University of California - San Diego, BioCircuits Institute, La Jolla, CA 92093-0402; August 1, 2011.
Based on the modeling of consciousness and modified general relativity, it is concluded that the phenomena of qualia (subjectivity) is inherited by the ordinary matter from the dark matter. Existence of a new particle - mediator between dark and ordinary matter (_{do}) is suggested.
The phenomena of consciousness can be considered as hierarchy of observations and control [1]. Hierarchical structures appear naturally in systems with strong interaction of many degrees of freedom. Typical signatures of such hierarchy are so-called similarity laws. Particularly, in turbulence the concept of scale-similarity was developed and was associated with the infinitely-divisible distributions [2]. The activity of the human brain also revealed the regime of scale-similarity, which was discovered by using the multi-channel MEG (magnetoencephalogram) [3,4] and EEG (electroencephalogram)[5] (see also [6,7]). Hundreds of billions of interconnected neurons and surrounding sells (particularly, astroglia), apparently, is favorable playground for hierarchical structures in the brain.
The electrochemical brain activity is taking place in wet and warm surroundings. To reproduce such activity in artificial systems, even approximately, seems impossible. However, modeling of the effects of consciousness [8-12] can be used to enhance performance of artificial stochastic systems[1].
In the modeling [9-12], the subjective experiences were divided into three major groups: sensations (S), emotions (E) and reflections (R). Note, that subjective S should be distinguished from the automatic sensory input into the neuron system of the brain [13]. Consider quaternion:
q=+i_{p}_{p} #1
Here (t,x) is the current density perpendicular to the cortical surface, _{p}(t,x) represent the indicated above (S, E, R) - effects, summation is assumed on repeated subscripts from 1 to 3 and imaginary units i_{p} satisfy conditions: i₁²=i₂²=i₃²=-1,i₁i₂=-i₂i₁=i₃ and so on cyclically. The model equation for the quaternion q has the form [9-12]:
Here k is the relaxation coefficient, f represents the sigmoidal firing rate of neurons [for example, f()=tanh()], v is typical propagation velocity of signals in the neuron system of the cortex, is the two-dimensional spatial Laplacian, quaternion =s+i_{p}_{p} is the sensory input, which has real component s and imaginary components _{p}(for so-called extra-sensory effects, if they exist) and parameters m∼k∼v/l, where l is the connectivity scale. If we put _{p}=0,_{p}=0 and =0, than equation for will be similar in spirit to equation used for interpretation of EEG and MEG spatial patterns ( see [14] and references therein).
The essential point of modeling (1) -(2) is that imaginary fields produce real effects because of the nonlinear firing rate of neurons. Note, that complex fields have been used [15] to eliminate classical electromagnetic divergencies, namely, the infinite self-energy of electrons and the paradoxical self-acceleration. The same (algebraic) approach works for the quantum interaction of charges. In new interpretation of quantum theory [16] imaginary trajectory and corresponding momentum play an important role.
Modeling (1) - (2) is designed for description of the effects of consciousness on the electric currents in the human brain. In order to advance in the problem of qualia (subjectivity) we now turn to a new type of cosmology, which is based on modified general relativity (MGR) [17-19]. The modification does not introduce new fields, but takes into account the effect of spacetime stretching (divergency) along with classical spacetime curvature. The modification is especially important when global spacetime curvature R is close to zero, which is the case in our universe.
The following exact analytical solution of MGR equations was obtained [20,21]:
Here a is the scale factor of the universe, subscript 0 indicates present epoch, c is the speed of light, G is the gravitational constant, w=+p is the heat function ( - energy density, p - pressure) and H₀ is the Hubble constant (H=a⁻¹da/d). This solution (without any fitting parameters) shows good quantitative agreement with cosmological observations (SnLa, SDSS-BAO, see details in [20,21]). Solution (3) corresponds to continuous and metric-affecting production of dark matter particles out of vacuum, with its density ₀=w₀c⁻² being retain constant during the expansion of spatially flat universe. This solution is shown [20] to be stable in the regime of cosmological expansion until t_{max} about 38 billions years.
Mass m₀ of corresponding dark matter particles is estimated [20,21]:
m₀∼ħ(G_{∗}₀)^{1/2}∼10⁻⁶⁶gram, #4
where ħ is the Plank constant. So, these primary dark matter particles (PDMP) are ultralight.
According to solution (3), our universe was born in infinite past out of small fluctuation. The averaged density of PDMP is very high: n=₀/m₀∼10³⁶cm⁻³. With such density we can expect multiple hierarchical collisions and formation of more heavy particles in some sort of "natural selection". During the steady and stable expansion of the universe, the ordinary matter was synthesized in this way, probably, starting with light particles. This process was accompanied by radiation, which is reflected in the cosmic microwave background (CMB). The eqilibrium character of CMB and the global condition R≈0 are naturally explained by the large amount of time available for the evolution. Some peculiarities of CMB can be associated with synthesis of various particles in expanding universe. In context of such evolution of our universe, what we call ordinary matter is, in fact, an exotic matter, which was synthesized from PDMP and, sofar, constitute only small fraction of the total mass of the universe. The theory of elementally particles should be modified by inclusion dark matter as primary basis for all particles.
From cosmological observation it is suggested, that dark matter interacts with ordinary matter only gravitationally and seems indifferent to electromagnetic, strong and week interactions. Note, that gravitation is resisting quantization, unlike the other three interactions. In a sense, interaction of ordinary matter with dark matter can be presented in the form of quaternion (1) with gravitation as real component and other three components imaginary (see also Ref. 9). If we continue with this analogy, than (apart from gravitation) some indirect form of interaction, similar to nonlinear firing rate of neuron, can exist between dark and ordinary matter. Indeed (see above), ordinary matter was synthesized from dark matter as result of multiple hierarchical collisions. In this sense, dark matter is working similarly to neural system.
The qualia (subjectivity) was historically considered as otherworldly. In contemporary cosmology we got the dark matter, which is unusual in indicated above respects. From what was described in this paper, it seems natural to suggest that qualia is inherited from dark matter. The ultralight PDMP with mass (4) are constantly produced by the vacuum everywhere, including our body and our brain. Perhaps, so called biophotons (see [22] and references therein) are related to production of PDMP. Inside neuron we have special conditions, which potentially can facilitates interaction with PDMP.
The best way to investigate these effects is, probably, during events of extremal qualia, such as pain or orgasm (preferable). Orgasm has many definitions [23], none of them totally satisfactory. Generally, orgasm has different feeling depending of sources of stimulation (including mental stimulation) and corresponding nerves. Combinations of sources in simultaneous stimulation produce so-called blended orgasms, which are, generally, more powerful. The physical nature of orgasm is a total mystery. The electrochemical signals repeatedly reach brain and than something happens, which reminds lightning, but in a "mental world".
The modeling (1)-(2) of the effects of consciousness suggests existence of a particle - mediator between dark and ordinary matter (_{do}). PDMP can produce _{do} spontaneously, or, more likely, during collisions. _{do} in turn produce additional ordinary photons during the nonlinear process of firing. So, the one thing, which can be tested during orgasm is enhanced radiation with a peculiar spectrum (details will be presented elsewhere).
Similar scheme can be applied to cosmic events. Collisions of PDMP produce _{do} - sparks of dark matter. In nonlinear process of hierarchical collisions, the "plasma" of PDMP and _{do} produces particles of ordinary matter, including ordinary photons. Note, that only small fraction of PDMP collisions produces ordinary matter. Cosmological observations (for example, [24]) indicate that more substantial portion of such collisions produce some lumps and clouds of dark matter.
Do dark matter, which we now observe only by the gravitational effect, has some sort of qualia? If so, are they similar to indicated above SER-qualia, which we possess? And, finally, can we communicate with dark matter? The positive answer to this question can produce revolution in the history of humankind.
The main conclusion of this paper is that such seemingly divorced phenomena as consciousness and dark matter, in fact, are closely connected. These two very important areas of research can greatly benefit each other from their proper coordination.
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