> I've always thought that Planck's constant defines the discreteness of time
Most certainly not! Amusingly, this is an incredibly common assumption that undegrad physics students I teach make, probably because of some pop-sci exposure.
All we know is that the Planck constant defines a scale where we do not know what happens. This is a scale at which we can see that the math behind our current theory breaks, but we have absolutely no reason to expect that the way to fix that math is to use some form of discretization related to that constant.
The "quantum" in quantum mechanics really should not be taken that literally. Photons as described by quantum mechanics for instance do not have a discrete spectrum (nothing literally "quantum" there).
There are fascinating conjectures on why maybe the Plank scale should be discrete, but they are way more subtle than "quantum mechanics is discrete" (because it is not always discrete).
Most certainly not! Amusingly, this is an incredibly common assumption that undegrad physics students I teach make, probably because of some pop-sci exposure.
All we know is that the Planck constant defines a scale where we do not know what happens. This is a scale at which we can see that the math behind our current theory breaks, but we have absolutely no reason to expect that the way to fix that math is to use some form of discretization related to that constant.
The "quantum" in quantum mechanics really should not be taken that literally. Photons as described by quantum mechanics for instance do not have a discrete spectrum (nothing literally "quantum" there).
There are fascinating conjectures on why maybe the Plank scale should be discrete, but they are way more subtle than "quantum mechanics is discrete" (because it is not always discrete).