Now for some seriousness...
Hope you enjoy!
(
@Ren I thought of you when I read this and thought this might add some side ponderances to your notebook or kick you some new angles to play with.)
Cosmology, 2014, Vol. 18. 212-230
Cosmology.com, 2014
Consciousness, the Paranormal and Higher Dimensions
Horace W. Crater1 and Stan V. McDaniel2
1The University of Tennessee Space Institute Tullahoma, TN
2Sonoma State University (Emeritus), Rohnert Park, CA
Abstract:
In the 1800s it was hypothesized by some scientists that the actions of things or beings in a realm of four spatial dimensions, relative to which we might occupy an embedded hypersurface of only three spatial dimensions, might account for some paranormal phenomena perceived by us.
That idea was subsequently dismissed.
We here consider what issues might be involved if the hypothesis regarding paranormal phenomena were to be re-evaluated in view of the type of contemporary extra-dimensional theory proposed in Randall and Sundrum (Randall, 1999) and Randall (Randall 2005).
1 Paranormal Phenomena and Extra-Dimensional Theory
In his 1884 book Flatland: A Romance of Many Dimensions, Edwin A. Abbott described how things, including beings like ourselves, who live in a realm with three spatial dimensions (width, length and depth), might appear to those limited to a flat embedded surface (Flatland) having just two spatial dimensions (width and length) and unable to perceive depth. In the 1800s it was argued even by prominent scientists that our realm of three spatial dimensions might be embedded in a universe of four spatial dimensions, and that 4-dimensional beings within that larger spatial realm might be experienced by us as ghosts or spirits. These would perhaps be knowable only by mediums or clairvoyants. (A good historical account of this is to be found in Kaku, 1994).
Although this idea was eventually abandoned, here we explore whether such paranormal phenomena as reincarnation, telepathy, communication with the dead and memories of past lives might fit into an updated analogy based on the theory that our four-dimensional universe (3 dimensions of space plus one of time) may be embedded within a five-dimensional universe (4 dimensions of space plus one of time) as such a universe is proposed in Randall and Sundrum (Randall, 1999) and Randall (Randall 2005). Our examination of the issues involves correlating various unique features of the theory with aspects of such paranormal phenomena. Our aim is not a rigorous verification of the validity of these correlations but rather an attempt at determining their degree of plausibility or implausibility; and if they appear to be plausible, what further experimental determinations may be necessary to raise the level of plausibility.
2 Higher Physical Dimensions
Renewed speculations about "extra" or "higher" dimensions have appeared in many different varieties in the physics literature since the work of Kaluza (Kaluza, 1921) and Klein (Klein, 1926) in the 1920s, and more recently with the advent of modern string theory (Green, 1984); Zwiebach, 2004). Kaluza and Klein showed that by extending Einstein’s equation to a universe of five space-time dimensions they could unify the forces of gravity and electromagnetism into a single equation. In string theory, strings were hypothesized as one- dimensional objects within a space which has nine spatial dimensions, (six in addition to length, width and depth). Although infinitesimally small, strings are not points, which have no spatial extension at all.
Advances in string theory in the 1990’s brought about the proposal that there could be other structures in space-time with zero thickness in one or more dimensions up to one less than the proposed 9 spatial directions. Thus, for example, the possibility of two-dimensional surfaces with zero thickness was considered. Just as the string was not limited to straight, zero thickness lines, but could have arbitrary curvature and in fact be closed, so the two-dimensional surfaces could be curved and be closed like a spherical surface. The concept of "branes" then followed, being objects that had zero thickness in one or more dimensions--The electron, quark, and other fundamental particles are thought to be true points, 0D objects in 4D space-time, but always accompanied by electromagnetic or chromodynamic fields. They have the effect of giving atoms and nuclei an effective size--angstrom and fermi respectively.
The authors have borrowed the concept of branes from the extended string theory but limit themselves to only one, two, or three extra spatial dimensions. We focus our attention on the Randall-Sundrum model (Randall, 1999, 2005) which proposes just one extra spatial dimension. In that model, the term brane describes our four-dimensional space-time (4D) as an "object" within a five dimensional (5D) space-time, called the bulk. The bulk, in addition to the time dimension, has four spatial dimensions corresponding to coordinates x, y, z and w. The brane has zero thickness in the w dimension and thus in effect has only three measurable spatial dimensions. The brane is an idealization just like the point electron, but although there is no universally accepted and tested theory for branes, like QED for the electron, treating the brane as a 0 w thickness object, as discussed later, gives results of a very profound nature, solving the Hierarchy problem. The brane and bulk are related in that the brane is said to be a kind of boundary of the bulk. As a result there will be a relation between the "size" of the bulk and that of the brane. The bulk must extend in some of its dimensions as far as does its "boundary" i.e. the brane. In the original Randall-Sundrum model (Randall, 1999), the bulk or 5-dimensional realm extends between our brane and a parallel brane (See Fig. 1). The forms of this and the following 5 figures were based on those given in (Randall, 2005).
Figure 1. Randall-Sundrum Higher Dimensional Model
Returning for the moment to the "Flatland" idea, we engage in a thought experiment. Consider the model of a hand. (The content of this paragraph first appeared as a contribution of one of the authors (HWC) to a recently published book (Weiss 2012).) Take your hand and place the fingertips on a flat surface (a large enough flat surface would represent a Flatlander’s Universe) Now, suppose the impression made by the tips of your fingers on the flat surface represents a group of five Flatlanders. The bodies of the Flatlanders are two-dimensional, having only the dimensions of length and width. Their physical interactions would correspond to the tips of your fingers becoming sufficiently near to one another on the flat surface. The fingers, however, represent larger 3-dimensional bodies of which the two-dimensional flatlanders are a kind of extension. In this hypothetical scenario instead of "ghosts or spirits" these 3-dimensional bodies would be part of the Flatlanders themselves, but unseen by them and invisible to their physical science.
This consideration raises a question regarding the mental activities of these apparently divided beings. Since the "fingers" are connected with each other (by belonging to the same "hand"), we might imagine a possibility of the sharing of thoughts from one "finger" to another. This idea need only suppose that the mental activity of the total person is not limited to the two- dimensional body in Flatland but is a capability possessed by the total self comprised of both the Flatland body and the 3-dimensional extension of that body (the "finger"). Another consequence of such a proposal is that the sense of selfhood is divided between the two "bodies" such that the Flatlander, at least, is unable under normal circumstances to be aware of the higher dimensional component of itself. This particular idea will be addressed a bit later on. In the meantime let us refer to the Flatlander as the "ego self" and the addition of the "finger" to the Flatlander as the "total self." As to what the relation between the minds and the bodies of these beings may be, we take no position but leave that as the same question that exists in philosophy and science today and has not yet been resolved.
Now what happens when the two-dimensional Flatlander dies? Lift your finger from the flat surface, leaving behind the two-dimensional "body" of the three-dimensional entity. As time passes, that same finger arches back down toward the plane, and plants itself at a different location. The finger in effect becomes associated with another two-dimensional Flatlander body. Although again the newly "born" Flatlander would under normal circumstances be unaware of the existence of its extended self, if the 3-dimensional finger retains memories of its association with its previous Flatlander body, a phenomenon similar to that of reincarnation and memories of past lives would be implied.
In our thought experiment the physical Flatlander is the action of the "tip" of the three- dimensional "finger" on the surface of Flatland. The two-dimensional flatlander and the three- dimensional "finger" are in some sense a single entity sharing the same consciousness, but the conceptual framework within which the Flatlander is normally constrained renders it very difficult, though perhaps not impossible, for the Flatlander to become aware of the existence of the "finger." Although (in this hypothetical scenario) the self-awareness of any individual Flatlander dissipates upon death, the death of the Flatlander does not bring about the death of its 3-dimensional extended body.
Thus we have in effect a divided self. But by the "fingertip" analogy the lower- dimensional being and its higher-dimensional extension are connected, at the very least by some kind of energy exchange. What then might be the nature of this connection? To what degree might it be a reciprocal relation? (Strangely enough this dilemma is somewhat presaged by the problem encountered by Descartes, who argued that although mind and body are separate "substances" the link between them was through the pineal gland. There was no way to explain how this link might be accomplished, since the two substances were diametrically opposed). And why should the extended higher-dimensional "body" remain after the death of its lower- dimensional component? In what follows we will discuss some of these questions in relation to a version of the theory incorporating the Randall-Sundrum model.
3 Energy Relations of Bulk and Brane
Our investigation focuses on the question whether it is physically coherent to propose that conscious beings, seemingly dwelling only on a brane of zero thickness in the w direction, in fact extend into the w direction (the fourth spatial dimension). As described above, the Randall- Sundrum extra-dimensional concept posits a five-dimensional universe called the bulk, within which is embedded a four-dimensional universe called the brane. Applying this idea to our topic, we ask (a) whether there can be any energy exchange between bulk and brane, and (b) whether there can be enough complexity of structure within the 5D bulk to support the possibility of an extended 5D body of the 4D selves which are limited to the brane. In terms of the "finger- fingertip" analogy, the "fingertips" would be our 4D selves and the "fingers" would correspond to their 5D extended bodies located in the bulk. Also we need to address the issue of how the 5D structures might continue to exist after the death of the 4D selves.
In the models presented in (Arkani- Hamed, 1998) and (Randall, 1999) all energy forms, with one exception, are unable to leave the four-dimensional brane. That one exception is gravity, in the forms of static gravitational fields, gravitational waves and their quanta, the zero mass graviton, and its harmonic excitations, the so-called Kaluza Klein particles (Landsburg, 2006; Chatrchyan, 2012). Since gravity is intimately tied to the curvature of space, it would exist in any extension of space to a higher dimension, and thus in the bulk. We will use the term gravity to refer to any of the above manifestations either in our brane or more generally in the bulk. We will use the term matter to refer to all other energy forms including electrons, quarks, photons, and every quanta of all forms of energy which in the models of Arkani- Hamed (1998) and Randall (1999) are restricted to the brane and do not penetrate the bulk (see Fig. 2).
Figure 2. Matter is confined to our brane
In the Randall-Sundrum model, the five-dimensional bulk contains only gravitational energy. This would require that any extension of the material bodies of individuals in the brane would necessarily be some kind of structures, or organs, made up purely of gravity (as defined above). The total "body" of an individual would thus include a specifically gravitational component located within the bulk. How might this be possible? We consider two aspects: extension into a higher dimension and the field concept. Somewhat analogous to this is that of the point electron which by virtue of its electromagnetic field extends its influence from zero dimensions to three dimensions. Analogous to this would also be the reciprocal connection between a thin and dense material 2D plane and its gravitational field in the 3D space above and below it. The connection between the material body in the brane and its associated gravitational field in the bulk would also be reciprocal.
The third question posed at the end of the last section was "why should the extended higher-dimensional form remain after the death of its lower-dimensional component"? As an analogy, consider that the source of a traveling electromagnetic wave is an accelerating charge. However, when that charge stops accelerating, the traveling electromagnetic field continues on as a pulse. Granted, we are relying on electromagnetic and lower dimensional analogies. But building on analogies is at the very heart of progress in theoretical physics. (Think of the once bizarre concept of de Broglie’s matter waves and its progeny the Schrodinger equation.) However, these answers generate in turn further glaring questions. How would it be possible to detect gravitational signals from a higher dimensional space? And, wouldn’t gravity’s notorious weakness cut off at the start this idea of gravity being the medium through which communication between gravitational "bodies" in the bulk and material bodies in the brane might operate? Even if detectable, how could gravity waves convey information back and forth from the material bodies in the brane (presumably in particular the brains of those individuals) to its purely gravitational extension in the bulk? With these questions in mind we now review aspects of the Randall-Sundrum theory of higher dimensional gravity.
Randall and Sundrum proposed an extra-dimensional extension of Einstein's general relativity for the purpose of solving what is known as the Hierarchy Problem (Randall, 1999). It is known that at a reasonable energy scale the electromagnetic and the weak and strong nuclear forces have approximately the same strength. The gravitational interaction, however, remains in comparison extremely weak. For example, the ratio between the attractive gravitational force between two electrons and their electrostatic repulsive force at equal distances is on the order of 10-41.
In the simplest form of the Randall-Sundrum model they found a resolution of the problem of the relative weakness of the gravitational force by proposing a two brane plus bulk model, in which our locale is the so-called "weak" brane, while on the so-called "strong" brane the gravitational interaction is comparable in strength to the other three interactions--because of this it is also referred to as the "gravity brane", here we call it simply the "parallel brane.” Using very simple and plausible assumptions about the Einstein gravitational metric and source terms in the Einstein equations, in particular the tension or stress on the two branes, they then solved the resultant Einstein equations in the intervening "space" between the two branes, i.e. in the bulk. They found that the presence of tension on the branes had a dramatic effect on the strength of the gravitational interaction between the two branes. The strength decreases exponentially from the parallel brane to the weak brane by a factor of about 1016. The distance between the branes was very small (1 or 2 orders of magnitude greater than the Planck length) but the exponential factor explained the dramatic decrease in gravitational interaction. It turns out to be not so much an exponential decrease in the Newton gravitational constant as it is an exponential decrease in the inertial masses of the fundamental matter constituents in the weak brane. Because of the equivalence principle, this means that the gravitational mass of the matter constituents on the weak brane are also exponentially small compared with their counterparts on the parallel brane.
As noted above, in their model the only form of energy in the bulk is gravity as defined above, which includes the ordinary massless gravitons but also harmonic excitations of the gravitons, called Kaluza-Klein particles. In the bulk between the two branes, if ordinary gravitons bounce back and forth between the two branes so that they have an additional kinetic energy due to their motion perpendicular to the weak brane, they in effect turn into higher vibrational modes in a wave description (as with a vibrating string tied between two fixed points, a more energetic excitation will cause the string to have more nodes). If these excited graviton states in the bulk make their way into our brane, then two very counterintuitive circumstances arise. Unlike the hypothetical spin-two graviton (two units of Planck’s constant), which is massless, these excited states appear as massive spin-two particles (see Fig.3).
Figure 3. Imprint of higher dimensional world
To quote Randall (2005) these Kaluza Klein particles "are the four dimensional (space- time) imprint of the higher dimensional world." How do they pick up this extra mass? Strictly speaking, this comes from solving the 5D Einstein equation in the two brane configuration proposed by Randall and Sundrum [H. Davoudiasi, 1999]. However, one can gain heuristic insight into the origin of the Kaluza Klein masses in our 4D brane without using the 5D Einstein equation by an elementary extension of the Einstein energy mass relation E = mc2. Stated in words, the fourth spatial component of the momentum (perpendicular to the brane) of the graviton in the bulk can only be perceived in the brane as an effective mass.
The second counterintuitive circumstance that arises from the graviton excitations passing from the bulk into the brane, (again derived from the same set of Einstein equations which predict the possible spectrum of higher mode gravitons (KK particles)), is that unlike the ordinary graviton, which couples very weakly to matter with Newton’s constant G, the Kaluza- Klein excitations of the graviton would couple to the mass of matter in the brane with a Newton’s constant G multiplied by a huge exponential factor of about 1016 , allowing it to produce observable effects in ordinary matter. A zero mass graviton in the bulk traveling in the w direction perpendicular to the brane will be detected there in the brane as a spin-two Kaluza Klein particle with non-zero mass. Its appearance would appear to violate energy conservation in the brane. In principle such a massive particle could be detected passively by its decay to ordinary matter particles in the brane.
The same coupling of the KK particles from the bulk to ordinary matter in the brane that allows this decay would also permit the reverse of this process whereby matter particles in the brane collide with one another and produce a KK particle in the brane. Because of the connection between the KK particles and the bulk, the allowed spectrum of energies of the particles would be the same as that observed by the passive mode. In either case their subsequent decays could be detected with a clearly defined decay signature for a particle with spin 2. The model makes a range of predictions of the center of momentum energies of the excitations which will be tested at the new Large Hadron Collider (LHC). In early tests at the lower end of this range, no evidence of these excitations has been found (CMS, 2011). However, the fact that the tests have been and are actually being carried out attests that the expected strength of the interaction would be substantial.
The Einstein geodesic equations and the Einstein field equations show that when matter is restricted to the 4D weak brane, gravity-based energy forms in the bulk are directly affected by and have a direct effect on what takes place in the 4D brane. This provides a possible physical mechanism for the interchange of energy and information between matter-based organisms in the brane and gravitational energies in the bulk. Given the above considerations, we may ask what gravity-based energy forms might there be that could transfer back and forth between bulk and brane, and would they not be overwhelmed by other energy forms?
Since gravity in our brane is incredibly weak in comparison with the other interactions, one might think that any signals between brane and bulk would be overwhelmed by the noise of other interactions. If so it would be impossible to detect in the bulk any gravitational changes associated causally with, for example, human brain activity. But since matter and its interactions are forbidden to manifest directly in the bulk, gravity would not have to compete at all with any matter-based energy forms. Therefore the weakness of ordinary gravity in the brane would not be a factor in the bulk.
However, there are plenty of gravity-based noise sources in the brane that could influence the bulk in addition to ones originating in our brains or nervous systems. If I wave the little finger of my left hand I create a gravitational disturbance perhaps at least as great, and probably much greater, than any gravitational signals coming from my brain or nervous system. But if my (hypothetical) extended self in the bulk behaves like a tuning fork, resonating only with vibrations having a frequency characteristic of the fork, this would provide a way in which that part of the bulk associated with our own 4D selves would not be overwhelmed by other gravitational disturbances either from the brane or within the bulk. This would require, of course, that gravity-based energy forms originating in the brain/brane must have a very well defined frequency.
What about gravitational energy forms entering the brane from the bulk? To be detected by the brains of organisms in the brane they would not only have to compete with other gravitational energy forms but also the myriad of matter-based energy forms. Weak, ordinary zero-mode gravity signals coming from the bulk would be virtually impossible to be noticed because they would be drowned out by the much stronger matter-based reactions. However, this would not necessarily be true of higher mode gravitons propagating into the brane from the bulk. They would indeed be much more likely to be noticeable because they interact with matter by a factor up to 1016 times greater than the ordinary zero mode gravitons. This, then, might provide a mechanism whereby whatever system capable of sending a gravity-based energy form with a well-defined frequency should also be capable of receiving such forms and not be overwhelmed by the noise of other energy forms.
So if the human brain is such a system, it would have to have (or be?) a well-tuned receiver of such signals. The question, of course, is whether the brain is such a system and whether, or how, that might be verified or inferred. The 5D Einstein equations provide a derived mechanism for transferring these received higher mode gravity signals to macroscopic matter-based actions. The higher mode signals coming from the bulk would differ from the completely ineffectual zero mode gravity signals coming from elsewhere in the brane or from the bulk. Once these higher mode forms are received, evidently something of the nature similar to that which takes place with an observed quantum state must occur. Recall that an observation of a quantum state will result in what is known as the "collapse of the wave function." During this (irreversible) process, a macroscopic record (involving many atoms) of the event is made. In the case of the brain then, a quantum event gets magnified to such a state that the brain would be able to detect it. Thus the quantum event might be raised to a level of awareness.
This would, of course, require one to "quiet oneself" in order to limit surrounding disturbances. Such "quieting" may in fact take place in several circumstances: when concentrating on a problem, having an aesthetic experience, sleeping, entering into a deep state of meditation, and perhaps in a psychic trance. Since everyone sleeps, there could be an interchange of information between brane and bulk during the sleep cycle, with the other possibilities being ways of enhancing such exchange. If we extrapolate on such an idea, the possibility of some human individuals being especially sensitive to such possible signals would refer to those historically known as "psychics," clairvoyants, or mystics.
So the bulk, although devoid of any matter, of quanta of any form of energy other than gravitational, would indirectly not be devoid of the influence of all other forms of energy, since the bulk is bounded or encompassed by the brane and the energy forms there would influence not only gravity in the brane but also gravity in the bulk. Likewise, unlike zero mode gravity from the bulk which has only infinitesimal effects, higher mode gravity from the bulk could influence matter in the brane. The possibility of "quieting" any noise which would interfere with energy exchange between human organisms in the brane and gravitational forms in the bulk might then be related to the various methods of ego-transcendence and possibly through the sleep cycle.
4 Structural Characteristics of the Bulk
Generally speaking, complexity of structure is associated with the possibility of the existence of organisms or organs of an organic system. If therefore some entities in the bulk are to be associated, through energy exchanges as discussed above, with organic systems (e.g. brains) in the brane, there would seem to be a requirement for structural complexity of entities in the bulk. We therefore turn our attention to this question.
Gravity waves in the brane (our 4D realm) are generally understood to be created by the accelerated motions of material bodies. Because there is an energy interface between the brane and the bulk, gravity waves in the bulk may also be produced by matter in accelerated motion in the brane. Since the bulk is bounded by two branes, purely gravitational structures in the bulk might then take the form of complex gravitational standing waves (see Fig.4).
Figure 4: Gravitational Standing Waves
Could these waves also, like their electromagnetic counterparts be capable of conveying information? The wave equations for standing sound waves and standing electromagnetic waves in the brane are linear, meaning that the standing waves could be constructed from a linear superposition of two (or more) waves traveling in opposite directions. Without this linearity, information could not be conveyed by the usual linear Fourier superpositions. The obvious problem in trying to extend the concept of standing waves capable of conveying information to gravitational waves in the bulk is that the Einstein equations (in 4D or 5D) are nonlinear. This means that in general if you have two or more solutions of the Einstein equations, then the sum of those solutions will
not be a solution of the Einstein equations. This is in contrast to the linear theories in which the sum of two or more solutions of the linear wave equation is itself a solution of that wave equation. Weak gravitational standing waves would be possible in either brane or bulk since they satisfy approximately a linear wave equation. The difference between the two types of linear waves would be that in the 5D bulk there is a ‘w’ dependence of the wave amplitude and phase whereas in the brane there is no such dependence since ‘w’ is fixed at 0.
Even if the gravitational field is not weak so that the nonlinear terms in the equation would play an important role, a special class of standing waves solutions has been found by Stephani (2003). His testing grounds, however, are not in the context of the Randall- Sundrum model but in the "ordinary" 4D Einstein metric and equations. It would be relevant then to determine if such a class of exact standing wave solutions exists in the 5D Randall- Sundrum model. If that turns out to be the case, there would be no conflict between having stable gravitational standing waves in the bulk capable of conveying information and the nonlinearity of the 5D Einstein equations.
There are other factors which may affect the strength and/or complexity of formations in the bulk. In the two-brane Randall-Sundrum model, all massive particles in the parallel brane have an enormously larger inertial mass than they have in the weak brane. Disturbances there could therefore have greater effects within the bulk than disturbances in the weak brane. Also, although solitons and standing waves in the 5D bulk would appear mathematically similar to their counterparts in the 4D brane, their spatial extensions in the x, y, z direction may depend sensitively on the local value of w (the extra spatial dimension). Magnitudes would vary as w varies. Additionally, aside from static gravitational fields and gravity waves, there are also their quanta, the massless gravitons, and of course their excitations. Just what the strength and complexity of gravitational formations in the bulk would be remains for further research. But it is not at all beyond possibility that complex purely gravitational 5D formations capable of dynamically storing and/or transmitting information might exist in the bulk. For an idea as to just how very complex nonlinear standing waves may become, see the studies of wave formations in a fluid medium carried out in Schwenk 1996, and the work of the Institute for Flow Sciences (Institut fuer Stroemungswissenschaften).
Since in terms of the analogy the extended self would have to be made up of 5D complex energy forms in the bulk, and since no ordinary matter inhabits this realm, this provides an interesting match for the oft-stated idea that the "spiritual" realm is not physical (where "physical" is construed as "material"). The bulk is indeed not a "physical" realm in that sense; thus it may be considered "spiritual" in that it contains no
matter whatsoever as earlier defined.
We might emphasize this crucial distinction by referring to any entity made up of material substance as a
corporeal entity. Then we would say that an entity of pure gravity (in the sense taken here) would be non-corporeal but it would not be non-physical. Using this terminology the speculation would be that each individual has a corporeal and a non-corporeal component (see Fig. 5).
Figure 5. Corporeal (Brane), Noncorporeal (Bulk)
When the 4D corporeal component terminates, the 5D non-corporeal (but still physical) component may remain. If so, the idea of the extended "body" and mind surviving after the death of the corporeal form would be supported (recall that we make no postulation regarding the specific relation of body and mind).
Another aspect of gravity in the bulk that may bear on our investigation is the possibility of information transfer (in the form of energy) from one portion to another of the bulk itself; and therefore if there are extended selves in the bulk, between such extended selves. Again we have a suggestive parallel to various forms of paranormal phenomena. Thinking of claims of telepathy, the theory would allow such communication to take place either indirectly through the brane (by energy transfer from one standing wave (the non-corporeal entity) to the 4D (corporeal) individual and then from there to another individual by ordinary electromagnetic or sound wave communication and from there by gravitational transfer of energy through the brane to the bulk as described earlier), or directly, by complicated connections between standing waves in the bulk or possibly by gravitational solitons (see Fig 6.).
Figure 6: Gravitational connections
Gravitational solitons are a feature of the nonlinearity of the vacuum Einstein equation. These are objects that move in the appropriate space-time dimensions with their shape unchanged.
Bizon et al (2007) have studied gravitational solitons in higher dimensional gravity although they did not study the Randall-Sundrum model. Their focus is on the stability of the solitons. They found evidence of stability at the linearized level and beyond for moderate sized perturbations. Also, thinking of "communication with the dead," if the corporeal body of person A dies but the extended self of A in the bulk remains and is capable of exchanging information with the extended self in the bulk of person B, who is alive in the brane, this would suggest something of that nature. Whatever levels of transfer are envisaged, if there is a mechanism for a corporeal individual in the brane (likely through his or her brain) to receive such signals, the soliton or standing wave should be capable of conveying information. Electromagnetic waves are clearly capable of this, so their gravitational counterparts should also be capable of conveying information by similar means.
5 Is Verification Possible?
Based on the above analysis, it is our view that the Randall-Sundrum model, while subject to provisos as noticed frequently above, still provides an intriguing metaphor for the existence of certain paranormal phenomena as well as for the persistent views found in religion, philosophy and psychology asserting a wider concept of the self. In order to raise the level beyond physical metaphors into the realm of potential verification, at least four important studies would have to be undertaken. Four experimental and theoretical requirements that would support the possibility of raising physical metaphors into the realm of potential verification are 1) discovery of KK particles 2) demonstrating theoretically that gravitational standing waves and solitons exist in the "bulk" of the Randall Sundrum theory 3) detecting higher mode gravitational waves originating in the bulk capable of being received by individual human organisms and 4) the identification of a candidate for a specific locus in the human organism of reception and transmission of vibratory effects back and forth from brane to bulk. Below we discuss each of these in detail. Taken together they would constitute necessary but not sufficient conditions for verification.
1. A necessary condition is experimental confirmation of the existence of higher dimensions by the detection of Kaluza-Klein excitation decays in the brane. Because in the theory the bulk is exponentially warped, the KK particles should have a mass on the order of or higher than 10^12 electron volts (Randall, 2005). At the energies to be available at the LHC, confirmation or falsification should be possible.
2. A second requirement would be theoretical confirmation of the possibility of very complex forms of gravitational wave activity in the bulk, involving standing waves, solitons, gravitons and their excitations. In this respect there is a danger of relying too much on physical intuition from our ordinary 4D space-time, since the extra spatial dimension in the 5D bulk can lead to more complexity. For example, there are very powerful methods (such as conformal mapping) for solving certain equations in 3D (2 space dimensions), and if there is symmetry in the z direction (called axial symmetry) then the added spatial dimension from 3D to 4D space time does not complicate the solutions, and one can use intuition and experience based on the 3D space time. However, in general adding an extra spatial dimension does lead to more complexity. Such would equally be true for the 4D to 5D transition. The potential added complexity of gravitational wave phenomena in the 5D bulk has yet to be investigated.
This second set of requirements will be quite challenging even to the expert general relativist. We have here made a brief foray into this question, but the present paper is limited to a discussion of the possibilities, requirements and issues raised in pursuing the Flatlander analogy in terms of one type of contemporary extra-dimensional theory and does not extend to technical theoretical elaborations along these lines.
It may be objected that it is absurd to imagine that
any configuration of purely gravitational field energies in the 5D bulk, however complex, could function as some kind of extension, or organ, of our physical 4D forms. But aside from the point just made (that intuition and experience based on our current paradigm may be inadequate), we submit that our "physical" (i.e. corporeal) bodies are themselves made up of (matter) fields and particles, where the particles are expressions (as quanta) of such fields. It is certainly not clear that this constitutes a radical qualitative difference in the possibilities of organization. Furthermore although the energies making up our own corporeal form are predominantly non-gravitational, they may certainly involve gravitational influences. The reverse case might indeed be made: a complex structure made only of gravitational energies and particles might have capabilities of organization unknown when freed of the presence of the energies constituting "matter," particularly when an additional spatial dimension is a factor. Only more research may determine whether such is a possibility. We note however that this latter point is consistent with the traditional notions of the transcendence of existence beyond the "corporeal."
3. Next, experimental determination of the existence of higher mode gravitational waves originating in the bulk and capable of being received by individual human organisms is required. (Preliminary to this one would first have to detect such received gravitational interactions from the bulk in a passive laboratory setting, without the aid of the LHC!) This would have to include a detailed modeling of gravitational energy exchange mechanisms between bulk and brane. If we are bound to the assumption of mind-brain identity, this would appear to mean localizing a source of such wave frequencies within the human brain.
The idea of biological quantum coherence phenomena based on vibrational effects within active cells, although not directly related to the brain, has been studied by Frohlich [Frohlich,1968]. He has examined biological systems with branches of longitudinal electric modes at frequencies in the microwave range, based on the dipolar properties of cell membranes. In particular he has shown that if energy is supplied above a certain mean rate to such a branch, then a steady state will be reached in which a single mode of this branch is very strongly excited. What is remarkable is that the supplied energy is not completely thermalized but stored in a highly ordered fashion with long range phase correlations which has considerable similarity with the low-temperature condensation of a Bose gas. This is mentioned just to point out that coherent vibratory effects within the biological system of the brain may not be pure speculation. Penrose (1994) has even suggested that there may be a connection between these microwave frequencies and the much lower measured frequencies associated with alpha, beta, theta, and delta brain wave activity.
In regard to a gravity-brain connection, Penrose (1994) has also claimed that consciousness involves processes that may be intimately tied to large scale quantum-coherent phenomena (including state reduction) in the microtubules associated with the synapses branching off nerve pathways, related to the claims discussed above by Frohlich. And he also proposes that quantum state reduction must ultimately be a gravitational phenomenon in
spite of the weak interactions involved. This would appear to support the possibility of the effect of gravitational signals on conscious awareness. However, contrary to some of the speculations of artificial intelligence, Penrose also argues that the way that gravitational mechanisms mediate state reduction cannot be modeled by any computational, i.e., algorithmic, procedure.
Returning now to the problem of the weakness of gravity in regard to consciousness and paranormal phenomena, we point out that even gravitational waves produced by large systems are very weak. The Sun-Jupiter rotational system, for example, produces a power output about that of only a 40 watt bulb. Detecting much, much weaker gravity waves is certainly impossible with today's detection devices. This, however, does not imply that such extremely weak signals could not have an impact on the gravitational structures in the bulk. There are two reasons. First of all, no matter-based interfering energy transfers to the bulk can take place; and secondly, some form of frequency resonance could be involved. The extremely weak nature of the coupling of the gravitational field to all matter forms (mass or electromagnetic) makes the determination of a viable mechanism of their generation and reception within the brain the most problematic aspect of our analysis. However, as discussed above the two-brane theory of Randall and Sundrum provides an enormous factor of about 1016 in the strength with which gravitational signals originating in the bulk can affect matter particles in the brane. As stated by Randall (2005), the "KK particles pile up on the weak brane (because their probability function peaks there) and they have all the properties of weak brane particles." Here then is another unexplored avenue of theoretical research, the pressing question being whether Randall’s statement about the KK particles from the bulk could theoretically translate into them having effects on brains or bodies in the brane.
4. Finally, verification would require a candidate for a specific locus, or organ, of reception and transmission of vibratory effects back and forth from brane to bulk. One candidate region might be the so-called "god spot" which was thought to be a distinct area of the brain responsible for spiritual experiences. Recent research at the University of Missouri has indicated, however, that experiences thought to be associated with a "god spot" are actually a complex phenomenon involving multiple areas of the brain, not just a single location (News Bureau, University of Missouri, April 18, 2012). This observation brings into view recent critiques of the mind-brain identity theory in cognitive science, which argue that no sharp demarcation can be drawn between the brain and the entire nervous system. Whether self-awareness can be associated with any specific areas of the brain is unknown with those both arguing for and against the localization hypothesis.
There is also the consideration that mediums and clairvoyants make claims of perceiving information from other dimensions or planes of existence, such as the "astral plane," and also of perceiving one or more spiritual "bodies" of individuals which exist in other such planes or levels of reality. If there were some experimental determination, again, of an organ or region of the body possessed by, or more highly developed in, such individuals, this could also be a candidate for such a focus of reception and transmission between brane and bulk.
Some in the field of cognitive science have proposed a theory of "extended cognition" which attributes mental phenomena to an even larger spatiotemporal structure called a
behavioral field which, it is proposed, may be described by Dynamic Systems Theory (DST) (Rockwell, 2007, Chemero 2009). Under such a theory, any source of gravitational forms which might serve as a basis for energy exchange between humans in the brane and gravitational structures in the bulk would be a complex dynamic spatiotemporal field of activity. As such, this latter would perhaps be a more likely source than any single dedicated area of the brain. Such concerns, however, are at the cutting edge of mind-brain research and at present no experiments have been devised or proposed which might detect weak gravitational waves associated with human mental activity, whether localized in the brain or extended to the nervous system or beyond. In fact, although it may be nearly impossible to detect gravity waves in the brain associated with zero mode gravitons from the brane or bulk it remains an open question whether the same could be said for the higher mode excitations from the bulk.
5 Conclusion
Our aim has been limited to an investigation of how the extra-dimensional theory of Randall and Sundrum might apply to an extension of the 3D-4D Flatlander case, by analogy, to a 4D-5D situation. Specifically the theory being investigated is that 5D gravity-based structures in the bulk are non-corporeal but physical extensions (as defined above) of the bodies of 4D individuals in the brane and are engaged in energy exchanges with human individuals, as this updated analogue to the Flatlander case suggests. The requirement of the analogy is that evidence should either be found, or experiments proposed, which might indicate that our personal consciousness may be divided in some way between corporeal forms in the embedded 4D realm and non-corporeal (gravitational) forms in the larger 5D realm, of which (in the Randall-Sundrum model) our 4D space-time constitutes a boundary called a brane. Following up on our detailed exploration of this topic, we identified four experimental and theoretical results whose confirmation would constitute necessary, but not sufficient, conditions for verification of such a theory. Our conclusion, then, is that although the Randall-Sundrum extra-dimensional model is suggestive of that possibility, actual verification of the extension of the Flatlander analogy at the 4D-5D level does not appear to be within the purview of contemporary experimental capability. On the other hand, given the existence of the various possibilities mentioned, the analogy cannot be rejected out of hand as absolutely unverifiable but that the question of what would constitute sufficient conditions remains open.
Acknowledgments The authors would like to thank Dr. Conley Powell and Dr. James Strange for helpful comments on a preliminary version of the paper, to Mr. David Menard for pointing out to us the work of Carr, and to Natallia Kaptur for graphical support on the figures.
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