From the principle of least action to the conservation of quantum information in chemistry

From the principle of least action to the conservation of quantum information in chemistry Can one generalize the periodic table?

The 23rd annual conference of the International Society for the Philosophy of Chemistry (ISPC) 15-17 July 2019 Turin

Vasil Penchev

Dept of Logical Systems and Models, Institute for the Study of Societies and knowledge, Bulgarian Academy of Sciences vasildinev@gmail.com

Project: Đ”Đ? 15/14 - 18.12.2017 to the "Scientific Research" Fund, Bulgaria: "Non-Classical Science and Non-Classical Logics.

Philosophical and Methodological Analyses and Assessments"

Mass conservation In fact, the first law of conservation (that of mass) was found in chemistry It was generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2” One can continue: Information = I(E) ?

Emmy Noether’s theorems (1918) Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918), especially the first one: Then, infomation conservation can be implied by the generalization in the second theorem?

Energy conservation in chemistry Any chemical change in a conservative (i.e. “closed�) system can be accomplished only in the way conserving its total energy Only one pathway for any reaction is followed, but only in classical chemistry rather than in quantum one

Bohr’s foundation of the periodic table Bohr grounded Mendeleev’s periodic table by quantum mechanics Quantum mechanics implies a certain generalization: All quantum leaps are as if accomplished in all possible trajectories (e.g. according to Feynman’s viewpoint)

Generalizing energy conservation Therefore, the principle of least action is generalized: This needs a certain generalization of energy conservation as to any quantum change Thus, any reaction in quantum chemistry has to be accomplished in all pathways simultaneously

From the first to the second theorem The transition means chemically for the generalization of any reaction to be accomplished as if any possible “course of time” All of them are counterfactual as to each other as to the (f)actual one, in classical chemistry The second theorem implies immediately: as many “times” as many “trajectories” of the reaction

A comparison with the standard energy conservation The standard evenly running time is that of “least action”: Thus, it is equivalent to energy conservation according to the first theorem Time is arbitrarily “accelerated” in all other, “counterfactual” pathways

The problem: If any quantum change is accomplished in all possible “variations (i.e. “violations”) of energy conservation” (by different probabilities), what (if any) is conserved?

What is conserved is impossible to be energy (valid only for the “trajectory of least action”)

An answer: Quantum information is what is conserved Indeed, it can be particularly deďŹ ned as the counterpart to the physical quantity of action Emmy Noether’s theorems imply counterparts of all mechanical quantities complementing them to that of action (e.g. as energy is the counterpart of time in them)

To counterfactuality The conservation of quantum information is valid in any course of time rather than in the evenly running one All those pathways of a chemical reaction can be considered as “counterfactual� to the single one of energy conservation in classical chemistry

An illustration Observers in arbitrarily accelerated reference frames exchange light signals about the course of a single chemical reaction observed by all of them, Then, the universal viewpoint shareĐ°ble by all is that of quantum information

The universal viewpoint of quantum information The separable complex Hilbert space utilized by quantum mechanics can be equivalently represented as vectors of qubits Those vectors are infinitely dimensional in general Any qubit in turn is a generalization of “bit” as to infinite sets

A “Gedankenexperiment” in Einstein’s manner Let us imagine an observer of a certain chemical reaction occuring in an arbitrary reference frame: For example, an astrochemist observes from the earth a chemical reaction in a very remote celestial body in the universe by means of the spectral lines The observed spectral lines would be quite different from those of the same substances on the earth

In terms of wave functions A wave function of initial chemical substances would transform to that of another Energy conservation would imply for the operator transforming the initial wave function into the final one to be Hermitian (self-adjoint) operator However, the earthly astrochemist would observe a quite different operator for the same transformation

The earthly astrochemist’s obserbations The operator according to the earthly astrochemist would not be Hermitian in general Thus, it would suggest a certain violation of energy conservation in the course of chemical reaction The observed difference is due to the deviation of the real geodetic line, in which the spectral lines reach the earth, according to general relativity

The equivalence of a geodetic line to a change of spectral lines The equivalence between 1 and 2: 1: All arbitrary geodetic lines in the pseudo-Riemannian space of the universe 2: All possible deviations of the chemical reaction operators observed anywhere in the universe by the earthly astrochemist, to the Hermitian operator of the same reaction observed on the earth

The same chemical reaction at entanglement The astrochemist accomplishes another set of experiments about the course (i.e. the operator) of the reaction: 1. Rigorously restricted to be on the earth 2. At all possible entanglements of the initial chemical substances

Two classes of experiments: The latter: a certain chemical reaction at all possible entanglements of the initial chemical substances The former: the same chemical reaction observed in each point of the universe by an earthly astrochemist

What the conservation of quantum information implies Both classes are identical to each other for any certain chemical reaction Each geodetic line from any point in the universe to the earth is equivalent to a certain state of entanglement of the initial chemical substances for any certain chemical reaction

The “alchemical” periodic table Thr conservation of quantum information implies a generalization of the periodic table: It includes any continuous and smooth transformation between two chemical elements Thus it can be called the “alchemical” periodic table It conserves quantum information, not energy

Conclusions 1. The second of Emmy Noether’s theorems (1918) implies the conservation of quantum information 2. The conservation of quantum information in chemistry means a new domain: quantum chemistry of entanglement and its generalized periodic table

The full article (20 pages): at researchgate.net

Thank you for your kind attention!

Please, any questions?

The article at ResearchGate https://www.researchgate.net/publication/33205 8314_From_the_principle_of_least_action_to_t he_conservation_of_quantum_information_in_ chemistry_Can_one_generalize_the_periodic_t able