Why does our brain not break down? Why is it that this extremely complex structure, with 100 billion neurons interconnected by as many as 100 trillion synapses (Jahr, 2003), plus an estimated three trillion miles of axons for transmitting messages, does not obey Murphy's law? Each neuron makes several thousand connections with other cells, astrocytes included (Heuss, 2002), so imagine the challenge of talking on the phone with 1,000 or 10,000 people and keeping all conversations going (Dobson, 2000). Keep also in mind that the action potential can run with the speed of up to 250 miles per hour (Greenfield, 2000) and the so-called kiss-and-run neurotransmitter release varies from 6 ms down to 250 µs, if the neurotransmitter inside the vesicles is freely diffusible (Burgoyne and Barclay, 2002), so we really don't have much time to think. Besides, what kind of "computation" could be possible if the chance for transmitting the signal, in many cortical synapses, may be of the order of as little as 30 per cent (Albright et al., 2000; Donald, 2002)? Surely something some day must go wrong. But it doesn't. It didn't happen over the first few years of life when some 30,000 brand new synapses were created every second under each square centimeter of the brain's surface (Rose, 1999). It didn't happen even in our prenatal development, when our brain has been created with a rate of approximately 250,000 neurons per minute (O'Rahilly and Muller, 1994). And this same piece of jelly matter has the ability to act on itself -- we think about our brain, with our brain. That is a total mystery. We know from school that there are many unsolved mysteries, the greatest one being undoubtedly the creation of the Universe. Another mystery, perhaps not widely recognized, is the nature of gamma ray bursts, coming from the far depths of the Universe, billions of light years away from us (see current Gamma Ray Bursts Map and BATSE). These are extremely powerful energy bursts of nearly 3.1053 ergs (Harada et al., 2000), which unleash, within a few seconds, the whole energy that the Sun has released during its entire 10-billion-year lifetime. We can read in newspapers about other great challenges facing today's Weltbild, or physical picture of Nature (Wilford, 1998; Wilford, 1998a; Oberbye, 1998; Glanz, 1999). All these stories, however, stay somehow away from us, while we carry the great mystery of the human brain always with us, right above our neck (Vitiello, 1996; Alfinito et al., 2000; Schwartz and Russek, 1998; Barrett, 1998; Kent, 1999; Zeh, 1999; Samal, 2000; Mohrhoff, 2000). We certainly know a lot about it, having studied the brain and its mind with great technical precision (Brodal, 1981; Rees and Frith, 1998; Kosslyn, 1999; Gazzaniga, 1999; Albright et al., 2000; Grossberg, 2000; Haxby et al., 2000; Horwitz et al., 1999; Llinás et al., 1998; Neisser, 1997; Rind and Simmons, 1999; Atkinson et al., 2000; Gusnard et al., 2001; Radford, 2000), and yet we have no clear understanding of how our self is linked to our brain, which is certainly the first question we may ask about the human brain. The situation is pretty similar to that in quantum physics -- despite its enormous practical achievements, today's quantum theory (Fuchs and Peres, 2000) does not explain the occurrence of events (Bassi and Ghirardi, 2000), which is certainly the first thing we observe about the world around us. Suppose, just for the sake of the argument, that all unsolved mysteries are linked into one coherent structure, such that all pieces fit perfectly and none of them is unneeded nor redundant. Perhaps the physics of the brain could tell us more about other, seemingly unrelated, blank spots in present-day science. Perhaps we may need to know how the brain works in order to develop a complete theory of quantum gravity, and vice versa. I believe we first need to understand the nature of the quantum of action -- not for the purpose of revealing the physics of the brain but for reasons coming exclusively from quantum physics and modern cosmology (cf. Open questions in quantum theory). This effort is driven by my firm belief that there is a quantum reality 'out there' (Chakalov, 2000a, 2000d), just as we are confident that there is a sound from a falling tree in a forest even if there is nobody around to hear it. The next step would be to introduce a special 'universal time arrow' in that quantum reality (D.G. Chakalov, Physics of Human Intention, CD ROM Edition, 2004), for the simple reason that if something exists as reality, it should exist in time and should change in time -- "Der Herrgott würfelt nicht" (God casts the die, not the dice), Albert Einstein. Hence the task is to reveal the dynamics of quantum reality (Schrödinger, 1935) from a totally static 'timeless' picture (Ashtekar, 1993; Rovelli, 1999; Neumaier, 1999; Kitada, 1999; Warren, 1999; Castro, 2000; Castro and Granik, 2000; Castro et al., 2000; Barbour, 2000). I will try to model the Universe as a human brain (Chakalov, 2000d) and will suggest some 'universal time arrow' matching the psychological time arrow, in Ulric Neisser's cognitive cycle (Neisser, 1976; Neisser, 1997). As to the philosophical framework, I am forced, regrettably, to suggest a new term, trialism, stressing that it is neither monism nor dualism. The only critical assumption is that there are no ghosts nor any other immaterial agents operating in our brain. Only matter can act on matter. If so, what happens in the brain when it acts on itself should be relevant to physics, particularly to the quest for quantum gravity and the mystery of cosmic vacuum energy density (Straumann, 2000; Adler et al., 1995; Feynman, 1988). Going back to Schrödinger's cat (Schrödinger, 1935; Margenau, 1940), I suggest we need a 'remnant from the cat' (Chakalov, 2000d; Altaisky, 2000) as a quantum correlate of Platonic ideas. To put it differently, the bi-directional 'talk' between space and matter ("Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve", John A. Wheeler) yields classical gravity in the limiting case of a vanishing small 'remnant from the cat', while in the quantum realm the same bi-directional talk goes between the remnant from the cat, serving as a non-physical background (or 'forest', Chakalov, 2000b; 2000d), and the explicated (not "collapsed") values of physical quantities, just like in the case of the human brain. This putative mechanism of quantum gravity actualization (not "collapse") is observer-free, and hence we can talk about a quantum reality 'out there', which exist in time and change in time: "Der Herrgott würfelt nicht" (God casts the die, not the dice), Albert Einstein. We simply cannot observe it with inanimate devices -- they could only display a frozen 'snapshot' of the physical world (Neumaier, 1999), and we can not mathematically describe the dynamics of the explications from the 'remnant from the cat' along the universal time arrow (cf. Note 1). That's why quantum theory inevitably involves probabilities, while the underlying dynamics of the quantum world is fully deterministic in the sense that the Universe passes into its next state with probability unit: "before" moving into that next state (God casts the die, not the dice, Albert Einstein), all explications from the 'remnant from the cat' are "already" bootstrapped and EPR-like correlated, in line with Leibnitzian harmonia praestabilita in a Machian-type Universe. We can physically describe only one frozen 'snapshot' from the evolution of the Universe, and hence could only make probabilistic counterfactual statements about its evolution in the future and history in the past. It has to be stressed that the remnant from the cat, just like Platonic ideas, can never be directly observed, and the nature of its confinement is perhaps related to the Berry phase (Anastopoulos and Savvidou, 2000) and the nature of "negative" probabilities (Rothman and Sudarshan, 2000). If, however, there is some immaterial, out-of-this-world ghost operating in our brain, which can change its "knowledge" instantaneously (Unruh, 1993; 1993a), being totally independent from the brain, then everything said here may be wrong, and we may not need to worry about how to interpret quantum mechanics (Fuchs and Peres, 2000). I do not offer any breakthrough nor final solutions. The task is highly non-trivial (cf. Kuchar's perennials and Isham's program), it goes back to the foundations of quantum mechanics (Unruh, 1993; 1993a; Pospiech, 2000; Balachandran, 2000; Vuletic, 1999; Schrödinger, 1931; Schrödinger, 1935; Margenau, 1940; Baez, 1996; Vecchi, 2000; Chakalov, 2000b; 2000c; 2000d; Altaisky, 2000; Rothman and Sudarshan, 2000) and ends up with the problem of continuum and the very nature of motion (Zeno's first paradox and Aristotelian First Cause). "If all this damned quantum jumping (verdammte
Quantenspringerei) were really to stay, I should be sorry I ever got
involved with quantum theory", said Erwin Schrödinger in September 1926. This is
exactly my goal, from the perspective of the physics of the human brain. All
questions, critical comments and suggestions will be highly appreciated. Dimiter G. Chakalov
References and notes
Heuss C. (2002). How Glia
Sustain the Brain, 26 November 2002,
See also: Astrocytes,
How Do Nerve Cells Communicate?
Brain Facts,
Dobson R. (2000). The web gets a mind of its own. The Sunday Times, Sec. 9, January 16, 2000. Greenfield S. (2000). The Private Life of the Brain. London: Penguin, p. 7. Cf. also pp. 12-13, p. 43, pp. 61-62, p. 64 (an operational definition of mind), p. 164, and pp. 197-198. (To order the February 2002 edition of the book from Penguin Books, ISBN 0141007206, click here.) Harada T., Iguchi H., Nakao
K. (2000). Naked Singularity Explosion.
O'Rahilly R., Muller F. (1994). The embryonic brain: An atlas of developmental stages. New York: Wiley. Wilford J.N. (1998). Shocked Cosmologists Find Universe Expanding Faster. The New York Times, March 3, 1998. Wilford J.N. (1998a). Cosmologists Ponder 'Missing Energy' of the Universe. The New York Times, May 5, 1998. Oberbye D. (1998). A Famous Einstein 'Fudge' Returns to Haunt Cosmology. The New York Times, May 26, 1998. Glanz A. (1999). What Do Physicists Fret About? Nothing. The New York Times, November 30, 1999. Vitiello G. (1996).
Structure and Function.
Alfinito E.,
Viglione R.G. and Vitiello G. (2000). The decoherence criterion.
Schwartz G.E.R. and Russek L.G.S. (1998). The Origin of Holism and Memory in Nature: The Systemic Memory Hypothesis. Frontier Perspectives, Vol. 7(2), Fall 1998, pp. 23-30. Barrett J. (1998). The Quantum Mechanics of Minds and Worlds. Oxford: Oxford University Press. (To order the book from Amazon.com, click here.) Kent A. (1999). Night
Thoughts of a Quantum Physicist.
Zeh H.D. (1999). The Problem
of Conscious Observation in Quantum Mechanical Description.
Samal M.K. (2000). Can
Science 'explain' Consciousness?
Mohrhoff U. (2000). The Physics of Interactionism. In: The Volitional Brain. Towards a neuroscience of free will. Ed. by Benjamin Libet, Anthony Freeman and Keith Sutherland. London: Imprint Academic (September 2000). Ulrich Mohrhoff: "The causal efficacy of the self thus rests on the causal efficacy of the particles, or on the ability of the particles to modify their individual contributions to the electromagnetic field. The causal behaviour of particles (meaning, the way particles influence each other's motion, as distinct from the way particles move) accordingly comes in two modes: a physical mode which obeys the laws of physics, and a non-physical mode through which modifications of the physical mode are effected. But this means that the only causal agents in existence are the fundamental particles, and that the non-material self cannot be as non-material as dualists would have it. Interactionism thus cannot be the last word." Brodal A. (1981). Neurological Anatomy in Relation to Clinical Medicine. Oxford: Oxford University Press. Rees G. and Frith C.D. (1998). How do we select perceptions and actions? Human brain imaging studies. Phil. Trans. Roy. Soc. B 353, 1283-1293. Kosslyn S.M. (1999). If neuroimaging is the answer, what is the question? Philos. Trans. R. Soc. Lond. B 354(1387) 1283-1294. Gazzaniga M.S. (ed.) (1999). The NEW Cognitive Neurosciences. Cambridge, MA: MIT Press. Albright T.D., Jessell T.M., Kandel E.R., and Posner M.I. (2000). Neural Science: A Century of Progress and the Mysteries that Remain. Neuron, 25(S2), 1-55, February 18, 2000. Donald M.J. (2002). Neural
Unpredictability, the Interpretation of Quantum Theory, and the Mind-Body
Problem.
Matthew J. Donald:
"Estimates vary, but there are probably at least 1014 synapses in an
average human brain. Neurons fire at an average rate of order a few times per
second. If every synaptic transmission is an uncertain event with probability
significantly distinct from 0 or 1, then there will be at least 1014
such events per second in the brain. Thus uncertainty in ordinary everyday
neural functioning may overwhelm, by many orders of magnitude, many
conventionally recognized sources of observed "quantum" uncertainty and may, in
fact, be the major source of unpredictability in human affairs.
Burgoyne R.D. and Barclay
J.W. (2002). Splitting the quantum: regulation of quantal release during vesicle
fusion. Trends in Neurosciences, 25(4) 176-178.
Jahr C.E. (2003). Drooling and stuttering, or do synapses whisper? Trends in Neurosciences, 26(1) 7-9. Craig E. Jahr, p. 7: "Spillover and multivesicular release are likely to occur at a variety of synapses in the CNS. Although the latter could enhance the former, neither appears to require the other, even though both affect neuronal communication. In two recent papers, new techniques, as well as the careful use of old standards, provide compelling evidence for these formerly heretical mechanisms. "The exquisite alignment of pre and postsynaptic
specializations suggests that these point-to-point connections between neurons
serve as isolated pathways of information transfer. In addition, classical
physiological studies indicate that, at each active zone, release is binary:
when an action potential invades the presynaptic element, either a single
synaptic vesicle is released or no release occurs. However, in recent years,
reports of transmitter ‘spillover’ between synapses and of ‘multivesicular
release’ (MVR) have suggested that these rules are broken at several synapses,
if not in general. In most of these papers, either spillover or MVR could
explain at least qualitatively many of the observations but, as is our wont, the
authors have usually chosen to back one hypothesis or the other. This summer,
two compelling papers have appeared that each report one of the phenomena and
reject the other. Unfortunately for the goal of parsimony, one paper decides for
MVR whereas the other favors spillover. As two very different synapses were
examined in the two laboratories, these disparate interpretations do not come as
a complete surprise.
P. 9: "The two papers highlighted here illustrate that MVR and spillover can both occur. Which of these two mechanisms dominates at a given synapse will depend on several morphological and physiological characteristics, including release probability, intersynaptic distance and the density of surrounding glutamate transporters. Heresy or not, these mechanisms seem to be here to stay." Rose S. Brains, Minds and the World. In: From Brains to Consciousness? Ed. by Steven Rose. London: Penguin, 1999, pp. 1-17. Grossberg S. (2000). The complementary brain: unifying brain dynamics and modularity. Trends in Cognitive Sciences, 4(6) 233-246. Haxby J.V., Hoffman E.A., and Gobbini I. (2000). The distributed human neural system for face perception. Trends in Cognitive Sciences, 4(6) 223-233. Horwitz B., Tagamets M-A., and McIntosh A.R. (1999). Neural modeling, functional brain imaging, and cognition. Trends in Cognitive Sciences, 3(3) 91-98. Llinás R., Ribary U., Contreras D., and Pedroarena C. (1998). The neuronal basis for consciousness. Philos. Trans. R. Soc. B 353(1377) 1841-1849. Neisser U. (1997). The ecological study of memory. Philos. Trans. R. Soc. B 352(1362) 1697-1701. Rind F.C. and Simmons P.J. (1999). Seeing what is coming: building collision-sensitive neurones. Trends in Neurosciences, 22(5) 215-220. Anthony P. Atkinson,
Michael S.C. Thomas and Axel Cleeremans (2000).
Debra A. Gusnard, Erbil Akbudak, Gordon L. Shulman, and Marcus E. Raichle (2001). Medial prefrontal cortex and self-referential mental activity: Relation to a default mode of brain function. Proc. Natl. Acad. Sci. USA, 98(7), 4259-4264 (March 27, 2001). Radford T. (2000). Physics gets hit for six. The Guardian, February 24, 2000. http://www.guardianunlimited.co.uk/Archive/Article/0,4273,3966799,00.html Fuchs C.A. and Peres A. (2000). Quantum Theory Needs No "Interpretation". Physics Today, 51(3), 70-71. Chakalov D.G.
(2000a). Comments on
Quantum Theory Needs No "Interpretation", by Christopher A. Fuchs
and Asher Peres, Physics Today, 51(3), 70-71.
Kuchar K. (1993).
Canonical Quantum Gravity.
Karel Kuchar: "Our space is three-dimensional
and a theory which makes an effective use of this fact is not to be blamed.
"The dynamical variable F which satisfies this requirement, [Eq. 43] must have the same value on all spacelike hypersurfaces. Therefore, it is necessarily a constant of motion. This underscores the point which I already made: If we could observe only constants of motion, we could never observe any change. (...) Those observables which also satisfy Eq. (43) I shall call perennials. I want to argue that One can observe dynamical variables which are not perennial, and that Perennials are often difficult to observe.
"No perennial ever changes along a dynamical
trajectory.
"We do not know how to
construct perennials for canonical gravity. (...) Perennials in canonical
gravity may have the same ontological status as unicorns -- a priori, these are
possible animals, but a posteriori, they are not roaming on the Earth. According
to bestiaries, the unicorn is a beast of fabulous swiftness, strength, and
beauty, but, alas, it can be captured only by a virgin [38]. Corrupt as we are,
we better stop hunting mythical beasts.
"Once we have decided what dynamical variables
can be observed, we need to know what is the statistical distribution of their
observed values. In quantum mechanics, probabilities are determined by the inner
product in a Hilbert space. Therefore, we need to endow the space of physical
states with a Hilbert space structure. The proposals on how to find the inner
product depend on what position one
takes on observables. p. 25: "Secondly,
even when one disregards this difficulty, one should notice that the proposal as
it stands is self-contradictory. [Ashtekar's program, see: A. Ashtekar,
Lectures on Non-Perturbative Canonical Gravity, World Scientific, Singapore,
1991, Chapter 10: The quantization program -- D.C.]
"To talk about instantaneous states requires a
decision about what is an instant. An instant in a relativistic spacetime is a
spacelike hypersurface. However, spacelike hypersurfaces are not elements of the
gravitational phase space. (...) Such an observable is called an *internal
time*. (The adjective 'internal' means 'constructed solely from the phase-space
variables'.)
"These things are more easily said than done. The internal time proposal meets as many difficulties as the approach based on the concept of perennials. I discussed the problems of time in a recent review [40] which complements my present treatment of observables. "It is sometimes maintained that the approach
based on perennials somehow avoids the problems of time. It would be great if it
did, but I fear it does not. A closer look reveals that the problems of time and
the problem of perennials are rather closely related. A Czech saying has it that
the devil thrown out of the door returns through a window.
"The problem of what quantities can be observed
(and how they can be observed) is one of the most intriguing and important
questions in quantum gravity. A widely held view (which I dispute) is that one
can observe only perennials. No true perennials, classical or quantum, have so
far been found, and even if they exist, finding them is difficult. I feel we
should instead concentrate on formulating and proving (non?)existence theorems
about perennials.
"Another outstanding problem of canonical quantum gravity is the construction of the inner product. Quantum geometrodynamics has been unsuccessful in this task [22, 36], and connection dynamics has hardly done more than formulate broad guidelines on how one might try to proceed. These guidelines crucially depend on the existence of perennials. "In contrast, one knows how to construct (at the
formal level) the inner product for parametrized field theories [17]. Each
choice of an internal time casts canonical gravity into the mold of a
parametrized field theory and leads to an inner product. The procedure, however,
is not without problems [40]. One which is closely related to the problem of
perennials is that internal time may not exist globally [44]."
Ashtekar A. (1993)
Mathematical Problems of Non-perturbative Quantum General Relativity.
Abhay Ashtekar: "At a fundamental level, since there is no background metric, there is no a priori notion of time either. What does dynamics and evolution even mean if there is no background space-time? How is time born in the framework? (...) The probabilities for an exhaustive set of mutually exclusive alternatives should add up to one. In quantum mechanics, this is generally ensured by using an instant of time to specify such alternatives. What is one to do when there is no time and no instants? These are fascinating issues." Rovelli C. (1999). Quantum
spacetime: what do we know?
Carlo Rovelli: "The time "along which" things happen is a notion which makes sense only for describing a limited regime of reality. This notion is meaningless already in the (gauge invariant) general relativistic classical dynamics of the gravitational field. At the fundamental level, we should, simply, forget time." Neumaier A. (1999). On a
realistic interpretation of quantum mechanics.
Arnold Neumaier: "Physics essentially describes nature as if everything had already happened, and then expresses its laws as information about observed correlations. Since some of the correlations involve time, it is possible to partially predict the future from the past, or the past from the future, or an intermediate situation from past and future observations. This summary also explains neatly why questions such as the flow of time or free will cannot be discussed within the framework of physics. Whether or not time flows, whether or not our will is free, the four-dimensional picture resulting from the course of nature, whether or not influenced by us, can (in a gedankenexperiment) be replayed, after everything has happened, like a movie. In the replay, everything is determined, and there is only the illusion of free will, just as we are used from the cinema. But the physics, expressed in the correlations between the parts of the movie, is identical to that in the original version." Kitada H. (1999). A
possible solution for the non-existence of time.
"This equation implies that there is no global
time of the universe, as the state \Psi of the universe is an
eigenstate for the total Hamiltonian H , and therefore does not
change. (...) Here the total Hamiltonian H is an ideal
Hamiltonian that might be gotten by "God."
"In both cases the unbalance caused by the existence of an exterior region yields time. In other words, time is an indefinite desire to reach the balance that only the universe has." Warren G.D. (1999).
Coexistence of Global and Local Time Provides Two Ages for the Universe.
Castro C. (2000). Is
Quantum Spacetime Infinite Dimensional?
Castro C., Granik A.
(2000). On M Theory, Quantum Paradoxes and the New Relativity.
Castro C., Granik A.,
El Naschie M.S. (2000). Why we live in 3 Dimensions.
Peres A. (1995). Quantum Theory: Concepts and Methods. Dordrecht: Kluwer Academic Publishers, Ch. 9.4, p. 278. Barbour J. (2000). The End of Time. London: Phoenix. Neisser U. (1976). Cognition and Reality. Principles and Implications of Cognitive Psychology. San Francisco: Freeman, Fig. 2 and Chs. 2 and 4. Straumann N. (2000).
Reflections on Gravity.
Norbert Straumann: "It is recognized since quite
some time that this is a profound mystery. Indeed, we expect that quantum
fluctuations in the fields of the standard model of particle physics, cut off at
about the Fermi scale, contribute to the vacuum energy density, because there is
no symmetry principle in this energy range which would require a cancellation of
the various contributions (as in strictly supersymmetric theories).
Straumann N. (2002). On
the Cosmological Constant Problems and the Astronomical Evidence for a
Homogeneous Energy Density with Negative Pressure. Invited lecture at the First
Séminaire Poincaré, Paris, March 2002.
Norbert Straumann: "Without gravity, we do not
care about the absolute energy of the vacuum, because only energy differences
matter.
Straumann N. (2002).
The history of the cosmological constant problem.
Norbert Straumann: "In a letter to P. Ehrenfest
on 4 February 1917 Einstein wrote about his attempt: "I have again perpetrated
something relating to the theory of gravitation that might endanger me of being
committed to a madhouse. (Ich habe wieder etwas verbrochen in der
Gravitationstheorie, was mich ein wenig in Gefahr bringt, in ein Tollhaus
interniert zu werden.)"
"For more on this, see e.g. [23]
(and references therein), as well as other contributions to this meeting."
Adler R.J., Casey B., Jacob O.C. (1995). Vacuum catastrophe: An elementary exposition of the cosmological constant problem. American Journal of Physics, 63(7), pp. 620-626. From the abstract: "Quantum field theory predicts a very large energy density for the vacuum, and this density should have large gravitational effects. However these effects are not observed, and the discrepancy between theory and observation is an incredible 120 orders of magnitude. There is no generally accepted explanation for this discrepancy, although numerous papers have been written about it. As usually stated the problem requires a knowledge of quantum field theory and general relativity, topics not normally studied by undergraduates. We have tried to make the problem accessible to undergraduates by using only the simplest ideas of quantum theory, such as the uncertainty principle and the theory of the harmonic oscillator, and classical gravitational theory. We believe that such simplification is not only an amusing pedagogical exercise but clarifies how basic is the conflict between quantum theory and gravitational theory. We do not here discuss various proposed solutions to the problem, beyond the trivial and unsatisfactory one of assuming an ad hoc canceling term in the Hamiltonian or field equations." Richard Feynman, in: P.C.W. Davies and J. Brown (eds.) (1988). Superstrings, A Theory of Everything. Cambridge: Cambridge University Press, p. 201. R. Feynman: "In the quantum field theories, there is an energy associated with what we call the vacuum in which everything has settled down to the lowest energy; that energy is not zero-according to the theory. Now gravity is supposed to interact with every form of energy and should interact then with this vacuum energy. And therefore, so to speak, a vacuum would have a weight -- an equivalent mass energy -- and would produce a gravitational field. Well, it doesn't! The gravitational field produced by the energy in the electromagnetic field in a vacuum -- where there's no light, just quiet, nothing -- should be enormous, so enormous, it would be obvious. The fact is, it's zero! Or so small that it's completely in disagreement with what we'd expect from the field theory. This problem is sometimes called the cosmological constant problem. It suggests that we're missing something in our formulation of the theory of gravity." Note 1. I am trying to speculate about some non-linear theory which allows the description of a quantum system to have infinite degrees of freedom (Kitada, 1999). This cannot be done in a Hilbert space, as we know from Asher Peres (Peres, 1995). Let's call it 'base space'. Then, in the process of preparation, you put a 'context' and select a finite dimensional sub-space from that base space, and decompose the contextualized system in the sub-space into orthonormal vectors. The 'remnant' from Schrödinger's cat (shall we call it propensity?) is untouchable; it is in the base space, in the form of a "non-vanishing surplus knowledge with respect to other measurements (observables)" (Pospiech, 2000). Its possible projections, alive or dead, are in the contextualized sub-space. You make measurements in the sub-space only, where the remnant from the cat can project its possible 'shadows', dead or alive. The 'remnant from the cat' (Altaisky, 2000) is never really dead; it is supposed to evolve along the hypothetical universal time arrow -- if it is a reality 'out there', being an intact quantum reality, it should exist in time and evolve in time (Chakalov, 2000d). As John A. Wheeler put it, "Time is Nature's way to keep things from happening all at once" (Private communication, 22 May 1989). In other words, the 'remnant from the cat' should be able to accommodate (i) things that we know, (ii) things that we know that we don't know, and (iii) things that we still don't know that we don't know -- the unknown unknown modeled by an ideal Hamiltonian that might be given by God only (Kitada, 1999). What a nice starting point for quantum cosmology! Briefly, the distinction between base space where the remnant from the cat is residing, and the contextualized sub-space where the cat casts its 'shadows' (superposed states), is suggested as the first step toward reconciling the principles of superposition and general covariance ab initio. The quantum reality must be extended in time (Balachandran, 2000), which requires a universal time arrow and a new causal principle (Neisser, 1976) including the relativistic causality (Balachandran, 2000) as a limiting case, by setting one of the parameters of the universal time arrow (along the 'skewer', see below) to approach zero. If you replace the 'remnant from the cat' with 'Platonic idea', I believe the task will become quite clear (Chakalov, 2000d). How to describe it in mathematical terms, however, is by no means obvious. Let me explain. To visualize the hypothetical universal time arrow, imagine onion rings with ever-increasing diameter, which you stack on a skewer starting with the smallest one. The cosmological time arrow, following the expansion of the Universe, is "along" the 'onion rings' (local time), while the universal time arrow is "along" the skewer (global, absolute and mathematical time), and is orthogonal to these slices. We can't observe the universal time arrow with inanimate devices. (With our brain -- maybe, but that's very much an open question.) What we can physically observe is a state of the Universe in the past only (Neumaier, 1999; Altaisky, 2000), just like, when we look at the Sun, we see what the Sun should have been about 8 minutes ago, but not at the moment of observation. Briefly, the conjecture here is that there should be a minimal (bounded below) separation between two spacetime points in all 'onion rings'. Let's call it 'chronon'. Suppose the Universe is always shifted one chronon in the future toward the edge of the skewer, and is in superposition of all possible states, but we can't observe these propensity-like states. What we can observe is what the Universe has already chosen to be, having selected one of these propensity-like states. Physically, we always see this selection (or rather 'projection') post-factum, as in the example with the Sun. We can't leave our slice or 'onion ring' to observe the chronon. When the Universe moves 'up', our 'onion ring' is embedded into the next, a bit "wider" (and maybe one bit richer) 'onion ring', thanks to which we can happily write down a Hamiltonian and talk about 'unitary time evolution', but it is strictly valid for one static slice only (Neumaier, 1999). So, we gather the wrong impression that we live in one 'onion ring' with "increasing diameter", because we cannot physically observe the instant (chronon) of embedding our 'onion ring' into the next, wider one. When physicists write down the wave function of the Universe, however, they realize that this 'unitary time evolution' is frozen. Why? Because there is no 'background' (Chakalov, 2000b; 2000d) with respect to which one could describe that evolution. This 'background' is the chronon itself. It is totally hidden, because of the peculiar nature of the so-called "speed of light". Briefly, to model the Universe as a human brain, I assume that the Absolute, true and mathematical time (Newton) is orthogonal to the local one (along the 'onion rings'). The next conjecture is to introduce the 'length' of the chronon, as it could be projected in our 'onion rings'. The minimal separation of two spacetime points is what we may call 'fundamental length' corresponding to an infinitesimal time interval (Balachandran, 2000). Let us denote it with Lmin. There should be, however, a second projection of the same chronon, which is supposed to be bounded above, and which should be projected in our 'onion rings' as 'the maximal separation of two spacetime points' fixing the biggest possible 'onion ring' or size of the Universe. Let us denote it with Lmax. I suppose that the Universe cannot reach Lmax
for any finite time interval, firstly, and secondly -- that Lmax
Lmin = 1. And finally, I suppose that the chronon is nothing but
the 'projection' of the common source of mind and matter, the
Universal Mind. Physically, it may be a Hyperpoint
(Castro
et al., 2000) or some other fundamental entity at Planck scale. The
latter acts as a finite but physically unattainable boundary of our
world. A cut-off that is utterly needed for the physical world, but a cut-off
that is physically impossible to reach, like the "speed" of light (for tardyons)
or the absolute zero "temperature". It is certainly not God because it
has been
created by God (John 1:1-4). I believe God is "inside" the instant 'now'
(absolute vacuum), but I don't see how could
anyone prove or reject this statement. That's fine with me, for otherwise
theology would be reduced to science, and that would be the end of science.
Helfer A.D. (1998). The
Physics of Negative Energy Densities.
Adam D. Helfer: "The main surprise is that arbitrarily negative energy densities occur pervasively, even in tame, "everyday" situations. Much of this paper will outline how this occurs in a general quantum-field-theoretic setting. No one really knows, at present, how to resolve the difficulties pervasive negative energy densities might cause. I shall outline, at the end, some suggestions of mine, and their possible consequences, but this is very much an open area." Visser M., Barcelo C.
(2000). Energy conditions and their cosmological implications.
Matt Visser and Carlos Barcelo: "Many experimental physicists and observational astrophysicists react quite heatedly when the theoreticians tell them that according to our best calculations there should be plenty of "negative energy" (energy densities less than that of the flat-space Minkowski vacuum) out there in the real universe. However, to avoid the conclusion that quantum effects can and do lead to locally negative energy densities, and even violations of the ANEC, requires truly radical surgery to modern physics, and in particular we would have to throw away almost all of quantum field theory." Unruh B. (1993). The
Reality and Measurement of the Wavefunction.
Bill Unruh: "That physicists have long wanted to regard the wave function as having an ontological role is clear. That desire underlies the unease surrounding the "projection postulate", and the oft heard lament that the wave function cannot simultaneously obey deterministic dynamical equations of evolution, and indeterministic collapse in the ill defined "measurement" process. As an object with an ontological role, as an object corresponding to some element of physical reality such schizophrenic behaviour is highly unsatisfactory. On the other hand if the wave function is simply a tool by which we encode our knowledge into the theory, the change of the wavefunction under a change in knowledge is perfectly rational. It leaves one, however with uncomfortable questions about how knowledge differs from other physical processes." Unruh B. (1993a). Time,
Gravity, and Quantum Mechanics.
Bill Unruh: "(T)he controversy about the nature of knowledge is probably even deeper than controversy about the nature of measurement." Pospiech G. (2000).
Information - the Fundamental Notion of Quantum Theory.
Balachandran A.P.
(2000). Classical Topology and Quantum States.
A.P. Balachandran: "Time in conventional
quantum physics has a unique role. It is not a quantum variable, and all
elementary quantum observations are instantaneous. Now elementary measurements
-- those instantaneous in time -- can only measure commuting observables.
Vuletic M.I. (1999).
Philosophy and Quantum Mechanics,
Schrödinger E. (1931). Specielle Relativitätstheorie und Quantenmechanik. Sitzungsber. Preuss. Akad. Wiss., phys.-math. Kl., Bd. 12, S. 238-247. Schrödinger E. (1935). Die
gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften, Bd.
23, S. 807-812; 823-828; 844-849. Available online at
Erwin Schrödinger: "The rejection of realism has logical consequences. In general, a variable has no definite value before I measure it; then measuring it does not mean ascertaining the value that it has. But then what does it mean?" Margenau H. (1940). Reality in Quantum Mechanics. Philosophy of Science, 16, 287. (Quoted after: Margenau H. (1984). The Miracle of Existence. Ox Bow Press: Woodbridge (CT), pp. 108-109; cf. latent observable.) Baez J. (1996). A Chat With
Penrose. June 10, 1996,
John Baez: "In any event, I then mentioned that by "cosmological considerations" I'd meant his hypothesis that the Weyl curvature was low near initial singularities and high near final ones. He said yes, this too hinted at modifications of quantum theory in the presence of gravity that gave rise to some sort of irreversibility. He mentioned a thought experiment that I'd seen somewhere else, perhaps in his book. It goes as follows. 4
\
3 "Here a light bulb at 1 emits photons which hit
a half-mirrored surface and either go
through to 2 or bounce off to 3. If a single photon is emitted, it should wind
up in a superposition of 1/sqrt(2) being at 2 and 1/sqrt(2) being at 3, and we
confidently predict that it has a 50-50 chance of getting to 2 or 3. If,
however, we observe a photon at 2 and "retrodict" where it came from, quantum
mechanics (supposedly) gives that it must have been a superposition of 1/sqrt(2)
being at 1 and 1/sqrt(2) being at 4. This would seem to mean it had at 50-50
chance of coming from the lightbulb or from somewhere else! Blatant
nonsense.Ergo, there is some inherent time-reversal asymmetry about how we
apply quantum theory."
Note 2. John Baez
arguers further that "our world is in a condition of generally increasing
entropy that allows for the setup with a hot light bulb and cool walls to occur,
and we can't blame quantum mechanics for that time asymmetry", but I can't
accept that as an explanation. It is 'baiting its tail' -- the thermodynamical
time arrow is a great mystery which may be explained by quantum cosmology, which
in turns requires quantum gravity, which in turns requires a much better
understanding of quantum mechanics, and especially the phenomenon of
superposition (Schrödinger, 1935), which was the the crux
of the issue with which it all began. To solve the puzzle, I believe we need a
'remnant from Schrödinger's cat' (Chakalov, 2000d)
and a new quantum theory reconciling the principles of superposition and general
covariance from the outset (cf. Open questions in quantum
theory).
Vecchi I. (2000). Local
observer.
Chakalov D.G.
(2000b). Local observer: Reply to Italo Vecchi.
Chakalov D.G.
(2000c). Loop quantum teleportation.
Chakalov D.G.
(2000d). The product rule and the human brain: A remnant from the cat?
Altaisky M. (2000). What
can biology bestow to quantum mechanics?
Mikhail Altaisky: "Very often the biological studies are regarded as opposite to the physical ones in the sense that they are qualitative rather than quantitative. At the same time the biology yields a number of concepts and basic facts those are not displayed explicitly in inanimate phenomena. We suggest the following three facts to be of principle importance: 1. The properties of a living system are more than just a collection of its component properties. In other words, it is impossible to predict the whole set of properties of a complex biological system even having known all properties of its components and interactions. 2. The properties and functions of the components of a system depend on the state of the whole system. In other words, the same components being included in different systems may have different properties. 3. There is an Evolution -- a process of
creating new entities, forms and functions on the base of the existing
components.
Anastopoulos C. and Savvidou
N. (2000). Quantum mechanical histories and the Berry phase,
Int. J. Theor. Phys. 41, 529 (2002),
Charis Anastopoulos and Ntina Savvidou: "The
standard quantum mechanical formalism refers to properties of the system at a
single moment of time: it assigns probabilities to possible events and studies
the evolution of these probabilities. In this context, the phase of a Hilbert
space vector is not physically relevant, as it does not enter the single-time
probability assignment.
Rothman T., Sudarshan
E.C.G. (2000). Hidden Variables or Positive Probabilities?
Tony Rothman and George Sudarshan: "Regarding probabilities, we find ourselves in a strange situation. If one insists that probabilities remain positive-definite, we are forced to use vague and imprecise concepts, such as "local" or "nonlocal" to describe the outcome of the EPR experiment. On the other hand, we are able formulate the precise mathematical conditions necessary for the violation of the Bell and CHSH inequalities, although at the cost of introducing negative probabilities, which are also not easy to interpret. A unified, physical interpretation of negative probabilities is, in fact, exactly what is currently lacking. This does not imply that they are meaningless." Bassi A., Ghirardi G.
(2000). A General Argument Against the Universal Validity of the Superposition
Principle.
Angelo Bassi and GianCarlo Ghirardi: "The very
possibility of performing measurements on a
microsystem combined with the assumed general validity of the linear
nature of quantum evolution leads to a fundamental contradiction."
Chakalov D.G.
(2000e). Cretan paradox, Buridan donkey, and the human brain.
This page created on January 26, 2000.
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