Hi Ken,
I think my response to your email is more appropriately posted here, since others may benefit by our discussion.
You write,
" I'm quite interested in new ideas of how to get quantum behavior to emerge from classical fields".
This was also what attracted my attention to your essay, as this is exactly what I am doing in my essay. What I mathematically demonstrate is that Planck's Law for blackbody radiation can be derived using continuous processes, without using energy quanta and statistics. Since Planck's Law is at the very roots (historical as well as theoretical) of modern physics, this result is very significant.
But more than that! In my essay I show that Planck's Law is an exact mathematical tautology that describes the interaction of measurement! This, in my view, explains why Planck's Law fits so remarkably well the experimental data. Check the blackbody spectrum obtained from measurements and obtained from Planck's Law.. "The FIRAS data match the curve so exactly, with error uncertainties less than the width of the blackbody curve, that it is impossible to distinguish the data from the theoretical curve". Naturally, the measurements will be exactly the same as the tautology that describes the measurements.
I also show in my essay why it is mathematically true that energy is proportional to frequency and why the uncertainty principle must hold. But this is only just some of the results in my essay. Too many to list here in this post!
You further write,
"Really, I was stumped at "mathematical identity" -- at that point you are claiming to derive a physical conclusion with no physical assumptions...? Surely there is some link to physical reality in this math, or it wouldn't mean anything. So what's the underlying picture of reality that this math is assuming to be true? "
I fully understand why you were "stumpt" at the mathematical identity nature of Planck's Law. I was anticipating just such response!
But there is nothing unusal about finding mathematical tautologies in physics - and without these having a 'physical basis'! If I was to measure a distance of 3 miles going east and follow that with a measure of a distance of 4 miles going north, and then measure that I am a distance of 5 miles from where I started, do I need to have derived the Pythagorean Theorem using some 'physical basis' in order for this Theorem to apply to my physical measurements? Likewise with Planck's Law, as I show in my essay!
Conserning my photoelectric effect paper. I am surprised that you actually read it since I don't disucss this result in my essay!
You write,
"1) There is no experimental delay between the time that a weak photon source is turned on and the time that the detectors start registering the photons. If the energy had to "build up" over time, one would expect to see such a delay."
As I explain in the paper, the time required for an 'accumulation of energy' h to occur (the minimum threshold needed for energy to manifest) is h/kT. I think you will agree that this is a very short time! I don't think any experimental claims are for a shorter time.
But there is a more general principle about 'instantaneous' that you raise which I find very important. Do you really believe that if the 'source' is turned on at say t=s, the 'sensor' will detect the photon at t=s also? That 'instantaneously' (in the sense t=s) the photon will be detected? I show in my essay that The Second Law of Thermodynamics states that some positive duration of time is required for a physical event to manifest. Physical events have both 'extention' in space as well as 'duration' of time. Your view that events happen 'instantaneously' at t=s in my opinion violates this fundamental Law.
You further say,
"2) A related issue is when the average field is very weak everywhere, but there are many detectors. If the energy has to build up to hv on one particular detector, they would all take a long time to fire -- but in fact one of them will fire quite quickly, as if all the energy in the whole field somehow was "directed"."
This would be a paradox if you assumed 'ballistic photons' carrying an energy of hv (how? don't ask!) following a path trajectory and striking some one detector! But in my view, the 'photon emitted at the source' is not the same as the 'photon detected at the sensor'. These are separate by related events, as I also argue in my explanation of the double-slit experiment). A detector will 'fire' when it has 'a minimal accumulation of energy that can be manifested'. If a detector does not 'fire' it means that it does not have that threshold to 'trip' the detector. You may ask, what happens to the 'lower than threshold' energy at a detector? It's possible that eventually it just dissipates into the Cosmos, undetected and undetectable. Or it may linker around a bit for the next photon to 'strike'. Since all this is below our 'veil of observation', we just wont know.
Finally you say,
" I simply don't understand how you can simply assume that the energy is always exponentially increasing with time"
What is exponentially increasing with time is the 'time dependent local representation' E(t). But this is at the level of 'accumulation before manifestation'. When energy becomes 'manifested', an amount of energy hv (in agreement with the quantization hypothesis!) is absorbed and the 'exponential representation collapses' (see my essay for a fuller discription of this).
Ken in my essay I present exactly what you are also seeking: Quantum Theory without Quantization. This is what brought me to your corner!
Best wishes,
Constantinos
