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

Author: morandrea

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

@@ -144,9 +144,9 @@ Time is counted in the second context as a duration in terms of submultiples of
 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 $$c = \frac{l_P}{t_P}$$ 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 $t_P 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.*
+At scales near $t_P$ 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.*
 
-Planck epoch refers to the first $t_P  after the big bang. During this epoch, spacetime itself is believed to have been highly quantum and fluctuating. No existing theory can reliably describe physics earlier than this time and our current physical theories no longer make reliable predictions. Before this epoch there is no classical spacetime and no known physical 
+Planck epoch refers to the first $t_P$  after the big bang. During this epoch, spacetime itself is believed to have been highly quantum and fluctuating. No existing theory can reliably describe physics earlier than this time and our current physical theories no longer make reliable predictions. Before this epoch there is no classical spacetime and no known physical 
 
  laws are useful; furthermore, quantum gravity dominates. At the scale of Planck length quantum 
 fluctuations of spacetime become so strong that classical geometry breaks down.