dear Manooch,
welcome to Toe quest. In our currently accepted laws of physics there is a "law" which says your velocity can only be so great, but there is no such law which limits our rate of acceleration. So theoretically you may reach any acceleration you choose, according to known laws. Now, if you were to reach such a high acceleration that, upon reaching that acceleration, you would go from your current speed to the speed of light in a planck second or less, assuming constant acceleration, then you would be acting outside the known laws of relativity. You would essentially have an absolute rate of acceleration that would theoretically allow you to travel faster than the speed of light.
Also if you think of absolute continuous time as being smooth then there is stuff happening in between each planck second. In other words, in the highest density, where the speed of light is 1/0, there is no planck second. It is essentially 0.


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