|It follows from this that gravity cannot be regarded
as some kind of "emergent phenomenon," secondary to other
physical effects, but is a "fundamental component" of physical
There are strong arguments (e.g. Penrose, 1987; 1995) to suggest
that the appropriate union of general relativity (Einstein's theory
of gravity) with quantum mechanics - a union often referred to as
"quantum gravity" - will lead to a significant change
in both quantum theory and general relativity, and, when
the correct theory is found, will yield a profoundly new
understanding of physical reality. And although gravitational
forces between objects are exceedingly weak (feebler than, for
example, electrical forces by some 40 orders of magnitude), there
are significant reasons for believing that gravity has a fundamental
influence on the behavior of quantum systems as they evolve from
the micro to the macro levels. The appropriate union of quantum
gravity with biology, or at least with advanced biological nervous
systems, may yield a profoundly new understanding of consciousness.
According to modern accepted physical pictures, reality is rooted in 3-dimensional space and a 1-dimensional time, combined together into a 4-dimensional space-time. This space-time is slightly curved, in accordance with Einstein's general theory of relativity, in a way which encodes the gravitational fields of all distributions of mass density. Each mass density effects a space-time curvature, albeit tiny.
This is the standard picture according to classical physics. On the other hand, when quantum systems have been considered by physicists, this mass-induced tiny curvature in the structure of space-time has been almost invariably ignored, gravitational effects having been assumed to be totally insignificant for normal problems in which quantum theory is important. Surprising as it may seem, however, such tiny differences in space-time structure can have large effects, for they entail subtle but fundamental influences on the very rules of quantum mechanics.
Superposed quantum states for which the respective mass distributions differ significantly from one another will have space-time geometries which correspondingly differ. Thus, according to standard quantum theory, the superposed state would have to involve a quantum superposition of these differing space-times. In the absence of a coherent theory of quantum gravity there is no accepted way of handling such a superposition. Indeed the basic principles of Einstein's general relativity begin to come into profound conflict with those of quantum mechanics (cf. Penrose, 1996). Nevertheless, various tentative procedures have been put forward in attempts to describe such a superposition. Of particular relevance to our present proposals are the suggests of certain authors (i.e., Karolyhazy, 1996; 1974; Karolyhazy et al., 1986; Kibble, 1991, Diósi, 1989; Ghirardi et al, 1990; Pearle and Squires, 1995; Percival, 1995; Penrose, 1993; 1994; 1996) that it is at this point that an objective quantum state reduction (OR) ought to occur, and the rate or timescale of this process can be calculated from basic quantum gravity considerations. These particular proposals differ in certain detailed respects, and for definiteness we shall follow the specific suggestions made in Penrose (1194; 1996). Accordingly, the quantum superposition of significantly differing space-times is unstable, with a lifetime given by that timescale. Such a superposed state will decay - or "reduce" - into a single universe state, which is one or the other of the space-time geometries involved in that superposition.
Whereas such an OR action is not a generally recognized part of the normal quantum-mechanical procedures, there is no plausible or clear-cut alternative that standard quantum theory has to offer. This OR procedure avoids the need for "multiple universes" (cf. Everett, 1957; Wheeler, 1957, for example). There is no agreement, among quantum gravity experts, about how else to address this problem. For the purposes of the present article, it will be assumed that a gravitationally induced OR action is indeed the correct resolution of this fundamental conundrum.
|Figure 1 (adapted from Penrose, 1994, p. 338) schematically
illustrates the way in which space-time structure can be affected
when two macroscopically different mass distributions take part in
a quantum superposition. Each mass distribution gives rise to a separate
space-time, the two differing slightly in their curvatures. So long
as the two distributions remain in quantum superposition, we must
consider that the two space-times remain in superposition. Since,
according to the principles of general relativity, there is no natural
way to identify the points of one space-time with corresponding points
of the other, we have to consider the two as separated from one another
in some sense, resulting in a kind of "blister" where the
A bifurcating space-time is depicted in the lowest of the three diagrams, this being the union ("glued together version") of the two alternative space-time histories that are depicted at the top of Figure 1. The initial part of each space-time is at the lower end of each individual space-time diagram. The bottom space-time diagram (the bifurcating one) illustrates two alternative mass distributions actually in quantum superposition, whereas the top two illustrate the two individual alternatives which take part in the superposition. The combined space-time describes a superposition in which the alternative locations of a mass move gradually away from each other as we proceed in the upward direction in the diagram. Quantum- mechanically (so long as OR has not taken place), we must think of the "physical reality" of this situation as being illustrated as an actual superposition of these two slightly differing space-time manifolds, as indicated in the bottom diagram. As soon as OR has occurred, one of the two individual space-times takes over, as depicted as one of the two sheets of the bifurcation. For clarity only, the bifurcating parts of these two sheets are illustrated as being one convex and the other concave. Of course there is additional artistic license involved in drawing the space-time sheets as 2-dimensional, whereas the actual space-time constituents are 4-dimensional. Moreover, there is no significance to be attached to the imagined "3-dimensional space" within which the space-time sheets seem to be residing. There is no "actual" higher dimensional space there, the "intrinsic geometry" of the bifurcating space-time being all that has physical significance. When the "separation" of the two space-time sheets reaches a critical amount, one of the two sheets "dies" - in accordance with the OR criterion - the other being the one that persists in physical reality. The quantum state thus reduces (OR), by choosing between either the "concave" or "convex" space-time of Figure 1.
It should be made clear that this measure of separation is only very schematically illustrated as the "distance" between the two sheets in the lower diagram in Figure 1. As remarked above, there is no physically existing "ambient higher dimensional space" inside which the two sheets reside. The degree of separation between the space-time sheets is a more abstract mathematical thing; it would be more appropriately described in terms of a symplectic measure on the space of 4-dimensional metrics (cf. Penrose, 1993) - but the details (and difficulties) of this will not be important for us here. It may be noted, however, that this separation is a space-time separation, not just a spatial one. Thus the time of separation contributes as well as the spatial displacement. Roughly speaking, it is the product of the temporal separation T with the spatial separation S that measures the overall degree of separation, and OR takes place when this overall separation reaches the critical amount. [This critical amount would be of the order of unity, in absolute units, for which the Planck-Dirac constant h bar (=h/2ã), the gravitational constant G, and the velocity of light c, all take the value unity, cf. Penrose, 1994 - pp. 337-339.] Thus for small S, the lifetime T of the superposed state will be large; on the other hand, if S is large, then T will be small. To calculate S, we compute (in the Newtonian limit of weak gravitational fields) the gravitational self-energy E of the difference between the mass distributions of the two superposed states. (That is, one mass distribution counts positively and the other, negatively; see Penrose, 1994; 1995.) The quantity S is then given by:
|Schematically, since S represents three
dimensions of displacement rather than the one dimension involved
in T, we can imagine that this displacement is shared
equally between each of these three dimensions of space - and this
is what has been depicted in Figure 3 (below). However, it should
be emphasized that this is for pictorial purposes only, the appropriate
rule being the one given above. These 2 equations relate the mass
distribution, time of coherence, and space-time separation for a given
OR event. If, as some philosophers contend, experience is contained
in space-time, OR events are self-organizing processes in that
experiential medium, and a candidate for consciousness.
But where in the brain, and how, could coherent superposition and
OR occur? A number of sites and various types of quantum
interactions have been proposed. We strongly favor microtubules
as an important ingredient, however various organelles and biomolecular
structures including clathrins, myelin (glial cells), pre-synaptic
vesicular grids (Beck and Eccles, 1992) and neural membrane proteins
(Marshall, 1989) might also participate.
Properties of brain structures suitable for quantum coherent superposition, OR and relevant to consciousness might include: 1) high prevalence; 2) functional importance (for example regulating neural connectivity and synaptic function); 3) periodic, crystal-like lattice dipole structure with long range order; 4) ability to be transiently isolated from external interaction/observation; 5) functionally coupled to quantum-level events; 6) hollow, cylindrical (possible wave guide); and 7) suitable for information processing. Membranes, membrane proteins, synapses, DNA and other types of structures have some, but not all, of these characteristics. Cytoskeletal microtubules appear to qualify in all respect.
|Interiors of living cells, including the brain's neurons, are spatially and dynamically organized by self-assembling protein networks: the cytoskeleton. Within neurons, the cytoskeleton establishes neuronal form, and maintains and regulates synaptic connections. Its major components are microtubules, hollow cylindrical polymers of individual proteins known as tubulin. Microtubules ("MTs") are interconnected by linking proteins (microtubule-associated proteins: "MAPs") to other microtubules and cell structures to form cytoskeletal lattice networks (Figure 2).|
|MTs are hollow cylinders 25 nanometers (nm) in diameter whose lengths vary and may be quite long within some nerve axons. MT cylinder walls are comprised of 13 longitudinal protofilaments which are each a series of subunit proteins known as tubulin (Figure 3). Each tubulin subunit is a polar, 8 nm dimer which consists of two slightly different 4 nm monomers (alpha and beta tubulin - Figure 4). Tubulin dimers are dipoles, with surplus negative charges localized toward monomers (DeBrabander, 1982), and within MTs are arranged in a hexagonal lattice which is slightly twisted, resulting in helical pathways which repeat every 3, 5, 8 and other numbers of rows. Traditionally viewed as the cell's "bone-like" scaffolding, microtubules and other cytoskeletal structures also appear to fill communicative and information processing roles. Numerous types of studies link the cytoskeleton to cognitive processes (for review, cf. Hameroff and Penrose, 1996). Theoretical models and simulations suggest how conformational states of tubulins within microtubule lattices can interact with neighboring tubulins to represent, propagate and process information as in molecular-level "cellular automata," or "spin glass" type computing systems (Figure 5; e.g. Hameroff and Watt, 1982; Rasmussen et al, 1990; Tuszynski et al, 1995).|
|In Hameroff and Penrose (1996; and in summary form, Penrose and Hameroff, 1995), we present a model linking microtubules to consciousness, using quantum theory as viewed in the particular "realistic" way that is described in Shadows of the Mind (Penrose, 1994).|