The Physics of Densities and the Problem of Time

We communicate using words. Some of our words (though not all) carry meanings. We communicate our thoughts, idea, emotions. There are different levels of communication. The meaning of the word can be found in a dictionary or a thesaurus. But words put together into sentences, and sentences into blocks may carry meaning that are not in a dictionary. The "whole" is more than the sum of its parts. We know it from our experiences. But we also know from our experience that the communication can go deeper when we also listen to the pauses between words. Thus listening adds extra dimension to the reading experience alone. And when we see the body language, when we do feel the physical presence of the person, it adds even more dimensions.

But what exactly are thoughts? And what exactly is "communication?"

In 2006 two physicists, Elisabeth Rausher

and Russell Targ, 

published a paper in Proceedings of the conference of American Institute of Physics under the title  "Investigation of a Complex Space-Time Metric to Describe Precognition of the Future" [1]. In the original 2001 version of the paper [1a]  (still available here) the title was expanded by adding at the very beginning "The Speed of Thoughts:" - though the abstract of the paper was exactly the same.

Let me quote from the Introduction ofv this paper:

" (...) Now in the twenty-first century, the evidence has become overwhelming that our thoughts and bodies can be directly affected and influenced by the thoughts of another person or by events and activities at a distant location blocked from ordinary perception. (...)"

It is somewhat surprising that the American Institute of Physics, a serious institution,  allowed for a publication of such a statement. And "Precognition of the Future"? Is it not considered as pseudo-science? Or, in  the best case, as "fringe science"? Strange. I leave the Reader speculation about possible causes of such a "faux pas".

But let us return to the subject of thoughts and thinking. What is this THINKING? When I am thinking about thinking a handy phrase comes to my mind: Thinking is information processing". Happy? I m not in the least. Because what is "information" and what is "processing"? I am thinking (without processing) that perhaps it should be the other way around. Perhaps thoughts are primary, and information is a concept that has been abstracted by thinking from the data and put into a linear order of mathematical abstraction by organized thoughts of mathematicians? 

We notice that the paper by Rauscher and Targ has been published in a volume entitled "CP863, Frontiers of Time, Retrocausation—Experiment and Theory, edited by D. P. Sheehan". We see the term "Frontiers of Time". How time is related to thinking?  And what is the algebra of thinking and time? Because some math is certainly necessary, sooner or later. But which math? Logic? Topology? My answer is : algebra. Logic can be described in terms of algebra (Boolean algebra, matrices, commutative and non-commutative), and topology is a later concept, there would be no topology without algebra (homotopy groups, homology, Chern classes etc.)

Algebra? But which kind of algebra? The simplest one is probably the algebra of 2x2 complex matrices. It is good for toy models. But to describe states of pure awareness (densities) and transitions between them, we need infinite dimensional algebra. In mathematics we are being taught about Clifford algebras, and more general C* algebras. We also come across a strange structure of the "Calkin algebra". This is related to "phase transitions", and we will be interested in such transitions, except that for a popular in mathematical solid state physics "Ising model", as it is mathematically analyzed in [3]. But all this will come later. For now we will have to discuss the problem of thoughts, thinking, states of awareness, and, last but not least, time.

Mathematicians "classify" their structures, much like "taxonomy" in biology. These structures come into families, but there are also "exotic" structures. Physicists find many different applications for standard mathematical structures, within families, but what about those singular exotic structures. One such exotic structure is "octonions" and related "exceptional Jordan algebra", the algebra of 3x3 matrices over octonions. Physicists have their own exotic structures. One such structure is an elusive "magnetic monopole" (see [4]). What can be an application of such exotic structures? Elementary particle physics? That would be not exotic at all. Exotic structures are to be applied to exotic problems. The problem of consciousness and of time - is such a problem. But the problem of consciousness and the problem of time needs an infinite number of dimensions. How infinite? There is a hierarchy of infinities. Countable infinity is not sufficient.

Concerning "dimensions: The monograph [4] is devoted entirely to the problem of "time". It also talks about "topology" and "quantization of shapes" - rather advanced mathematics is required here. Then we find this piece:

"I  had  the  fortune  of  having  as  a  brother-in-law  one  of  the  greatest mathematicians of recent times, Bill Thurston. Bill and I lived a few blocks from each other in Berkeley, and we had many conversations about  careers  (as  a  graduate  student,  he  was  convinced  that  he would  never  find  a  good  job),  mathematics,  and  physics.  He  was fascinated with my description of what we knew about the universe. He asked me if anybody had seriously considered a multiconnected universe?  Did  he  mean  wormholes,  passageways  that  potentially connected  one  part  of  the  universe  with  another?  No,  he  had something far simpler and much more elegant in mind. Bill  was  ultimately  most  famous  for  his  advances  in  topology, complex  geometries  that  went  far  beyond  our  normal  imagination. He told me that he had actually mastered the skill of being able to think in four dimensions. Few people believed him, until he produced a  vast  array  of  wonderful  theorems  that  he  claimed  he  had discovered by simply looking at surfaces in 4D space in his mind. It turns out, oddly, that math problems in three and fewer dimensions are relatively easy, and problems in five or more dimensions are also relatively  easy,  but  dealing  with  four  dimensions  is  very  tough. Thanks  to  his  work  in  four  dimensions,  Bill  was  to  win  the  FieldsMedal, the “Nobel Prize of mathematics,” before he turned forty.

And yet, surprisingly, the author avoids the subject of Kaluza-Klein theories and our reality having more than three space and one time dimension. In this respect Rauscher and Targ go deeper, and beyond main stream physics, as they allow for a complex 8-dimensional spacetime with acausal connections. 

How do we go from a finite number of dimension to infinite number? Nowadays we know the answer - by "quantization". We quantize a mechanical system by considering the space of functions (waves) on the configuration space. We call it "first quantization". In this first quantization the number of degrees of freedom of the system is finite and sharp. But then we consider functions on the space of functions, we "second quantize" the system, and even the number of particles becomes "wavy". We can thus proceed to the third and fourth quantization etc., though no one has an idea where to end and why?

From quantum theory, so successful for not quite well understood reasons, new insights came. Richard Feynman developed a technique called "integral over trajectories". Every classical trajectory acquires a complex "amplitude", whose modulus squared can be interpreted as a "probability". Then "real" trajectories of Newtonian physics are simply those "most probable ones" ("extremal"). Yet all those other trajectories are also important if we want to make quantum theoretical calculation agree with the observed, sometimes strange indeed, reality. Somehow, it would seem, our consciousness, whatever reality is hiding behind this concept, makes the "most probable" "real". The naïve reality of tables and chairs is just the most probable effect of the process of actualization of quantum probability waves.  Or so it seems. The very process of this actualization is still an enigma known as "the quantum measurement problem".

Quantum theory, in fact, is about measurements. The fundamental uncertainty relations as well as the more general concept of complementarity deal with restrictions on measurements. When measuring the momentum we disturb the position, when measuring the postion, we disturb the momentum. Measuring position forces the quantum object to behave like a particle. Measuring its momentum we force the object exhibit its wave-like properties. Yet the very process of measurement, its dynamics, is still a puzzle - it escapes the theoretical description. The idea that there is no measurement problem and no "quantum jumps", that the quantum wave function is a "hidden variable" that somehow, for some reasons "pilots" the classical particle is attractive, but does not explain where the mysterious quantum force that tells the particle to wander in space against the standard laws of mechanics is incomplete and has limited applications. 

Another approach to the measurement problem has other attractive properties and other limitations [5]. It is an old story that "consciousness" is somehow involved automatically in quantum theory. As John Archibald Wheeler termed it "No phenomenon is a phenomenon unless and until it is an observed phenomenon". But then we need to explain "consciousness" and "observation". Wheeler then continued:

" no elementary quantum phenomenon is a phenomenon until, in Bohr's words [10], "It has been brought to a close" by  "an irreversible act of amplification."  What we call the past is built  on bits. (...)  

"Consciousness".  We have traveled what may seem a dizzying path. First,  elementary  quantum  phenomenon brought  to  a  close by an  irreversible act of  amplification.  Second,  the  resulting information expressed in  the  form  of bits.

Third,  this  information used by observer-participants — via communication — to establish  meaning.  Fourth, from  the past  through the  billeniums to  come, so many observer-participants,  so many bits,  so much exchange of information, as to  build what  we call existence. Doesn't  this  it-from-bit  view of existence seek to  elucidate  the  physical world, about  which we know something, in terms of an entity about  which we know almost nothing,  consciousness  [134-137]? "

And then:

"Six:  Capitalize  on  the  findings  and  outlooks  of information theory  [160-163], algorithmic  entropy  [164],  evolution  of organisms  [165-167]  and  pattern  recogni-tion  [168-175].  Search out  every link each has with  physics  at  the  quantum level. Consider, for instance,  the  string  of bits 1111111 . . .  and its representation as the sum of the  two strings 1001110...  and 0110001...  Explore  and exploit the  connection  between  this  information-theoretic statement  and  the findings of theory  and experiment on the correlation between the polarizations of the two photons  emitted in the  annihilation of singlet positronium  [176] and in like Einstein-Podolsky-Rosen experiments  [177],  Seek out, moreover, every realization  in the  realm of physics of the information-theoretic  triangle inequality recently discovered by  Zurek  [178]. Finally:  Deplore?  No,  celebrate  the  absence  of a  clean  clear  definition  of  the term  "bit"  as  elementary  unit  in  the  establishment  of meaning.  We reject  "that view  of science  which  used  to  say,  'Define  your  terms  before  you proceed.'  The truly  creative  nature  of any forward  step in human knowledge," we know,  "is such that theory, concept, law and method of measurement — forever inseparable — are born into the  world in union  [179]."  If and when we learn  how to  combine bits  in fantastically  large  numbers to  obtain  what  we call  existence,  we will know better what we mean  both  by bit  and by existence. A  single question  animates  this  report:  Can  we ever expect  to  understand  existence?  Clues  we have,  and  work to  do, to  make headway on that  issue.  Surely someday,  we  can  believe,  we will  grasp  the  central  idea  of it  all  as  so simple,  so beautiful,  so compelling that we will all say to each other,  "Oh, how -could it  have been otherwise!  How could we all have been so blind so long!" 

If "it" comes from "bit", which sounds true, if matter is actualized and organized information, if there are organization levels that we may call "densities" - then, contrary what Wheeler suggests [6], we must not celebrate the fact that we do not have a clear definition of "bit", that we talk about information without being able to define it. This job needs to be done, and it will.

References:

[1] Elizabeth A. Rauscher and Russell Targ, "Investigation of a Complex Space-Time Metric to Describe Precognition of the Future",  AIP Conference Proc. 863 (2006),  http://dx.doi.org/10.1063/1.2388752

[1a]Elizabeth A. Rauscher and Russell Targ,  "The Speed of Thought: Investigation of a Complex Space-Time Metric to Describe Psychic Phenomena", Journal of Scientific Exploration", Vol. 15, No. 3, pp. 331–354, 2001 0892-3310/01, DOI:10.1063/1.2388752

[2] A. L. Carey, "Algebras  Almost  Commuting  with Clifford  Algebras", JOURNAL  OF  FUNCTIONAL  ANALYSIS  88,  279-298  (1990) 

[3] R. A. Sventkovsky, "The Equations of Dirac and Maxwell as a Result of Combining Minkowski Space and the Space of Orientations into Seven-Dimensional Space-Time",     October 2020 Mathematical Notes 108(3-4):381-393, DOI: 10.1134/S0001434620090072

[4] Edward Anderson, "The Problem of Time: Quantum Mechanics Versus General Relativity", Springer International Publishing, Oct 3, 2017 - Science - 920 pages

(...) This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics.(...) This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation.  Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond.

[5] Henry P. Stapp "Mindful Universe Quantum Mechanics and the Participating Observer", The Frontiers Collection, Springer, 2011, ISBN: 9783642180750,9783642180767,3642180752,3642180760, 
The classical mechanistic idea of nature that prevailed in science during the eighteenth and nineteenth centuries was an essentially mindless conception: the physically described aspects of nature were asserted to be completely determined by prior physically described aspects alone, with our conscious experiences entering only passively. During the twentieth century the classical concepts were found to be inadequate. In the new theory, quantum mechanics, our conscious experiences enter into the dynamics in specified ways not fixed by the physically described aspects alone. Consequences of this radical change in our understanding of the connection between mind and brain are described. This second edition contains two new chapters investigating the role of quantum phenomena in the problem of free will and in the placebo effect.

[5] John Archibald Wheeler, "Information, Physics, Quantum: the Search for Links".

This  report  reviews what  quantum  physics  and information theory  have to  tell  us about  the  age-old  question,  How come  existence?  No escape is evident  from  four conclusions:  (1) The world cannot  be a giant  machine, ruled by any  preestablished continuum  physical  law.  (2)  There  is  no  such  thing  at  the  microscopic level  as space  or  time  or  spacetime  continuum.  (3) The  familiar  probability  function  or functional,  and  wave equation  or  functional wave equation, of standard  quantum theory  provide  mere  continuum  idealizations  and  by  reason  of this  circumstance conceal the  information-theoretic  source from  which they  derive. (4) No element  in the  description  of physics shows  itself  as closer  to  primordial than  the  elementary quantum phenomenon, that is, the  elementary  device-intermediated act of posing a yes-no physical question and  eliciting  an  answer or, in brief,  the  elementary  act of observer-participancy.  Otherwise stated,  every  physical  quantity,  every it,  derives its ultimate  significance from  bits, binary yes-or-no indications, a conclusion which

we epitomize in the  phrase,  it from  bit.

P.S. Here is a piece from the discussion with "us in the future"