Update vol-I-chap-5-sect-1.md

Author: morandrea

docs/vol-I/vol-I-chap-5-sect-1.md

@@ -142,7 +142,7 @@ Time is counted in the second context as a duration in terms of submultiples of
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 Let us consider first physical phenomena at the extreme of cosmic times and explain the meaning of Planck time. It is the time it takes light to travel one Planck length in vacuum $t_P = \sqrt{([\hbar G]/c^5)}$, where ℏ is the is the reduced Planck constant and represents quantum mechanics, 
-G is the gravitational is the gravitational constant and represents gravitation, and the speed of light  represents relativity. Planck length $l_P = \sqrt{([\hbar G]/c^3)}$ ~ 1.62 x 10−35 m  marks the boundary where these three theories collide. Distances smaller than one Planck length cannot be meaningfully defined with current physics. 
+G is the gravitational is the gravitational constant and represents gravitation, and the speed of light $$c = \frac{l_P}{t_P}$$ represents relativity. Planck length $l_P = \sqrt{([\hbar G]/c^3)}$ ~ 1.62 x 10−35 m  marks the boundary where these three theories collide. Distances smaller than one Planck length cannot be meaningfully defined with current physics. 
 
 At scales near quantum fluctuations of spacetime become important, there is no well-defined causal order, and “before” and “after” lose meaning. Below Planck time, the concept of time itself may lose physical meaning. It marks the scale where quantum gravity effects become dominant, gravity disrupts quantum measurements, motion cannot be defined and cause and effect blur; all of this indicates where new physics is required. Planck time defines the earliest meaningful moment in the universe’s history. It is the shortest “tick” the universe can meaningfully have, not because time stops, but because *our concepts of time stop working.*