New QM framework

I show the dimensionality of observable space is conditioned on objectivity. I explain distinction between measuring device and observer

I show any theory assuming state of an object, or even object’s existence, will be at odds with empirical evidence. I discuss QM relation with special relativity (SR). I argue all paradoxes are artifacts of factitious assumptions

I argue the unitary evolution of quantum state is imposed by implicit extraction of classical information. I show the generating self-adjoint operator of time-driven unitary transformation is entropy, not Hamiltonian

I critically assess some published values for decoherence times. I show there are two characteristic times inversely proportional to each other: decoherence time, and probability decay time, with second often mistaken for the first. I present formulas for decoherence and decay times

There are misconceptions that entanglement (e.g. with environment) causes decoherence, and that decoherence causes classicality. Yet in an entanglement, barring classical communication, no action taken by one party has any effect on another party, a fact known as no-signaling theorem. The presented analysis reveals, it is the measurement, not entanglement, which turns quantum state into classical event sample, resulting in a loss of correlation terms of density matrix

I critically analyze the fidelity measure used for state estimation. I discuss the impossibility of complete determination. As an alternative to traditional fidelity, I suggest a figure of merit called confidence in the knowledge of an arbitrary state

I prove teleportation protocol for an arbitrary qubit state can be implemented with one bit of information transmitted via classical channel, per preparation + measurement cycle. I show how teleportation protocol can be implemented in a classical setting. I discuss the contextual meaning of teleportation

It appears that every prime number greater than 3 can be represented as a sum of two (if a twin prime) + 0 (Goldbach's conjecture), or 3 prime numbers (Vinogradov's theorem), with the index of the sum prime equal the sum of indices of first two primes in the sum. For example: 31 = 13 + 11 + 7, and the corresponding indices: 11 = 6 + 5 199 = 139 + 37 + 23, and the corresponding indices: 46 = 34 + 12

I show the unitarily equivalent solutions of Schrödinger equation predict different measurement results in different observation bases. I identify the criterion for choosing an observation basis in which the predicted measurement results are consistent with observed macroscopic behavior

Understanding of physical reality is rooted in the knowledge obtained from observations. The knowledge is encoded in variety of forms, from sequence of letters in a book, to neural circuits in a brain. At the core, any encoded knowledge is a sample of correlated events (symbols). I show the event samples bear attributes of a physical reality: energy, temperature, momentum, mass. I show that treating measurement as event sampling is consistent with predictions of quantum mechanics (QM). I discuss QM basics: wave function, Born rule, and Schrödinger equation, emphasizing their true meaning, which is rarely, if ever, mentioned in textbooks. I derive similar expressions using event sample as base construct, demonstrating the connection between QM and the presented model. I explain the mechanics of observation, and the role of observer. I show how model extends to include dispersion, decoherence, transition from quantum to classical state. I prove decoherence is a key factor in Fermi's golden rule, in Planck's radiation law, and in emergence of time. The controversial aspects of QM, such as wave function collapse, and measurement problem, do not appear in presented framework, which I call the knowledge mechanics (KM)

I propose a model wherein a system is represented by a finite sequence of natural numbers. These numbers are thought of as population numbers in statistical ensemble formed as a sample with replacement of entities (microstates) from some abstract set. I derive the concepts of energy and of temperature. I show an analogy between energy spectra computed from the model and energy spectra of some known constructs, such as particle in a box and quantum harmonic oscillator. The presented model replaces the concept of wave function with knowledge vector. I derive Schrödinger-type equation for knowledge vector and discuss principal differences with Schrödinger equation. The model retains major QM hallmarks such as wave-particle duality, violation of Bell’s inequalities, quantum Zeno effect, uncertainty relations, while avoiding controversial concept of wave function collapse. Unlike standard QM and Newtonian mechanics, the presented model has the Second Law of Thermodynamics built-in; in particular, it is not invariant with respect to time reversal.

I suggest an object acted on by classical (i.e. non-coherent) force, in gravitational field, unavoidably decays. I estimate decay rates in some scenarios.

I propose a model wherein a system is represented by a finite sequence of natural numbers. These numbers are thought of as population numbers in statistical ensemble formed as a sample with replacement of entities (microstates) from some abstract set. I derive the concepts of energy and of temperature. I show an analogy between energy spectra computed from the model and energy spectra of some known constructs, such as particle in a box and quantum harmonic oscillator. The presented model replaces the concept of wave function with knowledge vector. I derive Schrödinger-type equation for knowledge vector and discuss principal differences with Schrödinger equation. The model retains major QM hallmarks such as wave-particle duality, violation of Bell’s inequalities, quantum Zeno effect, uncertainty relations, while avoiding controversial concept of wave function collapse. Unlike standard QM and Newtonian mechanics, the presented model has the Second Law of Thermodynamics built-in; in particular, it is not invariant with respect to time reversal.