# Traversing a proton within the Planck time

If I could travel a super small distance (proton) in an even smaller time (Planck time), how long would it take me to cross the observable universe?

One proton is $$8.414 \cdot 10^{-16}$$ meters wide, and one Planck time is $$5.391247 \cdot 10^{-44}$$ seconds. This means that we are traveling at $$\dfrac{8.414 \cdot 10^{28}}{5.391247} = 1.5606779 \cdot 10^{28}$$ meters per second. Dividing by $$299792458$$ m/s, or $$c$$, we get $$5.205861 \cdot 10^{19}c$$. The observable universe is 93 billion light years in size, so it would take $$\dfrac{93 \cdot 10^9 \cdot 86400 \cdot 365c}{5.205861 \cdot 10^{19}c} \approx 0.0564$$ seconds to traverse the observable universe. This obviously is impossible, as faster-than-light travel (username checks out) violates the rules of general relativity (as we know it).