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TGD Inspired Theory of Consciousness
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ER=EPR correspondence proposed by Leonard Susskind and Juan Maldacena in 2014 (see also this) has become the most fashionable fashion in theoretical physics. Even the idea that space-time could emerge from ER-EPR has been proposed.
ER (Einstein-Rosen) bridge in turn is purely classical notion associated with general relativity theory (GRT). ER bridge is illustrated in terms of a fold of space-time. Locally there are two sheets near to each other and connected by a wormhole: these sheets are actually parts of the same sheet. Along the bridge the distance between two systems can be very short. Along folded sheet it can be very long. This suggest some kind of classical non-locality in the sense that the physics around the two throats of wormhole can be strongly correlated: the non-locality would be implied by topology. This is not in accordance with the view of classical physics in Minkowski space-time.
EPR (Einstein-Podolsky-Rosen) paradox states that it is possible to measure both position and momentum of two particles more accurately than Heisenberg Uncertainty Principle allows unless the measurement involves instantaneous transfer of information between particles denied by special relativity. The conclusion of EPR was that quantum theory is incomplete and should be extended by introducing hidden variables. The argument was based on classical physics view a bout microcausality.
Later the notion of quantum entanglement became an established notion and it became clear that no classical superluminal transfer of information is needed. If one accepts the basic rules of quantum measurement theory - in particular tensor products of distant systems - EPR paradox disappears. Entanglement is of course a genuinely non-nonlocal phenomenon not encountered in classical physics and one could wonder whether it might have classical sace-time correlate after all. State function reduction becomes the problem and has remained the ugly duckling of quantum theory. Unfortunately, this ugly duckling has become a taboo and is surrounded by a thick cloud of messy interpretations. Hence the situation is still far from settled.
At time EPR and ER were proposed, there was no idea about possible connection between these two ideas. Both notions involve unexpected non-locality and one might however ask whether there might be a connection.
In some sense ER=EPR could be seen as kind of victory for Einstein. There could be after all a classical space-time correlate for entanglement and for what happens state function reduction for a system induces state function reduction in distant entangled system. It however seems that quantum theory does not allow a signal travelling along the wormhole throat connecting the entangled systems.
What ER= EPR says that maximal entanglement for blackholes is somehow dual to Einstein-Rosen bridge (wormhole). Susskind and Maldacena even suggests that this picture generalizes to entanglement between any kind of systems and that even elementary particles are connected by Planckian wormholes.
The next step has been to argue that entanglement is more fundamental than space-time, and that space-time would emerge. The attempts to realize the idea involve holography and already this means introduction of 2-D surfaces in 3-D space so that the argument becomes circular. To my opinion the emergence of space-time is doomed to remain one of the many fashions of theoretical physics, which last few years and are then lost to sands of time. These fashions reflect the deep crisis of theoretical physics, which has lasted for four decades, and are as such a good sign telling that people at least try.
The motivation for following TGD inspired arguments was one of the arguments against ER=EPR: ER=EPR does not conform with the linearity of quantum mechanics. The state pairs in the superposition defining entangled state are unentangled (separable) and there should be no wormhole connecting the systems in this case. In an entangled state there should be wormhole. This makes sense only if the space-time geometry couples to quantum dynamics so that one must give up the idea that one has Schödinger amplitudes in fixed background and linear superposition for them. This looks weird even in GRT space-time.
Some background about TGD
Before discussing what ER-EPR corresponds in TGD few words about quantum TGD are in order.
The counterpart of ER=EPR in TGD framework
The TGD variant of ER=EPR has been part of TGD for two decades but have remained un-noticed since superstring hegemony has dominated the theory landscape. There are still many profound ideas to be re-discovered but their realization in the framework of GRT is practically impossible since they relate closely the vision about space-times as 4-surfaces in M4× CP2. What ER=EPR then corresponds in TGD.
Cloning of maximally negentropic states is possible: DNA replication as cloning of this kind of states?
In Facebook discussion with Bruno Marchal and Stephen King the notion of quantum cloning as copying of quantum state popped up and I ended up to ask about approximate cloning and got a nice link about which more below. From Wikipedia one learns some interesting facts cloning. No-cloning theorem states that the cloning of all states by unitary time evolution of the tensor product system is not possible. It is however possible clone orthogonal basis of states. Does this have some deep meaning?
As a response to my question I got a link to an article of Lamourex et al showing that cloning of entanglement - to be distinguished from the cloning of quantum state - is not possible in the general case. Separability - the absence of entanglement - is not preserved. Approximate cloning generates necessarily some entanglement in this case, and the authors give a lower bound for the remaining entanglement in case of an unentangled state pair.
The cloning of maximally entangled state is however possible. What makes this so interesting is that maximally negentropic entanglement for rational entanglement probabilities in TGD framework corresponds to maximal entanglement - entanglement probabilities form a matrix proportional to unit matrix- and just this entanglement is favored by Negentropy Maximization Principle . Could maximal entanglement be involved with say DNA replication? Could maximal negentropic entanglement for algebraic extensions of rationals allow cloning so that DNA entanglement negentropy could be larger than entanglement entropy?
What about entanglement probabilities in algebraic extension of rationals? In this case real number based entanglement entropy is not maximal since entanglement probablities are different. What can one say about p-adic entanglement negentropies: are they still maximal under some reasonable conditions? The logarithms involved depend on p-adic norms of probabilities and this is in the generic case just inverse of the power of p. Number theoretical universality suggests that entanglement probabilities are of form
with ∑ ai= N with algebraic numbers ai not involving natural numbers and thus having unit p-adic norm.
With this assumption p-adic norms of Pi reduce to those of 1/N as for maximal rational entanglement. If this is the case the p-adic negentropy equals to log(pk) if pk divides N. The total negentropy equals to log(N) and is maximal and has the same value as for rational probabilities equal to 1/N.
The real entanglement entropy is now however smaller than log(N), which would mean that p-adic negentropy is larger than the real entropy as conjectured earlier (see this). For rational entanglement probabilities the generation of entanglement negentropy - conscious information during evolution - would be accompanied by a generation of equal entanglement entropy measuring the ignorance about what the negentropically entangled states representing selves are.
This conforms with the observation of Jeremy England that living matter is entropy producer (for TGD inspired commentary see this). For algebraic extensions of rationals this entropy could be however smaller than the total negentropy. Second law follows as a shadow of NMP if the real entanglement entropy corresponds to the thermodynamical entropy. Algebraic evolution would allow to generate conscious information faster than the environment is polluted, one might concretize! The higher the dimension of the algebraic extension rationals, the larger the difference could be and the future of the Universe might be brighter than one might expect by just looking around! Very consolating! One should however show that the above described situation can be realized as NMP strongly suggests before opening a bottle of champaigne.
The impossibility of cloning of entanglement in the general case makes impossible the transfer of information as any kind of entanglement. Maximal entanglement - and maybe be even negentropic entanglement maximal in p-adic sectors - could however make the communication without damaging the information at the source. Since conscious information is associated with p-adic sectors responsible for cognition, one could even allow the modification of the entanglement probabilities and thus of the real entanglement entropy in the communication process since the maximal p-adic negentropy depends only weakly on the entanglement probabilities.
NE is assigned with conscious experiences with positive emotional coloring: experience of understanding, experience of love, etc... There is an old finnish saying, which can be translated to "Shared joy is double joy!". Could the cloning of NE make possible generation of entanglement by loving attitude so that living entities would not be mere thieves trying to steal NE by killing and eating each other?
For background see the chapter Negentropy Maximization Principle. See also the article Is the sum of p-adic negentropies equal to real entropy?.
I encountered in Facebook discussion Wigner's friend paradox (see this and this). Wigner leaves his friend to the laboratory together with Schrödinger's cat and the friend measures the state of cat: the outcome is "dead" or "alive". Wigner returns and learns from his friend what the state of the cat is. The question is: was the state of cat fixed already earlier or when Wigner learned it from his friend. In the latter case the state of friend and cat would have been superposition of pairs in which cat was alive and friend new this and cat was dead also now friend new this. Entanglement between cat and bottle would have been transferred to that between cat+bottle and Wigner's friend. Recall that this kind of information transfer occur in quantum computation and quantum teleportation allows to transfer arbitrary quantum state but destroys the original.
The original purpose of Wigner was to demonstrate that consciousness is involved with the state function collapse. TGD view is that the state function collapse can be seen as moment consciousness. Or more precisely, self as conscious entity corresponds to the repeated state function reduction sequence to the same boundary of causal diamond (CD). One might say that self is generalized Zeno effect in Zero Energy Ontology (ZEO). The first reduction to the opposite boundary of CD means death of self and re-incarnation at opposite boundary as time reversed self. The experiencet flow of time corresponds to the shift of the non-fixed boundary of self reduction by reduction farther from the fixed boundary - also the state at it changes. Thus subjective time as sequence of reductions is mapped to clock time identifiable as the temporal distance between the tips of CD. Arrow of time is generated but changes in death-reincarnation.
In TGD inspired theory of consciousness the intuitive answerto the question of Wigner looks obvious. If the friend measured the state of cat, it was indeed dead or alive already before Wigner arrived. What remains is the question what it means for Wigner, the "ultimate observer", to learn about the state of the cat from his friend. The question is about what conscious communications are.
Consider first the situation in the framework of standard quantum information theory.
TGD inspired theory of consciousness predicts that during communication Wigner and his friend form a larger entangled system: this makes possible sharing of meaning. Directed attention means that subject and object are entangled. The magnetic flux tubes connecting the two systems would serve as a correlate for the attention. This mechanism would be at work already at the level of molecular biology. Its analog would be wormholes in ER-EPR corresponence proposed by Maldacena and Susskind. Note that directed attention brings in mind the generation of the Bell entangled pair A-B. It would make also possible quantum teleportation.
Wigner's friend could also symbolize the "pointer of the measurement apparatus" constructed to detect whether cats are dead of alive. Consider this option first. If the pointer is subsystem defining subself of Wigner, it would represent mental image of Wigner and there would be no paradox. If qubit in the brain in the brain of Wigner's friend replaces the pointer of measurement apparatus then during communication Wigner and his friend form a larger entangled system experiencing this qubit. Perhaps this temporary fusion of selves allows to answer the question about how common meaning is generated. Note that this would not require quantum teleportation protocol but would allow it.
Negentropically entangled objects are key entities in TGD inspired theory of consciousness and the challenge is to understand how these could be constructed and what their properties could be. These states are diametrically opposite to unentangled eigenstates of single particle operators, usually elements of Cartan algebra of symmetry group. The entangled states should result as eigenstates of poly-local operators. Yangian algebras involve a hierarchy of poly-local operators, and twistorial considerations inspire the conjecture that Yangian counterparts of super-symplectic and other algebras made poly-local with respect to partonic 2-surfaces or end-points of boundaries of string world sheet at them are symmetries of quantum TGD. Could Yangians allow to understand maximal entanglement in terms of symmetries?
I ended almost by accident to a fascinating and almost trivial theorem. Adelic theorem for information would state that conscious information represented as sum of p-adic negentropies (entropies, which are negative) is equal to real entropy. The more conscious information, the larger the chaos in the environment as everyone can verify by just looking around;-)
This looks bad! Luckily, it turned out that this statement is true for rational probabilities only. For algebraic extensions it cannot be true as is easy to see. That negentropic entanglement is possible only for algebraic extensions of rationals conforms with the vision that algebraic extensions of rationals characterize evolutionary hierarchy. The rationals represent the lowest level at which there either conscious information vanishes or if equal to p-adic contribution to negentropy is companied by equally large real entropy.
It is not completely obvious that the notion of p-adic negentropy indeed makes sense for algebraic extensions of rationals. A possible problem is caused by the fact that the decomposition of algebraic integer to primes is not unique. Simple argument however strongly suggests that the various p-adic norms of the factors do not depend on the factorization. Also a formula for the difference of the total p-adic negentropy and real entropy is deduced.
p-Adic contribution to negentropy equals to real entropy for rational probabilities but not for algebraic probabilities
The following argument shows that p-adic negentropy equals to real entropy for rational probabilities.
Formula for the difference of total p-adic negentropy and real entanglement entropy
In the following some non-trivial details related to the definition of p-adic norms for the rationals in the algebraic extension of rationals are discussed.
The induced p-adic norm Np(x) for n-dimensional extension of Q is defined as the determinant det(x) of the linear map defined by multiplication with x. det(x) is rational number. The corresponding p-adic norm is defined as the n:th root Np(det(x))1/n of the ordinary p-adic norm. Root guarantees that the norm co-incides with the ordinary p-adic norm for ordinary p-adic integers. One must perform now a factorization to algebraic primes. Below an argument is given that although the factorization to primes is not always unique, the product of p-adic norms for given algebraic rational defined as ratio of algebraic integers is unique.
Can one write an explicit formula the difference of total p-adic entanglement negentropy (positive) and real entanglement entropy using prime factorization in finite dimensional algebraic extension (note that for algebraic numbers defining infinite-dimensional extension of rationals factorization does not even exist since one can write a=a1/2a1/2=...)? This requires that total p-adic entropy is uniquely defined. There is a possible problem due to the non-uniqueness of the prime factorization.
Life has been hard for skeptics during last two decades. A typical skeptic has as building bricks of his ego the items in the list of notions that they regard as pseudoscientific. This allows to attack the people who have the gift of imagination and passion for genuine understanding, which skeptics unfortunately do not possess. What makes attacks easy that no arguments based on contents are needed and the skeptic need not waste his time by trying to understand the arguments of the person to be labelled as pseudoscientist or crackpot.
The typical rhetoric tricks used begin from replacement of Dr X with Mr X and end up with the "conclusion" that the work of Mr X is totally incomprehensible. I have learned that rather often skeptic of this kind is an academic dropout who never managed to do his MsC. Obviously, the role of skeptic became a manner to survive socially and retain the illusion "I am a scientist". During last decades the list of pseudoscientific notions has shortened item by item as quantum biology and quantum consciousness have emerged as respected branches of science. The notion of re-incarnation has been certainly regarded as one of safest pillars supporting the ego of skeptic but even this pillar is in danger to fall down. Poor skeptics.
It is indeed amusing how fast the attitudes change as ideas evolve and experimental data emerge. Only few years ago I could not say anything definite about reincarnation in the framework of TGD inspired theory of consciousness. Now it has become an unavoidable prediction of zero energy ontology (ZEO), which itself is a "must" in TGD framework.
The prediction related to re-incarnation is however not quite what one might have expected. In death of self a reincarnation as time reversed conscious entity takes place. For time reversed self subjective time evolution corresponds to evolution in a reverse direction of geometric time. The next death/reincarnation after this re-incarnation gives rise a mental image for which the arrow of geometric time is the original one.
Can one test this prediction? If one accepts the predicted fractal self hierarchy in which sub-selves correspond to mental images of self, this is possible. I am too lazy to retype basics about ZEO, CDs, and about how self as generalized Zeno effect emerges and just assume that reader knows the basic concepts or sees to trouble to refresh her knowledge about them.
For background see the chapter About the nature of time.
I learned about an interesting work, which relates to the relationship of experienced time and geometric time but ortodoxically assumes that these two and one and the same thing. The title of the popular article was Inverse Research on Decisions Shows Instinct Makes Us Behave Like Cyborgs, not Robots (see this). It tells about the work of Adam Bear and Paul Bloom. The article claims that our mind for some mysterious-to-me reason tricks us to believe that were are responsible for totally automatic or reflexive behaviours. In fact, these behaviors by definition are such that we do not feel of being responsible for them. Bear how allows us some subconscious free will so that we are not programmed robots but cyborgs whatever that might mean.
This work is an excellent example about how a dominating paradigm, which is wrong, leads to wrong interpretation of experimental findings, which as such are correct. The standard belief in neuroscience and standard physics is that causal effects propagate always in the same direction of the geometric time. This interpretation follows from the identification of geometric time (time of physicist) with subjective time. This despite the fact that these times have very different properties: consider only reversibility viz. irreversibility, existence of both future and past viz. only past exists.
The classical experiments of Libet challenge this dogma. Person decides to raise finger but neuro-activity begins fraction of second earlier. Mainstream neuroscientist of interprets this by saying that there is no free will. Second proposed interpretation is that the decision is made earlier at subconscious level and at our level the experience of free will is an illusion. One can of course wonder why this illusion.
The third manner to interpret the situation respects our immediate experience that we indeed have free will but in order to avoid mathematical contradictions must be accompanied by a new more general view about quantum physics accepting as a fact that there are two causalities: that of free will and that of deterministic laws of field equations. In TGD framework Zero Energy Ontology realizes this view. The outcome is prediction of signals which can propagate in both directions of geometric time. If the conscious decision generates a signal to geometric past it initiates a neural activity in geometric past. An excellent tool for survival in jungle or in modern market economy full or merciless predators.
In the experiment considered subject persons saw five dots and selected one. One of the dots became red with a varying time lag but subject person did not know when. Subject person had to tell whether her choice had been correct, wrong, or whether she had failed to make any choice at all before the change took place.
The surprising observation was that the shorter the time interval from the guess to change of color to red was, the better the reported ability to guess correctly was and in conflict with statistical model based on fixed arrow of time. If information can travel backwards in geometric time, the natural interpretation would be the same as in Libet's experiments and in the experiments of say Radin and Bierman claimed to demonstrate precognition. This is possible in zero energy ontology (ZEO). ZEO allows also a slightly different interpretation relies. In ZEO in which mental images correspond to causal diamonds (CDs). For sensory mental images their time scale would be of order .1 seconds so that below this scale one cannot anymore put events in precise time order and one indeed has precognition. What this means that one does not know whether the sensory input corresponds to the "upper" or "lower" boundary of CD so that these interpretations are equivalent.
Neuroscientist cannot of course publicly utter the word "precognition" associating immediately with really dirty word "paranormal". The orthodox conclusion is that subject persons are "cheating" themselves without knowing it. Very bizarre interpretation - if taken completely seriously it forces to question all our knowledge! One can also ask, why the subjects would tend to cheat themselves when the change occurred immediately after their choice: why not always? Certainly the interpretation is a heroic attempt to save the standard world view.
A simple modification of the experiment would be an addition of a keystroke telling the choice when it was done and before the change in color. This would immediately tell whether something like precognition was involved.For background see the chapter About the nature of time.
Number theoretical feats of some mathematicians like Ramanujan remain a mystery for those believing that brain is a classical computer. Also the ability of idiot savants - lacking even the idea about what prime is - to factorize integers to primes challenges the idea that an algorithm is involved. In this article I discuss ideas about how various arithmetical feats such as partitioning integer to a sum of integers and to a product of prime factors might take place. The ideas are inspired by the number theoretic vision about TGD suggesting that basic arithmetics might be realized as naturally occurring processes at quantum level and the outcomes might be "sensorily perceived". One can also ask whether zero energy ontology (ZEO) could allow to perform quantum computations in polynomial instead of exponential time.
The indian mathematician Srinivasa Ramanujan is perhaps the most well-known example about a mathematician with miraculous gifts. He told immediately answers to difficult mathematical questions - ordinary mortals had to to hard computational work to check that the answer was right. Many of the extremely intricate mathematical formulas of Ramanujan have been proved much later by using advanced number theory. Ramanujan told that he got the answers from his personal Goddess. A possible TGD based explanation of this feat relies on the idea that in zero energy ontology (ZEO) quantum computation like activity could consist of steps consisting quantum computation and its time reversal with long-lasting part of each step performed in reverse time direction at opposite boundary of causal diamond so that the net time used would be short at second boundary.
The adelic picture about state function reduction in ZEO suggests that it might be possible to have direct sensory experience about prime factorization of integers (see this). What about partitions of integers to sums of primes? For years ago I proposed that symplectic QFT is an essential part of TGD. The basic observation was that one can assign to polygons of partonic 2-surface - say geodesic triangles - Kähler magnetic fluxes defining symplectic invariance identifiable as zero modes. This assignment makes sense also for string world sheets and gives rise to what is usually called Abelian Wilson line. I could not specify at that time how to select these polygons. A very natural manner to fix the vertices of polygon (or polygons) is to assume that they correspond ends of fermion lines which appear as boundaries of string world sheets. The polygons would be fixed rather uniquely by requiring that fermions reside at their vertices.
The number 1 is the only prime for addition so that the analog of prime factorization for sum is not of much use. Polygons with n=3,4,5 vertices are special in that one cannot decompose them to non-degenerate polygons. Non-degenerate polygons also represent integers n>2. This inspires the idea about numbers 3,4,5 as "additive primes" for integers n>2 representable as non-degenerate polygons. These polygons could be associated many-fermion states with negentropic entanglement (NE) - this notion relate to cognition and conscious information and is something totally new from standard physics point of view. This inspires also a conjecture about a deep connection with arithmetic consciousness: polygons would define conscious representations for integers n>2. The splicings of polygons to smaller ones could be dynamical quantum processes behind arithmetic conscious processes involving addition.
For details see the chapter Conscious Information and Intelligence or the article Number Theoretical Feats and TGD Inspired Theory of Consciousness.
In given p-adic sector the entanglement entropy (EE) is defined by replacing the logarithms of probabilities in Shannon formula by the logarithms of their p-adic norms. The resulting entropy satisfies the same axioms as ordinary entropy but makes sense only for probabilities, which must be rational valued or in an algebraic extension of rationals. The algebraic extensions corresponds to the evolutionary level of system and the algebraic complexity of the extension serves as a measure for the evolutionary level. p-Adically also extensions determined by roots of e can be considered. What is so remarkable is that the number theoretic entropy can be negative.
A simple example allows to get an idea about what is involved. If the entanglement probabilities are rational numbers Pi=Mi/N, ∑i Mi=N, then the primes appearing as factors of N correspond to a negative contribution to the number theoretic entanglement entropy and thus to information. The factors of Mi correspond to negative contributions. For maximal entanglement with Pi=1/N in this case the EE is negative. The interpretation is that the entangled state represents quantally concept or a rule as superposition of its instances defined by the state pairs in the superposition. Identity matrix means that one can choose the state basis in arbitrary manner and the interpretation could be in terms of "enlightened" state of consciousness characterized by "absence of distinctions". In general case the basis is unique.
Metabolism is a central concept in biology and neuroscience. Usually metabolism is understood as transfer of ordered energy and various chemical metabolites to the system. In TGD metabolism could be basically just a transfer of NE from nutrients to the organism. Living systems would be fighting for NE to stay alive (NMP is merciless!) and stealing of NE would be the fundamental crime.
TGD has been plagued by a longstanding interpretational problem: can one apply the notion of number theoretic entropy in the real context or not. If this is possible at all, under what conditions this is the case? How does one know that the entanglement probabilities are not transcendental as they would be in generic case? There is also a second problem: p-adic Hilbert space is not a well-defined notion since the sum of p-adic probabilities defined as moduli squared for the coefficients of the superposition of orthonormal states can vanish and one obtains zero norm states.
These problems disappear if the reduction occurs in the intersection of reality and p-adicities since here Hilbert spaces have some algebraic number field as coefficient field. By SH the 2-D states states provide all information needed to construct quantum physics. In particular, quantum measurement theory.
One can also ask, whether the other mathematical feats performed by idiot savants could be understood in terms of their ability to directly experience - "see" - the prime composition (adelic decomposition) of integer or even rational. This could for instance allow to "see" if integer is - say 3rd - power of some smaller integer: all prime exponents in it would be multiples of 3. If the person is able to generate an NE for which probabilities Pi=Mi/N are apart from normalization equal to given integers Mi, ∑ Mi=N, then they could be able to "see" the prime compositions for Mi and N. For instance, they could "see" whether both Mi and N are 3rd powers of some integer and just by going through trials find the integers satisfying this condition.
For details see the chapter Negentropy Maximization Principle or the article TGD Inspired Comments about Integrated Information Theory of Consciousness.