- Email: [email protected]
Quantum gravity and life
BioSystems 46 (1998) 29 – 39
Quantum gravity and life Michael Conrad * Department of Computer Science, Wayne State Uni6ersity, Detroit, MI 48202, USA
Abstract New physical effects predicted by a quantum mechanistic model of gravity (the fluctuon model) may contribute significantly to the control and information processing capabilities of cells and organisms. © 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Quantum gravity; Fluctuon model; Anti-entropy; Biological organization; Control; Evolution; Bioinformational science
1. Paradigmatics Organisms are a giant step more elaborate in their structural and dynamic form than the objects that have been used to build up the theories of physics and chemistry. They are also clearly qualitatively more intricate and coordinated than the artifacts created by engineers. One of the chief differences is that the limit of simplification, so important in conventional physics, is not a tenable ideal. Of the many viewpoints that have been forwarded to account for the distinctive characteristics of organisms we can briefly mention five: (1) The friction-constraint theory. Weak, short range interactions that form the basis of friction (e.g. van der Waal’s interactions and hydrogen * E-mail: [email protected]
bonds) are sufficient to maintain the morphological form (or boundary conditions) requisite for biological life (Watson, 1965). Macromolecular self-assembly, based on specific shape-fitting and driven by free energy minimization, is the principal process. The folded shapes are largely implicit in the strongly (covalently) bonded sequences of amino acids in proteins (or the DNA sequences that code for these). The initial distribution of these and other molecules (lipids, carbohydrates,…) is in general also a precondition for the functional integrity of the whole. (2) Collecti6e phenomenon theory. Longer range interactions important for morphogenesis and functional coordination are mediated by propagation of local processes controlled by short range interactions and by nonlinear coupling of these local processes (Nicolis and Prigogine, 1977). En-
0303-2647/98/$19.00 © 1998 Elsevier Science Ireland Ltd. All rights reserved. PII S0303-2647(97)00078-6
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tropy increase is the primary driving force. (Examples: dissipative structures based on local reactions coupled by diffusion, hydrodynamic flow, mechanical properties of extended structures such as cytoskeleton and membrane, or on an even larger scale by membrane excitability and nerve impulse). (3) The coherent state theory. The morphological integrity and dynamic coordination of organisms draw on quantum coherence (i.e. correlations in quantum mechanical phase) of the type responsible for dynamic rigidity and thermal isolation of superfluid materials (Schro¨dinger, 1944; London, 1961; Pattee, 1968). Hydrogen bond ‘wires’ with coherent dynamics, based on the interaction of migratory protons with polarizable electrons at the water-membrane interface and on interactions with membrane proteins that reduce proton effective mass, are a possible example (Conrad, 1988a). Coherence in these cases is driven by energy minimization, since it is a property of the true ground state; but in principle similar states could also arise in an entropy driven manner through metabolic pumping (Fro¨hlich, 1983). (4) The circular complexity theory. Relational properties, in particular reprocessing interactions (self-reproduction, self-reference, autopoiesis), distinguish organisms from the ordinary objects of physical and chemical study (Maturana and Varela, 1980; Kampis, 1991; Rosen, 1991). In some discussions such circular interactions must be supported by the particular interactions afforded by the materials of life (carbon, hydrogen, nitrogen, oxygen) and in others it is supposed that they could in principle be abstracted and supported by alternate materials (the artificial life in silico position). (5) The li6ing uni6erse theory. The apparently distinguishing characteristics of organisms are extreme expressions of the true underlying physics of the universe. This underlying physics has built-in homeostatic dynamics that is mirrored, though with enormous elaboration, by the reprocessing dynamics of biological life (point 4 above). Forces of a gravitational nature, but broader than the gravitational force ordinarily observed, provide the underlying basis for the structural and dynamic
integrity of the body. This broader aspect of gravity is connected with randomization and recorrelation of quantum mechanical phase (i.e. with wave function collapse and re-formation of selfconsistent wave functions). Friction-constraint (point 1 above) and collective dynamics (point 2) demonstrably play a critical role in the biological life process. Quantum coherence (point 3) has not so far been convincingly demonstrated in biological matter, but it is easy to contemplate the contribution its existence would make to a wide variety of functionalities. Circular complexity (point 4) is also a fact, but with the reservation here that the relational aspect of the life process cannot be separated from its material basis in carbon chemistry (artificial life in silico is a no-go). Circularity could have its basis in friction, collective behavior or coherence (points 1–3). But an alternative conception, more akin to the one to be outlined here, is that it is an extension of circularities inherent in physics (Matsuno, 1989). The claim to be developed is this: all the above aspects (1 to 5) are sine qua non, but gravity is more sine qua non (‘more equal’) than the others. Systems of sufficiently high mass and with sufficiently high velocities are devoid of specific biological features. Yet, according to the quantum gravity theory to be outlined, they exhibit important features of biological life, such as significant random variation (superpositional collapse), significant control (or homeostasis), and variegated (chaotic) time evolution generated by inherent reprocessing dynamics. The universe as a whole has these properties. In the context of biological life they combine with the other necessities (friction, coherence, heredity-supporting polymers and highly specific self-referential mappings) to generate, through the evolutionary process, attractor structures whose complexity and equifinality would be unapproachable in the absence of the gravitational effect.
2. Quantum gravity (prelude) The fluctuon model of gravity, on which the above claim is based, has been presented in its
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technical aspect elsewhere.1 As prelude consider the main conceptual problem: general relativity and quantum mechanics provide antithetical models of acceleration. The former is an inherently nonlinear theory of acceleration, whereas the latter is linear, apart from measurement. The linchpin principle of general relativity is that of equivalence: gravity is locally indistinguishable from acceleration. However, gravity is a self-consistent field process (mass bends space, space curvature controls the motions of mass). Thus, equations of motion should be nonlinear, regardless of the nature of the forces at work. By contrast linear superposition is the linchpin principle of quantum mechanics: the state of a quantum mechanical system (its wave function) is a linear superposition of possible states that interfere with each other. Acceleration, or change of state of motion, occurs through the interference of possible states of different energy. The equations of motion must be linear, otherwise the linearity of the superposition would fail and superpositions would spontaneously collapse. If both principles, linear superposition and general relativity, are insisted upon this would mean all changes in the state of motion of all particles or systems of particles in the universe must at one and the same time be described by a linear map and by a nonlinear map, a frontal contradiction. Nonlinearity does enter into quantum mechanics in the measurement process (Penrose, 1989). However, this is an irreversible process treated as distinct from the reversible equations of motion that otherwise govern time evolution in standard formulations of quantum mechanics. Thus, when the superpositional description of a state is to be related to observation it is necessary to collapse the set of possible states into a particular classical description. This is where probability enters and also the choice of which variable to measure
1
For the most recent and complete presentation of gravity see Conrad (1996a); also Conrad (1996b) for a discussion of thermodynamic implications. For discussions of the model of force in general (including gravity) see Conrad (1989a,b, 1991, 1993a,b,c) and for the fluctuon principle Conrad (1986, 1988b). For qualitative presentations in a biological context see Conrad (1994, 1996c,d, 1997).
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precisely (e.g. position or momentum). So far as the equations of motion are concerned transitions between different energy levels (the quantum mechanical version of acceleration) are actually never seen. One is inclined to think that realistically an atom emits and absorbs photons even if it is not observed. However, until it is observed the formalism of quantum mechanics refers only to superpositions of interfering possibilities. The well known paradoxes of quantum mechanics are all connected with the fact that according to the equations of motion superpositions never collapse, whereas according to the measurement operations required to connect the wave function to experience they always collapse when a measurement is made. However, the even more basic contradiction to be noted here is this: quantum mechanics allows practically any transition compatible with conser6ation laws to occur with some probability, whereas general relati6ity requires that the obser6able distributions of mass be consistent with the unmanifest structure of spacetime. If the results of measurement are as arbitrary as allowed by the standard equations of quantum mechanics this means that general relativity must fail (failure of the first type). If the results are restricted in the way required by general relativity then standard quantum mechanics must fail (failure of the second type). According to the fluctuon model both types of failures are always occurring. Failures of the first type are somewhat analogous to mutations (since they involve random decorrelations in quantum mechanical phase). Failures of the second type are analogous to selection processes that bring order back into the system (since they involve recorrelations in quantum mechanical phase). This is the idea that motivates the hypothesis that a consistent theory of quantum gravity provides inherent attractor structures that are sufficiently strong and moldable to underlie the stability of a vast variety of dynamic organic forms. So far we have approached matters from the point of view of acceleration. Quantum mechanics and classical general relativity also differ as models of the influences, or forces, that produce acceleration. Quantum field theories treat interactions among particles (strong, electromagnetic, and
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weak forces) in terms of exchanges of virtual quanta (virtual gluons, photons, vector bosons). General relativity treats the gravitational force in terms of the geometry of space-time. A virtual particle interpretation (in terms of gravitons) must be consistent with this, and consistent with the fact that the virtual particle exchanges that mediate the strong, electromagnetic, and weak forces can co-exist with gravity without any detectable influence on the geometry of space-time. If gravity is to be identified with both acceleration and with the structure of space-time it might seem, on the purely geometrical view, to disappear as a force altogether (Misner et al., 1973). However, if gravity is mediated by the exchange of gravitons this cannot be so. Some interactions must maintain the consistency between the substratum of graviton excitations and the changing states of motion of manifest matter; whether this substratum is identified with space-time, or as a field whose structure is interpretable in terms of space and time, it must be drawn into the circle of action and reaction. Deviations from consistency correspond to the decorrelations noted above; restoration of consistency corresponds to the recorrelations. The decorrelation process is associated with superpositional collapse. The restoring force responsible for recorrelation is itself mediated by corrective alterations in graviton exchanges that spring into action as soon as consistency breaks down. These are the new, biologically relevant aspects of gravity predicted by the fluctuon theory.
3. Fluctuon model (brief overview) Picture a plenum of particles, somewhat analogous to a Dirac sea of negative energy particles (the so-called vacuum sea). The important point is that the particles of this sea are unmanifest. The mass of manifest particles is actually eventually to be interpreted in terms of lacunae in this vacuum sea. Negative energy turns out to be a formal property, roughly speaking inherited from the fact that the particles of the plenum are in a superposition of states that interact through the exchange of virtual quanta and states that do
not so interact (the unmanifest states proper). The space-curvature of general relativity (the metric structure of space-time) is interpreted as the density structure of the vacuum sea. Altogether there are three seas. The supersea of all vacuum particles mediates the gravitational force. This is the weakest force because, for reasons to be noted below, the strength of an interaction in the fluctuon model decreases as vacuum density increases. Gravitons are interpreted as excitations in this supersea. Photons mediating the electromagnetic force are interpreted as excitations in the much less dense subsea of vacuum electrons (and the related weak force as excitations in compressed regions of this subsea). The strong (chromodynamic) force is mediated by the very much less dense subsea of vacuum quarks. Photons are interpreted as chains of transient electron–positron pairs. The length of each link in the chain is determined by the density of vacuum electrons. Gluons, similarly, are interpreted as chains of transient quark–antiquark pairs. The vast majority of particles in the full sea are referred to as massons. Gravitons are interpreted as chains of masson–antimasson pairs propagating in the full sea of vacuum fermions (though higher energy excitations of other particles can also enter into such chains). The term ‘fluctuon’ refers to the nature of these propagating excitations. Consider a positive energy particle, to be referred to as an absorber. For concreteness, suppose that this is an electron. The unmanifest electrons in the surrounding sea are continually undergoing fluctuations in energy, due to the time-energy uncertainty principle. The fluctuation energy might be greater than or equal to the mass-energy required to form an electron– positron pair. Suppose it is equal. Then the transient appearance of the pair may be accompanied by the transmission of a definite quantity of momentum to the manifest electron that in all coordinate systems is compatible with conservation of momentum. The pair must decay in a time (referred to as the fluctuation time) compatible with the time-energy uncertainty principle. When it decays there is some chance that it will not give its momentum back to the electron, but to the vacuum sea. But this is not allowed, since it is
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incompatible with conservation of momentum in all coordinate systems. Thus, another particle – antiparticle pair must be created, and so on, until the chain reaches a second absorbing particle that can take up its momentum without violating conservation of momentum. The momentum carried by the pair decreases as vacuum density decreases, since the fluctuation energy required for propagation decreases; but the coupling strength increases, roughly because the probability of an initial fluctuation ‘dumping’ its fluctuation energy on a neighboring vacuum particle increases as the duration of the violation of time-energy uncertainty increases. (Actually the coupling probability increases quadratically with the duration of the violation, referred to as the fluctuation time). Absorbing particles obviously cannot directly repel unmanifest vacuum particles, since the latter only serve as carriers of momentum. However, recall that vacuum particles are in superpositions of unmanifest and manifest states (the latter being referred to as trapped fluctuons). Chains initiated by absorbing particles thus exert a depressing (or polarizing) effect on the surrounding vacuum sea. This effect is isotropically distributed in the cases of the strong and electromagnetic forces, since buildup of polarization is countered by the overall requirement for color and charge neutrality. This is not the case for the gravitational interaction, since mass comes in only one charge. The vacuum density of neighboring high mass collections of manifest particles will thus be highly depressed and the density of distant regions of space-time elevated. This is how mass controls the metric structure of space-time. The attractive gravitational interaction is actually indirect. Manifest particles are pushed together by gravitons emanating from trapped fluctuons in distant regions of space where the vacuum density is elevated. Mutual screening by the manifest particles allows the compressing effect to dominate over the direct repulsion. All the particles in the universe, both manifest and unmanifest, thus contribute to the gravitational interaction. This is the fluctuon model’s version of Mach’s principle. Now we can see why a geometrical theory of gravity is possible and why the strong and electromagnetic interactions can conform to this geome-
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try without introducing any geometrical effects of their own. The isotropy and low density of the electron and quark subseas means that interactions mediated by these subseas are not altered by the geometry of space-time, though the resulting particle motions are of course also subject to ubiquitous graviton bombardments. Changes in states of motion of absorbers resulting from electromagnetic and chromodynamic interactions must affect the density (or metric) structure of the vacuum sea, however. This is why gravity alone can be identified with acceleration, and why resistance to acceleration (or inertia) is solely dependent on gravitational mass. Mass would not be independent of electric charge if the electron subsea were so dense that the effect of charge on the density of the vacuum supersea were comparable to the effect of mass. We can also see why superpositions should collapse spontaneously. This follows from the self-consistency requirements of the theory. The mass formally assigned to vacuum particles must be consistent with the density of either the vacuum supersea or one of the subseas. If this were not the case the fluctuation energy required to create the initial transient pair would not match the fluctuation energy required for chain propagation. Whenever particles change their state of motion the distribution of mass in the universe must change. The density structure of the vacuum sea is altered. The effect on the density structure of the quark and electron subseas is negligible, apart from the local polarizations attached to the particles themselves. The density variations associated with these local polarizations are compensated by distortion waves of vacuum density that correspond to the wave aspect of chain propagation. The dependence of the strong and electromagnetic forces on the density of their respective subseas is thus effectively masked. Such masking is not possible in the case of gravity, however, since the density structure of the supersea changes whenever mass accelerates and does so regardless of which force produces the acceleration. The gravitational force between any two particles thus depends on the density structure of the supersea and accordingly must be redefined whenever accelerations occur. From the quantum mechanical
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point of view the wave function of the vacuum changes, and thus superpositional collapse must continually occur if a new density is to be continually defined. Consequently the forces between particles (the interaction structure of the universe) is to some degree subject to a continual random variation (a kind of mutation). We can also describe the situation equivalently, but more usefully for the present purposes, from the point of view of the interactions required to maintain self-consistency. As noted above, changes in the distribution of manifest particles must always be followed by readjustment of the vacuum density distribution. The consistency between the two distributions is not a ‘pre-established harmony’ and is never perfect. It must be maintained by interactions between manifest particles and trapped fluctuons. The greater the rearrangement of manifest mass the greater the deviation from consistency. The strength of the gravitational interaction between particles will be altered. For example, if the density of the supersea is locally too low the masson-antimasson mass will be too high for graviton chains to be initiated. The repulsive effect of manifest particles will decrease and consequently the local vacuum density will undergo a corrective increase. If the local density is too high, the lower energy fluctuations that allow for propagative chains that jump over vacuum particles will be possible, thereby increasing the strength of the gravitational interaction, again leading to a corrective effect. The interactional picture brings out the control system aspect of gravity. Deviations from selfconsistency can be viewed as error. When such deviations occur the motions of manifest particles become decorrelated from the vacuum density structure. A random fluctuation of energy occurs. Each of the components of the superposition is multiplied by a random phase factor. The interference terms are thus altered in a random way. This is the basis of superpositional collapse (Bohm, 1951). The term superpositional mutation would actually be more accurate, since the superposition is redefined rather than eliminated. This corresponds to the fact that interference effects disappear completely only when the results of many measurements are averaged, since the random al-
terations of phase then cancel out. Randomness here can be defined, without philosophical prejudice, in terms of the incompressibility of a description (in the fashion of algorithmic information theory, Chaitin, 1990). However, as noted earlier, the degree of incompressibility associated with the phase altering fluctuations must be greater than that allowed by relativity, since in the latter case incompressibility is constrained by a self-consistency requirement, whereas in the former case it is not (since the fluctuations are deviations from self-consistency). It is at this point that the graviton exchanges that recorrelate the phases in a way that moves back in the direction of self-consistency spring into action. Again we see a random error aspect analogous to genetic mutation and an error correction aspect analogous to natural selection and homeostatic regulation.
4. Self-regulation in the case of gravitational collapse Black hole phenomena, according to the fluctuon theory, are an extreme manifestation of such self-regulation. When the number of positive energy particles (or vacuum lacunae) collected in a region of the vacuum sea becomes so great that photons cannot escape, then gravitational collapse to a black hole begins. According to the fluctuon theory gravitons are also trapped. Thus, on the surface it would appear that the black hole should no longer exert any gravitational attraction on particles outside the region, an immediate contradiction to the collapse concept. However, recall that in the fluctuon model, gravity is an indirect attractive force. Actually particles will continue to be pushed into the black hole region by gravitons emanating from high vacuum density regions of distant space. The elevated density of these regions was originally induced by the repelling effects of the positive energy particles whose coalescence traps photons and gravitons. Trapping eliminates these inducing effects. The compressing effect of gravitons emanating from distant regions accordingly falls off. Direct repulsive effects of graviton exchanges within the hole come to the fore, and the particles within it fly
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outwards. The collapse process is reversed. Trapped fluctuons are again repelled into distant regions of space, and the normal (indirect) attractive force of gravity reinstated. The reversal of collapse is of great conceptual importance, since ultimate gravitational collapse is incompatible with the conservation of energy and would therefore lead inevitably to the complete breakdown of physics. The point to note here is that the mechanism of gravitational collapse is the same as the mechanism of superpositional collapse. The alterations of graviton exchanges initiated by particles in the black hole region is a massive analog of the alterations accompanying superpositional collapse. The random alterations in the motions of particles concomitant to the shutting down of graviton initiations corresponds to the decorrelation process, while the reinstatement of the indirect attractive interaction corresponds to the recorrelation process.
5. Potential reversal and anti-entropy The self-regulatory aspect of gravitational collapse illustrates in dramatic fashion an important feature of the fluctuon theory: the sign of the gravitational interaction can change (Conrad, 1996b). This is due to the fact that the compressing effect of gravitons from distant regions of the vacuum sea dominates only when these regions have high density; when the density falls off the direct repulsive effect dominates. The ordinary potential energy minimum is thus the coalesced state in the former (normal) case. However, as this minimum is approached overly closely the dispersed state becomes the minimum. What appears to be the high potential energy state (the atypical initial condition) under ordinary conditions of the physics laboratory is thus one region of a cyclic attractor. Actually, the real evolution of the universe would follow a highly chaotic course, since stability or instability of different manifest distributions of matter depends on the unmanifest structure of the vacuum sea. Two similar distributions could have very different stability properties, depending on far distant features
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of this sea, and therefore depending on the historical pathway of their formation. Minima representing ultimate gravitational collapse (big bang, big crunch) would almost certainly disappear before they are ever reached. Such reversals of potential are, according to fluctuon theory, always associated with acceleration. This is due to the close relationship between superpositional collapse (or mutation) and gravitational collapse (really massive gravitational reversal). The recorrelation processes that follow changes in states of motion in the low energy, low mass domain mirror those in the black hole domain, with the difference that the alterations in gravitational interactions are so much smaller and less coherent that deviations from the normal (indirect) attractive force of gravity are undetectable. Nevertheless the decorrelation–recorrelation cycle in this domain points to the existence of basins of attraction whose structure is history dependent, just as it is in the case of the universe in the large. The decorrelation–recorrelation process points to a broadened concept of entropy. Decorrelation is associated with entropy increase, whereas recorrelation is associated with entropy decrease. This is particularly clear in the case of gravitational collapse and reversal of collapse. An atypical initial condition arises dynamically when collapse is reversed, due to the fact that the minimum potential energy state toward which particles fall is the dispersed state at this stage. When the attractive gravitational interaction is reinstated the dispersed state becomes the high potential energy state. A perfectly elastic bouncing ball cycles between low and high potential energy states, but not because the potential is reversed. An incompletely elastic ball thus eventually comes to rest in the low potential energy state, due to the fact that its kinetic energy is distributed over the heat bath. Entropy therefore increases and consequently the high potential energy state becomes unavailable. The existence of a decorrelation–recorrelation cycle means that the system arrives again at a high potential energy state even though entropy increased as it approached the initial potential energy minimum, due to the fact that this state appears on an attractor. The recorrelation part of
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the cycle, since it is associated with movement towards an atypical state, represents an anti-entropy process. The same considerations apply to superpositional collapse, except that the entropy process always dominates the anti-entropy process. A source of high grade energy is still necessary to defeat the general increase in entropy. However, the anti-entropy process nevertheless plays an important role in regulation, since it is the indication of an attractor structure. The universe in the fluctuon model is always in one particular quantum state, even if the wave function changes in a random, irreversible manner whenever changes in states of motion occur. The occurrence of these transitions is not contingent on a measurement process, since decorrelation (connected with randomization of quantum mechanical phase) is an endogenous process. Thus the wave function becomes partially actualized (which is why we are entitled to think of photons radiating even in the absence of their being observed). Entropy in some sense increases, but in some sense it cannot increase (since the universe is only in one state). The latter fact is the content of the Liouville theorem, which applies in the fluctuon model. This ambiguity (which is faced both by classical and quantum statistical mechanics) is redressed in the following way in the fluctuon theory. The entropy and anti-entropy associated with the correlation and decorrelation cycle are measured by the number of complexions compatible with the macrostate of the universe. The entropy increases on decorrelation because the macrostate of the manifest universe becomes more symmetrical (e.g. gradients of temperature, pressure, chemical potential diminish). Decorrelation leads to this situation because it leads to a wave function in which the probability amplitudes are more equal. Recorrelation represents an anti-entropy process since it is associated with the restoration of a consistent relationship between the manifest organization of matter and the unmanifest structure of the vacuum sea. The probability amplitudes therefore become less equal and the number of possible wave functions compatible with the same manifest macroscopic organization therefore decreases.
The new feature of the fluctuon model is that systems can dynamically return to higher symmetry states after undergoing a transition to a lower symmetry state due to restrictions on access imposed by self-consistency (the assumption that all states are equally probable does not apply). In the normal regime, where indirect attractive interaction dominates, the increase in entropy associated with decorrelation is greater than the decrease associated with decorrelation. In the anti-normal regime the situation is reversed. Such changes in overall symmetry actually are only apparent, since they are compensated by symmetry changes in the unmanifest vacuum structure. Thus, when particles coalesce and become randomized by collision due to the attractive force of gravity the density gradients in the vacuum sea become more pronounced.
6. Percolation network The effects noted above would be entirely undetectable in the simple systems studied in the physics laboratory. A single electron undergoing acceleration in a given coordinate system would undergo repeated radiation of photons and gravitons. According to the fluctuon theory the occurrence of these radiative transitions is not contingent on the intervention of an observer. The random effects of vacuum density alterations on interference terms involving states of different energy serves to actualize these transitions. This decorrelation process is followed by a recorrelation which, because of the negligibility of the departure from self-consistency, would reform the wave function in a way that for all practical purposes would have the aspect of a continuous, deterministic evolution, as in the standard theory. The motions of particles in ordinary multiparticle systems (gases, liquids, solids) should exhibit slight deviations from what in principle follows from the standard time evolution equations, but this would have no effect on average properties. If the systems are out of equilibrium some component of the entropy increase would be due to the decorrelation entropy; but this would be swamped by the general increase in entropy attributable to
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the evolution of a larger and larger number of complexions compatible with the macroscopic state. The organization of cells and organisms is entirely different. Some terms that are descriptive include: vertical flow of information, cross-scale interactions, percolation network, hypercircle of influence flow (Conrad, 1993a,d, 1994, 1995, 1996c). First picture influences as flowing horizontally through a system, in general with recurrent interactions. So far this is just like a current day technological computing system. Next picture such horizontal flows occurring at many different levels. To this add vertical flows across levels (or across scale). Influences impinging on the system from the environment are filtered in the downscale direction to selectively set the state of micro components of the system and are selectively amplified in the upscale direction to control its actions. A measurement apparatus directed to micro-properties has this cross-scale characteristic. However, the organism is different from existing technical measurement systems in a fundamental respect. The cross-scale flow of influence proceeds in small steps through multiple levels, each with unique scale dependent physicalchemical capabilities. The hypercircle image is intended to evoke this picture. However, it is a hypercircle with many inner hyper-epicycles. Furthermore, the picture of distinct levels with definite dimensions is inadequate. The system incorporates diverse ultra-integrated subcomponents and processes that combine different physical dimensions in diverse ways. The mitochondrion, the chloroplast, the cytoskeleton, tissues, and organ systems are examples that could be described structurally in this multi-scale fashion. Genetic-developmental systems, the immune system, and the brain are examples that could be described functionally as percolation networks that process information from macro input influences to macro output action in a multiscale fashion. Each such percolation network can be abstractly conceptualized as a cross-scale decision tree. The many optional directions in which the downward filtration and upward percolation of influences can proceed means that averaging is no
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longer the dominant fact. Events at the smallest levels of scale, for example involving the state changes of electrons in macromolecules, are critical for controlling the macro behavior. The vacuum structure must, according to the fluctuon model, be drawn into the hypercircular decision tree. The distribution of manifest particles currently constituting the body of the organism must be consistent with the vacuum density structure, which we can refer to as its body image in the vacuum sea. When the manifest body particles rearrange themselves the vacuum body image must change. They will become inconsistent. Graviton flows will spring into action to bring them back into a consistent relationship. These flows will be too weak, given the masses and velocities involved, to affect the motion of macromolecules as a whole. However, the mass of electrons and of various quasi particle excitations of the manifest body is sufficiently small for vacuum decorrelation and recorrelation processes to effect transitions. In the percolation network type architecture of biological organisms this is sufficient to exert a critical controlling effect on macro behavior. The decorrelation processes can contribute to the randomness of mutation or other search processes. Recorrelation generally means that some electronic transitions will be selectively triggered, potentially playing a critical role in the cross-scale decision tree. The integration of influences within the vacuum sea thus contributes to decision processes that eventually culminate in the macro actions of the organism. Or, at a more global level, the body image in the vacuum sea may provide a basin of attraction which helps to pull the organism back to its dynamic form subsequent to perturbing influences from the outside by influencing widely distributed electronic and quasi particle transitions. Or the body image in the vacuum may in this manner contribute to the reliable functioning of the organism in the face of various internal noise processes. It is at this stage difficult to assess how important these various contributions are in comparison to the paradigms mentioned at the front of this paper. The argument might be made that the effects predicted would be so small at biological energies that we could give an adequate account,
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in principle, of the information and control capabilities of organisms without any reference to quantum gravity; quantum gravity would then only be relevant by virtue of the fact that the universe would not be what it is without it. The counter argument is this: if the effects are so small then the nonlinearities requisite for life would have to be added to the equations of motion in an ad hoc manner, whereas they are inherent in fluctuon theory. The circular (self-reprocessing) dynamics are inherent in the underlying physics. The elaborate form and coordination of biological matter maintainable through frictional interactions is greater than could be accounted for on the basis of models that leave out this underlying physics. The nonlinearities and initial-boundary conditions prerequisite for form and coordination to develop through collective processes, such as dissipative structures, would have an intrinsic basis, since the existence of these prerequisites cannot themselves be justified on the basis of the dynamics to which they give rise. Interaction structures sufficiently intricate to support quantum coherence are also more supportable, opening the possibility for a more global underpinning of biological form. Each increment along any of these lines would elaborate the crossscale, percolative aspect of the organization, further shaping the vacuum image and thereby further eliciting the control capabilities nascent in the interactions between the vacuum sea and manifest matter. The image serves to regulate the manifest organization’s responses to perturbations directly affecting it; the manifest organization serves to regulate the image’s responses to the changing arrangements of manifest mass. The present state of the manifest organism is no longer a full statement of all its relevant past history. Its image in the vacuum sea also represents aspects of this history. The whole organization boots to greater and greater self-regulatory capacity and complexity, including complexity that supports the manifest hereditary apparatus. A new feature of heredity enters though. Two material organizations with the same form would have different stability properties if the pathway of their evolution were different. History is locked not only into the manifest hereditary apparatus,
and into the manifest structures requisite to the operations of this apparatus, but as well into the hidden structure of the vacuum sea.
Acknowledgements This research was supported by the National Science Foundation under grant ECS-9409780.
References Bohm, D., 1951. Quantum Theory. Prentice-Hall, Englewood Cliffs, N.J. Chaitin, G.J., 1990. Algorithmic Information Theory. Cambridge University Press, Cambridge, UK. Conrad, M., 1986. Reversibility in the Light of Evolution, Mondes en De´veloppement, vol. 14, no. 54 – 55, pp. 111 – 121. [Also In: Prigogine, I., Sanglier, M. (Eds.), Laws of Nature and Human Conduct. Task Force on Research Information and Study on Science, Brussels, pp. 111 – 121, 1987]. Conrad, M. The water-membrane interface as a substrate for H – H superflow. Int. J. Quantum Chem: Quantum Biol. Symp. 14 (1988) 167 – 188 (Printer’s Erratum in vol. 33 (1988) 503 – 504). Conrad, M., 1988b. Quantum mechanics and molecular computing: mutual implications. Int. J. Quantum Chem.: Quantum Biol. Symp. 15, 287 – 301. Conrad, M., 1989a. Physics and biology: towards a unified model. Appl. Math. Comput. 32, 75 – 102. Conrad, M., 1989b. Force, measurement, and life. In: Casti, J., Karlquist, A. (Eds.), Newton to Aristotle: Toward a Theory of Models for Living Systems. Birkhauser, Boston, pp. 121 – 199. Conrad, M., 1991. Transient excitations of the Dirac vacuum as a mechanism of virtual particle exchange. Phys. Lett. A 152, 245 – 250. Conrad, M., 1993a. The fluctuon model of force, life, and computation: a constructive analysis. Appl. Math. Comput. 56, 203 – 259. Conrad, M., 1993b. Fluctuons I. operational analysis. Chaos, Solitons Fractals 3, 411 – 424. Conrad, M., 1993c. Fluctuons II. electromagnetism. Chaos, Solitons Fractals 3, 563 – 573. Conrad, M., 1993d. Emergent computation through self-assembly. Nanobiology 2, 5 – 30. Conrad, M., 1994. From brain structure to vacuum and back again: the great chain of being model. Nanobiology 3, 99 – 121. Conrad, M., 1995. Multiscale synergy in biological information processing. Opt. Mem. Neural Netw. 4 (2), 89 – 98. Conrad, M., 1996a. Fluctuons-III. gravity. Chaos, Solitons Fractals 7, 1261 – 1303.
M. Conrad / BioSystems 46 (1998) 29–39 Conrad, M., 1996b. Anti-entropy and the origin of initial conditions. Chaos, Solitons Fractals 7, 725–745. Conrad, M., 1996c. Percolation and collapse of quantum parallelism: a model of qualia and choice. In: Hameroff, S.R., Kaszniak, A.W., Scott, A.C. (Eds.). MIT Press, Cambridge, MA, pp. 469–492. Conrad, M., 1996d. Cross-scale information processing in evolution, development and intelligence. BioSystems 38, 97– 109. Conrad, M., 1997. Origin of life and the underlying physics of the universe. Biosystems 42, 177–190. Fro¨hlich, H., 1983. Evidence for coherent excitation in biological systems. Int. J. Quantum Chem. 23, 1589–1595. Kampis, G., 1991. Self-Modifying Systems in Biology and Cognitive Science. Pergamon, Oxford, UK. London, F., 1961. Superfluids, vol I. Dover Publications, New York. Maturana, H.R., Varela, F.J., 1980. Autopoiesis and Cognition. Reidel, Dordrecht, The Netherlands.
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Matsuno, K., 1989. Protobiology: Physical Basis of Biology. CRC Press, Boca Raton, FL. Misner, C.W., Thome, K.S., Wheeler, J.A., 1973. Gravitation. W.H. Freeman and Co., New York. Nicolis, G., Prigogine, I., 1977. Self-Organization in Nonequilibrium Systems. Wiley-Interscience, New York. Pattee, H.H., 1968. The physical basis of coding and reliability in biological evolution. In: Waddington, C.H. (Ed.), Prolegomena to Theoretical Biology. University of Edinburgh Press, Edinburgh, pp. 67 – 93. Penrose, R., 1989. The Emperor’s New Mind. Oxford University Press, Oxford, UK. Rosen, R., 1991. Life Itself. Columbia University Press, New York. Schro¨dinger, E., 1944. What is Life? Cambridge University Press, Cambridge, UK. Watson, J.D., 1965. Molecular Biology of the Gene. W.A. Benjamin, New York.
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Quantum gravity and life Michael Conrad * Department of Computer Science, Wayne State Uni6ersity, Detroit, MI 48202, USA
Abstract New physical effects predicted by a quantum mechanistic model of gravity (the fluctuon model) may contribute significantly to the control and information processing capabilities of cells and organisms. © 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Quantum gravity; Fluctuon model; Anti-entropy; Biological organization; Control; Evolution; Bioinformational science
1. Paradigmatics Organisms are a giant step more elaborate in their structural and dynamic form than the objects that have been used to build up the theories of physics and chemistry. They are also clearly qualitatively more intricate and coordinated than the artifacts created by engineers. One of the chief differences is that the limit of simplification, so important in conventional physics, is not a tenable ideal. Of the many viewpoints that have been forwarded to account for the distinctive characteristics of organisms we can briefly mention five: (1) The friction-constraint theory. Weak, short range interactions that form the basis of friction (e.g. van der Waal’s interactions and hydrogen * E-mail: [email protected]
bonds) are sufficient to maintain the morphological form (or boundary conditions) requisite for biological life (Watson, 1965). Macromolecular self-assembly, based on specific shape-fitting and driven by free energy minimization, is the principal process. The folded shapes are largely implicit in the strongly (covalently) bonded sequences of amino acids in proteins (or the DNA sequences that code for these). The initial distribution of these and other molecules (lipids, carbohydrates,…) is in general also a precondition for the functional integrity of the whole. (2) Collecti6e phenomenon theory. Longer range interactions important for morphogenesis and functional coordination are mediated by propagation of local processes controlled by short range interactions and by nonlinear coupling of these local processes (Nicolis and Prigogine, 1977). En-
0303-2647/98/$19.00 © 1998 Elsevier Science Ireland Ltd. All rights reserved. PII S0303-2647(97)00078-6
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tropy increase is the primary driving force. (Examples: dissipative structures based on local reactions coupled by diffusion, hydrodynamic flow, mechanical properties of extended structures such as cytoskeleton and membrane, or on an even larger scale by membrane excitability and nerve impulse). (3) The coherent state theory. The morphological integrity and dynamic coordination of organisms draw on quantum coherence (i.e. correlations in quantum mechanical phase) of the type responsible for dynamic rigidity and thermal isolation of superfluid materials (Schro¨dinger, 1944; London, 1961; Pattee, 1968). Hydrogen bond ‘wires’ with coherent dynamics, based on the interaction of migratory protons with polarizable electrons at the water-membrane interface and on interactions with membrane proteins that reduce proton effective mass, are a possible example (Conrad, 1988a). Coherence in these cases is driven by energy minimization, since it is a property of the true ground state; but in principle similar states could also arise in an entropy driven manner through metabolic pumping (Fro¨hlich, 1983). (4) The circular complexity theory. Relational properties, in particular reprocessing interactions (self-reproduction, self-reference, autopoiesis), distinguish organisms from the ordinary objects of physical and chemical study (Maturana and Varela, 1980; Kampis, 1991; Rosen, 1991). In some discussions such circular interactions must be supported by the particular interactions afforded by the materials of life (carbon, hydrogen, nitrogen, oxygen) and in others it is supposed that they could in principle be abstracted and supported by alternate materials (the artificial life in silico position). (5) The li6ing uni6erse theory. The apparently distinguishing characteristics of organisms are extreme expressions of the true underlying physics of the universe. This underlying physics has built-in homeostatic dynamics that is mirrored, though with enormous elaboration, by the reprocessing dynamics of biological life (point 4 above). Forces of a gravitational nature, but broader than the gravitational force ordinarily observed, provide the underlying basis for the structural and dynamic
integrity of the body. This broader aspect of gravity is connected with randomization and recorrelation of quantum mechanical phase (i.e. with wave function collapse and re-formation of selfconsistent wave functions). Friction-constraint (point 1 above) and collective dynamics (point 2) demonstrably play a critical role in the biological life process. Quantum coherence (point 3) has not so far been convincingly demonstrated in biological matter, but it is easy to contemplate the contribution its existence would make to a wide variety of functionalities. Circular complexity (point 4) is also a fact, but with the reservation here that the relational aspect of the life process cannot be separated from its material basis in carbon chemistry (artificial life in silico is a no-go). Circularity could have its basis in friction, collective behavior or coherence (points 1–3). But an alternative conception, more akin to the one to be outlined here, is that it is an extension of circularities inherent in physics (Matsuno, 1989). The claim to be developed is this: all the above aspects (1 to 5) are sine qua non, but gravity is more sine qua non (‘more equal’) than the others. Systems of sufficiently high mass and with sufficiently high velocities are devoid of specific biological features. Yet, according to the quantum gravity theory to be outlined, they exhibit important features of biological life, such as significant random variation (superpositional collapse), significant control (or homeostasis), and variegated (chaotic) time evolution generated by inherent reprocessing dynamics. The universe as a whole has these properties. In the context of biological life they combine with the other necessities (friction, coherence, heredity-supporting polymers and highly specific self-referential mappings) to generate, through the evolutionary process, attractor structures whose complexity and equifinality would be unapproachable in the absence of the gravitational effect.
2. Quantum gravity (prelude) The fluctuon model of gravity, on which the above claim is based, has been presented in its
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technical aspect elsewhere.1 As prelude consider the main conceptual problem: general relativity and quantum mechanics provide antithetical models of acceleration. The former is an inherently nonlinear theory of acceleration, whereas the latter is linear, apart from measurement. The linchpin principle of general relativity is that of equivalence: gravity is locally indistinguishable from acceleration. However, gravity is a self-consistent field process (mass bends space, space curvature controls the motions of mass). Thus, equations of motion should be nonlinear, regardless of the nature of the forces at work. By contrast linear superposition is the linchpin principle of quantum mechanics: the state of a quantum mechanical system (its wave function) is a linear superposition of possible states that interfere with each other. Acceleration, or change of state of motion, occurs through the interference of possible states of different energy. The equations of motion must be linear, otherwise the linearity of the superposition would fail and superpositions would spontaneously collapse. If both principles, linear superposition and general relativity, are insisted upon this would mean all changes in the state of motion of all particles or systems of particles in the universe must at one and the same time be described by a linear map and by a nonlinear map, a frontal contradiction. Nonlinearity does enter into quantum mechanics in the measurement process (Penrose, 1989). However, this is an irreversible process treated as distinct from the reversible equations of motion that otherwise govern time evolution in standard formulations of quantum mechanics. Thus, when the superpositional description of a state is to be related to observation it is necessary to collapse the set of possible states into a particular classical description. This is where probability enters and also the choice of which variable to measure
1
For the most recent and complete presentation of gravity see Conrad (1996a); also Conrad (1996b) for a discussion of thermodynamic implications. For discussions of the model of force in general (including gravity) see Conrad (1989a,b, 1991, 1993a,b,c) and for the fluctuon principle Conrad (1986, 1988b). For qualitative presentations in a biological context see Conrad (1994, 1996c,d, 1997).
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precisely (e.g. position or momentum). So far as the equations of motion are concerned transitions between different energy levels (the quantum mechanical version of acceleration) are actually never seen. One is inclined to think that realistically an atom emits and absorbs photons even if it is not observed. However, until it is observed the formalism of quantum mechanics refers only to superpositions of interfering possibilities. The well known paradoxes of quantum mechanics are all connected with the fact that according to the equations of motion superpositions never collapse, whereas according to the measurement operations required to connect the wave function to experience they always collapse when a measurement is made. However, the even more basic contradiction to be noted here is this: quantum mechanics allows practically any transition compatible with conser6ation laws to occur with some probability, whereas general relati6ity requires that the obser6able distributions of mass be consistent with the unmanifest structure of spacetime. If the results of measurement are as arbitrary as allowed by the standard equations of quantum mechanics this means that general relativity must fail (failure of the first type). If the results are restricted in the way required by general relativity then standard quantum mechanics must fail (failure of the second type). According to the fluctuon model both types of failures are always occurring. Failures of the first type are somewhat analogous to mutations (since they involve random decorrelations in quantum mechanical phase). Failures of the second type are analogous to selection processes that bring order back into the system (since they involve recorrelations in quantum mechanical phase). This is the idea that motivates the hypothesis that a consistent theory of quantum gravity provides inherent attractor structures that are sufficiently strong and moldable to underlie the stability of a vast variety of dynamic organic forms. So far we have approached matters from the point of view of acceleration. Quantum mechanics and classical general relativity also differ as models of the influences, or forces, that produce acceleration. Quantum field theories treat interactions among particles (strong, electromagnetic, and
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weak forces) in terms of exchanges of virtual quanta (virtual gluons, photons, vector bosons). General relativity treats the gravitational force in terms of the geometry of space-time. A virtual particle interpretation (in terms of gravitons) must be consistent with this, and consistent with the fact that the virtual particle exchanges that mediate the strong, electromagnetic, and weak forces can co-exist with gravity without any detectable influence on the geometry of space-time. If gravity is to be identified with both acceleration and with the structure of space-time it might seem, on the purely geometrical view, to disappear as a force altogether (Misner et al., 1973). However, if gravity is mediated by the exchange of gravitons this cannot be so. Some interactions must maintain the consistency between the substratum of graviton excitations and the changing states of motion of manifest matter; whether this substratum is identified with space-time, or as a field whose structure is interpretable in terms of space and time, it must be drawn into the circle of action and reaction. Deviations from consistency correspond to the decorrelations noted above; restoration of consistency corresponds to the recorrelations. The decorrelation process is associated with superpositional collapse. The restoring force responsible for recorrelation is itself mediated by corrective alterations in graviton exchanges that spring into action as soon as consistency breaks down. These are the new, biologically relevant aspects of gravity predicted by the fluctuon theory.
3. Fluctuon model (brief overview) Picture a plenum of particles, somewhat analogous to a Dirac sea of negative energy particles (the so-called vacuum sea). The important point is that the particles of this sea are unmanifest. The mass of manifest particles is actually eventually to be interpreted in terms of lacunae in this vacuum sea. Negative energy turns out to be a formal property, roughly speaking inherited from the fact that the particles of the plenum are in a superposition of states that interact through the exchange of virtual quanta and states that do
not so interact (the unmanifest states proper). The space-curvature of general relativity (the metric structure of space-time) is interpreted as the density structure of the vacuum sea. Altogether there are three seas. The supersea of all vacuum particles mediates the gravitational force. This is the weakest force because, for reasons to be noted below, the strength of an interaction in the fluctuon model decreases as vacuum density increases. Gravitons are interpreted as excitations in this supersea. Photons mediating the electromagnetic force are interpreted as excitations in the much less dense subsea of vacuum electrons (and the related weak force as excitations in compressed regions of this subsea). The strong (chromodynamic) force is mediated by the very much less dense subsea of vacuum quarks. Photons are interpreted as chains of transient electron–positron pairs. The length of each link in the chain is determined by the density of vacuum electrons. Gluons, similarly, are interpreted as chains of transient quark–antiquark pairs. The vast majority of particles in the full sea are referred to as massons. Gravitons are interpreted as chains of masson–antimasson pairs propagating in the full sea of vacuum fermions (though higher energy excitations of other particles can also enter into such chains). The term ‘fluctuon’ refers to the nature of these propagating excitations. Consider a positive energy particle, to be referred to as an absorber. For concreteness, suppose that this is an electron. The unmanifest electrons in the surrounding sea are continually undergoing fluctuations in energy, due to the time-energy uncertainty principle. The fluctuation energy might be greater than or equal to the mass-energy required to form an electron– positron pair. Suppose it is equal. Then the transient appearance of the pair may be accompanied by the transmission of a definite quantity of momentum to the manifest electron that in all coordinate systems is compatible with conservation of momentum. The pair must decay in a time (referred to as the fluctuation time) compatible with the time-energy uncertainty principle. When it decays there is some chance that it will not give its momentum back to the electron, but to the vacuum sea. But this is not allowed, since it is
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incompatible with conservation of momentum in all coordinate systems. Thus, another particle – antiparticle pair must be created, and so on, until the chain reaches a second absorbing particle that can take up its momentum without violating conservation of momentum. The momentum carried by the pair decreases as vacuum density decreases, since the fluctuation energy required for propagation decreases; but the coupling strength increases, roughly because the probability of an initial fluctuation ‘dumping’ its fluctuation energy on a neighboring vacuum particle increases as the duration of the violation of time-energy uncertainty increases. (Actually the coupling probability increases quadratically with the duration of the violation, referred to as the fluctuation time). Absorbing particles obviously cannot directly repel unmanifest vacuum particles, since the latter only serve as carriers of momentum. However, recall that vacuum particles are in superpositions of unmanifest and manifest states (the latter being referred to as trapped fluctuons). Chains initiated by absorbing particles thus exert a depressing (or polarizing) effect on the surrounding vacuum sea. This effect is isotropically distributed in the cases of the strong and electromagnetic forces, since buildup of polarization is countered by the overall requirement for color and charge neutrality. This is not the case for the gravitational interaction, since mass comes in only one charge. The vacuum density of neighboring high mass collections of manifest particles will thus be highly depressed and the density of distant regions of space-time elevated. This is how mass controls the metric structure of space-time. The attractive gravitational interaction is actually indirect. Manifest particles are pushed together by gravitons emanating from trapped fluctuons in distant regions of space where the vacuum density is elevated. Mutual screening by the manifest particles allows the compressing effect to dominate over the direct repulsion. All the particles in the universe, both manifest and unmanifest, thus contribute to the gravitational interaction. This is the fluctuon model’s version of Mach’s principle. Now we can see why a geometrical theory of gravity is possible and why the strong and electromagnetic interactions can conform to this geome-
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try without introducing any geometrical effects of their own. The isotropy and low density of the electron and quark subseas means that interactions mediated by these subseas are not altered by the geometry of space-time, though the resulting particle motions are of course also subject to ubiquitous graviton bombardments. Changes in states of motion of absorbers resulting from electromagnetic and chromodynamic interactions must affect the density (or metric) structure of the vacuum sea, however. This is why gravity alone can be identified with acceleration, and why resistance to acceleration (or inertia) is solely dependent on gravitational mass. Mass would not be independent of electric charge if the electron subsea were so dense that the effect of charge on the density of the vacuum supersea were comparable to the effect of mass. We can also see why superpositions should collapse spontaneously. This follows from the self-consistency requirements of the theory. The mass formally assigned to vacuum particles must be consistent with the density of either the vacuum supersea or one of the subseas. If this were not the case the fluctuation energy required to create the initial transient pair would not match the fluctuation energy required for chain propagation. Whenever particles change their state of motion the distribution of mass in the universe must change. The density structure of the vacuum sea is altered. The effect on the density structure of the quark and electron subseas is negligible, apart from the local polarizations attached to the particles themselves. The density variations associated with these local polarizations are compensated by distortion waves of vacuum density that correspond to the wave aspect of chain propagation. The dependence of the strong and electromagnetic forces on the density of their respective subseas is thus effectively masked. Such masking is not possible in the case of gravity, however, since the density structure of the supersea changes whenever mass accelerates and does so regardless of which force produces the acceleration. The gravitational force between any two particles thus depends on the density structure of the supersea and accordingly must be redefined whenever accelerations occur. From the quantum mechanical
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point of view the wave function of the vacuum changes, and thus superpositional collapse must continually occur if a new density is to be continually defined. Consequently the forces between particles (the interaction structure of the universe) is to some degree subject to a continual random variation (a kind of mutation). We can also describe the situation equivalently, but more usefully for the present purposes, from the point of view of the interactions required to maintain self-consistency. As noted above, changes in the distribution of manifest particles must always be followed by readjustment of the vacuum density distribution. The consistency between the two distributions is not a ‘pre-established harmony’ and is never perfect. It must be maintained by interactions between manifest particles and trapped fluctuons. The greater the rearrangement of manifest mass the greater the deviation from consistency. The strength of the gravitational interaction between particles will be altered. For example, if the density of the supersea is locally too low the masson-antimasson mass will be too high for graviton chains to be initiated. The repulsive effect of manifest particles will decrease and consequently the local vacuum density will undergo a corrective increase. If the local density is too high, the lower energy fluctuations that allow for propagative chains that jump over vacuum particles will be possible, thereby increasing the strength of the gravitational interaction, again leading to a corrective effect. The interactional picture brings out the control system aspect of gravity. Deviations from selfconsistency can be viewed as error. When such deviations occur the motions of manifest particles become decorrelated from the vacuum density structure. A random fluctuation of energy occurs. Each of the components of the superposition is multiplied by a random phase factor. The interference terms are thus altered in a random way. This is the basis of superpositional collapse (Bohm, 1951). The term superpositional mutation would actually be more accurate, since the superposition is redefined rather than eliminated. This corresponds to the fact that interference effects disappear completely only when the results of many measurements are averaged, since the random al-
terations of phase then cancel out. Randomness here can be defined, without philosophical prejudice, in terms of the incompressibility of a description (in the fashion of algorithmic information theory, Chaitin, 1990). However, as noted earlier, the degree of incompressibility associated with the phase altering fluctuations must be greater than that allowed by relativity, since in the latter case incompressibility is constrained by a self-consistency requirement, whereas in the former case it is not (since the fluctuations are deviations from self-consistency). It is at this point that the graviton exchanges that recorrelate the phases in a way that moves back in the direction of self-consistency spring into action. Again we see a random error aspect analogous to genetic mutation and an error correction aspect analogous to natural selection and homeostatic regulation.
4. Self-regulation in the case of gravitational collapse Black hole phenomena, according to the fluctuon theory, are an extreme manifestation of such self-regulation. When the number of positive energy particles (or vacuum lacunae) collected in a region of the vacuum sea becomes so great that photons cannot escape, then gravitational collapse to a black hole begins. According to the fluctuon theory gravitons are also trapped. Thus, on the surface it would appear that the black hole should no longer exert any gravitational attraction on particles outside the region, an immediate contradiction to the collapse concept. However, recall that in the fluctuon model, gravity is an indirect attractive force. Actually particles will continue to be pushed into the black hole region by gravitons emanating from high vacuum density regions of distant space. The elevated density of these regions was originally induced by the repelling effects of the positive energy particles whose coalescence traps photons and gravitons. Trapping eliminates these inducing effects. The compressing effect of gravitons emanating from distant regions accordingly falls off. Direct repulsive effects of graviton exchanges within the hole come to the fore, and the particles within it fly
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outwards. The collapse process is reversed. Trapped fluctuons are again repelled into distant regions of space, and the normal (indirect) attractive force of gravity reinstated. The reversal of collapse is of great conceptual importance, since ultimate gravitational collapse is incompatible with the conservation of energy and would therefore lead inevitably to the complete breakdown of physics. The point to note here is that the mechanism of gravitational collapse is the same as the mechanism of superpositional collapse. The alterations of graviton exchanges initiated by particles in the black hole region is a massive analog of the alterations accompanying superpositional collapse. The random alterations in the motions of particles concomitant to the shutting down of graviton initiations corresponds to the decorrelation process, while the reinstatement of the indirect attractive interaction corresponds to the recorrelation process.
5. Potential reversal and anti-entropy The self-regulatory aspect of gravitational collapse illustrates in dramatic fashion an important feature of the fluctuon theory: the sign of the gravitational interaction can change (Conrad, 1996b). This is due to the fact that the compressing effect of gravitons from distant regions of the vacuum sea dominates only when these regions have high density; when the density falls off the direct repulsive effect dominates. The ordinary potential energy minimum is thus the coalesced state in the former (normal) case. However, as this minimum is approached overly closely the dispersed state becomes the minimum. What appears to be the high potential energy state (the atypical initial condition) under ordinary conditions of the physics laboratory is thus one region of a cyclic attractor. Actually, the real evolution of the universe would follow a highly chaotic course, since stability or instability of different manifest distributions of matter depends on the unmanifest structure of the vacuum sea. Two similar distributions could have very different stability properties, depending on far distant features
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of this sea, and therefore depending on the historical pathway of their formation. Minima representing ultimate gravitational collapse (big bang, big crunch) would almost certainly disappear before they are ever reached. Such reversals of potential are, according to fluctuon theory, always associated with acceleration. This is due to the close relationship between superpositional collapse (or mutation) and gravitational collapse (really massive gravitational reversal). The recorrelation processes that follow changes in states of motion in the low energy, low mass domain mirror those in the black hole domain, with the difference that the alterations in gravitational interactions are so much smaller and less coherent that deviations from the normal (indirect) attractive force of gravity are undetectable. Nevertheless the decorrelation–recorrelation cycle in this domain points to the existence of basins of attraction whose structure is history dependent, just as it is in the case of the universe in the large. The decorrelation–recorrelation process points to a broadened concept of entropy. Decorrelation is associated with entropy increase, whereas recorrelation is associated with entropy decrease. This is particularly clear in the case of gravitational collapse and reversal of collapse. An atypical initial condition arises dynamically when collapse is reversed, due to the fact that the minimum potential energy state toward which particles fall is the dispersed state at this stage. When the attractive gravitational interaction is reinstated the dispersed state becomes the high potential energy state. A perfectly elastic bouncing ball cycles between low and high potential energy states, but not because the potential is reversed. An incompletely elastic ball thus eventually comes to rest in the low potential energy state, due to the fact that its kinetic energy is distributed over the heat bath. Entropy therefore increases and consequently the high potential energy state becomes unavailable. The existence of a decorrelation–recorrelation cycle means that the system arrives again at a high potential energy state even though entropy increased as it approached the initial potential energy minimum, due to the fact that this state appears on an attractor. The recorrelation part of
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the cycle, since it is associated with movement towards an atypical state, represents an anti-entropy process. The same considerations apply to superpositional collapse, except that the entropy process always dominates the anti-entropy process. A source of high grade energy is still necessary to defeat the general increase in entropy. However, the anti-entropy process nevertheless plays an important role in regulation, since it is the indication of an attractor structure. The universe in the fluctuon model is always in one particular quantum state, even if the wave function changes in a random, irreversible manner whenever changes in states of motion occur. The occurrence of these transitions is not contingent on a measurement process, since decorrelation (connected with randomization of quantum mechanical phase) is an endogenous process. Thus the wave function becomes partially actualized (which is why we are entitled to think of photons radiating even in the absence of their being observed). Entropy in some sense increases, but in some sense it cannot increase (since the universe is only in one state). The latter fact is the content of the Liouville theorem, which applies in the fluctuon model. This ambiguity (which is faced both by classical and quantum statistical mechanics) is redressed in the following way in the fluctuon theory. The entropy and anti-entropy associated with the correlation and decorrelation cycle are measured by the number of complexions compatible with the macrostate of the universe. The entropy increases on decorrelation because the macrostate of the manifest universe becomes more symmetrical (e.g. gradients of temperature, pressure, chemical potential diminish). Decorrelation leads to this situation because it leads to a wave function in which the probability amplitudes are more equal. Recorrelation represents an anti-entropy process since it is associated with the restoration of a consistent relationship between the manifest organization of matter and the unmanifest structure of the vacuum sea. The probability amplitudes therefore become less equal and the number of possible wave functions compatible with the same manifest macroscopic organization therefore decreases.
The new feature of the fluctuon model is that systems can dynamically return to higher symmetry states after undergoing a transition to a lower symmetry state due to restrictions on access imposed by self-consistency (the assumption that all states are equally probable does not apply). In the normal regime, where indirect attractive interaction dominates, the increase in entropy associated with decorrelation is greater than the decrease associated with decorrelation. In the anti-normal regime the situation is reversed. Such changes in overall symmetry actually are only apparent, since they are compensated by symmetry changes in the unmanifest vacuum structure. Thus, when particles coalesce and become randomized by collision due to the attractive force of gravity the density gradients in the vacuum sea become more pronounced.
6. Percolation network The effects noted above would be entirely undetectable in the simple systems studied in the physics laboratory. A single electron undergoing acceleration in a given coordinate system would undergo repeated radiation of photons and gravitons. According to the fluctuon theory the occurrence of these radiative transitions is not contingent on the intervention of an observer. The random effects of vacuum density alterations on interference terms involving states of different energy serves to actualize these transitions. This decorrelation process is followed by a recorrelation which, because of the negligibility of the departure from self-consistency, would reform the wave function in a way that for all practical purposes would have the aspect of a continuous, deterministic evolution, as in the standard theory. The motions of particles in ordinary multiparticle systems (gases, liquids, solids) should exhibit slight deviations from what in principle follows from the standard time evolution equations, but this would have no effect on average properties. If the systems are out of equilibrium some component of the entropy increase would be due to the decorrelation entropy; but this would be swamped by the general increase in entropy attributable to
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the evolution of a larger and larger number of complexions compatible with the macroscopic state. The organization of cells and organisms is entirely different. Some terms that are descriptive include: vertical flow of information, cross-scale interactions, percolation network, hypercircle of influence flow (Conrad, 1993a,d, 1994, 1995, 1996c). First picture influences as flowing horizontally through a system, in general with recurrent interactions. So far this is just like a current day technological computing system. Next picture such horizontal flows occurring at many different levels. To this add vertical flows across levels (or across scale). Influences impinging on the system from the environment are filtered in the downscale direction to selectively set the state of micro components of the system and are selectively amplified in the upscale direction to control its actions. A measurement apparatus directed to micro-properties has this cross-scale characteristic. However, the organism is different from existing technical measurement systems in a fundamental respect. The cross-scale flow of influence proceeds in small steps through multiple levels, each with unique scale dependent physicalchemical capabilities. The hypercircle image is intended to evoke this picture. However, it is a hypercircle with many inner hyper-epicycles. Furthermore, the picture of distinct levels with definite dimensions is inadequate. The system incorporates diverse ultra-integrated subcomponents and processes that combine different physical dimensions in diverse ways. The mitochondrion, the chloroplast, the cytoskeleton, tissues, and organ systems are examples that could be described structurally in this multi-scale fashion. Genetic-developmental systems, the immune system, and the brain are examples that could be described functionally as percolation networks that process information from macro input influences to macro output action in a multiscale fashion. Each such percolation network can be abstractly conceptualized as a cross-scale decision tree. The many optional directions in which the downward filtration and upward percolation of influences can proceed means that averaging is no
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longer the dominant fact. Events at the smallest levels of scale, for example involving the state changes of electrons in macromolecules, are critical for controlling the macro behavior. The vacuum structure must, according to the fluctuon model, be drawn into the hypercircular decision tree. The distribution of manifest particles currently constituting the body of the organism must be consistent with the vacuum density structure, which we can refer to as its body image in the vacuum sea. When the manifest body particles rearrange themselves the vacuum body image must change. They will become inconsistent. Graviton flows will spring into action to bring them back into a consistent relationship. These flows will be too weak, given the masses and velocities involved, to affect the motion of macromolecules as a whole. However, the mass of electrons and of various quasi particle excitations of the manifest body is sufficiently small for vacuum decorrelation and recorrelation processes to effect transitions. In the percolation network type architecture of biological organisms this is sufficient to exert a critical controlling effect on macro behavior. The decorrelation processes can contribute to the randomness of mutation or other search processes. Recorrelation generally means that some electronic transitions will be selectively triggered, potentially playing a critical role in the cross-scale decision tree. The integration of influences within the vacuum sea thus contributes to decision processes that eventually culminate in the macro actions of the organism. Or, at a more global level, the body image in the vacuum sea may provide a basin of attraction which helps to pull the organism back to its dynamic form subsequent to perturbing influences from the outside by influencing widely distributed electronic and quasi particle transitions. Or the body image in the vacuum may in this manner contribute to the reliable functioning of the organism in the face of various internal noise processes. It is at this stage difficult to assess how important these various contributions are in comparison to the paradigms mentioned at the front of this paper. The argument might be made that the effects predicted would be so small at biological energies that we could give an adequate account,
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M. Conrad / BioSystems 46 (1998) 29–39
in principle, of the information and control capabilities of organisms without any reference to quantum gravity; quantum gravity would then only be relevant by virtue of the fact that the universe would not be what it is without it. The counter argument is this: if the effects are so small then the nonlinearities requisite for life would have to be added to the equations of motion in an ad hoc manner, whereas they are inherent in fluctuon theory. The circular (self-reprocessing) dynamics are inherent in the underlying physics. The elaborate form and coordination of biological matter maintainable through frictional interactions is greater than could be accounted for on the basis of models that leave out this underlying physics. The nonlinearities and initial-boundary conditions prerequisite for form and coordination to develop through collective processes, such as dissipative structures, would have an intrinsic basis, since the existence of these prerequisites cannot themselves be justified on the basis of the dynamics to which they give rise. Interaction structures sufficiently intricate to support quantum coherence are also more supportable, opening the possibility for a more global underpinning of biological form. Each increment along any of these lines would elaborate the crossscale, percolative aspect of the organization, further shaping the vacuum image and thereby further eliciting the control capabilities nascent in the interactions between the vacuum sea and manifest matter. The image serves to regulate the manifest organization’s responses to perturbations directly affecting it; the manifest organization serves to regulate the image’s responses to the changing arrangements of manifest mass. The present state of the manifest organism is no longer a full statement of all its relevant past history. Its image in the vacuum sea also represents aspects of this history. The whole organization boots to greater and greater self-regulatory capacity and complexity, including complexity that supports the manifest hereditary apparatus. A new feature of heredity enters though. Two material organizations with the same form would have different stability properties if the pathway of their evolution were different. History is locked not only into the manifest hereditary apparatus,
and into the manifest structures requisite to the operations of this apparatus, but as well into the hidden structure of the vacuum sea.
Acknowledgements This research was supported by the National Science Foundation under grant ECS-9409780.
References Bohm, D., 1951. Quantum Theory. Prentice-Hall, Englewood Cliffs, N.J. Chaitin, G.J., 1990. Algorithmic Information Theory. Cambridge University Press, Cambridge, UK. Conrad, M., 1986. Reversibility in the Light of Evolution, Mondes en De´veloppement, vol. 14, no. 54 – 55, pp. 111 – 121. [Also In: Prigogine, I., Sanglier, M. (Eds.), Laws of Nature and Human Conduct. Task Force on Research Information and Study on Science, Brussels, pp. 111 – 121, 1987]. Conrad, M. The water-membrane interface as a substrate for H – H superflow. Int. J. Quantum Chem: Quantum Biol. Symp. 14 (1988) 167 – 188 (Printer’s Erratum in vol. 33 (1988) 503 – 504). Conrad, M., 1988b. Quantum mechanics and molecular computing: mutual implications. Int. J. Quantum Chem.: Quantum Biol. Symp. 15, 287 – 301. Conrad, M., 1989a. Physics and biology: towards a unified model. Appl. Math. Comput. 32, 75 – 102. Conrad, M., 1989b. Force, measurement, and life. In: Casti, J., Karlquist, A. (Eds.), Newton to Aristotle: Toward a Theory of Models for Living Systems. Birkhauser, Boston, pp. 121 – 199. Conrad, M., 1991. Transient excitations of the Dirac vacuum as a mechanism of virtual particle exchange. Phys. Lett. A 152, 245 – 250. Conrad, M., 1993a. The fluctuon model of force, life, and computation: a constructive analysis. Appl. Math. Comput. 56, 203 – 259. Conrad, M., 1993b. Fluctuons I. operational analysis. Chaos, Solitons Fractals 3, 411 – 424. Conrad, M., 1993c. Fluctuons II. electromagnetism. Chaos, Solitons Fractals 3, 563 – 573. Conrad, M., 1993d. Emergent computation through self-assembly. Nanobiology 2, 5 – 30. Conrad, M., 1994. From brain structure to vacuum and back again: the great chain of being model. Nanobiology 3, 99 – 121. Conrad, M., 1995. Multiscale synergy in biological information processing. Opt. Mem. Neural Netw. 4 (2), 89 – 98. Conrad, M., 1996a. Fluctuons-III. gravity. Chaos, Solitons Fractals 7, 1261 – 1303.
M. Conrad / BioSystems 46 (1998) 29–39 Conrad, M., 1996b. Anti-entropy and the origin of initial conditions. Chaos, Solitons Fractals 7, 725–745. Conrad, M., 1996c. Percolation and collapse of quantum parallelism: a model of qualia and choice. In: Hameroff, S.R., Kaszniak, A.W., Scott, A.C. (Eds.). MIT Press, Cambridge, MA, pp. 469–492. Conrad, M., 1996d. Cross-scale information processing in evolution, development and intelligence. BioSystems 38, 97– 109. Conrad, M., 1997. Origin of life and the underlying physics of the universe. Biosystems 42, 177–190. Fro¨hlich, H., 1983. Evidence for coherent excitation in biological systems. Int. J. Quantum Chem. 23, 1589–1595. Kampis, G., 1991. Self-Modifying Systems in Biology and Cognitive Science. Pergamon, Oxford, UK. London, F., 1961. Superfluids, vol I. Dover Publications, New York. Maturana, H.R., Varela, F.J., 1980. Autopoiesis and Cognition. Reidel, Dordrecht, The Netherlands.
.
39
Matsuno, K., 1989. Protobiology: Physical Basis of Biology. CRC Press, Boca Raton, FL. Misner, C.W., Thome, K.S., Wheeler, J.A., 1973. Gravitation. W.H. Freeman and Co., New York. Nicolis, G., Prigogine, I., 1977. Self-Organization in Nonequilibrium Systems. Wiley-Interscience, New York. Pattee, H.H., 1968. The physical basis of coding and reliability in biological evolution. In: Waddington, C.H. (Ed.), Prolegomena to Theoretical Biology. University of Edinburgh Press, Edinburgh, pp. 67 – 93. Penrose, R., 1989. The Emperor’s New Mind. Oxford University Press, Oxford, UK. Rosen, R., 1991. Life Itself. Columbia University Press, New York. Schro¨dinger, E., 1944. What is Life? Cambridge University Press, Cambridge, UK. Watson, J.D., 1965. Molecular Biology of the Gene. W.A. Benjamin, New York.
.