Information (Theory)

John G

The Living Force
obyvatel said:
[quote author=whitecoast]
What I find interesting is how to work into this understanding what Gurdjieff taught about how different food, breathing, and impressions nourish our organism in different ways, and can contribute to the growth of an entirely new body.

Applying the traditional thermodynamic concept of entropy to living organisms creates confusion. It is perhaps a case where a computational concept which was found useful to describe certain macroscopic phenomena in well specified boundary conditions is over-extended to an extent where it no longer provides useful insight. Traditional thermodynamic entropy (2nd law) is valid for isolated systems in thermal equilibrium. Living systems at various scales are neither isolated nor generally in thermal equilibrium...

The question about the relationship between information and energy straddles the boundaries between physics and metaphysics. From the "information is physical" perspective, energy and information are closely tied together...

If we come to the metaphysical level, then Gurdjieff's concept of "table of hydrogens" which Bennett elaborated and developed further in the book linked above is one candidate for a framework of explanation. In that framework, "hydrogen" can be treated as a metaphysical structure (in-formation) which is characterized and described by the term energy. No essential separation of information/energy exists in this metaphysical framework as far as I understand at present - which is consistent with Gurdjieff's claim of "materialism".

Now, there are other frameworks where information is treated as primary. The probabilistic (uncertain) nature of reality lends credence to the primacy of information. From the 4th Way perspective, Bennett tackled the uncertainty in his work on "hazard" (discussed here), but I am not aware of a work tying it to information. Quantum computing is a developing field where some scientists support the primacy of information in the bigger scheme of things - but I do not know much about it.
[/quote]

Yeah you kind of end up with the whole universe being the isolated system with entropy inversely proportional to vacuum energy density thus the universe gets thinned out energy density-wise while entropy increases for the whole universe. Living systems being such a small part of the total universe entropy/energy makes entropy not an overly useful concept for living systems as you say.

The physics - metaphysics relationship with information is interesting. This is kind of like looking at one spot in the system and using information theory to say what could be there. It's not an evolving thing like increasing entropy or thinning out energy density. The Enneagram for me gives a nice information theory for the food, air and impressions octaves of the table of hydrogens. The system could be different things: physics; hydrogens; the Enneagram is a modern personality model; densities matching what Laura did with the Tree of Life.

For hydrogens, you kind of have shock and self remembering giving a new spiritual body. For personality/organizational behavior you could get development and consulting giving a new process. For quantum physics, matter and antimatter giving a "new" spacetime. For densities something like evolving and channeling giving a new service orientation. The information theory can give parallels for different systems like: inward self remembering; inward perfecting of process; internal (Kaluza Klein) symmetry space; inward service to self orientation. For different systems, something like inward could seem good, bad, or neutral.

To really show the information theory, you have to show an actual bit structure. In generic metaphysics terms, you could use something like fire-earth and water-air for bits. To get say a personality/organizational behavior model, you could add the fixed-mutable and introversion-extraversion you find for Zodiac descriptions or better yet just use the 8 Jungian MBTI factors. This gives you a Cl(8) Clifford algebra information theory structure. For quantum physics X,Y,Z,T and four more Kaluza-Klein-like internal symmetry factors (basis vectors) can be useful. For densities maybe there's things like: spiritual-physical, linear-nonlinear time, subjective-objective, and fall-ascend for your Cl(8) factors. Again there can be parallels like with linear-nonlinear time and fixed-mutable.
 

zak

Dagobah Resident
Hi Keyhole, some stuffs here and there that i came accross.
Further ahead in this thread Shijing brought:
Even more strikingly, in the 1970s Jacob Bekenstein and Stephen Hawking discovered that a black hole's surface area is also its entropy (in suitable units). Hence information, too, must be an exact quantity, like area.
And in the chapter Cosmology of Entropy in Wiki:
Since a finite universe is an isolated system, the Second Law of Thermodynamics states that its total entropy is constantly increasing. It has been speculated, since the 19th century, that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source.

If the universe can be considered to have generally increasing entropy, then – as Roger Penrose has pointed out – gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. The entropy of a black hole is proportional to the surface area of the black hole's event horizon. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size. This makes them likely end points of all entropy-increasing processes, if they are totally effective matter and energy traps.[citation needed] However, the escape of energy from black holes might be possible due to quantum activity, see Hawking radiation. In 2014 Hawking changed his stance on some details, in a paper which largely redefined the event horizons of black holes, positing that black holes do not exist.

The role of entropy in cosmology remains a controversial subject since the time of Ludwig Boltzmann. Recent work has cast some doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly, moving the universe further from the heat death with time, not closer. This results in an "entropy gap" pushing the system further away from the posited heat death equilibrium. Other complicating factors, such as the energy density of the vacuum and macroscopic quantum effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult.

Current theories suggest the entropy gap to have been originally opened up by the early rapid exponential expansion of the universe

With the Boltzmann others ENTROPY:
https://en.wikipedia.org/wiki/Boltzmann%27s_entropy_formula
https://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)#Gibbs_entropy_formula
https://en.wikipedia.org/wiki/Von_Neumann_entropy
http://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf
https://en.wikipedia.org/wiki/Entropy_(information_theory)
It is Boltzmann's equation which establishes that the logarithm of the probability that an atom is in a particular state of energy is proportional to a quantity called "entropy" of the system, in short a measure of its degree of disorder .
This constancy of proportionality is called "Constance de Boltzmann".
Represented by the symbol k, this is one of the fundamental constants of physics. The more information about a system can be obtained, the less its degree of disorder must be.
The same principle also applies to a system of electrical oscillations.
The frequency can only be measured with perfect accuracy if the oscillation persists for an infinite time.
In practice, it must always be implemented and interrupted; We have to go up the clock and let it run until it stops, so we have only a finite number of ticks, cycles of oscillations, heartbeats over a lifetime, On which to base our estimate of the frequency. This limits the accuracy of the coherence that can be achieved within the limits of space and time. Smith/Best

About structured information in livings system:
The quintessence of the wave genome theory may be represented as following:

genome of the highest organisms is considered to be a bio-computer which forms the space-time grid framework of a bio-systems.

In that bio-system, as the carriers of a field epi-gene-matrix - wave fronts are being used, which are assigned by gene-holograms and so-called solitons on DNA – distinct type of acoustic and electromagnetic fields, produced by biogenetic apparatus of the organism/bio-system under consideration and being a medium of strategic regulatory data/information exchange between cells, tissues and organs of the bio-system.

It is also vital to note that the holographic grids/frameworks, which are also the elements of fluctuating structures of solitons, are, in fact, discrete simplest cases of code-originated information, anchored in chromosome continuum of an organism.
The rest HERE

A video interview:

https://youtu.be/et4yvfuSv80

I am going now with some excerpts from the book "Electromagnetic man" of Smith and Best:
Dr. Peter Gariaev and Dr. Georges Tertishny of the Institute of Control Sciences of the Russian Academy of Sciences consider that the phenomenon of quantified optical activity is the basis on which an organism can obtain unlimited information on its own metabolism. This information is read by the endogenous coherent radiation of chromosomes, which due to coherence passes into radio-regulatory frequencies containing what the authors consider to be a genome computer. These processes could have the capabilities of the human brain in data processing and function capabilities making it possible to remotely control information processes in biological systems and actively protect against the destructive effects of exogenous radiation.
Let us suppose, as the theologians maintain, that knowledge or information possesses an objective existence outside the constraints of space and time, and that it is possible that a system becomes more ordered as a result of an entry of information. These two extremes are respectively a material system perfectly linked to chance without any other than an average kinetic energy corresponding to its temperature, and on the other hand a pure information system and a non-material order which does not contain or transport d 'energy

Within the material world, all systems combine these two magnitudes to varying degrees. Mathematically, they can be treated as a complex quantity (combining real and imaginary parts); The real component will represent the energy related to chance, the imaginary component the pure information. The mathematical laws governing complex quantities apply so that by multiplying the "position of the real system" by its complex conjugate, one obtains the energy content linked to chance/hazard.
If the system is "thermodynamically closed", an increase in the information will result in a drop in temperature.
If the system is "thermodynamically open", it delivers information, the energy required to maintain the constant temperature will be taken from the flow of energy flowing through the system. This must be the way in which a living system interacts with information and organization. For a physical system to be influenced by energy equivalent to zero, an increase in information must be used to search for chaotic energy surplus, also allowing the system to dominate the thermal environment
.

In electronics, the "super-heterodyne" receptors invented at the beginning of the radio, provide a comparative element very close to this concept. This reception process was invented because radio tubes were scarce and amateur radio wanted to have the most sensitive receivers possible. These types of receivers are no longer used today, because their circuit radiates electromagnetic energy while detecting it. This circuit allows the oscillation to appear and enter into action before it can be deleted. The instant in which the oscillation begins to start and the rate at which it occurs, depends on the amount of information present, superimposed on the electrical background noise of the circuit.
A superheterodyne circuit could be used to determine the limits of the human ability to influence and be influenced by electronic circuits since this circuit also emits. Such experiments should show whether the sensibility of a living system can exceed the limits set by the laws of physics.

REDOX:
Redox_Halves_text.svg


Pethig evaluated in 1973 the total number of chemical reactions (redox) causing an electron transport along each metabolic pathway in the body, and concluded that a total current of about 200 amperes implementation. Since the energy bandwidth of a protein is about 5eV, this current represents an electrical energy of about 1 kW and is about equal to the maximum power output of the body, somewhat higher than the metabolic rate basic. A man, with his arms stretched out in the air, would look like a quarter-wavelength dipole antenna at a frequency of 30 MHz (wavelength 10 meters), the highest frequency that can be easily reflected around the world by the ionosphere. If a man was able to synchronize all of his chemical reactions to produce energy metabolism at a frequency of 30 MHz, he could communicate with a hypersensitive man anywhere in the world simply by using electromagnetic radiation. Based on the inverse square law for electromagnetic propagation and for an emitted power density of 1kW / m2 to be received by a sensor sensitive to 0.7pW / m2, the range should be 3.7x10m2 (Almost twice the required range since the average circumference of the Earth is 4.0x10m2).
Thus the dimensions of the planet provide the limits of the simple communication from man to man on earth. Going further or reaching less sensitive people would require a more powerful radiation source. This could be achieved by using, to transmit, a group of people holding hands to synchronize their respective output power powers (as may occur in substitution kinesiology). The sunlight, with an oblique incidence (at sunrise or sunset), shining through the aura of a man/woman, a group of men, or perhaps stones, could be modulated by non-linearities in the surrounding water vapor (analogous to the "Luxembourg effect", where the ionosphere had been disturbed by this powerful radio transmitter of the 1930s, and thus allow sunlight to propagate of the messages anticipated in relation to the sun's rays, in the manner of an early-warning radar.We wonder if this activity was possible from places like Stonehenge, where the alignments are favorable to phenomena related to sunrise.
This concept is even more pertinent as a result of the success of the experiments before, during and after the flight of Apollo 8 astonauts. During these experiments, all the physiological functions of these astronauts were quantitatively controlled by the earth Detection and analysis of their signals. These signals were received through the walls of the space capsule, except when the capsule was in the shadow of the moon, even on its terrestrial side of the earth, implying that the sunlight scattered from the capsule was modulated from inside.
 

whitecoast

The Living Force
FOTCM Member
Hi Whitecoast,

In case you are interested, JG Bennett's Energies - Material-Vital-Cosmic is a work that expands on Gurdjieff's hints.


Thanks for the recommendation Obyvatel. I've started in on it. :)
 

Jeffrey of Troy

Padawan Learner
From Scientific American magazine article Why Do Computers Use So Much Energy? (October 4, 2018)

[cooling] issues don’t only arise in artificial, digital computers. There are many naturally occurring computers, and they, too, require huge amounts of energy. To give a rather pointed example, the human brain is a computer.
...
Indeed, the comparison of thermodynamic costs in artificial and cellular computers can be extremely humbling for modern computer engineers. For example, a large fraction of the energy budget of a cell goes to translating RNA into sequences of amino acids (i.e., proteins), in the cell’s ribosome. But the thermodynamic efficiency of this computation—the amount of energy required by a ribosome per elementary operation—is many orders of magnitude superior to the thermodynamic efficiency of our current artificial computers.
...
We now understand that the second law does not say that the entropy of a closed system cannot decrease, only that its expected entropy cannot decrease.


They're trying to walk back the pure materialist dismissal of life pretty slyly now..
 

monotonic

The Living Force
In electronics, the "super-heterodyne" receptors invented at the beginning of the radio, provide a comparative element very close to this concept. This reception process was invented because radio tubes were scarce and amateur radio wanted to have the most sensitive receivers possible. These types of receivers are no longer used today, because their circuit radiates electromagnetic energy while detecting it. This circuit allows the oscillation to appear and enter into action before it can be deleted. The instant in which the oscillation begins to start and the rate at which it occurs, depends on the amount of information present, superimposed on the electrical background noise of the circuit.
A superheterodyne circuit could be used to determine the limits of the human ability to influence and be influenced by electronic circuits since this circuit also emits. Such experiments should show whether the sensibility of a living system can exceed the limits set by the laws of physics.

That is fascinating, but the author doesn't seem to know much about this since what he described is a superregenerative receiver, not a superheterodyne. He makes it sound as if it's an experiment just waiting for someone to put it together, but I don't think it works the way he sees it in his imagination. Combining the reception and transmission in a single circuit for the purpose of such an experiment could easily be a massive overcomplication, as any engineer has experienced. Furthermore you would not be learning anything about the known effects of EMF such as insulin, intracellular calcium, etc. Research has already learned a lot about the effect of radio waves on humans via other methods.
 

John G

The Living Force
Zizzi (whose Wikipedia page I linked to earlier) does start the big bang with the beginning entropy of a Planck mass black hole. Both Zizzi and Tony Smith (who uses Zizzi's model) have a Clifford algebra protospace. Already when you have a Planck mass black hole, there's been symmetry breaking of the protospace. I agree though I would have no idea how one would get back to the protospace. Getting past the material world is a little easier to think of than getting to the Planck scale. Ark's conformal gravity allows hyperdimensional possibilities and thinking of massless particles having quantum transactions gets beyond materialistic thinking too. A Clifford algebra universe state is quite natural number related (and real numbers if you think of time-like branching between universe states) so I'm not worried in a categorical sense.

Thank you for this description, but I would like to ask you to develop this idea.


Paola Zizzi says: ... we have three "degrees" (or phases) for the beginning of the universe:

  • The (perhaps eternal) presence of the proto space-time below the Planck scale.
  • The beginning of (quantum) inflation at the Planck time.
  • The end of inflation and beginning of existence.
... the semiclassical arguments of black holes evaporation might fail at the Planck scale. When the black hole reaches the Planck mass [about 10^19 proton masses], strong quantum gravity effects might stop the evaporation process ...[and]... there would be a remnant, which should store all the information collapsed in the original black hole. ... the remnant Planckian black hole gives rise to a QGN ... This idea is similar to the original one of Dyson [... Institute of Advanced Study preprint, 1976, unpublished...], that the black hole disappears completely, but one or more new universes branch off and carry away the information. ... the "unphysical time" t_(-1) = 0 (corresponding to a singularity in the classical theory) is unphysical for the new born universe, but not for the mother universe. ... in the mother universe, t_(-1) is the latest instant of evaporation of the black hole which will originate the child universe. The fact that there is this "leap" from physical time to unphysical time, in the passage from one universe to another, means that the two universes are not causally related. ...


... generalization ( related to loopoids) of the von Neumann hyperfiniteII1 Clifford tensor product

... x Cl x Cl x Cl x Cl x Cl x Cl x Cl x ...
where Cl = Mat2(C) to a similar structure with Cl = Mat16(R).

  • Begin by considering the Clifford tensor product as a linear chain of Cl's.
  • Consider each Cl in the linear chain as a node in a linear pregeometry.
  • Let the linear pregeometry, like a long line of yarn, "fold" or "weave" it into a higher-dimensional "array" or "tapestry" of Cl's.
  • Prior to the folding/weaving, each Cl node in the linear pregeometry would have 2 nearest neighbors in the chain
... Cl--Cl--Cl--Cl--Cl--Cl--Cl ...
that corresponds to the 1-dim lattice of Natural Numbers.
  • After the folding/weaving, each Cl pregeometry node in the tapestry could have more nearest neighbors.
 

John G

The Living Force
However, the current theories, including LQG (loop quantum gravity), face some problems, e.g. Loop quantum gravity - Wikipedia

LQG is nice in that it gives you a foamy spacetime of vertices from which you can do quantum transactions. It's not so nice in that it is too small to include forces other than gravity in the foamy structure. One good thing about the Paola Zizzi/Tony Smith foamy Clifford algebra structure Cl-Cl-Cl... mentioned earlier is that it is big. The Mat16(R) mentioned is Cl(8) via 16x16=2^8=256 degrees of freedom. This bit-like structure also hints at Clifford algebra being very information theory-like. Cl(8) has an 8-fold Bott periodicity which enables it to be a foamy spacetime. Tony actually used it for a Feynman Checkerboard model but like LQG, it's a lattice that's relativistic and has embedded Feynman paths. Tony under his given name Frank is cited as a source for Wikipedia's Feynman Checkerboard article.

Getting past the material world is a little easier to think of than getting to the Planck scale. Ark's conformal gravity allows hyperdimensional possibilities and thinking of massless particles having quantum transactions gets beyond materialistic thinking too.
I have seen you posting on Ark's Polish blog so I know you have some familiarity with Ark's work. I have a Polish last name but unfortunately did not pick up the language from my grandparents so I have to use a translator there. From a Clifford algebra point of view, Ark's conformal gravity would be the bivectors of the Cl(6) part of Cl(8). I think I'll eventually try to go through the complete information theory structure of Cl(8) here. As for massless particles:


Since massless light-cone particles, such as photons, live on the boundaries of light-cones, they do not experience linear time like massive material particles.

They see which part of their world-line is at what time by the value of its quantum U(1) phase, so that a world line look like a helix.

Andrew Gray's History Selection formulation of Many-Worlds Quantum Theory is based on the point of view of a Massless Lightcone life form that perceives the whole of its space-time world line.
 

Cleopatre VII

Padawan Learner
LQG is nice in that it gives you a foamy spacetime of vertices from which you can do quantum transactions. It's not so nice in that it is too small to include forces other than gravity in the foamy structure. One good thing about the Paola Zizzi/Tony Smith foamy Clifford algebra structure Cl-Cl-Cl... mentioned earlier is that it is big. The Mat16(R) mentioned is Cl(8) via 16x16=2^8=256 degrees of freedom. This bit-like structure also hints at Clifford algebra being very information theory-like. Cl(8) has an 8-fold Bott periodicity which enables it to be a foamy spacetime. Tony actually used it for a Feynman Checkerboard model but like LQG, it's a lattice that's relativistic and has embedded Feynman paths. Tony under his given name Frank is cited as a source for Wikipedia's Feynman Checkerboard article.


I have seen you posting on Ark's Polish blog so I know you have some familiarity with Ark's work. I have a Polish last name but unfortunately did not pick up the language from my grandparents so I have to use a translator there. From a Clifford algebra point of view, Ark's conformal gravity would be the bivectors of the Cl(6) part of Cl(8). I think I'll eventually try to go through the complete information theory structure of Cl(8) here. As for massless particles:

I have seen you posting on Ark's Polish blog so I know you have some familiarity with Ark's work.
Yes, that's true, but I am currently dealing with consciousness from a neurobiological perspective. I am about to adapt quantum models.

In the near future, I also plan to write an article on the time operator in quantum theory (If this interests you, I can more or less describe the main problems).

I am not so familiar with what you write about and I would have to read a lot. My main problems are time and consciousness and the relationship between them.

I read about LQG mainly in Rovelli's book "The order of Time". Do you know this book?
 

John G

The Living Force
In the near future, I also plan to write an article on the time operator in quantum theory (If this interests you, I can more or less describe the main problems)... I read about LQG mainly in Rovelli's book "The order of Time". Do you know this book?

If it's a time operator in the Hamiltonian sense especially the Heisenberg Hamiltonian sense that definitely interests me since Tony's use of Clifford algebra is very similar to using the Heisenberg group; Tony uses H92 embedded in Cl(8).


In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest. For example, the similarity between the Heisenberg equation in the Heisenberg picture of quantum mechanics and the Hamilton equation in classical physics should be built in.

One of the earliest attempts at a natural quantization was Weyl quantization, proposed by Hermann Weyl in 1927. Here, an attempt is made to associate a quantum-mechanical observable (a self-adjoint operator on a Hilbert space) with a real-valued function on classical phase space. The position and momentum in this phase space are mapped to the generators of the Heisenberg group, and the Hilbert space appears as a group representation of the Heisenberg group.

I first learned about LQG via online discussions between Tony and John Baez. Haven't really read much about it beyond that. Smith and Baez both agreed that E6/F4 would be great for LQG since it could handle more than gravity if only it was "foamy". Tony then went on to talk about using Clifford algebra to get around the "foamy" problem.
 

Cleopatre VII

Padawan Learner
If it's a time operator in the Hamiltonian sense especially the Heisenberg Hamiltonian sense that definitely interests me since Tony's use of Clifford algebra is very similar to using the Heisenberg group; Tony uses H92 embedded in Cl(8).




I first learned about LQG via online discussions between Tony and John Baez. Haven't really read much about it beyond that. Smith and Baez both agreed that E6/F4 would be great for LQG since it could handle more than gravity if only it was "foamy". Tony then went on to talk about using Clifford algebra to get around the "foamy" problem.
My initial goal was to answer the question about the existence of the time operator in quantum mathematical theory (non-relativistic and relativistic). I initially analyzed other works on this subject, many problems appeared in them (Pauli theorem, Hegerfeldt Lemma etc.) First of all, the time operator constructed by other authors was often either not self-adjoint (but e.g. maximally symmetrical) or did not fulfill the canonical commutation relation with the Hamiltonian. I did not take it as an absolute criterion, but it was a preliminary assumption. I wanted to construct a time operator that would be similar to other observables.

I was inspired by the dispute between Newton and Leibniz about the nature of time. The philosophical properties that Leibniz expected from time were transferred to the time operator. Nevertheless, a specific mathematical structure, partly derived from lattice theory, was required from the time operator. Constructions based on the generalized concept of an observable (POVM) were not perceived as satisfying.

Ultimately, the important point was that a time operator that satisfied these properties could be created when there was a field of interaction. I have constructed such an operator, among others for the harmonic oscillator, for the Hehl's Hamiltonian and the Hehl's Hamiltonian in the non-relativistic limit, and for the Hamiltonian in a homogeneous electric field.

However, I lack the proof that the time operator that meets the properties I require can only exist in the fields of interaction. The time operator (without interaction fields) created, among others Kijowski, however, his relation of canonical commutation is not entirely satisfactory, as the sign plays an important role. However, this is, in my opinion, the most satisfactory mathematical construction of the time operator for the free Hamiltonian.

At the moment, I am missing a clear proof that the time operator requires the existence of an interaction, and therefore a mathematical argument that time is only a manifestation of changes/phenomena (on the basis of quantum mechanics, because such arguments exist, but on the basis of thermodynamics, where time is a parameter). Here it is quite close to the relationship between time and consciousness.

Additionally, I have to consider the structure of quantum mechanics, hence my considerations of it as a categorical or non-categorical theory. And also another important question: Why is there such a problem with the time operator, and not with another physical quantity? Of course, there are also numerous considerations regarding the representation of physical quantities, tensors (including scalars, vectors) or perhaps operators. Is it purely mathematical or also philosophical? And I have many other unanswered questions here. What I currently have are some mathematical premises, but it is not enough for me. I have no conclusive proof.
 

John G

The Living Force
My initial goal was to answer the question about the existence of the time operator in quantum mathematical theory (non-relativistic and relativistic). I initially analyzed other works on this subject, many problems appeared in them (Pauli theorem, Hegerfeldt Lemma etc.) First of all, the time operator constructed by other authors was often either not self-adjoint (but e.g. maximally symmetrical) or did not fulfill the canonical commutation relation with the Hamiltonian. I did not take it as an absolute criterion, but it was a preliminary assumption. I wanted to construct a time operator that would be similar to other observables.

I was inspired by the dispute between Newton and Leibniz about the nature of time. The philosophical properties that Leibniz expected from time were transferred to the time operator. Nevertheless, a specific mathematical structure, partly derived from lattice theory, was required from the time operator. Constructions based on the generalized concept of an observable (POVM) were not perceived as satisfying.

Ultimately, the important point was that a time operator that satisfied these properties could be created when there was a field of interaction. I have constructed such an operator, among others for the harmonic oscillator, for the Hehl's Hamiltonian and the Hehl's Hamiltonian in the non-relativistic limit, and for the Hamiltonian in a homogeneous electric field.

However, I lack the proof that the time operator that meets the properties I require can only exist in the fields of interaction. The time operator (without interaction fields) created, among others Kijowski, however, his relation of canonical commutation is not entirely satisfactory, as the sign plays an important role. However, this is, in my opinion, the most satisfactory mathematical construction of the time operator for the free Hamiltonian.

At the moment, I am missing a clear proof that the time operator requires the existence of an interaction, and therefore a mathematical argument that time is only a manifestation of changes/phenomena (on the basis of quantum mechanics, because such arguments exist, but on the basis of thermodynamics, where time is a parameter). Here it is quite close to the relationship between time and consciousness.

Additionally, I have to consider the structure of quantum mechanics, hence my considerations of it as a categorical or non-categorical theory. And also another important question: Why is there such a problem with the time operator, and not with another physical quantity? Of course, there are also numerous considerations regarding the representation of physical quantities, tensors (including scalars, vectors) or perhaps operators. Is it purely mathematical or also philosophical? And I have many other unanswered questions here. What I currently have are some mathematical premises, but it is not enough for me. I have no conclusive proof.
I do think it's good to have a math structure that forces you to stick to the canonical commutation relation so this is kind of my favorite presentation of this topic:


Your state has to be a complete universe state in order to handle entanglement in time and even just relativity. Your propagator/time operator could math-wise propagate to any time with time being a complex plane thing thus really you just go to a particular phase of a time circle. So yes if you can in theory jump to any time in a transaction; time for you is kind of just counting quantum transactions, in other words just a manifestation of changes as you say.

Interesting that you refer to fields of interaction because yes even with a math structure that sticks to the canonical commutation relation and has a full set of boson and fermion creation/annihilation operators, it still lacks a local field description of its current location. It has operators to go to new states but not a complete enough description of the current state. It's math-wise like the central element of your math structure which has only the propagator/time operator, needs to be joined by field operators. Something like Ark's description of a conformal bimetric plus Standard model fields added in maybe a Kaluza Klein Hodge dual structure would be good.
 

Cleopatre VII

Padawan Learner
I do think it's good to have a math structure that forces you to stick to the canonical commutation relation so this is kind of my favorite presentation of this topic:


Your state has to be a complete universe state in order to handle entanglement in time and even just relativity. Your propagator/time operator could math-wise propagate to any time with time being a complex plane thing thus really you just go to a particular phase of a time circle. So yes if you can in theory jump to any time in a transaction; time for you is kind of just counting quantum transactions, in other words just a manifestation of changes as you say.

Interesting that you refer to fields of interaction because yes even with a math structure that sticks to the canonical commutation relation and has a full set of boson and fermion creation/annihilation operators, it still lacks a local field description of its current location. It has operators to go to new states but not a complete enough description of the current state. It's math-wise like the central element of your math structure which has only the propagator/time operator, needs to be joined by field operators. Something like Ark's description of a conformal bimetric plus Standard model fields added in maybe a Kaluza Klein Hodge dual structure would be good.
Thank you very much for your reply and for your observations. I will keep them in mind. At the moment, however, I am expanding what I already have regarding the time operator. When I write an article about it, I will think about what to do next.

On the other hand, I currently deal with the study of consciousness from a different perspective. Namely, I am participating in a neurobiology grant that deals with the structure and function of the GABA receptor.

Then I will have to create some synthesis and make time and consciousness meet. So I have a lot of work to do, but thank you very much for the ideas. Perhaps they will become important when my vision is at a more advanced stage.
 

John G

The Living Force
I think I'll eventually try to go through the complete information theory structure of Cl(8) here.

First of all, the time operator constructed by other authors was often either not self-adjoint (but e.g. maximally symmetrical) or did not fulfill the canonical commutation relation with the Hamiltonian.


The basis elements satisfy the commutation relations:

[X,Y] = Z; [X,Z]=0; [Y,Z]=0
The name "Heisenberg group" is motivated by the preceding relations, which have the same form as the canonical commutation relations in quantum mechanics:

[x,p]=ihI; [x,ihI]=0; [p,ihI]=0
where x is the position operator, p is the momentum operator, and h is Planck's constant.

OK mostly just because it's fun, I'm going to try as I mentioned earlier to go through the information theory structure of Cl(8). I'm going to start with the Heisenberg group because it has a form similar to Cl(8) and as mentioned above it has the form of the canonical commutation relations which is good for time operator construction. The Heisenberg group most similar to Cl(8) is H92. H92 has the graded dimensions 92 1 92. The 92s could be for the position and momentum operators mentioned above and the 1 would be for the time operator (or propagator phase) dimension. However to eventually match up with Tony Smith's use of Cl(8), we will use the 92s for different operators that are functions of position and momentum:


Let us define the creation operator ˆa†(φ) by its action on an arbitrary state... The destruction or annihilation operator ˆa(φ) is then defined as the adjoint of ˆa†(φ)... If the (identical) particles are bosons, the operators ˆa(φ) obey canonical commutation relations. If the (identical) particles are Fermions, the operators ˆa(φ) obey canonical anticommutation relations... X and P, the coordinate [position] and momentum Hermitian operators satisfy canonical commutation relations... We now define the creation and annihilation operators a† and a as a = 1/√2[√mω/h X + i P/√mωh] a† = 1/√2[√mω/h X −i P/√mωh]...

So we are still using the Heisenberg group but have switched from position/momentum to creation/annihilation operators for bosons (force particles/fields) and fermions (matter/antimatter). We also now have graded dimensions for H92 of 8 28 56 1 56 28 8. 8+28+56=92 so it's still H92. The odd grades (1-3-5-7) give you 8+56+56+8=128 dimensions to use for fermions and the even grades (2-4-6) give you 28+1+28=57 dimensions for boson (force particle/field) operators. This is due to the following math property of the grades:


even grades commute, odd grades anticommute.

This fits with the idea mentioned earlier that bosons obey canonical commutation relations and fermions obey canonical anticommutation relations. Even though we are still with H92 and not Cl(8), we can still see an information theory forming. The 8 one-grade fits with 8 ways to put one 1 in 8 bits; the 28 two-grade fits with 28 ways to put two 1s in 8 bits; the 56 three-grade fits with 56 ways to put three 1s in 8 bits; the 56 five-grade fits with 56 ways to put five 1s in 8 bits; the 28 six-grade fits with 28 ways to put six 1s in 8 bits; and the 8 seven-grade fits with 8 ways to put seven 1s in 8 bits. There are 70 ways to put four 1s in 8 bits so the 1 for H92 is going to become a 70 for Cl(8). Also there is one way to zero 1s and one way to put eight 1s in 8 bits. Thus Cl(8) will add 1 for the zero grade and 1 for the eight-grade. These extra Cl(8) dimensions for Tony Smith add fields for relativity and the Higgs mechanism to the H92 quantum mechanics. The graded Cl(8) dimensions are 1-8-28-56-70-56-28-8-1 which add to 2^8=256, the number of possibilities represented by 8 bits. I'll later start going through the bit structure for the different fermion and boson/field dimensions.
 

John G

The Living Force
So we... have switched from position/momentum to creation/annihilation operators for bosons (force particles/fields) and fermions (matter/antimatter)... The graded Cl(8) dimensions are 1-8-28-56-70-56-28-8-1 which add to 2^8=256, the number of possibilities represented by 8 bits. I'll later start going through the bit structure for the different fermion and boson/field dimensions.


The Lorentz transformation is a linear transformation. It may include a rotation of space; a rotation-free Lorentz transformation is called a Lorentz boost. In Minkowski space—the mathematical model of spacetime in special relativity—the Lorentz transformations preserve the spacetime interval between any two events... Given the strong resemblance to rotations of spatial coordinates in 3d space in the Cartesian xy, yz, and zx planes, a Lorentz boost can be thought of as a hyperbolic rotation of spacetime coordinates in the xt, yt, and zt Cartesian-time planes of 4d Minkowski space... The second equation is satisfied for spacetime translations in addition to Lorentz transformations leading to the Poincaré group or the inhomogeneous Lorentz group. The first equation (or the second restricted to lightlike separation) leads to a yet larger group, the conformal group of spacetime.

First thing to do is to label the Cl(8) bits. Four of them will simply be the XYZT of spacetime. I call the other four GMAC which are a Kaluza Klein internal spacetime. G is green/greater than (color/positive charge); M is magenta/minus (anticolor/negative charge); A is anti-DeSitter (a group that has spacetime translations); C is conformal (adds the special conformal transformations of Ark's conformal gravity). Now we can look at the bits for Ark's conformal gravity. First we need the XY, YZ and ZX rotations mentioned above plus the XT, YT and ZT boosts also mentioned above:

1626855195657.png1626855261840.png

The picture hints at the idea of a rotation (including rotations in time) via just rotating around at the black starting dot. These have two one bits so the are part of the first 28 Cl(8) grading (there are 28 ways to put two one bits in 8 bits). These would be creation operators. For the annihilation operators all ones become zeros and zeros become ones and I do mean all. The pictures for the annihilation rotation/boost operators thus will look like one white starting dot with the rest black. There will be two zero bits and six one bits for the annihilation operators thus they will be part of the second 28 in the Cl(8) grading (there are 28 ways to put six one bits in 8 bits). Which bits become the zeros isn't where the ones were however. The T bit for example is the far left bit and is represented by 1-1-1 digitally. You have to change this to 0-0-0 (you really do have to change all ones to zeros) thus if the far left (1-1-1) T bit is a one for the creation operator then the corresponding annihilation operator bit will be a zero in the far right (the 0-0-0 bit). I'll continue later with the translation and conformal bosons of Ark's gravity.
 
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John G

The Living Force
Here are the translation and special conformal transformation bosons of Ark's conformal gravity:

1627246758591.png
1627246826719.png

The strait line picture for the translations hints at the idea of translations being a straight ahead motion. The conformal transformations relate to things like complex numbers/phases and the picture has a phase-like look. The picture also relates to spacetime details with time, longitudinal space (straight ahead direction) and transverse spaces (different directions than straight ahead). There's one more degree of freedom in the conformal group called the dilation; it sets a Higgs mechanism energy level in Tony's model (relates to the masses of particles).

1627247850647.png
These are creation operators (two one-bits); the corresponding annihilation operators (six one-bits) are derived as previously described for rotations and boosts via changing ALL one-bits to zero-bits. This as mentioned earlier makes the picture have black pixels where there used to be white and vice-versa (you can though have a different set of pictures associated with the creation operators starting with a white dot instead of black and the annihilation operators starting with a black dot instead of white). The alternative pictures for example allow these translation annihilation operators to have some spacetime detail like what was described for the special conformal transformations:

1627248799999.png
 
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