If your apparent relative time was seven days while the physical universe experienced 15 billion years, we can determine how close to the speed of light you were traveling using time dilation.
The time dilation formula from special relativity is:
t' = t / √(1 - (v^2/c^2))
Where: t' is the time experienced by the moving observer (seven days in this case) t is the time experienced by a stationary observer (15 billion years) v is the velocity of the moving observer c is the speed of light (299,792,458 meters per second)
Rearranging the formula, we can solve for v:
v = c * √(1 - (t'/t)^2)
Plugging in the values, we get:
v = 299,792,458 m/s * √(1 - (7 days / 15 billion years)^2)
Note that we need to convert the time units to seconds for consistency. 7 days is approximately 604,800 seconds, and 15 billion years is approximately 4.73 × 10^17 seconds.
v = 299,792,458 m/s * √(1 - (604,800 s / 4.73 × 10^17 s)^2)
After performing the calculations, the velocity would be extremely close to the speed of light, but not quite there. The exact value depends on the precise calculations and rounding used, but it would be a very high fraction of the speed of light.
Please note that this hypothetical scenario assumes a constant velocity throughout the entire duration since the Big Bang, which is not realistic as the expansion of the universe, gravitational forces, and other factors would influence the actual motion of objects.