Now I put that same energy into a relativistic system. The velocity I achieve isn't as high (and perhaps noticeably different, if the energy/mass ratio is large) so I don't travel that same distance as fast. However, the distance I need to travel (according to my system's frame of reference) is decreased due to the increased velocity. So the time it appears to take to travel that distance (from the moving object reference frame) isn't just the reduced velocity divided by the original distance. I did some math to see what the comparison was, and I was surprised by the result. I was hoping people here could comment on my math and my approach as I am not confident in either. I do static structures for a living: not relativity.

I ran some mathcad code for a Newtonian velocity of 1.5*c, I've tried to translate as best as possible into forum readable code (x

_{n}refers to "Newtonian" values and X

_{r}refers to "relativistic" values)

d

_{0}= 1*ly = 9.461e15 m

m

_{0}= 1 kg

c = 2.998e8 m/s

Newtonian:

v

_{n}= 1.5*c

t

_{n}= d

_{0}/v

_{n}= 2.104e7 s

E

_{n}= 1/2 * m

_{0}* v

_{n}

^{2}= 1.011e17 J

Relativistic:

E

_{r}= E

_{n}+ m

_{0}*c

^{2}

rho

^{2}*c

^{2}= -m

_{0}

^{2}*c

^{4}+ (m*c

^{2})

^{2}

E

_{r}= sqrt(rho

^{2}*c

^{2}+ (m

_{0}*c

^{2})

^{2})

==> MATH <==

v

_{r}= c * sqrt(E

_{r}

^{2}- c

^{4}* m

_{0}

^{2}) / E

_{r}

v

_{r}= 2.645e8 m/2 = 0.882 * c

d

_{r}= d

_{0}* sqrt(1 - v

_{r}

^{2}/ c

^{2})

d

_{r}= 4.452e15 m = 0.471 * ly

t

_{r}= d

_{r}/ v

_{r}= 1.683e7 s

t

_{n}/ t

_{r}= 1.25

So basically, it actually takes less time (as observed by the traveler) to travel in a relativistic universe as compared to a Newtonian one. Thoughts or comments?