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One of the issues of going past the speed of light is that M is inversely proportional to the square root of $c^2-v^2$. So the faster one goes, the smaller the denominator gets, the bigger the M gets, the more energy it takes to accelerate ... with an asymptote of $v = c$.

So could there be a (logical) way to bump speed by, say, 100 miles/hour at a time, so you instantaneously go from just under the speed of light to just above the speed of light?

And if it would be possible, what would an $i$ length or mass mean physically?

I know that in our universe it's quite impossible. My question is would such a concept make sense?

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    $\begingroup$ you know, a quantum leap covers the SMALLEST distance possible to exist. $\endgroup$ – Mindwin Dec 16 '16 at 21:41
  • $\begingroup$ Welcome to Worldbuilding, sppe, an interesting and tricky question. This could only happen in an alternative universe. To may need to clarify elements of your question. M, I presume, is mass, if so say so because it helps understand your hypothetical scenario. The only known instantaneous velocity change applies to photons when they are emitted where their velocity goes from zero to c. You are considering doing something similar, but not quite the same, to positive mass objects. A definite alternative universe situation. $\endgroup$ – a4android Dec 16 '16 at 22:26
  • $\begingroup$ @Mindwin No it doesn't. Kindly provide sources and citations for your assertion. The OP isn't suggesting quantum changes in distance, this concerns instantaneous quantized velocity changes. The smallest distance possible, conceptually, is the Planck length. Electrons shift considerably more than that when raised to a higher energy level inside atoms. $\endgroup$ – a4android Dec 16 '16 at 22:34
  • $\begingroup$ Because this is an alternative universe question this can be simply one of its properties. if instantaneous acceleration happens, then there is no reason, especially if you assume this is how your universe works, why vehicles couldn't "jump" the lightspeed barrier. The rest of your question is about what special relativity looks like at superluminal velocities. This is a controversial area of theoretical physics. $\endgroup$ – a4android Dec 16 '16 at 22:40
  • $\begingroup$ This is somewhat in the realm of the site but it would be best asked at Physics SE (although it may be rejected as too theoretical) $\endgroup$ – Zxyrra Dec 17 '16 at 5:01
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What you need is discreet time that means every change in velocity is an instantaneous one. Now when the huge force is applied in a single instant all the change happens in that instant. (or the next maybe)

The math might be expected to be non-recursive each tick or to use approximation at some point to keep the system solvable. There may be room for a bug or buffer overflow at edge cases.

Without the source code experimentation is the only way to analyze a bug. Caution: relying on undefined behavior is the leading cause of nasal daemons.

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