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Re: [Phys-L] what's quantized and what's not



Thanks, Moses.
I have been anxiously awaiting some clarification of this point - and would yet welcome more.

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
www.sciamanda.com

-----Original Message----- From: Moses Fayngold
Sent: Sunday, April 24, 2016 12:06 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] what's quantized and what's not

On Friday, April 15, 2016 6:59 PM, John Denker <jsd@av8n.com> wrote:



Einstein emphasized quantization of light i.e. electromagnetic
radiation, but the idea was soon applied more generally.

There's only one problem. The basic idea is wrong. Anybody
who thought carefully about it in 1921, or even in 1905,
should have known it was wrong.

Many controversies originate from fuzziness of human language. Here I can only try to formulate again what has been proved right by an overwhelming scientific evidence, starting from 1905. Mathematically, quantization is the reduction of the set of allowed values of some characteristic from continuous range down to a discrete set. In QM, this is manifest in representation of observables by their respective operators whose eigenvalues may form a discrete set. Particularly, the Hamiltonian operator representing energy E of a system may have a discrete set of eigenvalues. In this sense, the system's energy is quantized. Actually, quantization is known already in CM, e.g., frequency quantization of a finite string or elastic rod. Physically, energy quantization in QM is observed in interactions and energy exchange between different systems. The system's evolution may be continuous and described by the corresponding wave equation or unitary transformation. But the observed interaction outcomes may be discontinuous with the instant finite energy changes. In this sense, energy is quantized, while still satisfying conservation laws (when averaged over vacuum fluctuations). That such changes may fall below available experimental sensitivity, thus appearing continuous (e.g., low frequency limit of EM radiation), falls short of "conflicting evidence". Otherwise, one could pronounce seemingly continuous flows of fluid an abundant evidence against the existence of atoms. By contrast, the frequency threshold and practically instant photo-emission in PEE, discrete spectra in atomic and molecular Optics, etc., are the solid evidence of quantization of light. We should be very vigilant to avoid the interpreting classical limits of QM as an evidence against Quantum.
Moses Fayngold,NJIT
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