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Year 2017

About the double-slit experiment of Dean Radin

Dean Radin and his team have done a very interesting experiment (see this and this) testing the idea that observer induces state function reduction.


The experiment is a modified double slit experiment. In double slit experiment a laser beam arrives to the screen via two slits and interference pattern is generated as if photons would behave like waves localized at screen. If one adds detectors at the slits, either detector fires and detects the passing-by by photon, and interference pattern disappears with optimal detection efficiency.

The idea is to add a subject person (S) at distance of two meters. S imagines of measuring that electron passes through either slit. One can say that S intends to add a "detector" to either slit or both of them so that a state function reduction selecting either slit occurs. This experiment differs from experiments in which S tries to affect the ratio of frequencies of 0:s and 1:s in random series of bits: S does not try to force the electrons to pass by either slit. There is a feedback represented as sound/yellow light whose height/intensity coded for the amount of the reduction of the height of the peak. There are two kinds of participants: meditators and those who have no experience in meditation.

The results of the experiment are thoroughly discussed in the Youtube lecture or Radin (see this). To my opinion the results are amazing. In one experiment it was found that the height of the peak of the Fourier transform of the intensity distribution of the diffraction pattern is reduced. In second experiment the depth of bottom of the through of distribution was reduced. As if the intention would induce with some probability to perform the measurement selecting the photon path. The effect was small but appeared systematically for a group consisting of meditators. For persons without experience in meditation the effect averaged out also in this case it was present in the beginning of the experiment when subject person were not bored by the repetitive character of the experiment. The longer attention span of meditators could partially explain this.

Even more amazing finding was that in a variant of the experiment realized in internet the results were also positive although the persons intending to induce the experiment.

Arguments of different skeptic

The standard argument of skeptic is that statistics is poor, that the experiment is even fraud, etc... One can however consider more refined and more imaginative objections. Let us make a digress from the usual behavior of skeptic and assume that the effect was real.

If the meditators could induce the measurement by intention, one expects that also the experimenter could have done it. To how high degree the outcome was due to the experimenters and how much due to the meditators? Experimenter also had the theoretical expectation that meditators are better in inducing the slit detection. Could the wish that the theory is correct have caused subconscious intention about performing the detection in the case of meditators or not doing it in the case of non-meditating subject persons?

In the case of net experiment situation becomes even more problematic. One can imagine that also in this case the intention of experimenter could induce the detection - at least if experimenter is near to the system. Should experimenters have spent the period of experiments in Mars or at least in a distant holiday resort! Experimenters studying remote mental interactions are usually not rich people and presumably they did not do this.

The experimenter effect is well-known in parapsychology. Some experimenters are extremely successful. Could one think that they have strong intentional powers? Ironically, this would demonstrate the reality of paranormal effects of this kind but in a manner that can never convince the skeptics. There is evidence for this kind of effect in the testing of new medicines. Good results are obtained when the testers are enthusiastic and dream of a positive result. When they do same tests after some years, the results are worse.

TGD based model

The challenge is to understand how the S imagining a measurement telling that photon went through either slit could realize this intention. What does the detection mean and what it demands?

  1. The measurement should involve a state function reduction selecting between the slits entangled with observer. In principle it is enough to have an interaction of photon in either slit localing the path of the photon to that slit. It is enough that photon interacts with charged particles in either slit with some probability. This measurement is of course not optimal since the interference diagram is only partially changed. Only some fraction of these measurements take place and produce single slit pattern so that the observer pattern is a weighted average of double slit and single slit patterns. In principle one can estimate the probability for single slit pattern from the data.
  2. Quantum classical correspondence requires that in order that the intention to detect could be realized, one must have a physical connection from the S to both slits or at least either of them. Also charged particles assignable to the connection should be involved to make scattering of photon possible. Also entanglement entangling detector fires/does not fire with corresponding states of some other system, say the S would be needed.

How could one realize these connections in TGD?

  1. In TGD framework the magnetic flux tubes serve as correlates of entanglement and directed attention. To direct attention to a system means to connected with it by flux tubes. Flux tubes carry dark charged particles essential for TGD view about quantum biology.
  2. Every system has U-shaped flux tubes emanating from it and acting as kind of tentacles scanning the environment. As a U-shaped flux tube from system A encounters another similar flux tube from system B, a reconnection takes place if the quantized fluxes are same. The outcome is a pair of flux tubes connection A and B. The flux tube pair can carry Cooper pairs with members of the pair at the flux tubes. The photons from laser could scatter from the charged particles.
  3. The dark particles the flux tube are dark with heff/h=n satisfying an additional condition implying that n is proportional to the mass of the charged particle in turn implying that cyclotron energies Ec= hbareff eB/m are universal and assumed to correspond energies in the range of visible and UV.

    In order that photon scatters from the charged particles it must have the same value of heff as the particles at magnetic flux tubes emanating from the S. Some fraction of laser photons could satisfy this condition. Note that if perturbative quantum theory applies, the classical predictions are same as lowest order quantum predictions so that heff makes it visible only in higher orders assuming that perturbation theory works when heff/h=n holds true. Unfortunately, it is not possible to estimate the probability that photon enters to the flux tube. Note that the probability depends also on the density of the flux tubes.

The effect is reported in net experiments for which distances can be long and there is no visual contact. Can one understand this?
  1. If there quantum entanglement between A and B already exists one can increase the distance without spoiling the entanglement. But how to achieve the entanglement if n the systems are at large distance from beginning?
  2. The length of the magnetic flux tubes is not a problem. The size scale for the layers of magnetic flux tube corresponding to EEG frequency 7.8 Hz is circumference of Earth. The condition that the size of the flux tube is at least of the order of the cyclotron wavelength λ for cyclotron photons at the flux tube implies that length of the flux tube of of the order of the size scale of Earth for EEG frequencies.

    In fact, our MBs could have much larger layers if biological rhythms have cyclotron frequencies as counterparts. The size scales could be of order light-life-time or even longer. This changes totally the view about the role of length scales in biology and consciousness. There is some evidence that galactic day defines the natural rhythm for precognitive phenomena: precognitive phenomena tend to occur at galactic midday. Galactic cyclotron frequencies (the galactic magnetic field is of order nT) could correspond to bio-rhythms up to 12 hours.

In net experiment the problem is how to generate the connection to a correct target. The same problem is encountered in the attempts to explain the claimed results of remote viewing experiments. Could the density of flux tubes of personal magnetic body (MB) be so high that the connection is generated with high enough probability. S receives data through the web. Could this help to build the desired connection.
  1. Skeptic would explain the reported positive result in web experiments by saying that the results were actually induced by the intention of the experimenter who was near to the system. This might of course be the case.
  2. The first possibility is that an entanglement is generated between the camera monitoring the system and slits involving flux tubes. The communication of the image from the camera to computer builds another flux tube bridge. The radiation reflected in satellite to the computer at Earth involves propagation along flux tubes. At the receiver ends similar bridges are build. There is therefore a flux tube connection with the computer of used by S, who generates the last piece of the connection. This kind of flux tube connection would be between all communicating systems. Also the experiments would belong to this entanglement network.
  3. MB has layers with size scale of order Earth size. Could it be able to meet the challenge by using the information coming from web. Could the U-shaped flux tubes be so dense as to be able to build a contact with the experimental arrangement with high enough probability? If they are to represent Maxwellian magnetic field in good approximation, they should be dense. What is important that these flux tubes correspond do different space-time sheets for distinct observers: this is actually the basic distinction between the field concepts of Maxwell and TGD.

    Could it be that the feedback from S at her computer via the net to the computer at the other end generates quantum correlated events and this correlation has as correlates magnetic flux tubes connecting the distant systems.

  4. The hyper-imaginative option is that S can delegate the problem with collective consciousness assignable to the magnetosphere of Earth and having all the engineering knowledge that Earth has! Could we be neurons of a gigantic brain of Mother Gaia, which would help S to realize their intention. Can single neuron realize its intention on a distant neuron in brain in the similar manner? Could some kind of resonance mechanism be involved? Could MB detect correlations between distant events and generate flux tube connection and entanglement between these places? Could brain do the same for neutrons?

See the chapter TGD inspired view about remote mental interactions and paranormal.

NMP and self

The preparation of an article about number theoretic aspects of TGD forced to go through various related ideas and led to a considerable integration of the ideas. In this note ideas related directly to consciousness and cognition are discussed.

  1. Adelic approach strongly suggests the reduction of NMP to number theoretic physics somewhat like second law reduces to probability theory. The dimension of extension rationals characterizing the hierarchy level of physics and defined an observable measured in state function reductions is positive and can only increase in statistical sense. Therefore the maximal value of entanglement negentropy increases as new entangling number theoretic degrees of freedom emerge. heff/h=n identifiable as factor of Galois group of extension characterizes the number of these degrees of freedom for given space-time surfaces as number of its sheets.
  2. State function reduction is hitherto assumed to correspond always to a measurement of density matrix which can be seen as a reaction of subsystem to its environment. This makes perfect sense at space-time level. Higher level measurements occur however at the level of WCW and correspond to a localization to some sector of WCW determining for instance the quantization axes of various quantum numbers. Even the measurement of heff/h=n would measure the dimension of Galois group and force a localization to an extension with Galois group with this dimension. These measurements cannot correspond to measurements of density matrix since different WCW sectors cannot entangle by WCW locality. This finding will be discuss in the following.
1. Evolution of NMP

The view about Negentropy Maximization Principle (NMP) has co-evolved with the notion of self and I have considered many variants of NMP.

  1. The original formulation of NMP was in positive energy ontology and made same predictions as standard quantum measurement theory. The new element was that the density matrix of sub-system defines the fundamental observable and the system goes to its eigenstate in state function reduction. As found, the localizations at to WCW sectors define what might be called self-measurements and identifiable as active volitions rather than reactions.
  2. In p-adic physics one can assign with rational and even algebraic entanglement probabilities number theoretical entanglement negentropy (NEN) satisfying the same basic axioms as the ordinary Shannon entropy but having negative values and therefore having interpretation as information. The definition of p-adic negentropy (real valued) reads as Sp= -∑ Pklog(|Pk|p), where | . |p denotes p-adic norm. The news is that Np= -Sp can be positive and is positive for rational entanglement probabilities. Real entanglement entropy S is always non-negative.

    NMP would force the generation of negentropic entanglement (NE) and stabilize it. NE resources of the Universe - one might call them Akashic records- would steadily increase.

  3. A decisive step of progress was the realization is that NTU forces all states in adelic physics to have entanglement coefficients in some extension of rationals inducing finite-D extension of p-adic numbers. The same entanglement can be characterized by real entropy S and p-adic negentropies Np, which can be positive. One can define also total p-adic negentropy: N= ∑p Np for all p and total negentropy Ntot=N-S.

    For rational entanglement probabilities it is easy to demonstrate that the generalization of adelic theorem holds true: Ntot=N-S=0. NMP based on Ntot rather than N would not say anything about rational entanglement. For extensions of rationals it is easy to find that N-S>0 is possible if entanglement probabilities are of form Xi/n with |Xi|p=1 and n integer. Should one identify the total negentropy as difference Ntot=N-S or as Ntot=N?

    Irrespective of answer, large p-adic negentropy seems to force large real entropy: this nicely correlates with the paradoxical finding that living systems tend to be entropic although one would expect just the opposite: this relates in very interesting manner to the work of biologists Jeremy England \citebbio/England1. The negentropy would be cognitive negentropy and not visible for ordinary physics.

  4. The latest step in the evolution of ideas NMP was the question whether NMP follows from number theory alone just as second law follows form probability theory! This irritates theoretician's ego but is victory for theory. The dimension n of extension is positive integer and cannot but grow in statistical sense in evolution! Since one expects that the maximal value of negentropy (define as N-S) must increase with n. Negentropy must increase in long run.
2. Number theoretic entanglement can be stable

Number theoretical Shannon entropy can serve as a measure for genuine information assignable to a pair of entanglement systems. Entanglement with coefficients in the extension is always negentropic if entanglement negentropy comes from p-adic sectors only. It can be negentropic if negentropy is defined as the difference of p-adic negentropy and real entropy.

The diagonalized density matrix need not belong to the algebraic extension since the probabilities defining its diagonal elements are eigenvalues of the density matrix as roots of N:th order polynomial, which in the generic case requires n-dimensional algebraic extension of rationals. One can argue that since diagonalization is not possible, also state function reduction selecting one of the eigenstates is impossible unless a phase transition increasing the dimension of algebraic extension used occurs simultaneously. This kind of NE could give rise to cognitive entanglement.

There is also a special kind of NE, which can result if one requires that density matrix serves a universal observable in state function reduction. The outcome of reduction must be an eigen space of density matrix, which is projector to this subspace acting as identity matrix inside it. This kind NE allows all unitarily related basis as eigenstate basis (unitary transformations must belong to the algebraic extension). This kind of NE could serve as a correlate for "enlightened" states of consciousness. Schrödingers cat is in this kind of state stably in superposition of dead and alive and state basis obtained by unitary rotation from this basis is equally good. One can say that there are no discriminations in this state, and this is what is claimed about "enlightened" states too.

The vision about number theoretical evolution suggests that NMP forces the generation of NE resources as NE assignable to the "passive boundary of CD for which no changes occur during sequence of state function reductions defining self. It would define the unchanging self as negentropy resources, which could be regarded as kind of Akashic records. During the next "re-incarnation after the first reduction to opposite boundary of CD the NE associated with the reduced state would serve as new Akashic records for the time reversed self. If NMP reduces to the statistical increase of heff/h=n the consciousness information contents of the Universe increases in statistical sense. In the best possible world of SNMP it would increase steadily.

3. Does NMP reduce to number theory?

The heretic question that emerged quite recently is whether NMP is actually needed at all! Is NMP a separate principle or could NMP reduced to mere number theory? Consider first the possibility that NMP is not needed at all as a separate principle.

  1. The value of heff/h=n should increase in the evolution by the phase transitions increasing the dimension of the extension of rationals. heff/h=n has been identified as the number of sheets of some kind of covering space. The Galois group of extension acts on number theoretic discretizations of the monadic surface and the orbit defines a covering space. Suppose n is the number of sheets of this covering and thus the dimension of the Galois group for the extension of rationals or factor of it.
  2. It has been already noticed that the "big" state function reductions giving rise to death and reincarnation of self could correspond to a measurement of n=heff implied by the measurement of the extension of the rationals defining the adeles. The statistical increase of n follows automatically and implies statistical increase of maximal entanglement negentropy. Entanglement negentropy increases in statistical sense.

    The resulting world would not be the best possible one unlike for a strong form of NMP demanding that negentropy does increaes in "big" state function reductions. n also decrease temporarily and they seem to be needed. In TGD inspired model of bio-catalysis the phase transition reducing the value of n for the magnetic flux tubes connecting reacting bio-molecules allows them to find each other in the molecular soup. This would be crucial for understanding processes like DNA replication and transcription.

  3. State function reduction corresponding to the measurement of density matrix could occur to an eigenstate/eigenspace of density matrix only if the corresponding eigenvalue and eigenstate/eigenspace is expressible using numbers in the extension of rationals defining the adele considered. In the generic case these numbers belong to N-dimensional extension of the original extension. This can make the entanglement stable with respect to state the measurements of density matrix.

    A phase transition to an extension of an extension containing these coefficients would be required to make possible reduction. A step in number theoretic evolution would occur. Also an entanglement of measured state pairs with those of measuring system in containing the extension of extension would make possible the reduction. Negentropy could be reduced but higher-D extension would provide potential for more negentropic entanglement and NMP would hold true in the statistical sense.

  4. If one has higher-D eigen space of density matrix, p-adic negentropy is largest for the entire subspace and the sum of real and p-adic negentropies vanishes for all of them. For negentropy identified as total p-adic negentropy SNMP would select the entire sub-space and NMP would indeed say something explicit about negentropy.
4. Or is NMP needed as a separate principle?

Hitherto I have postulated NMP as a separate principle. Strong form of NMP (SNMP) states that Negentropy does not decrease in "big" state function reductions corresponding to death and re-incarnations of self.

One can however argue that SNMP is not realistic. SNMP would force the Universe to be the best possible one, and this does not seem to be the case. Also ethically responsible free will would be very restricted since self would be forced always to do the best deed that is increase maximally the negentropy serving as information resources of the Universe. Giving up separate NMP altogether would allow to have also "Good" and "Evil".

This forces to consider what I christened weak form of NMP (WNMP). Instead of maximal dimension corresponding to N-dimensional projector self can choose also lower-dimensional sub-spaces and 1-D sub-space corresponds to the vanishing entanglement and negentropy assumed in standard quantum measurement theory. As a matter fact, this can also lead to larger negentropy gain since negentropy depends strongly on what is the large power of p in the dimension of the resulting eigen sub-space of density matrix. This could apply also to the purely number theoretical reduction of NMP.

WNMP suggests how to understand the notions of Good and Evil. Various choices in the state function reduction would correspond to Boolean algebra, which suggests an interpretation in terms of what might be called emotional intelligence . Also it turns out that one can understand how p-adic length scale hypothesis - actually its generalization - emerges from WNMP.

  1. One can start from ordinary quantum entanglement. It corresponds to a superposition of pairs of states. Second state corresponds to the internal state of the self and second state to a state of external world or biological body of self. In negentropic quantum entanglement each is replaced with a pair of sub-spaces of state spaces of self and external world. The dimension of the sub-space depends on which pair is in question. In state function reduction one of these pairs is selected and deed is done. How to make some of these deeds good and some bad? Recall that WNMP allows only the possibility to generate NNE but does not force it. WNMP would be like God allowing the possibility to do good but not forcing good deeds.

    Self can choose any sub-space of the subspace defined by k≤ N-dimensional projector and 1-D subspace corresponds to the standard quantum measurement. For k=1 the state function reduction leads to vanishing negentropy, and separation of self and the target of the action. Negentropy does not increase in this action and self is isolated from the target: kind of price for sin.

    For the maximal dimension of this sub-space the negentropy gain is maximal. This deed would be good and by the proposed criterion NE corresponds to conscious experience with positive emotional coloring. Interestingly, there are 2k-1 possible choices, which is almost the dimension of Boolean algebra consisting of k independent bits. The excluded option corresponds to 0-dimensional sub-space - empty set in set theoretic realization of Boolean algebra. This could relate directly to fermionic oscillator operators defining basis of Boolean algebra - here Fock vacuum would be the excluded state. The deed in this sense would be a choice of how loving the attention towards system of external world is.

  2. A map of different choices of k-dimensional sub-spaces to k-fermion states is suggestive. The realization of logic in terms of emotions of different degrees of positivity would be mapped to many-fermion states - perhaps zero energy states with vanishing total fermion number. State function reductions to k-dimensional spaces would be mapped to k-fermion states: quantum jumps to quantum states!

    The problem brings in mind quantum classical correspondence in quantum measurement theory. The direction of the pointer of the measurement apparatus (in very metaphorical sense) corresponds to the outcome of state function reduction, which is now 1-D subspace. For ordinary measurement the pointer has k positions. Now it must have 2k-1 positions. To the discrete space of k pointer positions one must assign fermionic Clifford algebra of second quantized fermionic oscillator operators. The hierarchy of Planck constants and dark matter suggests the realization. Replace the pointer with its space-time k-sheeted covering and consider zero energy energy states made of pairs of k-fermion states at the sheets of the n-sheeted covering? Dark matter would be therefore necessary for cognition. The role of fermions would be to "mark" the k space-time sheets in the covering.

The cautious conclusion is that NMP as a separate principle is not necessary and follows in statistical sense from the unavoidable increase of n=heff/h identified as dimension of extension of rationals define the adeles if this extension or at least the dimension of its Galois group is observable.

See the chapter Life and Death and Consciousness.

Are all quantum jumps measurements of density matrix?

The preparation of an article about number theoretic aspects of TGD forced to go through various related ideas and led to a considerable integration of the ideas. In this note ideas related directly to consciousness and cognition are discussed.

  1. Adelic approach strongly suggests the reduction of NMP to number theoretic physics somewhat like second law reduces to probability theory. The dimension of extension rationals characterizing the hierarchy level of physics and defined an observable measured in state function reductions is positive and can only increase in statistical sense. Therefore the maximal value of entanglement negentropy increases as new entangling number theoretic degrees of freedom emerge. heff/h=n identifiable as factor of Galois group of extension characterizes the number of these degrees of freedom for given space-time surfaces as number of its sheets.
  2. State function reduction is hitherto assumed to correspond always to a measurement of density matrix which can be seen as a reaction of subsystem to its environment. This makes perfect sense at space-time level. Higher level measurements occur however at the level of WCW and correspond to a localization to some sector of WCW determining for instance the quantization axes of various quantum numbers. Even the measurement of heff/h=n would measure the dimension of Galois group and force a localization to an extension with Galois group with this dimension. These measurements cannot correspond to measurements of density matrix since different WCW sectors cannot entangle by WCW locality. This finding will be discuss in the following.
The notion of self can be seen as a generalization of the poorly defined definition of the notion of observer in quantum physics. In the following I take the role of skeptic trying to be as critical as possible.

The original definition of self was as a subsystem able to remain unentangled under state function reductions associated with subsequent quantum jumps. The density matrix was assumed to define the universal observable. Note that a density matrix, which is power series of a product of matrices representing commuting observables has in the generic case eigenstates, which are simultaneous eigenstates of all observables. Second aspect of self was assumed to be the integration of subsequent quantum jumps to coherent whole giving rise to the experienced flow of time.

The precise identification of self allowing to understand both of these aspects turned out to be difficult problem. I became aware the solution of the problem in terms of ZEO (ZEO) only rather recently (2014).

  1. Self corresponds to a sequence of quantum jumps integrating to single unit as in the original proposal, but these quantum jumps correspond to state function reductions to a fixed boundary of causal diamond CD leaving the corresponding parts of zero energy states invariant - "small" state function reductions. The parts of zero energy states at second boundary of CD change and even the position of the tip of the opposite boundary changes: one actually has wave function over positions of second boundary (CD sizes roughly) and this wave function changes. In positive energy ontology these repeated state function reductions would have no effect on the state (Zeno effect) but in TGD framework there occurs a change for the second boundary and gives rise to the experienced flow of time and its arrow and self: self is generalized Zeno effect.
  2. The first quantum jump to the opposite boundary corresponds to the act of "free will" or birth of re-incarnated self. Hence the act of "free will" changes the arrow of psychological time at some level of hierarchy of CDs. The first reduction to the opposite boundary of CD means "death" of self and "re-incarnation" of time-reversed self at opposite boundary at which the the temporal distance between the tips of CD increases in opposite direction. The sequence of selves and time reversed selves is analogous to a cosmic expansion for CD. The repeated birth and death of mental images could correspond to this sequence at the level of sub-selves.
  3. This allows to understand the relationship between subjective and geometric time and how the arrow of and flow of clock time (psychological time) emerge. The average distance between the tips of CD increases on the average as along as state function functions occur repeatedly at the fixed boundary: situation is analogous to that in diffusion. The localization of contents of conscious experience to boundary of CD gives rise to the illusion that universe is 3-dimensional. The possibility of memories made possibly by hierarchy of CDs demonstrates that this is not the case. Self is simply the sequence of state function reductions at same boundary of CD remaining fixed and the lifetime of self is the total growth of the average temporal distance between the tips of CD.
One can identify several rather abstract state function reductions selecting a sector of WCW.
  1. There are quantum measurements inducing localization in the moduli space of CDs with passive boundary and states at it fixed. In particular, a localization in the moduli characterizing the Lorentz transform of the upper tip of CD would be measured. The measured moduli characterize also the analog of symplectic form in M4 strongly suggested by twistor lift of TGD - that is the rest system (time axis) and spin quantization axes. Of course, also other kinds of reductions are possible.
  2. Also a localization to an extension of rationals defining the adeles should occur. Could the value of n=heff/h be observable? The value of n for given space-time surface at the active boundary of CD could be identified as the order of the smallest Galois group containing all Galois groups assignable to 3-surfaces at the boundary. The superposition of space-time surface would not be eigenstate of n at active boundary unless localization occurs. It is not obvious whether this is consistent with a fixe value of n at passive boundary.

    The measured value of n could be larger or smaller than the value of n at the passive boundary of CD but in statistical sense n would increase by the analogy with diffusion on half line defined by non-negative integers. The distance from the origin unavoidably increases in statistical sense. This would imply evolution as increase of maximal value of negentropy and generation of quantum coherence in increasingly longer scales.

  3. A further abstract choice corresponds to the the replacement of the roles of active and passive boundary of CD changing the arrow of clock time and correspond to a death of self and re-incarnation as time-reversed self.
Can one assume that these measurements reduce to measurements of a density matrix of either entangled system as assumed in the earlier formulation of NMP, or should one allow both options. This question actually applies to all quantum measurements and leads to a fundamental philosophical questions unavoidable in all consciousness theories.
  1. Do all measurements involve entanglement between the moduli or extensions of two CDs reduced in the measurement of the density matrix? Non-diagonal entanglement would allow final states states, which are not eigenstates of moduli or of n: this looks strange. This could also lead to an infinite regress since it seems that one must assume endless hierarchy of entangled CDs so that the reduction sequence would proceed from top to bottom. It looks natural to regard single CD as a sub-Universe.

    For instance, if a selection of quantization axis of color hypercharge and isospin (localization in the twistor space of CP2) is involved, one would have an outcome corresponding to a quantum superposition of measurements with different color quantization axis!

    Going philosophical, one can also argue, that the measurement of density matrix is only a reaction to environment and does not allow intentional free will.

  2. Can one assume that a mere localization in the moduli space or for the extension of rationals (producing an eigenstate of n) takes place for a fixed CD - a kind of self measurement possible for even unentangled system? If there is entanglement in these degrees of freedom between two systems (say CDs), it would be reduced in these self measurements but the outcome would not be an eigenstate of density matrix. An interpretation as a realization of intention would be approriate.
  3. If one allows both options, the interpretation would be that state function reduction as a measurement of density matrix is only a reaction to environment and self-measurement represents a realization of intention.
  4. Self measurements would occur at higher level say as a selection of quantization axis, localization in the moduli space of CD, or selection of extension of rationals. A possible general rule is that measurements at space-time level are reactions as measurements of density matrix whereas a selection of a sector of WCW would be an intentional action. This because formally the quantum states at the level of WCW are as modes of classical WCW spinor field single particle states. Entanglement between different sectors of WCW is not possible.
  5. If the selections of sectors of WCW at active boundary of CD commute with observables, whose eigenstates appear at passive boundary (briefly passive observables) meaning that time reversal commutes with them - they can occur repeatedly during the reduction sequence and self as a generalized Zeno effect makes sense.

    If the selections of WCW sectors at active boundary do not commute with passive observables then volition as a choice of sector of WCW must change the arrow of time. Libet's findings show that conscious choice induces neural activity for a fraction of second before the conscious choice. This would imply the correspondences "big" measurement changing the arrow of time - self-measurement at the level of WCW - intentional action and "small" measurement - measurement at space-time level - reaction.

    Self as a generalized Zeno effect makes sense only if there are active commuting with passive observables. If the passive observables form a maximal set, the new active observables commuting with them must emerge. The increase of the size of extension of rationals might generate them by expanding the state space so that self would survive only as long at it evolves. Self would die and re-incarnate when it could not generate any new observables communicating with those assignable to active boundary to be measured. From personal experience I can say that ageing is basically the loss of the ability to make new choices. When all possible choices are made, all observables are measured or self-measured, it is time to start again.

    Otherwise there would be only single unitary time evolution followed by a reduction to opposite boundary. This makes sense only if the sequence of "big" reductions for sub-selves can give rise to the time flow experienced by self: the birth and death of mental images would give rise to flow of time of self.

The overall conclusion is that the notion of WCW is necessary to understand intentional free will. One must distinguish between measurements at WCW level as localizations, which do not involved measurement of density matrix and measurements space-time level reducible to measurements of density matrix (taking the density matrix to be function of product of commuting observables one can measure all these observables simultaneously by measuring density matrix. WCW localizations correspond to intentional actions - say decision fixing quantization axis for spin and space-time reductions correspond to state function reductions at the level of matter. By reading Krishnamurti I learned that eastern philosophies make a sharp distinction between behavior as mere reactivity and behavior as intentional actions which are not reactions. Furthermore, death and reincarnation happen when self has made all choices.

For details see the chapter Negentropy Maximization Principle or the article Re-examination of the basic notions of TGD inspired theory of consciousness.

See the chapter Life and Death and Consciousness.

Adelic physics, imagination, and dark matter

An important step in the progress has been the discovery of Strong Form of Holography (SH). 2-dimensional surfaces (string world sheets and partonic 2-surfaces) are fundamental objects and 4-D physics is a kind of algebraic continuation from this intersection of reality and various p-adicities in both real and p-adic sectors of the adelic Universe. 4-D space-time surfaces are preferred extremals of Kähler action making them effectively 2-D in the sense that the 2-D surfaces serve as "space-time genes". Also the quantum states assignable to the 2-D surfaces can be algebraically continued to the entire 4-D space-time.

It is however quite possible that the continuation in the real sector to a preferred extremal of Kähler action fails. In p-adic sectors the possibility of p-adic pseudo constants, which are piecewise constant functions with vanishing derivative, makes the continuation much easier. This inspires the idea that imagination corresponds to these p-adic continuations. p-Adic continuation might be possible whereas real continuation could fail: one would have imagined world, which cannot be realized as often happens!

This argument becomes more precise as one realizes that SH is slightly broken: even information theoretically one has only effective 2-dimensionality. This means that 4-surfaces as preferred extremals are dictated by the data at string world sheets and possibly also partonic 2-surfaces and by data discrete set of points with preferred imbedding space coordinates in the extension of rationals defining the adele structure by inducing the extensions of p-adic number fields. For p-adic number fields pseudo-constants make it easy to construct the algebraic continuation to a preferred extremal containing the discretization. For reals this is possible only in special cases. These discretizations correspond to realizable imaginations.

Note that Galois group acts as symmetries in the space of space-time discretizations and under certain conditions gives rise to a space-time surface, which is a covering space with n sheets, n a factor of the order of Galois group. The identification heff/h=n is natural and reduces the hierarchy of Planck constants and dark matter to adelic physics. Ramified primes for the extension of rationals involved are preferred for extension and if the extension allows especially many realizable imaginations, it is surviver in the number theoretic fight for survival. Ramified primes for these extensions should be winners in the number theoretic evolution. Whether p-adic length scale hypothesis and its generalization follow from this conjecture, remains an open question.

See the chapter Life and Death and Consciousness.

Why metabolism is needed?

The simplest and at the same time most difficult question that innocent student can make about biology class is simple: "Why we must eat?". Or using more physics oriented language: "Why we must get metabolic energy?". The answer of the teacher might be that we do not eat to get energy but to get order. The stuff that we eat contains ordered energy: we eat order. But order in standard physics is lack of entropy, lack of disorder. Student could get nosy and argue that excretion produces the same outcome as eating but is not enough to survive.

We could go to a deeper level and ask why metabolic energy is needed in biochemistry. Suppose we do this in TGD Universe with dark matter identified as phases characterized by heff/h=n. At deeper level metabolic energy should closely relate to negentropic entanglement (NE) and thus information. Identification of these two is however not possible. I have considered several answers to the question why metabolic energy is needed. Here two answers will be discussed.

  1. Conscious information could be the basic currency and the transfer of metabolic energy and metabolites would make possible transfer of NE. Is the transfer of metabolic energy essentially transfer of NE? Could the transfer of NE require metabolic energy? NE transfer could be transfer of systems consisting of negentropically entangled parts or it could be transfer of NE with larger system, even Earth. NMP would force the systems to fight for NE and this would lead to the fight for metabolic resources. The transfer of entanglement is the basic mechanism in quantum computation and would mean in biology stealing of NE, the fundamental crime!
  2. Could metabolic energy needed to generate NE from scratch? For this option the molecules providing the metabolic energy contain dark atoms. Of course, the nutrients could already contain the negentropic entanglement and photosynthesis could serve as fundamental generator of NE. The following naive model for dark atoms obtained by replacing h with heff supports this view.
    1. The binding energy spectrum of dark hydrogen atom is scaled by 1/n2, n=heff/h (do not confuse this n with the integer n labelling the states of hydrogen atom!) so that generation of dark hydrogen atoms would require energy. Dark atoms have smaller binding energies and their creation by a phase transition increasing the value of n demands a feed of energy - metabolic energy! If the metabolic energy feed stops, n is gradually reduced. System gets tired, loses consciousness, and eventually dies. Also in case of cyclotron energies the positive cyclotron energy is proportional to $h_{eff}$ so that metabolic energy is needed to generate larger heff and prerequisites for negentropy.
    2. The analogy of weak form of NMP following from mere adelic physics makes it analogous to second law. Could one consider the purely formal generalization of dE=TdS-.. to dE= -TdN-... where E refers to metabolic energy and N refers to entanglement negentropy? No: the situation is different. The system is not closed system; N is not the negative of thermodynamical entropy S; and E is the metabolic energy feeded to the system, not the system's internal energy. dE= TdN - ... might however make sense for a system to which metabolic energy is feeded.

      The identification of N is still open: N could be identified as N= ∑pNp -S where one has sum of p-adic entanglement negentropies and real entanglement entropy S or as N = ∑pNp. For the first option one would have N=0 for rational entanglement and N>0. for extensions of rationals. Could rational entanglement be interpreted as that associated with dead matter?

    3. Bio-catalysis and ATP→ ADP$ process need not require metabolic energy. A transfer of negentropy from nutrients to ATP to acceptor molecule would be in question. Metabolic energy would be needed to reload ADP with negentropy to give ATP by using ATP synthase as a mitochondrial power plant. Metabolites could be carriers of dark atoms of this kind possibly carrying also NE. They could also carry NE associated with the dark cyclotron states as suggested earlier and in this case the value of heff=hgr would be much larger than in the case of dark atoms.

      What is remarkable that the scale of atomic binding energies decreases with n only in dimension D=3. In other dimensions it increases and in D=4 one cannot even speak of bound states! This can be easily found by a study of Schrödinger equation for the analog of hydrogen atom in various dimensions. Life based on atomic metabolism seems to make sense only in spatial dimension D=3. Note however that there are also other quantum states than atomic states with different dependence of energy on heff.

See the chapter Life and Death and Consciousness.

What happens in bio-catalysis?

Bio-catalysis is a key mechanism of biology and its extreme efficacy remains to be understood. Enzymes are proteins and ribozymes RNA sequences acting as biocatalysts.

1. Conditions on bio-catalysis

What catalysis demands?

  1. Catalyst and reactants must find each other. How this could happen is very difficult to understand in standard biochemistry in which living matter is seen as soup of biomolecules. I have already already considered the mechanisms making it possible for the reactants to find each other. For instance, in the translation of mRNA to protein tRNA molecules must find their way to mRNA at ribosome. The proposal is that reconnection allowing U-shaped magnetic flux tubes to reconnect to a pair of flux tube connecting mRNA and tRNA molecule and reduction of the value of heff=n× h inducing reduction of the length of magnetic flux tube takes care of this step. This applies also to DNA transcription and DNA replication and bio-chemical reactions in general.
  2. Catalyst must provide energy for the reactants (their number is typically two) to overcome the potential wall making the reaction rate very slow for energies around thermal energy. The TGD based model for the hydrino atom having larger binding energy than hydrogen atom claimed by Randell Mills suggests a solution . Some hydrogen atom in catalyst goes from (dark) hydrogen atom state to hydrino state (state with smaller heff/h and liberates the excess binding energy kicking the either reactant over the potential wall so that reaction can process. After the reaction the catalyst returns to the normal state and absorbs the binding energy.
  3. In the reaction volume catalyst and reactants must be guided to correct places. The simplest model of catalysis relies on lock-and-key mechanism. The generalized Chladni mechanism forcing the reactants to a two-dimensional closed nodal surface is a natural candidate to consider. There are also additional conditions. For instance, the reactants must have correct orientation. For instance, the reactants must have correct orientation and this could be forced by the interaction with the em field of ME involved with Chladni mechanism.
  4. One must have also a coherence of chemical reactions meaning that the reaction can occur in a large volume - say in different cell interiors - simultaneously. Here MB would induce the coherence by using MEs. Chladni mechanism might explain this if there is there is interference of forces caused by periodic standing waves themselves represented as pairs of MEs.
2. Phase transition reducing the value of heff/h=n as a basic step in bio-catalysis

Hydrogen atom allows also large heff/h=n variants with n>6 with the scale of energy spectrum behaving as (6/n)2 if the n=4 holds true for visible matter. The reduction of n as the flux tube contracts would reduce n and liberate binding energy, which could be used to promote the catalysis.

The notion of high energy phosphate bond is somewhat mysterious concept. There are claims that there is no such bond. I have spent considerable amount of time to ponder this problem. Could phosphate contain (dark) hydrogen atom able to go to the a state with a smaller value of heff/h and liberate the excess binding energy? Could the phosphorylation of acceptor molecule transfer this dark atom associated with the phosphate of ATP to the acceptor molecule? Could the mysterious high energy phosphate bond correspond to the dark atom state. Metabolic energy would be needed to transform ADP to ATP and would generate dark atom.

Could solar light kick atoms into dark states and in this manner store metabolic energy? Could nutrients carry these dark atoms? Could this energy be liberated as the dark atoms return to ordinary states and be used to drive protons against potential gradient through ATP synthase analogous to a turbine of a power plant transforming ADP to ATP and reproducing the dark atom and thus the "high energy phosphate bond" in ATP? Can one see metabolism as transfer of dark atoms? Could possible negentropic entanglement disappear and emerge again after ADP→ATP.

Here it is essential that the energies of the hydrogen atom depend on hbareff=n× h in as hbareffm, m=-2<0. Hydrogen atoms in dimension D have Coulomb potential behaving as 1/rD-2 from Gauss law and the Schrödinger equation predicts for D≠ 4 that the energies satisfy En∝ (heff/h)m, m=2+4/(D-4). For D=4 the formula breaks since in this case the dependence on hbar is not given by power law. m is negative only for D=3 and one has m=-2. There D=3 would be unique dimension in allowing the hydrino-like states making possible bio-catalysis and life in the proposed scenario.

It is also essential that the flux tubes are radial flux tubes in the Coulomb field of charged particle. This makes sense in many-sheeted space-time: electrons would be associated with a pair formed by flux tube and 3-D atom so that only part of electric flux would interact with the electron touching both space-time sheets. This would give the analog of Schrödinger equation in Coulomb potential restricted to the interior of the flux tube. The dimensional analysis for the 1-D Schrödinger equation with Coulomb potential would give also in this case 1/n2 dependence. Same applies to states localized to 2-D sheets with charged ion in the center. This kind of states bring in mind Rydberg states of ordinary atom with large value of n.

The condition that the dark binding energy is above the thermal energy gives a condition on the value of heff/h=n as n≤ 32. The size scale of the dark largest allowed dark atom would be about 100 nm, 10 times the thickness of the cell membrane.

See the chapter Life and Death and Consciousness.

Symplectic structure for M4, CP breaking, matter-antimatter asymmetry, and electroweak symmetry breaking

The preparation of an article about number theoretic aspects of TGD forced to go through various related ideas and led to a considerable integration of the ideas. In this note idea about the symplectic structure of M4 is discussed although it is not directly related to number theoretic aspects of TGD.

  1. Twistor lift of TGD suggests strongly a symmetry between M4 and CP2. In particular, M4 should have the analog of symplectic structure.
  2. It has been already noticed that this structure could allow to understand both CP breaking and matter-antimatter asymmetry from first principles. A further study showed that it can also allow to understand electroweak symmetry breaking.
Consider now the delicacies of this picture.
  1. Should assign also to M4 the analog of symplectic structure giving an additional contribution to the induced Kähler form? The symmetry between M4 and CP2 suggests this, and this term could be highly relevant for the understanding of the observed CP breaking and matter antimatter asymmetry. Poincare invariance is not lost since the needed moduli space for M4 Kähler forms would be the moduli space of CDs forced by ZEO in any case, and M4 Kähler form would serve as the correlate for fixing rest system and spin quantization axis in quantum measurement.
  2. Also induced spinor fields are present. The well-definedness of electro-magnetic charge for the spinor modes forces in the generic case the localization of the modes of induced spinor fields at string world sheets (and possibly to partonic 2-surfaces) at which the induced charged weak gauge fields and possibly also neutral Z0 gauge field vanish. The analogy with branes and super-symmetry force to consider two options.

    Option I: The fundamental action principle for space-time surfaces contains besides 4-D action also 2-D action assignable to string world sheets, whose topological part (magnetic flux) gives rise to a coupling term to Kähler gauge potentials assignable to the 1-D boundaries of string world sheets containing also geodesic length part. Super-symplectic symmetry demands that modified Dirac action has 1-, 2-, and 4-D parts: spinor modes would exist at both string boundaries, string world sheets, and space-time interior. A possible interpretation for the interior modes would be as generators of space-time super-symmetries.

    This option is not quite in the spirit of SH and string tension appears as an additional parameter. Also the conservation of em charge forces 2-D string world sheets carrying vanishing induced W fields and this is in conflict with the existence of 4-D spinor modes unless they satisfy the same condition. This looks strange.

    Option II: Stringy action and its fermionic counterpart are effective actions only and justified by SH. In this case there are no problems of interpretation. SH requires only that the induced spinor fields at string world sheets determine them in the interior much like the values of analytic function at curve determine it in an open set of complex plane. At the level of quantum theory the scattering amplitudes should be determined by the data at string world sheets. If induced W fields at string world sheets are vanishing, the mixing of different charge states in the interior of X4 would not make itself visible at the level of scattering amplitudes! In this case 4-D spinor modes do not define space-time super-symmetries.

    This option seems to be the only logical one. It is also simplest and means that quantum TGD would reduce to string model apart from number theoretical discretization of space-time surface bringing in dark matter as heff/h=n phases with n identifiable as factor of the order of the Galois group of extension of rationals. This would also lead to adelic physics, predict preferred extensions and identify corresponding ramified primes as preferred p-adic primes.

  3. Why the string world sheets coding for effective action should carry vanishing weak gauge fields? If M4 has the analog of Kähler structure, one can speak about Lagrangian sub-manifolds in the sense that the sum of the symplectic forms of M4 and CP2 projected to Lagrangian sub-manifold vanishes. Could the induced spinor fields for effective action be localized to generalized Lagrangian sub-manifolds? This would allow both string world sheets and 4-D space-time surfaces but SH would select 2-D Lagrangian manifolds. At the level of effective action the theory would be incredibly simple.

    Induced spinor fields at string world sheets could obey the "dynamics of avoidance" in the sense that both the induced weak gauge fields W,Z0 and induced Kähler form (to achieve this U(1) gauge potential must be sum of M4 and CP2 parts) would vanish for the regions carrying induced spinor fields. They would coupleonly to the induced em field (!) given by the vectorial R12 part of CP2 spinor curvature for D=2,4. For D=1 at boundaries of string world sheets the coupling to gauge potentials would be non-trivial since gauge potentials need not vanish there. Spinorial dynamics would be extremely simple and would conform with the vision about symmetry breaking of weak group to electromagnetic gauge group.

    The projections of canonical currents of Kähler action to string world sheets would vanish, and the projections of the 4-D modified gamma matrices would define just the induced 2-D metric. If the induced metric of space-time surface reduces to an orthogonal direct sum of string world sheet metric and metric acting in normal space, the flow defined by 4-D canonical momentum currents is parallel to string world sheet. These conditions could define the "boundary" conditions at string world sheets for SH.

To sum up, the notion M4 symplectic structure is now on rather firm basis both physically and mathematically.

See the chapter Topological Geometrodynamics: Basic Visions or the article Some questions related to the twistor lift of TGD.

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