I would like to thank Mehran Shaghaghi for initiating a discussion on their recent paper, “The Physical Foundations of Quantum Theory”, based on their recent paper published in February 2023 in Springer Link: https://link.springer.com/article/10.1007/s10701-023-00673-2.

Abstract:

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems with only one adjustable property cannot carry more than a single message at a time. We demonstrate that this is true for the photons in the double-slit experiment, and that this is what leads to the fundamental limit on measuring the complementary aspect of the photons. Next, we illustrate that systems with a single adjustable property exhibit other quantum behaviors, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert space formalism of quantum mechanics as well as the Born probability rule. Our derivation demonstrates the physical foundation of quantum theory.

5 days later

The paper presents a fascinating perspective and is likely to make a significant contribution to the field. It has successfully resolved several complex issues. This makes me wonder, if quantum systems are just a special case of single-message systems, do we really need a theory of everything?

    Robert McEachern

    Replace one member of an entangled pair, with an exact, pixel-by-pixel, identical (negative) copy of the other member, instead of retaining the original, in which the entangled pairs are only "statistically" identical rather than being "exactly" identical. That simple substitution changes everything...

    that simple change in the nature of the inputs ("identical twins" versus "fraternal twins") entirely changes the nature of the observed correlations between the entangled pairs.

      Robert McEachern
      I suspect those are the same concept. In his definition, a single-message system consists of a single piece of information, which can be any sequence of bits of data, not just one bit (↑ / ↓) of data.

          Michael No, they are quite different in a very important way. It has nothing to do with the number of bits of data in a message; the only thing that matters is the amount of information. The Time-Bandwidth product in Shannon's Capacity expression for the amount of information (corresponding to the product in the Heisenberg Uncertainty Principle [HUP]), limits the number of independent (uncorrelated) measurements that can be made on a system. But the other term (signal-to-noise ratio) in Shannon's Capacity, that has no equivalent in the HUP, limits the number of significant bits in that measurement. Hence, when both the number of uncorrelated measurements and the number of bits-per-measurement become extremely limited, strange things happen. But it is important to realize that a single bit of information, can be encoded in a variety of ways; by increasing the time-bandwidth product (and thus the number of uncorrelated measurements that can be made) while simultaneously reducing the signal-to-noise ratio, or vice-versa.

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