As a corresponding scheme, we present below for the emergence of molecular semiotic controls a quantum mechanical frame. We introduce it in relation to the directly observable, algorithmically, materially mediated, “abstract”, genetic code software. We present it as being in direct relation to the origin and contemporary existence of the genetic code-protein synthetizing system. We will find the invariance of the code vocabulary to satisfy the requirements of being a special source of spontaneous, integrative autonomy of a semiotic nature. It also serves as a clue to investigate the integrated causal cellular organization, i.e., the causal macromolecular network. This maintains and mediates the invariant abstract, virtual existence of the code vocabulary.
We note here that time evolution in quantum mechanics is twofold: in between quantum measurements, time evolution is a unitary one, subject to the linear superpositional (paralell evolutionary) dynamical principle of a many-to-many nature on one hand, and the nonlinear, projective, many-to-one evolutionary, quantum measurement nature, on the other. The former is a real quantal process, while the latter is heavily debated but agreed to involve some kind of classical component.
3.1.1. Quantum Measurement Schemes
There are three distinct, but related quantum measurement schemes of biological significance, denoted below by letters a, b, c, having bearings on our scenario of the emergence of semiotic controls in chemical evolution.
These schemes can be classified according to the kind of the arbitrary position of the so-called “Heisenberg-cut” [
29], which divides the underlying quantum object and the classical device (and record and memory states),
i.e., it specifies
where the “reduction of the wave packet” occurs. Accordingly, Neumann’s infinite regress analysis [
20] permits the introduction of the projection operator, along with this cut, to be placed at any level of this regress (the “projection
postulate”)
.(a) External (“orthodox”, “holistic”) Measurements
Here belongs the ordinary case, where the Heisenberg-cut is placed between the consciousness and memory of the human observer and his brain, his body in general. This is the ultimate solution of Neumann [
20]. Later Wigner relaxed the idea to embrace biological organisms in general [
30]. Here it is the “subject” of the organism,
depending on its whole body, which
is the place of reduction, “projection”. All material components: object, device, and the body of the observer form a chain of interacting physical systems. Record and memory states are thus objectively contingently, holistically-organizationally biological. Also, there comes about a mapping of the measurement outcome relations upon the “subject”, as the ultimate realization of the reduction of the wavepacket. This stage must have been preceded by “internal”- and, the already strongly related “mixed” measurements, with the biological “subject” identified in the latter as the
global virtually coherent organization of the “measurer” biological system.
(b) “Internal” Measurement
Though this concept was not introduced exclusively in biology, it has shown its primary use in protobiology [
11,
17].
Here we place the Heisenberg-cut, and the level of projection, between a macromolecular object and its macromolecular measurement device with its record and memory states
within the same system, so that, e.g., a biopolymer “measures” its “object” biopolymer (see further e.g., [
2,
4,
5,
6,
7]). The basic idea is that a molecular measurement on a larger quantum system cannot be instantenous according to special relativity,
i.e., takes
internal dynamical time. In this scheme, we introduce, accordingly, “internal” quantum measurement and internal quantum dynamics on equal footings. The measurement does not depend directly on an interaction Hamiltonian of the influence of an “environment”, rather, on specific
gross 3D relations. The latter is governed by the fitting of the “device” and “object” subsystems in
internal dynamical time. In this way, 3D relations are “lifted” to the (composite) Hilbert space. Mathematically, it is a constrained linear combination set of molecular projection operators, yielding a 3D steric
classical selection
and specific
quantal overlaps (compare with molecular projections [
31]). The result is a highly constrained time dependence, measurement dynamics, in our context a set of paralell evolutionary many-to-one processes, each resulting in one of a highly limited number of “similar” outcomes. In this way, the dynamics of internal measurement proceeds as
where Π is product, the
P’s are the molecular projectors (characterized below), belonging to the same molecular “device”, Ψ(t) is the object wavefunction, with L>M>N . The limiting expression is the integral
where “
n” is a smaller number. This is a natural expression for a dynamical-measuremental evolutionary
approximate sterical fitting.
(c) “Mixed” Measurements
We introduce this special case of internal measurement as a mediating process between molecular internal and human “orthodox”, external, instantaneous measurements. Here, we place the cut between the
external object and the
internal device, with the latter being part of the “body” of the macromolecular network “observer”, forming an interacting quantum dynamical system. That is, we place the cut at the border between the two worlds. However,
by the measurement, the projected object state as
record and memory state is, through the device state, locally coupled to, and globally mapped onto, the holistic, overall pre-existent
gross biological organization. Thus, it becomes a part of the same quantum dynamical network. In this way, the setting
internally represents these
external measurement characteristics. This type of measurement occurs at the interface of internal/external measurements: the object is essentially external but the measuremental device
and the following record and memory states are internal. Here, the reduction by projection occurs, finally, by internal mapping operators, mapping the measurement outcomes on the internal causal dynamical network. This completes and fixes the measurements. In fact, these mapping operators fix the object/device relations, the outcomes of the measurements, acting upon the device/record and memory wavefunctions. Additionally, there emerges, as a novel phenomenon an
entangled, nonseparable state of the measurement device and the object system similarly to pure “external” processes [
24]. However, in mixed measurements, this entangled state is internal to the global measuring system.
As to the general nonlinear nature of projection operators, we note that
any projection operator depends on the specific, projected state of its “object”. In our case of biological semiotic control functions
, this state is predetermined by the corresponding projection operator, projecting out this specific state from the quantal superposition, the existing possibilities. It satisfies, thus, the specific requirement of internal biological
control. Quantum measurements, as discussed below, are of this usual control type:
3.1.2. The Origin Problem: Chemical Evolution as the Evolution of Nonlinearity
To understand the origin of certain invariant biological semiotic controls and, as their function, those of the informational symmetry breakings/restorations, is basic for the understanding the deeper significance and action of these controls. The fundamental elementary biological semiotic controls are those of the genetic mechanism, the code assignments, forming possibly the basic evolutionary division line between pure chemical and biological systems and their evolution.
The transition from chemical evolution to biological evolution was due to roughly five distinct successive stages, where the evolution of the nonlinear nature of the corresponding processes played the central role. To arrive at our goal, we briefly review these well-known stages of chemical evolution.
I. Symmetry-Breaking Instabilities and Dissipative Structures
Here belong in chemical evolution those auto-and cross-catalytic networks which were nonlinear in their
concentrations,
a statistical constraint was exerted upon the underlying dynamics [
32]. These structures were evidently present in early chemical evolution probably with spatio-temporal periodic patterns [
33], subject to statistical closure.
As shown by Kauffman’s analysis, in these processes, at “the edge of chaos”,
i.e., conforming to both stability and adaptability as variance, autocatalysis is more stable than simple catalysis in the polymeric network. Even more important, polymeric
size in general increases in the evolution of these structures [
34].
II. Dynamical Nonlinearity
With increasing polymeric mass (length) and complicated 3D structure, conformation and the resultantly evolving higher quantum specificity, i.e., acting on specific quantum states of their object in the catalytic process, the characteristics of the process shift towards individual polymers. They shift, in fact, towards individual macromolecular quantum dynamics. Here, nonlinearity is a dynamical one, its object, in autocatalytic activity, is implied in its time dependent potential energy operator. The system has, accordingly, a dynamic closure and nonlinearity; hence, the polymeric dynamical network is causal in the quantum mechanical sense of unitary time evolution. With individual large auto-catalytic and cross-catalytic polymers, primeval proteins and RNAs with high quantum specificity, there may have emerged stage III.
III. Internal Measurement
Sufficiently evolved enzymes and ribozymes perform internal measurements [
11,
17,
18]. They act as molecular projection operators [
18], projecting out specific quantum states of their objects by their 3D classical conformational structure, lifted to the Hilbert space, and their quantum-specific degrees of freedom. The nonlinearity of their action is thus evolved to a pre-informational structural-molecular
projective one. However, they still do not have real semiotic control on the internal protobiological processes. By the modern
language of decoherence, the “pointer state” of the “preferred observable”, which is least perturbed by the internal measurement, here the state of molecular shape [
35], provides a spontaneous symmetry breaking of the unitary time evolution of the quantum dynamic superposition of the “object”. There is an informational gain, in open system dynamics. For the first time, coupled to this dynamics, the above projection operators appear [
24].
IV. Pre-Formed Structures towards Internal Semiotic Controls
Concerning the ultimate step towards the emergence of semiotic controls, we must make a specific supposition. According to this, we have “autocatalytic”
internal measurements of RNAs on themselves. This supposition is usually made in the “RNA-World” scenarios, as, e.g., in [
36], with the difference that we here do not appeal to the usual template-dependent reactions, rather, to a reversal of the self-cleavage function. It emerges as the transition from spontaneously formed oligomers to the build-up of RNA polymers. We also take the further, widely accepted, view of polymerases as catalytically building RNAs [
17]. This model amounts to a “strong” (“direct”) self-reference, nonlinearity of RNAs dynamics, with the corollary that there was a similar internal measurement “catalysis” by primordial proteins, which in general terms is, in fact, a compromise between the RNA-and Protein-World views.
V. Mixed Measurements and the Emergence of Invariant Genetic Assignments as the Fundamental Semiotic Controls
This crucial step may have emerged when the auto-and cross-catalytic network, the proto-organism, the “
measuring agent”, was well developed to “perform” external, holistical measurements. It possibly had internal global virtual coherence (“self-distinction”), and faced externally emerging short ribonucleic acid oligomers as objects (compare with [
17,
37,
38]).
Concerning individual primordial codons, it follows from stage
IV that ancient, undeveloped polymerases performed “catalytic” internal measurements as measurement devices in a naturally nonlinear projective way. The emergence of primordial longer RNAs may have been the measurement outcomes. Also, these RNAs were involved in strongly nonlinear “
autocatalysis”. This suggested process has certain similarities to Dyson’s concept [
38] of a two-step evolution as metabolism followed by the internalization of the later informational, macromolecular RNAs(/DNAs). However, in our scheme the coding function is concomitant with the measurement interaction, see also [
17,
25]. Individual amino acid-codon pairs may have evolved during the gradual, in some aspects dynamical, internal measurements of the molecular shape class. The process was governed by gradual 3D fitting of specific sequence shorter-longer polymers. We do not wish in this paper go into a possible detailed stereochemical argument. Perhaps it is enough here to point out that several alternative mechanisms may have been involved. For instance, the protein
device may have acted as an envelope around specific shorter RNA oligomers as a stereochemical structure. The stereochemically decisive amino acid residues as loop-producing turning points in the conformations could evolve to code the similarly stereochemically crucial codon units, nucleotide sequences. The chemical evolutional existence of the protein device must have been a statistically and occasionally emerging internal event. This tentative process may have formed the dynamical, “stereochemical” evolutionary aspect, as accompanied by a correspondingly constrained probabilistic quantum transition during the measurement dynamics. The latter random measurement aspect then resulted in a stereochemically “constrained” probability choice outcome,
i.e., the probabilistic choice is made from a set of sterically related molecular measurement alternatives. This tentative process of
both chance
and 3D dependence in evolution, resulting in a few, “similar”, degenerate codons, then may have resulted in a both stereochemical
and a constrained frozen accident emergence of the code (see originally e.g., Woese [
39]
vs. Crick [
40]; for the possibly stereochemical origin of the presumably most ancient coding of
tRNAs, see [
4]).
By mixed measurements, which are contingent upon a clear spatial-causal distinction between the internal and external world (see “Semantic Closure” [
41]), the internal macromolecular record and memory electronic wavefunctions, depending on the steric molecular nuclear structural frame, were then mapped onto the underlying global virtually coherent internal causal network by the assignation operators. They were, in fact, encoding the object/device measurement outcome. The
internalization of the record and memory states was due to the dynamical, internal measurement aspect of mixed measurements. The mapping itself, as the ultimate “reduction of the wave packet”, may have been a manifestation of the external measuremental aspect. There thus presumably appeared, by conforming to this external aspect, a set of integrated, global-”abstract” correlation-conserving entities, quantum mechanical global-virtual ultimate measurement outcomes. They were thus internally virtually
representing the original macromolecular measurement outcome,
i.e., the record and memory state. The record and memory states, in this way, were possibly encoding by their steric structures the contingently arisen
reversed object/device relations. The latter relation, presumably, must have emerged by these
newly internalized, coupled record and memory states becoming the natural internal
causal predecessor to the state of the internal device and, through it, to the cycles of the global network.
In this way, the
possibility of an
internal reversal of the original object/device relations may have emerged, the two components together forming a retrocausated one-to-many local dynamical process. The splitting into probability branches of the record and memory states post-measurement might have been then due to an inducing effect of the particular perturbing time-dependent nonlinear interaction Hamiltonian, acting through the protein device state, at the “edge of chaos”
nonlinear complex case [
34]. Thus, the original cause, the protein device realizing a causal reversal, depends on its own future as its own effect,
i.e., projected RNA. Its mechanism, thus, is the coupling of RNA to the internal network through the “
ab initio” internal, dynamically coupled protein device state. In this context, we refer to the kind of reverse case of partial measurements [
42].
In this way, the states of the projected RNAs will depend nonlinearly on their protein effects and in general, the global network through the assignment operators, which is our point here: assignation is a function of the global network (compare with [
25]).
The resultant fixed global causal entities as outcome functions of the mapping (assignation) operations could be the abstract-virtual, semiotic classical rules, encoding the reversed object/device relations. They may be quantum dynamical correlation functions, global spatio-temporal “software correlations” over the structural hardware, the macromolecular device and record and memory spatial structural states. Actually, these naturally emerging classical semiotic rules, encoding the measurement outcome relations, may have emerged as represented by internal causally maintained quantum mechanical entanglemental correlations by a virtually coherent internal dynamical network background. They might have emerged according to the well-known entanglement relation between the quantum mechanical device and its object.
In this way, the measurement phenomenon involved a macromolecular hardware and a globally-semiotically interpreted software, assignment. In a natural way, as pointed out above, the latter emerged as a function (representation) of the former, as “self-distinction”.
Thus, at this presumed final, rather singular molecular evolutional stage, all components of the set “object”, “device”, “record” and “memory” was internalized into the system
by the measurement. It should be stressed, that by the chemical evolutionally emerged mixed measurements, there was a concomitant cause-effect, causal break in the dynamics of the object as is usual in ordinary holistic quantum measurements. (We recall that a many-to-one process cannot be
causally a predecessor of a many-to-many one. The von Neumann entropy changes during the event [
20], see essentially, e.g., [
19]. In this case, however, the causal break was mapped to internal
causally reversed projected object state/device state relations. In this way, semiotic controls could emerge as an internal global
reverse causal representation. So the causal break was eliminated from the system by a retrocausal dynamics.)
In concrete terms, by the presumed evolutionary, measurement coupling of the two nonlinear molecular “catalytic” processes of Protein→RNA and RNA→RNA, i.e., by the introduction of a certain semiotic reversal of the processes, a reversal of the original internal measurement relations happens, leading to an RNA→Protein→RNA dynamics. A time symmetric future is constructed by symmetrically following, in a regressive way, the past of the system. (Thus, this reversal does not correspond to simple antiunitarity; the arrows denote “producing”.)
The fundamental reason for this construction of a time-symmetric one-to-one regressive quantum dynamics is that it is required by “external” quantum measurements in an “internal” context (“mixed” measurements). A continuously causal dynamics was being able to come about only by following the reverse process, the past, i.e., in a retrocausal way. In fact, this route of the quantum dynamics of the record and memory RNA structures was the only continuously causal quantum dynamical future of these ancient, measurement (“catalytically”) built RNAs, encoding the assignments. This choice possibility arose as they were coupled to the continously causal quantum dynamical internal organizational network through the protein device state. Thus a dynamically, causally continuous dynamics of the record and memory RNAs was possible to emerge post-measurement, just by coupling to the continuously causal organizational network. It was, in fact, an alternative to a highly unstable post-measurement acausal superposition, as supported by possibly strong protobiological evolutional pressure. Its alternative, the acausally emerging superposition was subject to unavoidable uncontrolled random internal fast decoherence.
The necessary continuously causal future of these upbuilt, projected macromolecular RNA record and memory systems was tentatively needed to be regressively constructed in a real-time, time-symmetric manner, just as they were coupled to the rest of the macromolecular network. Actually, the process had to be stepwise highly constrained, i.e., constructed from its origin, since it was evolving in a regressive one-to-many way upon the only available retrocausal time direction, not following any special reverse assignment history. The projected, assigned object wavefunctions, here those of tRNA-like coding RNA structures, became the projective controlling ones on the wavefunction of the former device protein. Accordingly, the process possibly arose by the many-to-one relation of the original measurement constraint becoming a peculiar underlying energizing one-to-many relation concerning the component macromolecular wavefunctions. In fact, the causal interaction with the global enzymatic virtually coherent network might have resulted in the concatenation of the complementer (“anti”-) N! primordial codons of the tRNA-like structures, yielding a sequence of nucleotide bases, the coding RNA/DNA polymer, in an energizing quantum mechanical one-to-many process. (N here denotes the serial, not necessarily different, codons.) The quantal superposition of each (“anti”-) “codon” was then constrained by the control-setting many-to-one projection of the internal assignment rule of the full causal network. Selection might have then favored the emergence of specialized polymerases.
Thus the resultant recursive process, as successive projection constraints upon the post-measurement successive time evolutions, right from the very origin emerges as an observable energized one-to-one correspondence (rule) chain.
The ambiguity in the post measurement time evolution of the projected object system, hardware RNAs, was so probably having, within a short term in evolution, a pay-off in favor of a semiotically constructed stable internal causality. From this stage on, they were the RNAs with a global software which acted as symmetry constructing “internal measurement devices”. They were the carriers of the reversed assignments as tRNA-like ribozyme species, with the genetic code, carried by them, interpreted by the whole intracellular macromolecular machinery. In this way, the molecular hardware as nucleotide sequence is correspondingly local, while the software as abstract-virtual genetic codes is global. In a natural way, there must have existed systems following the acausal route with undeveloped internal causality conditions.
Accordingly, these evolutionary semiotic constraints are but descendants of the above “direct” assignments, arising from the measurements, as embodying “reversed” assignments. They are, on one hand, fairly arbitrarily set as an evolutional choice of retrocausality, while, by their consequent fundamental causality, are strongly constrained. This is what we suggest here as a certain kind of special “biological freedom”. This overall process is amounting to the emergence of semantic nonlinearity in direct context with the symmetry restoration dynamical cell cycle.
This is, tentatively, how and why physical records and memories of internal measuremental sterical relation origins may have evolved into global-virtual semiotic natural projection operators. They act upon the underlying reversed dynamics, yielding the necessary constructing “initial symbols” of the entanglement correlations in terms of the molecular algorithm, as their projective role. They are existing in relation to the intact cell cycle in a holistic organizationally maintained and mediated, dynamical virtual coherence. Concerning mathematical representation, they are projection operators corresponding to this deeply quantal, if virtual, quantum correlation (
Section 3.2.). They are built on (are representations of) internal “coding” record and memory states of RNAs(/DNAs) as the dual wavefunctions of them by the assignation operators, and embody an evolutionally robust, invariant, also global-virtual and self-distinctioning, assignment relation.
In terms of internal chemistry, the origin of the observable protein synthetizing process was in a way natural, taking into account the resolution of direct (“strong”) RNA nonlinearity into a “weak”, protein mediated one. In fact, the cause-effect relations of a dynamical nonlinearity with quantum specific interactions were opened up by the perturbing effect of the proto-protein, and its
effect in turn becomes the effect of an other, more stable (
mediated) nonlinearity (compare with [
43]). This amounts to chemical assignments and their semiotic reversal. It comes about by a dynamical change of the object/device relations and, by the nature of the process, it was, and contemporarily also is, a regressive, real positive time, phenomenon.
3.1.3. The Process of Semiotic Symmetry Breaking/Restoring: on the Source of Biomolecular Information
It follows from the above tentative scenario, that the emergence of biological semiotic controls was presumably of a fairly singular, quantum measurement, origin. As was noted above, subsequently to the primeval mixed measurements, the reversedly emerging superpositions contain as branches the different reverse assignment possibilities as alternative histories. The primary “initial symbols” of the following protein synthetizing translational algorithms are the stable entanglemental global-virtual reverse assignment projection operators. They can be conceived grammatically as a simple declarative “sentence” of a virtual language, to be translated to another, molecular, material language. These projections select, as semiotic controls, the proper reverse histories, reverse assignments. They set the right physical initial conditions of the measuremental-dynamical (internal measurement) recursion.
The successive process corresponds to the well-known steps of the genetic translational apparatus, the whole molecular dynamics being comprised of retrocausal, discrete algorithmic steps. These algorithmic discrete steps are thus internal measuremental, recursive-regressive steps where one macromolecule is once a measured, once a measuring entity in the algorithm [
11] (compare also with [
44]), corresponding to the important phenomenon of “quantum update”.
It is a primary result of the above discussion that time-invariant semiotic controls could only emerge by a causal break, i.e., breaking of time inversion symmetry, forming a possibility of setting the kind of “arbitrary” unitary symmetry breaking special constraints on the post-measurement superpositions, i.e., the process arose as the introduction of the element of choice. There emerged in evolution a new, constructed kind of causality, at the expense of external physical matter and energy sources, to be gained. It is an emergence from the universal natural history, the universal continuous unidirectional dynamical time evolution. We consider, thus, biological autonomy, spontaneity and internally controlled causality as the strongest evidence of the above discussed evolutionary vital mechanism.
This special overall symmetry restoring process is in line with similar suggestions in the literature of “perpetual inconsistency-restoration force” schemes [
11,
14,
15,
43]. However, it is the primary advantage of our frame, that even if it belongs to this family of concepts, it is special in that it corresponds to the strong requirement to account for this internally generated spontaneous
energized activity. That these semiotic controls had to be born concomitant with the very origin of life was pointed out long ago by Pattee [
6,
7,
17]. Also, according to the above scenario, this symmetry restoring dynamics of internal origin is a liberated one by the break in causality, providing the
possibility of the evolution of the aforementioned element of physical “freedom” as choice.
It is implied by the above discussions, that the emerging
information, in the present context, is defined as the probability measure of the right, projectional choice of the branch in each reverse superposition, belonging to each assignment,
Here,
pi is the square of the time dependent probability coefficient of the
ith, special unique branch in the proper reverse superposition of assignment histories, summed over the paralell reverse different assignment superpositions in creating a protein macromolecule.
Thus, they are these downward causational, virtual-global, evolutional semiotic controls which make biological organisms so integrated, spontaneous and distinct in face of the rest of the Universe. In fact, they are these which can account for the
origin of the internally generated spontaneous activity, corresponding to the internal, liberated efficient cause of biological “motion”, generalized dynamics (see also
Section 2.2. and
Section 5.3. and [
16]). Actually, it appears that they are these pre-set, organizationally integrated “abstract” semiotic assignment relations which are the central
cause and at the same time also the nonlinear
effect of the overall biological generalized dynamics. Possibly, it is this semiotic relation which is often simplified by the concept of “autocatalysis”.
The controlling global-virtual quantum mechanical correlation primavelly may have arisen from a common, primordial material origin of the two molecular species as internal measurement “outcome” relations of codons and amino acids, evolving into mixed measurement outcome relations, as primeval correspondance. There are in this way a chemical evolution maintained coherence, in fact entanglement relation, between codons and the proper amino acids. The measurement assignment operators, corresponding to mixed measurements, may have evolved upon these inherent entanglement correspondances, setting initial conditions for the macromolecular algorithm. As to the contents of these quantum correlations, measuring one molecular species immediately sets the measurement outcome of the other, which is a solid component of our understanding of the “genetic language”.