Why is physics quantized?

This equation is the general form of a Wiener process, in economics it is known as the no arbitrage condition. p(x,t) is a polynomial with integer, positive coefficients and gives us the range of combintations or arrangements that can be made at any given x. In physics it gives the Wave Solution in Schrodinger.

What it t?

Physicists call it time, but it really is a global variable representing steps along a yard stick.  The Polynomial in t tells us what notches are on the yard stick and their size.

Why are notches separated?

Because the yardstick has to be kept updated, so a uncertainty constant is maintained between notches in which yard sticks can slightly shift their nothes as needed to maintain the boundary conditions.  This is the bandwidth needed to update the decoding table in a Shannon solution.  That buffer is the fine structure constant in the atom.

This happens because there are no fields in nature, everything is local.  And the locality constraint requires yardstick updates, and that means an uncertainty buffer, and that means we a separation between particles and waves.  All of this derives from the locality constraint, and the locality constraint requires conservation of the 'grid' and that implies Lucas numbers when we work the hyperbolic form. That is why the set of Lucas angles along Tanh gives Pi/2 and the fine strcuture.

An adiabatic process is one that occurs without transfer of heat or matter between a system and its surroundings. A key concept in thermodynamics, the adiabatic process provides a rigorous conceptual basis for the theory used to expound the first law of thermodynamics.

That adiabasis is in the fine structure constant.  It is all having the spectrum to about update the yardstick in measure theory.