What should we call the quantity m*t? Is there already a name for it?
m0*t0 = m1*t1
m0 = rest mass
m1 = m0 / sqr(1 - (v/c)^2)
t1 = (m0 / m1)*t0 = sqr(1 - (v/c)^2) * t0
t1 <= t0
Remember that this is t and not dt. t0 & t1 represent the actual position in time of an object relative to the other object or reference frame. This isn't very useful.
What should we call the quantity m*t? Is there already a name for it?