system
Given the following post, respond as if you're commenting on Reddit:
human
Pauli exclusion principle: how fast does 'this state is occupied' information travel?

Assuming it travels with c, does this mean that PEP can be violated for short amount of time?
gpt
As the other poster stated, it's a man-made rule to explain what we observe. But the math tells us that this information is embedded in a field. So there is no "this state is occupied" information. You just have a wave behaving as it naturally will. 

Unfortunately, in this case, the wave is a bit too hard to think about intuitively to give a satisfying explanation as to why it won't. You merely learn to accept it as a physicist that it won't. 

Fermions are described by what we call "spinor" fields. A spinor is vaguely described as the square root of geometry the same way the imaginary number `i` is the square root of a number. We find mathematically that spinor's don't commute with each other the way a normal number will. IE 3 x 4 = 4 x 3 but ab !=  ba if a & b are spinors. Rather ab = - ba. 

A spinor-valued field fundamentally has this property. So what we find is that a normal classical field is perfectly willing to double itself (f*f = f^(2)) but a spinor field can't since a*a = -a*a and the only number that equals negative itself is 0. So we simply find that this field won't let itself double. 

So a quick example. An ocean wave can be simply compared to a spin-less boson's field. An ocean wave is obviously willing to cross another wave and the amplitudes of the two waves just combine. But a spinor field won't!