I don't want your cookie. It's probably what caused that "typo."
More fibre needed.

There's no minimum energy, E, nor minimum frequency, f
I don't think this is right. I'm not trying to outsmart you or anything, I'm not waving my dick about. I just believe this contradicts Planck's discovery, where he assumed a minimum energy value to predict the black body spectrum, and his "hack" solved the problem of predictions failing to match observations, aka the Ultraviolet Catastrophe. The "hack" in question was to assume that energy is quantum, that it is found in integer values. Planck himself expected his "constant" to be zero, but instead it was a very small but non-zero number. This was the birth of quantum mechanics. Well, perhaps not the birth. The maturity. Planck's work was built on foundations laid during the 19th century, but his constant was confirmation that light comes in discrete packets - photons - and allowed physicists of the day to develop quantum theory.



I could definitely be jumping to conclusions, failing to fully understand what Planck actually discovered, but it seems to me to be the first concrete evidence of the quantum nature of the universe, including space, time, length, and indeed energy. That is, a minimum integer value. It's so tiny that from the pov of the macro world, it appears infinitely divisible, but this doesn't seem to be the case.

By the way, I made a schoolboy error with my assumptions. Where I say "minimum frequency", I actually mean "maximum frequency", or "minimum wavelength". But of course, shorter wavelengths mean more energy, not less. So there would likely still be a "minimum frequency" associated with the lowest energy level possible for a photon. But that "minimum frequency" or "maximum wavelength" could be larger than the universe, frankly I can't even begin to guess at that.