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There's a couple questions that I've been trying to figure out that I have not been able to make much progress on.

1. Time Dilation

the equation states that T' = Lorentz Factor * T0

So the Lorentz factor will always be > 1 because v < c

So then, if, let's say, there's 2 events, A and B. There are 2 reference frames, a guy on Earth and a guy moving in a spaceship at a very high speed.

Event A: a stopwatch on Earth displays t = 0 s

Event B: a stopwatch on Earth displays t = 30 s

So, on earth, T0 = 30

Let's assume the lorentz factor = 2

Doesn't this mean, then, according to the equation, that the guy on the spaceship measures 60 seconds between events A and B? Doesn't this mean that in the duration of 30 seconds passing on earth, 60 seconds has passed for the guy in the spaceship, meaning that the guy on the spaceship is aging faster than the guy on earth, completely counter to the established theory?

2. Lorentz Contraction Derivation

I understand that to derive the Lorentz contraction, you use

l0 = x2-x1 reference frame of earth

l = x2' - x1' reference frame of spaceship

so then, since x1 = L (x1' + vt')

x2 = L (x2' + vt')

you can write x2-x1 = L (x2'-x1')

So, l = l0/L, the Lorentz contraction formula.

My question is, why couldn't you have also used the reverse set of equations

x1' = L (x1-vt)

x2' = L (x2-vt)

to get x1'-x2' = L (x1-x2)

and then, in this case, l = l0 * L, which is the exact opposite result?

I think I'm probably thinking about this the wrong way, so if someone could give me some help that would be really appreciated.