Fleeting thoughts: God in terms of experimental science

There are two dogmas dividing the study of God from science and especially from the experimental science:

I. The perception of God generates a specific domain of human experience: religion. God being omnipresent is within all spheres of human activity and cognition, and He is their unity. Nevertheless, the finiteness and limitedness of all human beings imposes that area of religion.

II. Science and especially experimental science is inappropriate for the cognition or study of God as to human beings for science addresses the repetition, reiteration, recurrence, and resettability of result as well as the materiality of phenomena. Thus God is fundamentally inaccessible in science for He is creative and nonmaterial.

The talk doubts those two dogmas stating that quantum mechanics is an experimental science, in which God is properly cognizable, knowable, and cognoscible probably in a definitive hypostasis.

Firstly, arguments contra the second dogma:

1. Quantum mechanics calls much criticism ostensibly violating the fundamental principles of scientific content requiring just the repetition, reiteration, recurrence, and resettability of all experimental data. Any given result in quantum mechanics is initially random and thus it cannot be forecast in principle. What is forecastable is only the probability distribution of a big enough statistical ensemble of experimental data, which changes gradually and causally in time. Nevertheless some rather incredible state of any quantum system can occur with some nonzero probability and thus as a given result of measuring.

2. Quantum mechanics describes the state of any quantum system as a wave function. That wave function can be represented as a point in Hilbert space and interpreted both as a trajectory in space-time
(a “fermion”) and as a coherent mix (i.e. a “superposition”, using the proper term of quantum mechanics) of possible states (a “boson”). Whether “belonging” to a fermion or a boson, wave function can be interpreted as a form of generalized information: quantum information which is furthermore a nonmaterial generalization of matter. That is: Matter is a particular case of quantum information, which is nonmaterial in general.

3. Quantum information is not less another generalization of the usual concept of information, according to which information is the quantity of elementary choices such as bits (an abbreviation of “binary digits”). A bit is defined as the choice between two equiprobable alternatives and thus any finite series of choices of an element among any finite sets can be exactly calculated as a real number of bits, i.e. as that information containing in the series in question. Consequently, the nontrivial generalization of information should refer both to infinite series of choices and to the choice of an element among any infinite set therefore requiring the axiom of choice to be involved. Quantum information is that generalization of “information” though it is introduced by quantum mechanics as still one interpretation of wave function in terms of information. So a qubit (an abbreviation of “quantum bit”) is both the above equivalence of transfinite series and a choice among an infinite set and the normed superposition of any two orthogonal subspaces of Hilbert space in spirit of quantum mechanics. Furthermore, quantum information is the quantity of those “infinite choices”, i.e. qubits. Any wave function is a given value of quantum information, and Hilbert space can be interpreted as that variable of quantum information.

About a scientific notion of God in terms of quantum mechanics and thermodynamics (which are experimental sciences)

The thesis is: God can be discussed in a properly scientific way as a concept definable by certain properties in terms of quantum mechanics, quantum information theory, thermodynamics, and furthermore inherently linked to set theory and the foundation of mathematics. Those properties might be: the universal course of time; choice and even free will (in a sense) of any item or entity in the universe; wholeness as a fundamental emergent property as it is studied by thermodynamics; the relation between any entity in the universe and its disposition within the universe; the interpretation of information as the quantity of choices and thus quantum information as that generalization of information, which refers to infinite series or sets; Skolem’s “relativeness” of the concept of set if the axiom of choice is granted and thus relativeness both of countable and uncountable set, on the one hand, and of finite and infinite set, on the other hand.

That understanding of God claiming to be scientific can be featured as pantheistic for it would suggest that nature should be seen as having free will and even consciousness in a sense rather than as that absolutely inert nature opposed to mankind.

A few general comments of the thesis:

1. One can object that any attempt for any scientific definition of God is self-contradictory and thus should fail for God is absolutely universal and thus inherently opposed to any definition being always some limiting of what is to be defined: Any definition suggests something more universal than what is defined, and that approach is unacceptable to God. The same argument allows of a polar interpretation: any “razor” such as those of Occam, Russell’s “barber” or Mach’s “economy of thought” removes any absolutely universal concept such as that of God as redundant.
   The definition of God being suggested can be interpreted only as a projection of Him in the limited areas of enumerated scientific disciplines. Thus it is a kind of particular understanding of the absolutely universal however consistent and hence irredundant for these sciences.
   Furthermore, the boundaries of any last, actual scientific theory are not known in principle. Any preliminary restriction (as to it) is self-contradictory in turn for that restriction would be founded on some meta-viewpoint to it, which would mean that its boundaries should be known.

2. Infinity, wholeness, quantum information, and the course of time are involved as a kind of “particular universalities”, that is as universalities featuring universality as to the corresponding particular scientific theories: set theory, thermodynamics, quantum mechanics and information. The suggested concept of God would mean their community and thus a certain option for their unification. This means that they might be synthesized between each other “a priori” if one utilizes Kant’s terms and conceptions. Thus, the concept of God might be consider as the fundamental justification for any aprioristic synthesis.
3. That concept of God is consistent to occasionalism, that special kind of causation, which assigns it to God. One can say that there exists a hidden direction both of causality and time opposed to the usual one: It flows from the coherent state of absolutely unorderable future to the always well-ordered past by the meditation of all choices made in the present, including those of the human beings. This is a way relevant to exact science for choice and free will to be introduced ontologically: Indeed the transformation from unordreable future to the well-ordered past needs the so-called well-ordering theorem in set theory equivalent to the axiom of choice.

A few featured arguments in favor of the thesis:

1. According to quantum mechanics: The Schrödinger equation being fundamental in it can be interpreted as a quantitatively description for the way of how time flows: It is that generalization of energy conservation, which allows of a certain mismatch between future and the present unlike the standard energy conservation suggesting their identification. Thus, such a kind of mismatch between energies of future and the past implies some nonzero value of a new kind of energy ascribable to the past properly.
2. According to thermodynamics both phenomenological and statistical, both classical and quantum: The wholeness of the system at issue is necessary for any thermodynamic consideration and thus any element belonging to it turns out to doubled therefore allowing of some nonzero mismatch between it by itself and again it but in relation of the system as a whole. One can say that quantum mechanics is a thermodynamic theory in a sense for it needs unconditionally an apparatus equivalent to the system as a whole: quantum mechanics is a theory both about some quantum entities and their corresponding measured images in the apparatus suggesting even on a fundamental level for them „by themselves“ and their measured „images“ not to coincide.
3. According to the theory of information and of quantum information particularly: The universe can be consider as a single quantum computer and thus all physical processes both as informational and computational once information is relevantly generalized to quantum information as to infinite series and sets. Indeed the standard definition of quantum information as the normed superposition of two orthogonal subspaces of Hilbert space is equivalent to its definition as the quantity of choices between an infinite set of alternatives and its elementary units of quantum bits (qubits). Furthermore, any wave function being the exhausted description of some quantum system is representable as a series of qubits and thus as a value of quantum information. The free variable of quantum information represents the Hilbert space itself, and then any “point” in it is a value of quantum information.
4. At last, according to set theory and mathematics foundation: Infinity can be consitently discussed as a second and independent finiteness complementary to the usual „first“ one. That „second“ finiteness called in tradition infinity can be ascribed to wholeness. Furtermore both finiteness allows of Gentzen‘s transfinite foundation to be translated in the language of two Peano‘s arithmetic.