Do you already believe in emergent gravity?

Popular writer Sabine Hossenfelder gave a highly authoritative explanation for what emergent gravity is (see this). Actually, she started by bravely expanding the notion of emergence: not only gravitation but also free will, cell, and brain emerge. You are fundamentally just a lot of fundamental particles. Get over it! I can only admire Bee's intuitive powers: not a single argument for why this would be the case was needed. Only the great (and somewhat aggressive) insight transcending over the boundaries of sciences. But why this strange emotionality about free will, life and consciousness not typical for scientist? As an outsider I can only try to guess the reasons.

The idea of emergence of gravitation is the newest fashion in the long sequence of fashions that has plagued theoretical physics during more than four decades. GUTs, supergravity, loop gravity, super string models, M-theory and its descendents, multiverse, AdS/CFT, reduction of physics to that of blackholes... Now it is fashionable to believe that Einstein was wrong: gravitation has a non-geometric origin: gravity as entropic force, emergence of gravition and 3-space and even space-time.

Verlinde argues that the origin is thermodynamical. That it cannot be became clear already for 6 years ago experimentally. I have written about this in more detail in previous blog posting. Gravitational potential appears in the Schrödinger equation of neutron: it should not if gravitational potential is a thermodynamical quantity: thermodynamical quantities should not appear in quantal equations since they are derived from the statistical predictions of quantum theory. This elementary fact was noticed by Kobakidzhe. For some funny reason, this simple observation has not got through and it is probably too late now: during next years entropic gravity will produce a lot of stuff in archives for the future sociologists of science. We are living post-truth period and theoretical physics has been the forerunner in this respect.

Bee mentions as an example about emergent gravity the model of Xiao-Gang Wen and collaborators. As usual, the model turned out to be a disappointment. Space-time emerges from space-time as it does also in other models in the best tradition of circular logic. One replaces space-time with a lattice keeping the 4-dimensionality: assigns finite-D Hilbert space at points of this 4-D lattice: essentially a discretization of quantum field theory is in question. One constructs Hamiltonian as sum of local Hamiltonians for a symmetric tensor field in such a manner that one obtains Einstein's equations in lowest order as continuum limit. Why I am not happy with this?

One of course should not have any lattice assumed to have structure of 4-D lattice. One should have no tensor fields. One should have only Hilbert space. One however starts from fields in continuous space-time, discretizes, it and makes continuous again! I have always wondered why these naive mathematically primitive tricks familiar already from loop gravity. Superstring theories were not physically correct simple because the dimension of fundamental objects was too small (1 instead of 3) and this actually led to the idea that space-time energes: either by compactication or as 3-brane or as it seems as both;-). String model was however based on refined mathematics. I can only imagine the pains suffered by Witten as he sees this intellectual degeneration of theoretical physics.

I have tried to explain that discretization occurs naturally due to the finite measurement resolution for both sensory experience and cognition. This however requires that consciousness and cognition are something which does not reduce to dynamics of particles. This leads to a notion of manifold involving naturally both discretization in terms of algebraic extensions of rationals and continuum aspects and also fusion of various number fields so that one can speak about adelic space-time - already Leibniz dreamed about this as he talked about monads. Most importanly, in this framework discretization does not lead to a loss of fundamental space-time symmetries: this is what killed loop gravity. Both the symmetries of special relativity and general coordinate invariance are exact and new infinite-dimensional symmetry algebras - in particular huge extension of conformal symmetries, are predicted.

I have also talked about emergence: very many things emerge in TGD. Elementary bosons and actually also elementary fermions emerge from induced spinor fields and topology of wormhole contact pairs. Standard model and general relativity emerge as approximation to many-sheeted space-time having most important application to biology, neuroscience, and consciousness. These are definitely not emergent for point like particles! Generalizations of the usual positive energy ontology to zero energy ontology and of quantum measurement theory are needed.

Classical gauge fields and gravitational fields at the level of single space-time sheet emerge from the dynamical geometry of space-time as a 4-D surface. The outcome is ridiculously simple: by general coordinate invariance there are only 4 fundamental field like degrees of freedom: for instance CP₂ coordinates at macroscopic limit. Gravitational field of GRT and gauge fields of standrad model emerge as the sheets of the many-sheeted space-time are lumped together and the gauge potentials and deviation of metric from Minkowski metric sum up to gauge
potentials and gravitational field of GRT.

Space-time does not however emerge! Only the conscious experience about 3-space - proprioception - emerges through tensor nets formed by magnetic flux tubes meeting at nodes defined by 3-surfaces. How rapid the progress in physics would be if colleagues could finally accept that also the conscious observer must be understood physically.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Mersenne integers and brain

I received a link to an interesting the article "Brain Computation Is Organized via Power-of-Two-Based Permutation Logic" by Kun Xie et al in Frontiers in Systems Neuroscience (see this).

The proposed model is about how brain classifies neuronal inputs and suggests that the classification is based on Boolean algebra represents as subsets of n-element set for n inputs. The following represents my attempt to understand the model of the article.

1. One can consider a situation in which one has n inputs identifiable as bits: bit could correspond to neuron firing or not. The question is however to classify various input combinations. The obvious criterion is how many bits are equal to 1 (corresponding neuron fires). The input combinations in the same class have same number of firing neurons and the number of subsets with k elements is given by the binomial coefficient B(n,k)= n!/k!(n-k)!. There are clearly n-1 different classes in the classification since no neurons firing is not a possible observation. The conceptualization would tell how many neurons fire but would not specify which of them.
   
   
2. To represent these bit combinations one needs 2ⁿ-1 neuron groups acting as unit representing one particular firing combination. These subsets with k elements would be mapped to neuron cliques with k firing neutrons. For given input individual firing neurons (k=1) would represent features, lowest level information. The n cliques with k=2 neurons would represent a more general classification of input. One obtains M_n=2ⁿ-1 combinations of firing neurons since the situations in which no neurons are firing is not counted as an input.
   
   
3. If all neurons are firing then all the however level cliques are also activated. Set theoretically the subsets of set partially ordered by the number of elements form an inclusion hierarchy, which in Boolean algebra corresponds to the hierarchy of implications in opposite direction. The clique with all neurons firing correspond to the most general statement implying all the lower level statements. At k:th level of hierarchy the statements are inconsistent so that one has B(n,k) disjoint classes.
   
   

The M_n=2ⁿ-1 (Mersenne number) labelling the algorithm is more than familiar to me.

1. For instance, electron's p-adic prime corresponds to Mersenne prime M₁₂₇ =2¹²⁷-1, the largest not completely super-astrophysical Mersenne prime for which the mass of particle would be extremely small. Hadron physics corresponds to M₁₀₇ and M₈₉ to weak bosons and possible scaled up variant of hadron physics with mass scale scaled up by a factor 512 (=2^(107-89)/2). Also Gaussian Mersennes seem to be physically important: for instance, muon and also nuclear physics corresponds to M_G,n= (1+i)ⁿ-1, n=113.
   
   
2. In biology the Mersenne prime M₇= 2⁷-1 is especially interesting. The number of statements in Boolean algebra of 7 bits is 128 and the number of statements that are consistent with given atomic statement (one bit fixed) is 2⁶= 64. This is the number of genetic codons which suggests that the letters of code represent 2 bits. As a matter of fact, the so called Combinatorial Hierarchy M(n)= M_M(n-1) consists of Mersenne primes n=3,7,127, 2¹²⁷-1 and would have an interpretation as a hierarchy of statements about statements about ... It is now known whether the hierarchy continues beyond M₁₂₇ and what it means if it does not continue. One can ask whether M₁₂₇ defines a higher level code - memetic code as I have called it - and realizable in terms of DNA codon sequences of 21 codons (see this).
   
   
3. The Gaussian Mersennes M_G,n n=151,157,163,167, can be regarded as a number theoretical miracles since the these primes are so near to each other. They correspond to p-adic length scales varying between cell membrane thickness 10 nm and cell nucleus size 2.5 μm and should be of fundamental importance in biology. I have proposed that p-adically scaled down variants of hadron physics and perhaps also weak interaction physics are associated with them.
   
   

I have made attempts to understand why Mersenne primes M_n and more generally primes near powers of 2 seem to be so important physically in TGD Universe.

1. The states formed from n fermions form a Boolean algebra with 2ⁿ elements, but one of the elements is vacuum state and could be argued to be non-realizable. Hence Mersenne number M_n=2ⁿ-1. The realization as algebra of subsets contains empty set, which is also physically non-realizable. Mersenne primes are especially interesting as sine the reduction of statements to prime nearest to M_n corresponds to the number M_n-1 of physically representable Boolean
   statements.
   
   
2. Quantum information theory suggests itself as explanation for the importance of Mersenne primes since M_n would correspond the number of physically representable Boolean statements of a Boolean algebra with n-elements. The prime p≤ M_n could represent the number of elements of Boolean algebra representable p-adically (see this).
   
   
3. In TGD Fermion Fock states basis has interpretation as elements of quantum Boolean algebra and fermionic zero energy states in ZEO expressible as superpositions of pairs of states with same net fermion numbers can be interpreted as logical implications. WCW spinor structure would define quantum Boolean logic as "square root of Kähler geometry". This Boolean algebra would be infinite-dimensional and the above classification for the abstractness of concept by the number of elements in subset would correspond to similar classification by fermion number. One could say that bosonic degrees of freedom (the geometry of 3-surfaces) represent sensory world and spinor structure (many-fermion states) represent that logical thought in quantum sense.
   
   
4. Fermion number conservation would seem to represent an obstacle but in ZEO it can circumvented since zero energy states can be superpositions of pair of states with opposite fermion number F at opposite boundaries of causal diamond (CD) in such a manner that F varies. In state function reduction however localization to single value of F is expected to happen usually. If superconductors carry coherent states of Cooper pairs, fermion number for them is ill defined and this makes sense in ZEO but not in standard ontology unless one gives up the super-selection rule that fermion number of quantum states is well-defined.
   
   

One can of course ask whether primes n defining Mersenne primes (see this) could define preferred numbers of inputs for subsystems of neurons. This would predict n=2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257,.. define favoured numbers of inputs. n=127 would correspond to memetic code.

See the article Why Mersenne Primes Are So Special? or the chapter Unified Number Theoretical Vision of "Physics as Generalized Number Theory".

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Does the presence of cosmological constant term make Kähler coupling strength a genuine coupling constant classically?

The addition of the volume term to Kähler action has very nice interpretation as a generalization of equations of motion for a world-line extended to a 4-D space-time surface. The field equations generalize in the same manner for 3-D light-like surfaces at which the signature of the induced metric changes from Minkowskian to Euclidian, for 2-D string world sheets, and for their 1-D boundaries defining world lines at the light-like 3-surfaces. For 3-D light-like surfaces the volume term is absent. Either light-like 3-surface is freely choosable in which case one would have Kac-Moody symmetry as gauge symmetry or that the extremal property for Chern-Simons term fixes the gauge.

The known non-vacuum extremals are minimal surface extremals of Kähler action and it might well be that the preferred extremal property realizing SH quite generally demands this. The addition of the volume term could however make Kähler coupling strength a manifest coupling parameter also classically when the phases of Λ and α_K are same. Therefore quantum criticality for Λ and α_K would have a precise local meaning also classically in the interior of space-time surface. The equations of motion for a world line of U(1) charged particle would generalize to field equations for a "world line" of 3-D extended particle.

This is an attractive idea consistent with standard wisdom but one can invent strong objections against it in TGD framework.

1. All known non-vacuum extremals of Kähler action are minimal surfaces and the minimal surface vacuum extremals of Kähler action become non-vacuum extremals. This suggest that preferred extremals are minimal surface extremals of Kähler action so that the two dynamics apparently decouple. Minimal surface extremals are analogs for geodesics in the case of point-like particles: one might say that one has only gravitational interaction. This conforms with SH stating that gauge interactions at boundaries (orbits of partonic 2-surfaces and 2-surfaces at the ends of CD) correspond classically to the gravitational dynamics in the space-time interior.
   

   Note that at the boundaries of the string world sheets at light-like 3-surfaces the situation is different: one has equations of motion for geodesic line coupled to induce Kähler gauge potential and gauge coupling indeed appears classically as one might expect! For string world sheets one has only the topological magnetic flux term and minimal surface equation in string world sheet. Magnetic flux term gives the Kähler coupling at the boundary.
   
   

2. Decoupling would allow to realize number theoretical universality since the field equations would not depend on coupling parameters at all. It is very difficult to imagine how the solutions could be expressible in terms of rational functions with coefficients in algebraic extension of rationals unless α_K and Λ have very special relationship. If they have different phases, minimal surface extremals of Kähler action are automatically implied. If the values of α_K correspond to complex zeros of Riemann ζ, also Λ should have same complex phase, in order to have genuine classical coupling. This looks somewhat un-natural but cannot be excluded.
   

   The most natural option is that Λ is real and α_K corresponds to zeros of zeta. For trivial zeros the phases are different and decoupling occurs. For trivial zeros Λ and α_K differ by imaginary unit so that again decoupling occurs.
   
   

3. One can argue that the decoupling makes it impossible to understand coupling constant evolution. This is not the case. The point is that the classical charges assignable to super-symplectic algebra are sums over contributions from Kähler action and volume term and therefore depend on the coupling parameters. Their vanishing conditions for sub-algebra and its commutator with entire algebra give boundary conditions on preferred extremals so that coupling constant evolution creeps in classically!
   

   The condition that the eigenvalues of fermionic charge operators are equal to the classical charges brings in the dependence of quantum charges on coupling parameters. Since the elements of scattering matrix are expected to involve as building bricks the matrix elements of super-symplectic algebra and Kac-Moody algebra of isometry charges, one expectes that discrete coupling constant evolution creeps in also quantally via the boundary conditions for preferred extremals.
   
   

Although the above arguments seem to kill the idea that the dynamics of Kähler action and volume term could couple in space-time interior, one can compare this view (Option II) with the view based on complete decoupling (Option I).

1. For Option I the coupling between the two dynamics could be induced just by the condition that the space-time surface becomes an analog of geodesic line by arranging its interior so that the U(1) force vanishes! This would generalize Chladni mechanism! The interaction would be present but be based on going to the nodal surfaces! Also the dynamics of string world sheets is similar: if the string sheets carry vanishing W boson classical fields, em charge is well-defined and conserved. One would also avoid the problems produced by large coupling constant between the two-dynamics present already at the classical level. At quantum level the fixed point property of quantum critical couplings would be the counterparts for decoupling.
   
   
2. For Option II the coupling is of conventional form. When cosmological constant is small as in the scale of the known Universe, the dynamics of Kähler action is perturbed only very slightly by the volume term. The alternative view is that minimal surface equation has a very large perturbation proportional to the inverse of Λ so that the dynamics of Kähler action could serve as a controller of the dynamics defined by the volume term providing a small push or pull now and then. Could this sensitivity relate to quantum criticality and to the view about morphogenesis relying on Chladni mechanism in which field patterns control the dynamics with charged flux tubes ending up to the nodal surfaces of (Kähler) electric field (see this)? Magnetic flux tubes containing dark matter would in turn control and serve as template for the dynamics of ordinary matter.
   
   

Could the possible coupling of the two dynamics suggest any ideas about the values of α_K and Λ at quantum criticality besides the expectation that cosmological constant is proportional to an inverse of p-adic prime?

1. Number theoretic vision suggests the existence of preferred extremals represented by rational functions with rational or algebraic coefficients in preferred coordinates. For Option I one has preferred extremals of Kähler action which are minimal surfaces so that there is no coupling and no constraints on the ratio of couplings emerges: even better, both dynamics are independent of the coupling. All known non-vacuum extremals of Kähler action are indeed also minimal surfaces. For Option II the ratio of the coefficients Λ/8π G and 1/4πα_K should be rational or at most algebraic number. One must be however very cautious here: the minimal option allowed by strong form of holography is that the rational functions of proposed kind emerge only at the level of partonic 2-surfaces and string world sheets.
   
   
2. I have proposed that that the inverse of Kähler coupling strength has spectrum coming as zeros of zeta or their imaginary parts (see this). The phases of complexified 1/α_K and Λ/2G must be same in order to avoid the decoupling of Kähler action and minimal surface term implying minimal surface extremals of Kähler action.
   

   This conjecture is consistent with the rational function property only if α_K and vacuum energy density ρ_vac appearing as the coefficient of volume term are proportional to the same possibly transcendental number with proportionality coefficient being an algebraic or rational number.
   

   If the phases are not identical (say Λ is real and one allows complex zeros) one has Option I and effective decoupling occurs. The coupling (Option2)) can occur for the trivial zeros of zeta if the volume term has coefficient iΛ/8πG rather than Λ/8π G to guarantee same phase as for 1/4πα_K. The coefficient iΛ/8πG would give in Minkowskian regions large real exponent of volume and this looks strange. In this case also number theoretical universality might make sense but SH would be broken in the sense that the space-time surfaces would not be analogous to geodesic lines.
   
   

3. At quantum level number theoretical universality requires that the exponent of the total action defining vacuum functional reduces to the product of roots of unity and exponent of integer existing in finite-dimensional extension of p-adic numbers. This would suggest that total action reduces to a number of form q₁+iq₂π, q_i rational number, so that its exponent is of the required form. Whether this can conform with the properties of zeros of zeta and properties of extremals is not clear.
   
   

ZEO suggests deep connections with the basic phenomenology of particle physics, quantum consciousness theory, and quantum biology and one can look the situation for both these options.

1. Option I: Decoupling of the dynamics of Kähler action and volume term in space-time interior for all values of coupling parameters.
   
2. Option II: Coupling of dynamics for trivial zeros of zeta and Λ→ iΛ.
   

Particle physics perspective

Consider a typical particle physics experiment. There are incoming and outgoing free particles moving along geodesics, these particles interact, and emanate as free particles from the interaction volume. This phenomenological picture does not follow from quantum field theory but is put in by hand, in particular the idea about interaction couplings becoming non-zero is involved. Also the role of the observer remains poorly understood.

The motion of incoming and outgoing particles is analogous to free motion along geodesic lines with particles generalized to 3-D extended objects. For both options these would correspond to the preferred extremals in the complement of CD within larger CD representing observer or measurement instrument. Decoupling would take place. In the interaction volume interactions are "coupled on" and particles interact inside the volume characterized by causal diamond (CD). What could be the TGD view translation of this picture?

1. For Option I one would still have decoupling and the interpretation would be in terms of twistor picture in which
   one always has also in the internal lines on mass shell particles but with complex four-momenta. In TGD framework the momenta would be always complex due to the contribution of Euclidian regions defining the lines of generalized scattering diagrams. As explained coupling constant evolution can be understood also in this case and also classical dynamics depends on coupling parameters via the boundary conditions. The transitory period (control action) leading to the decoupled situation would be replaced by state function reduction, possibly to the opposite boundary.
   
   
2. For Option II the transitory period would correspond to the coupling between the two classical dynamics and would take place inside CD after a phase transition identifiable as "big state function reduction" to time reversed mode. The problem is that in the interacting phase α_K would not have a value approximately equal to the U(1) coupling strength of weak interactions (see this) so that the physical picture breaks down.
   
   

Quantum measurement theory in ZEO.

1. For Option I state preparation and state function reduction would be in symmetric role. Also now there would be inherent asymmetry between zero energy states and their time reversals. With respect to observer the time reversed period would be invisible.
   
   
2. For Option II state preparation for CD would correspond to a phase transition to a time reversed phase labelled by a trivial zero of zeta and Λ→ iΛ. In state function reduction to the original boundary of CD a phase transition to a phase labelled by non-trivial zero of zeta would occur and final state of free particles would emerge. The phase transitions would thus mean hopping from the critical line of zeta to the real axis and back and change the values of α_K and possibly Λ. There would be strong breaking in time reversal symmetry.
   

   One cannot of course take this large asymmetry as an adhoc assumption: it should be induced by the presence of larger CD, which could also affect quite generally the values of α_K and Λ (having also a spectrum of values).
   
   

TGD inspired theory of consciousness

What happens within sub-CD could be fundamental for the understanding of directed attention and sensory-motor cycle.

1. The target of directed attention would correspond to the volume of CD - call it c - within larger CD - call it C representing the observer - attendee having c as part of its perceptive field. c would serve as a target of directed attention of C and thus define part of the perceptive field of c. c would correspond also to sub-self giving rise to a mental image of C. This would also allow to understand why the attention is directed rather than being completely symmetric with respect to C and c. For both options directed attention would correspond to sub-self c interpreted as mental image. There would be no difference.
   
   
2. Quite generally, the self and time-reversed self could be seen as sensory input and motor response (Libet's findings). Directed attention would define the sensory input and sub-self could react to it by dying and re-incarnating as time-reversed subself. The two selves would correspond to sensory input and motor action following it as a reaction. Motor reaction would be sensory mental image in reversed time direction experienced by time reversed self. Only the description for the reaction would differ for the two options.
   

   The motor action would be time-reversed sensory perception for Option I. For Option II motor action would correspond
   to a different phase in which Kähler action and volume term couple classically.
   

TGD inspired quantum biology

The free geodesic line dynamics with vanishing U(1) Kähler force indeed brings in mind the proposed generalization of Chladni mechanism generating nodal surfaces at which charged magnetic flux tubes are driven (see this).

1. For Option I the interiors of all space-time surfaces would be analogous to nodal surfaces and state function reductions would correspond to transition periods between different nodal surfaces. The decoupling would be dynamics of avoidance and could highly analogous to Chladni mechanism.
   
   
2. For Option II the phase labelled by trivial zeros of zeta would correspond to period during which nodal surfaces are formed. This view about state function reduction and preparation as phase transitions in ZEO would provide classical description for the transition to the phase without direct interactions.
   
   

To sum up, it seems that the complete decoupling of the two dynamics (Option I) is favored by both SH, realization of preferred extremal property (perhaps as minimal surface extremals of Kähler action, number theoretical universality, discrete coupling constant evolution, and generalization of Chladni mechanism to a dynamics of avoidance.

For background see the new chapter How the hierarchy of Planck constants might relate to the almost vacuum degeneracy for twistor lift of TGD? of "Towards M-matrix" or the article with the same title.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

More precise interpretation of gravitational Planck constant

The notion of gravitational Planck constant h_gr=GMm/v₀ was introduced originally by Nottale. In TGD it was interpreted in terms of astrophysical quantum coherence. The interpretation was that h_gr characterizes a gravitational flux tube connecting masses M and m and v₀ is a velocity parameter - some characteristic velocity assignable to the system.

It has become clear that a more precise formulation of the rather loose ideas about how gravitational interaction is mediated by flux tubes is needed.

1. The assumption treats the two masses asymmetrically.
   
   
2. A huge number of flux tubes is needed since every particle pair M-m would involve a flux tube. It would be also difficult to understand the fact that one can think the total gravitational interaction in Newtonian framework as sum over interactions with the composite particles of M. In principle M can be decomposed into parts in many manners - elementary particles and their composites and larger structures formed from them: there must be some subtle difference between these different compositions - all need not be possible - not seen in Newtonian and GRT space-time but maybe having representation in many-sheeted space-time and involving h_gr.
   
   
3. Flux tube picture in the original form seems to lead to problems with the basic properties of the gravitational interaction: namely superposition of gravitational fields and absence or at least smallness of screening by masses between M and m. One should assume that the ends of the flux tubes associated with the pair pair M-m move as m moves with respect to M. This looks too complex.
   

   Linear superposition and absence of screening can be understood in the picture in which particles form topological sum contacts with the flux tubes mediating gravitational interaction. This picture is used to deduce QFT-GRT limit of TGD. Note that also other space-time sheets can mediate the interaction and pairs of MEs and flux tubes emanating from M but not ending to m are one possible option. In the following I however talk about flux tubes.
   
   

These problems find a solution if h_gr characterizes the magnetic body (MB) of a particle with mass m topologically condensed to a flux tube carrying total flux M. m can also correspond to a mass larger than elementary particle mass. This makes the situation completely symmetric with respect to M and m. The essential point is that the interaction takes place via touching of MB of m with flux tubes from M.

1. In accordance with the fractality of the many-sheeted space-time, the elementary particle fluxes from a larger mass M can combine to a sum of fluxes corresponding to masses M_i<M with ∑ M_i=M at larger flux tubes with hbar_gr=GMM_i/v_0,i> hbar. This can take place in many manners, and in many-sheeted space-time gives rise to different physical situations.
   

   Due to the large value of h_gr it is possible to have macroscopic quantum phases at these sheets with a universal gravitational Compton length L_gr= GM_im/v₀. Here m can be also a mass larger than elementary particle mass. In fact, the convergence of perturbation theory indeed makes the macroscopic quantum phases possible. This picture holds true also for the other interactions. Clearly, many-sheeted space-time brings in something new, and there are excellent reasons to believe that this new relates to the emergence of complexity - say via many-sheeted tensor networks (see this).
   
   

2. Quantum criticality would occur near the boundaries of the regions from which flux runs through wormhole contacts from smaller to larger flux sheets and would be thus associated with boundaries defined by the throats of wormhole contacts at which the induced metric changes from Minkowskian to Euclidian.
   
   
3. This picture implies that fountain effect - one of the applications of large h_gr phase is a kind of antigravity effect for dark matter - maybe even for non-microscopic masses m - since the larger size of MB implies larger average distance from the source of the gravitational flux and the experienced gravitational field is weaker. This might have technological applications some day.
   
   

This picture is a considerable improvement but there are still problems to ponder. In particular, one should understand why the integer n= h_eff/h= h_gr/h interpreted as a number of sheets of the singular covering space of MB of m emerges topologically. The large value of h_gr implies a huge number of sheets.

Could the flux sheet covering associated with M_i code the value of M_i using as unit Planck mass as the number of sheets of this covering? One would have N=M/M_Pl sheeted structure with each sheet carrying Planckian flux. The fluxes experienced by the MB of m in turn would consist of sheets carrying fusion n_m= M_Plv₀/m Planckian fluxes so that the total number of sheets would be reduced to n= N/n_m= GMm/v₀ sheets.

Why this kind of fusion of Planck fluxes to larger fluxes should happen? Could quantum information theory provide clues here? And why v₀ is involved?

For background see the chapter Criticality and dark matter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy".

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

About interactions of selves and their time reversals (and few words about ghosts)

I have been thinking about the time-reversed zero energy states and corresponding conscious entities predicted by Zero Energy Ontology (ZEO). I find that forcing myself to even write about this is difficult. The fear is that the whole nice scenario falls down by predicting something totally absurd. I however force myself to make the questions. What could these ghostly time-reversed entities be? Do they interact with those with standard time orientation? How could they do so?

In ZEO self corresponds to a generalized Zeno effect that is sequence of state function reductions leaving the passive boundary of CD unaffected as also the members of state pairs associated with 3-surfaces at it. At active boundary the members of state pairs change and the active boundary drifts reduction by reduction farther away from passive boundary. The temporal distance between the tips of CD increases gradually and corresponds to the experience about flow of time.

Negentropy Maximization Principle (NMP) forces eventually self to die by making the first reduction to the passive boundary of its causal diamond (CD), which now becomes the active boundary: a new time reversed self is born. This option is forced because it produces more negentropy. For this self the arrow of geometric time would be opposite since now the formerly passive boundary would be active and shift in opposite direction of time: in this manner CD would steadily increase in size.

Also the time-reversed self would eventually die and make the first reduction to the opposite - the original - boundary of CD. The position of the boundary of active boundary in first reduction would be shifted to the geometric future from the original position. The first and - as will be found - probably wrong guess for the size of shift towards geometric future from the position at the moment of previous death would be as the average increase of the temporal distance between tips of CD during Zeno period. This increment could be rather small as compared to the size of CD itself.

This picture raises questions.

1. Do we make this kind jump to time-reverse life at some level of our personal self hierarchy as we fall sleep? If wake-up period corresponds to re-incarnation in the original time direction, time increment of CD from its previous value would be the duration of sleeping period as seen by a larger conscious system. This is much longer than the subjective chronon for sensory mental images about .1 seconds.
   

   Remark: Note that EEG splits to pieces of duration about 300 ms as found by Fingelkurz brothers (see this) and it might be possible to identify in EEG periods, which correspond to mental images and their time reversals. These periods could differ by a phase conjugation although the power spectrum would have the same typical behavior (sound wave and its phase conjugate have same power spectrum but we can distinguish sound and its time-reversal from each other).
   

   Could the first big reduction correspond to a time increment, which is of the same order of magnitude as the total time duration of life-cycle of the time-reversed self? The size of 3-surfaces at the boundary of time-reversed CD has increased by about life-time. Could the first reduction to the opposite boundary increase the size of the 3-surface at this boundary by the same amount? If so, the re-incarnations for human life cycles would take roughly life-time after the death.
   

   Could one identify negative energy time reversed signal as time-reversed self at some level of hierarchy? If so
   then the selves associated with CDs could gradually increase their energy by dying and re-incarnating repeatedly since the opposite boundary would increase also the magnitude of the negative energy at the opposite boundary. This is in principle possible since conservation laws hold true by the very definition of zero energy states as well as for classical time evolutions appearing in their quantum superposition. The average energy for a given member of pair defining zero energy state would increase gradually. The size of the CD associated with re-incarnating self could become arbitrary large and gain an arbitrary high total energy: the wildest speculation is that cosmologies correspond to very large selves (see this).
   
   

2. Could selves/systems living in opposite directions of time have direct interactions? If the vision that motor actions are realized as negative energy signals travelling to brain of the geometric past and induce neural activity fraction of second earlier than the conscious decision was made (Libet's finding), this could be the case. Motor action could correspond to a death of sensory self, reincarnation as time-reversed motor-self, and a re-incarnation as sensory self in time scale of .1 seconds. Sensory-motor cycle would correspond to a sequence of re-incarnations as time reversed sub-self.
   
   
3. How the time reversed selves could reveal themselves? If their presence can be indeed detected, a key signature would be the opposite direction of the thermodynamical arrow of time for them. Heat would be apparently transferred in wrong direction: from cold to hot. This kind of apparent breakings of second law have been observed: phase conjugate laser waves and acoustic signals represent examples of this. Fantappie suggested that they occur routinely in living matter and introduce the notion of syntropy as time reverse counterpart of entropy. The strange cooling of the air at magnetic walls associated with the rotating magnetic systems (see this) provides second example.
   
   
4. Good music is claimed to send cold shivers in spine and sensations of cold are assigned also with the perception of ghosts. Could the claims about encounters of ghosts be due to a perception of time reversed selves? I remember that in my personal great experience for three decades ago the entire body went into a state analogous to that created by a good music. Did I interact with a time reversed conscious entity? My experience indeed was that I was in contact with what I called Great Mind. This is of course just a subjective experience and the skeptic scientist knows that I was in a psychotic state since it is completely obvious from my scientific work even without reading it that I am a madman;-).
   
   

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Weight change for electrets and "weight of soul"

Also the weight of electrets have been found to change as the Research Gate conference article or Schreiber and Tajmar reports (see this). They refer also to other works reporting anomalous looking weight changes. Recall that electrets are systems possessing spontaneous electric polarization and therefore analogous to magnets. Electret property allows to transform electric signals to mechanical and vice versa. Living systems are full of electrets.

Electrets were produced from organic materials (organic origin might be relevant) by a procedure described in the article beginning with melting at temperature 120 degrees Celsius to a molten state followed by an application of an external high voltage (10 kV) electrostatic field forcing the microscopic electric dipoles to orient in parallel leading to complete solidification until room temperature was reached.

Fig. 3 describes the schematic model for the resulting electret containing parallel electric dipoles and free positive and negative charges. The polarization of the electret its not completely stable and can change or disappear. There are two kinds of free charges near the ends of the electret: the region near negative pole contains more positive than negative charges and the region near positive pole more negative than positive charges. There are two kinds of charges known as heterocharges and homocharges and these charges have different relaxation times. Therefore the relaxation can lead to change of the polarization voltage and even of its direction.

Two kinds of measurement were performed. Both the resulting polarization of electret and its weight were measured in the first experiment (see Fig. 7 of this). The voltage for these electrets changed after half an hour: the voltage dropped first from 3 kV to about 2.82 kV and then suddenly jumped to 3.425 kV. The weight showed after an initial fluctuation period a sharp increase to a saturation value taking place after 5.5 hour so that there was 5 hour lag. For an unpolarized electret the weight was found to increase steadily (see Figure 9 of this). The overall change of the weight during 20 hours was Δ g/g∼ 2× 10^-4 in both measurements.

The change of the electric field of the polarized electret was accompanied by an increase of weight followed by a fluctuating period with vanishing average weight increase followed by a sudden increase after 5 hours followed by steady increase. The overall change in both cases was about Δ g/g∼ 2× 10^-4. Maybe the behavior of polarized electret could be seen as that of a depolarized electret perturbed by the change in the value of polarization. There was 5 hour lag before the sudden change in Δ g/g: as if the steady weight increase occurring for electret with no polarization had been prevented by the change of the polarization and transformed to a fluctuation lasting for about 5 hours before returning to nearly normal value.

The challenge is to understand the cause of weight increase and why it was affected by the change in polarization.
The models for the weight change of a rotating magnetic system and for the weight change induced by the presence of light-box suggests that the continual feed of dark photons transformed to ordinary photons was involved. One can consider two options in this framework: the electret sends negative energy dark photons to some system below the electret able to receive them or the source system located above the electret sends positive energy dark photons to the electret.

1. Since the electret system consists of organic material one might think that it could still be able to regenerate a connection to its magnetic body carrying magnetic field - say the endogenous magnetic field B_end=.2 Gauss. Perhaps the transformation to electret returned the ability to regenerate this connection by generating an ordered phase of dipoles: could one say that the external field "revived the organic material.
   
   
2. The magnetic body located above the system send dark positive energy photons to the electret in which they are partially transformed to ordinary photons. B_end can have flux tubes also below the Earth's surface and the electret could get energy by remote metabolism by sending negative energy dark photons downwards constantly. This would give rise to a increase of the effective weight.
   
   

What other models can one imagine?

1. One can also imagine that dark mass of order Δ m/m∼ 2× 10^-4 flows from magnetic body to the system and transforms to ordinary matter.
   
   
2. I have already earlier encountered the number 2× 10^-4 assigned with endogenous magnetic field B_E=.2 Gauss . The proposed interpretation was that the flux tubes of B_end correspond to gravitational flux tubes for dark mass M_D∼ 2× 10^-4 M_E . Could one think that the revived system regenerates gravitational flux tube connections to this mass and experiences the gravitational field generated by it?
   

   The arguments used however strongly suggest that M_D must reside at the distance of Moon at a spherical layer: this conforms with the vision about how the condensation of visible matter around dark matter creates the astrophysical objects. In Newton's theory however the net gravitational force should be very small at the surface of Earth since different contributions to the force would interfere. M_D should reside considerably below the surface of Earth for this model to make sense.
   

   Flux tube picture distinguish between TGD and Newton's theory could however save the situation: the gravitational flux would arrive along flux tubes through wormhole contacts below the surface of Earth and then spread out radially and give an additional contribution to the Earth's gravitational field and cause the weight increase. This explanation does not apply to rotating magnetic systems nor to the change of weight due to light.
   

   The objection is that the system cannot just decouple from the flux tubes. Also the conservation of gravitational flux which could correspond basically to the conservation of Kähler magnetic monopole flux prevents this.
   
   

3. The third option is that the mass of electret has also dark contribution coming perhaps from its own personal MB - its "soul"! MB as intentional agent indeed behaves in many respect like "soul". This is just what I have proposed many years ago: as the ageing biological body gets uninteresting, MB finds more interesting target of attention. In this case death would mean the loss of MB and also loss of weight Δ m/m≈ 2× 10^-4. Also Earth could have magnetic body and it could indeed correspond to the dark mass at distance of Moon if the ratio M_D/M is universal.
   

   Also Earth could have MB and it could indeed correspond to the dark mass at distance of Moon. Could the flux tubes from Earth carrying monopole flux go at this distance to another space-time sheet through wormhole contacts carrying quantum numbers of dark matter particles at their throats and return near Earth's core, where they would return to the original space-time sheet and turn back to form a loop? Could these loops be just elementary particles with h_eff=h_gr?
   

An interesting test is to see what happens as organism dies: is it weight changed - reduced - as these experiments would suggest? For a weight of 100 kg the weight reduction would be 20 g if one can extrapolate from the above measurements. Amusingly, the "weight of soul" has been measured and - believe or not - the average result is 21 g (see this! Of course, one can invent many explanations for the weight change and also challenge its occurrence, and skeptics of course ridiculize the idea about detecting the possible weight change because some-one has uttered the word "soul" in this context.

For details see the article The anomalies in rotating magnetic systems as a key to the understanding of morphogenesis?

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Could the presence of light affect weight?

We had an intense Facebook discussion yesterday with Ulla, Joseph, and Sebastian on rotating magnetic systems and some-one gave a link to a very interesting experiment in which light arrives horizontally in a box and is reflected there in forth and back in a 6-layered structure (see this). It is reported that the presence of light-box reduces the gravitational force on an object above the box and increases it for an object below the light-box.

Could TGD explanation be similar to that as for the reduction of weight of rotating system in Godin-Roschin experiment? This might be the case although the reduction of weight is fraction of order .1 per cent and much smaller than the maximal reduction of 35 per cent in G&R experiment. This could be understood if dark photons with energies scale up by a factor h_eff/h=n= h_gr result as a small leakage from ordinary photons or vice versa. In G&R experiments the beam of photons arriving the system is dark.

In the intense FB discussion I misunderstood the system: laser light is not used and it seems that the photons travelling back and forth in the light-box can have almost arbitrary direction due to the repeated reflections. I hope that I understand correctly at this time. I must admit that could not fully understand the illustration of the light-box. Anyone with better visual skills is well-come to help!

The next trial to explain the effect led to a strange conclusion: the momentum direction for the dark photons exchanged between the light-box and test mass must be opposite to the momentum. This violates Quantum Classical Correspondence (QCC) , which is basic principle of TGD. In the light-hearted brainstorming mood I was ready to accept this but soon realized that this won't go. After that it was easy to see that Zero Energy Ontology (ZEO) solves this problem. This however leads to a dramatically new manner to interpret gravitation and also other interactions. This interpretation is however not in conflict with existing physics although it would conform with the vision of Sheldrake.

Consider first how gravitational force by dark gravitons giving rise to momentum exchange along the flux tubes connecting the test mass to Earth could work.

1. The weight gets momentum increments Δp assignable to gravitons with some rate and this gives rise to net momentum transfer rate dp/dt defining gravitational force. Reaction law holds in the sense that mass gets a momentum increment Δp when a momentum -Δp travels along flux tube to Earth getting opposite momentum increment. Note that the direction of Δp is opposite to the direction of travel of graviton
   in positive energy ontology! Also the energy of the graviton is negative.
   
   
2. This does not conform with the classical expectation about (virtual) gravitons as a localized wave packets. Momentum increment -Δp can be said to travel in direction of Δp rather that in its own direction as one might expect!
   
   

How could one cure this problem?

1. Should one give up QCC although it is basic principle of TGD? Could one argue that gravitation is quantum macroscopic interaction - something totally different from say entropic gravity - and one must speak of non-localized waves of momentum Δp in the scale of the entire system even in astrophysical situations so that classical intuition fails. This is what TGD indeed predicts via h_eff/h=n= h_gr hypothesis.
   
   
2. Or should one replace positive energy ontology with ZEO and interpret the momentum exchange as taking place in reverse time direction. ZEO could allow to achieve this correspondence in terms of remote metabolism in which test mass sends negative energy dark gravitons travelling in reversed direction of geometric time to a system able to absorb them and gains positive energy as a recoil.
   

   Test mass would send to the geometric negative energy dark gravitons with momentum -Δp (this momentum is directed upwards to the light box getting positive energy gain and downwards direct Δp as a recoil. The QCC would not be lost because of time reversal. Since the virtual graviton propagates backwards in time, QCC is true: situation is PT reversal of a positive energy dark graviton with momentum Δp propagating in its own direction.
   
   

3. Are planets then primitive conscious entities soaking up gravitational energy from Sun?! From this there is not a long way to the idea that living organisms on Earth soak up energy from Sun also a dark photons. All physical systems are trying to steal energy from each other! One can safely give up the belief that Nature is somehow innocent. This sounds a pre-Keplerian idea but in ZEO it need not be inconsistent with basic laws of physics. This picture conforms with the views of Sheldrake about learning and morphogenesis.
   
   

Consider now the experiment in this picture. What would happen as one adds light-box below the test mass?

1. This picture about gravitational force as remote metabolism generalizes to the recent case by replacing negative energy dark gravitons with negative energy dark photons. Test mass would be a primitive living system and would gradually learn to utilize light-box as an energy source using remote metabolism. This would conform with the observation that it takes time for the effect to emerge.
   
   
2. Test mass would send negative energy dark photons along gravitational flux tubes and some fraction of them would be absorbed by the light-box as they transform to negative energy bio-photons with some rate - at least if quantum criticality in some sense is realized: in what sense remains an open question. Does quantum criticality develop during the time needed for the effect to emerge. Certainly the fact that the photons in the light-box have energies in the range covered by bio-photon energies matters.
   
   
3. If negative energy dark photons have Δ p parallel to the direction of motion with reversed arrow of time, Δ p is directed downwards and the effective weight increases if the box is below the test mass. If the box is above the test mass the effective weight is reduced. This is what has been reported in the article. From the size of the reduction of mass about 1 per cent one in principle could get idea about the rate for the transformation of dark photons to ordinary visible photons.
   
   
4. A related TGD inspired suggestion is that topological light rays (MEs) parallel to the magnetic flux tubes mediating the gravitational interaction are generated and dark photons can be assigned to them. The fundamental property of MEs is that pulses can propagate only in single direction and this could relate closely to the sign of the force. Dark photon Bose-Einstein condensate propagating in single direction is generated as photons from the light-box transform to dark bosons. For given ME all dark photons must be collinear just like the classical pulses inside ME propagate only in single direction. The direction would be towards the test mass and opposite to the direction of momentum exchange involved to make the interaction attractive. Also now the TGD analogs of standing waves might be involved and would correspond to pairs of "plane wave" MEs such that the sums of their em fields are standing waves.
   
   
5. What is interesting that this model could also explain the well-known fluctuations in the value of gravitational constant measurements (see this and this ). Also Sheldrake has noticed the variation (see this).
   

   The largest variation is about one percent from the average value, and there is evidence that the measured value varies periodically with a period of one sidereal day (galaxy as rest system). This suggests that the test mass soaks energy from the flux tubes of galactic magnetic field: I have indeed proposed that they mediate the gravitational interaction of Earth (the local geometric entanglement of galactic flux tubes could be essential for the formation of various biological or even more general material structures). The effectiveness of soaking could depend on the angle characterizing the orientation of the gravitational flux tubes with respect to the line connecting Earth to Galactic center varying in the range [0,π]. The effectiveness could also depend on the position of Earth at its orbit around Sun giving annual variation: could the local density of the galactic flux tubes have periodic variation? There are also other interesting appearances of sidereal day and year in living matter (see this).
   

   The long measurement times should tend to affect the measured value of the gravitational constant G. One should arrange the instruments so that the are not below or above the test mass.
   

One can criticize the idea.

1. Skeptic of course argues that the assumption about all matter having some aspects assigned to living systems
   is worst kind of pseudo-science that they have ever met and that now these quantum crackpots try to bring physics back to pre-Keplerian times. ZEO is however completely consistent with basic laws of classical physics and quantum physics. The fact is that TGD predicts that dark matter as a key aspect of what it is to be living. Adelization of physics means that cognition is present in all scales - already in elementary particle length scales as the success of p-adic mass calculations suggests. TGD also predicts hierarchy of conscious entities. Also skeptics explain all our activities in terms of conscious choices. Maybe also skeptics should finally accept free will as a fact and try to explain it scientifically. The consolating news for skeptics is that in ZEO one can indeed assign to consciousness causal powers without ending up with conflict with the laws of physics.
   
   
2. Physicalist would argue that one can just assume that light-box has additional attractive interaction with test mass analogous to gravitational interaction. This interaction should be electromagnetic, certainly not the extremely weak gravitational interaction. Coulomb attraction is probably not in question. The interaction energy for this interaction should increase as the distance between test mass and light-box decreases to give attractive force as gradient of interaction energy - just as in the case of gravitation. If this picture is correct, one should be able to express this interaction in more familiar terms.
   
   

For details see the new chapter The anomalies in rotating magnetic systems as a key to the understanding of morphogenesis? of "TGD and fringe physics" or the article with the same title.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

The anomalies in rotating magnetic systems as a key to the understanding of morphogenesis?

During almost two decades I have returned repeatedly to the fascinating but unfortunately un-recognized work of Roschin and Godin about rotating magnetic systems. With the recent advances in TGD it has become clear that the reported strange effects such as the change of weight proportional to the rotation velocity of rollers taking place above 3.3 Hz rotation frequency and rapid acceleration above 9.2 Hz up to frequency 10 Hz could provide clues for developing a general vision about morphogenesis of magnetic body, whose flux quanta can carry Bose-Einstein condensates of dark charged ions with given mass and charge if the hypothesis h_eff=n× h=h_gr identifying dark matter as phases with non-standard value of Planck constant holds true.

At this time my friend Samuli Pentikäainen re-stimulated my interest by sending some links to the files describing the patent of Godin and Roschin. We had a nice brain storming about the system, which eventually inspired the preparation of this article to clarify my recent views about the system. One can find from web a brief description of the rotating magnetic system (see this) and the english translation of the patent (see (see this). I am grateful for Samppa for these links and interesting discussions.

The generalization of Chladni mechanism would provide a general model for how magnetic flux tubes carrying charged particles with given mass at given flux tube drift to the nodal surfaces giving rise to magnetic walls in the field of standing or even propagating waves assignable to "topological light rays" (MEs). Ordinary matter would in turn condense around these dark magnetic structures so that Chladni mechanism would serve as a general mechanism of morphogenesis. This mechanism could be universal and work even in astrophysical systems (formation of planets).

The change of weight correlating with the direction of rotation (parity breaking) and rapid acceleration could be understood in terms of momentum and angular momentum transfer by dark photons liberated in the quantum phase transition of many-particle states of dark charged particles to from cyclotron Bose-Einstein condensates giving rise to analogs of superconductivity and spontaneous magnetization.

For details see the article The anomalies in rotating magnetic systems as a key to the understanding of morphogenesis?

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Emergent gravity and dark Universe

Eric Verlinde has published article with title Emergent Gravity and the Dark Universe > (see this). The article represents his recent view about gravitational force as thermodynamical force described earlier and suggests an explanation for the constant velocity spectrum of distant stars around galaxies and for the recently reported correlation between the real acceleration of distant stars with corresponding acceleration caused by baryonic matter. In the following I discuss Verlinde's argument and compare the physical picture with that provided by TGD. I have already earlier discussed Verlinde's entropic gravity from TGD view point (see this). The basic observation is that Verlinde introduces long range quantum entanglement appearing even in cosmological scales: in TGD framework the hierarchy of Planck constants does this in much more explicit manner and has been part of TGD for more than decade. It is nice to see that the basic ideas of TGD are gradually popping up in literature.

Before continuing it is good to recall the basic argument against the identification of gravity as entropic force. As Kobakidzhe notices neutron diffraction experiments suggests that gravitational potential appears in the Schrödinger equation. This cannot be the case if gravitational potential has thermodynamic origin and therefore follows from statistical predictions of quantum theory: to my opinion Verlinde mixes apples with oranges.

Verlinden's argument

Consider now Verlinde's recent argument.

1. Verlinde wants to explain the recent empirical finding that the observed correlation between the acceleration of distant stars around galaxy with that of baryonic matter (see this) in terms of apparent dark energy assigned with entanglement entropy proportional to volume rather than horizon area as in Bekenstein-Hawking formula. This means giving up the standard holography and introducing entropy proportional to volume.
   

   To achieve this he replaces anti-de-Sitter space (AdS) with de-Sitter space(dS) space with cosmic horizon expressible in terms of Hubble constant and assign it with long range entanglement since in AdS only short range entanglement is believed to be present (area law). This would give rise to an additional entropy proportional to volume rather than area. Dark energy or matter would corresponds to a thermal energy assignable to this long range entanglement.
   
   

2. Besides this Verlinde introduces tensor nets as justification for the emergence of gravitation: this is just a belief. All arguments that I have seen about this are circular (one introduces 2-D surfaces and thus also 3-space from beginning) and also Verlinde uses dS space. What is to my opinion alarming that there is no fundamental approach really explaining how space-time and gravity emerges. Emergence of space-time should lead also to the emergence of spinor structure of space-time and this seems to me something impossible if one really starts from mere Hilbert space.
   
   
3. Verlinde introduces also analogy with the thermodynamics of glass involving both short range crystal structure and amorphous long range behaviour that would correspond to entanglement entropy in long scales long range structure. Also analogy with elasticity is introduced. Below Hubble scale the microscopic states do not thermalize below the horizon and display memory effects. Dark gravitational force would be analogous to elastic response due to what he calls entropy displacement.
   
   
4. Verlinde admits that this approach does not say much about cosmology or cosmic expansion, and even less about inflation.
   
   

The long range correlations of Verlinde correspond to hierarchy of Planck constants in TGD framework

The physical picture has analogies with my own approach (see this) to the explanation of the correlation between baryonic acceleration with observed acceleration of distant stars. In particular, long range entanglement has the ieentification of dark matter in terms of phases labelled by the hierarchy of Planck constants as TGD counterpart.

1. Concerning the emergence of space and gravitation TGD leads to a different view. It is not 3-space but the experience about 3-space - proprioception -, which would emerge via tensor nets realized in TGD in terms of magnetic flux tubes emerging from 3-surfaces defining the nodes of the tensor net (see this) . This picture leads to a rather attractive view about quantum biology (see for instance this).
   
   
2. Twistor lift of TGD has rapidly become a physically convincing formulation of TGD (see this). One replaces space-time surfaces in M⁴× CP₂ with the 12-D product T(M⁴× CP₂) of the twistor spaces T(M⁴) and T(CP₂) and Kähler action with its 6-D variant.
   

   This requires that T(M⁴) and T(CP₂) have Kähler structure. This is true but only for M⁴ (and its variants E⁴ and S⁴) and CP₂. Hence TGD is completely unique also mathematically and physically (providing a unique explanation for the standard model symmetries). The preferred extremal property for Kähler action could reduce to the property that the 6-D surface as an extremal of 6-D Kähler action is twistor space of space-time surface and thus has the structure of S² bundle. That this is indeed the case for the preferred extremals of dimensionally reduced 4-D action expressible as a sum of Kähler action and volume term remains to be rigorously proven.
   
   

3. Long range entanglement even in cosmic scales would be crucial and give the volume term in entropy breaking the holography in the usual sense. In TGD framework hierarchy of Planck constants h_eff=n× h satisfying the additional condition h_eff=h_gr, where h_gr=GMm/v₀ (M and m are masses and v₀ is a parameter with dimensions of velocity) is the gravitational Planck constant introduced originally by Nottale , and assignable to magnetic flux tubes mediating gravitational interaction makes. This makes possible quantum entanglement even in astrophysical and cosmological long length scales since h_gr can be extremely large. In TGD however most of the the galactic dark matter and energy is associated with cosmic strings having galaxies along it (like pearls in necklace). Baryonic dark matter could correspond to the ordinary matter which has resulted in the decay of cosmic strings taking the role of inflaton field in very early cosmology. This gives automatically a logarithmic potential giving rise to constant spectrum velocity spectrum modified slightly by baryonic matter and a nice explanation for the correlation, which served as the motivation of Verlinde.
   
   
4. Also glass analogy has TGD counterpart. Kähler action has 4-D spin glass degeneracy giving rise to 4-D spin-glass degeneracy. In twistor lift of TGD cosmological term appears and reduces the degeneracy by allowing only minimal surfaces rather than all vacuum extremals. This removes the non-determinism. Cosmological constant is however extremely small implying non-perturbative behavior in the sense that the volume term for the action is extremely small and depends very weakly on preferred extremal. This suggests that spin glass in 3-D sense remains as Kähler action with varying sign is added.
   
   
5. The mere Kähler action for the Minkowskian (at least) regions of the preferred extremals reduces to a Chern-Simons terms at light-like 3-surfaces at which the signature of the induced metric of the space-time surface changes from Minkowskian to Euclidian. The interpretation could be that TGD is almost topological quantum field theory. Also the interpretation in terms of holography can be considered.
   

   Volume term proportional to cosmological constant given by the twistorial lift of TGD (see this) could mean a small breaking of holography in the sense that it cannot be reduced to a 3-D surface term. One must be however very cautious here because TGD strongly suggests strong form of holography meaning that data at string world sheets and partonic 2-surfaces (or possibly at their metrically 2-D light-like orbits for which only conformal equivalence class matters) fix the 4-D dynamics.
   

   Volume term means a slight breaking of the flatness of the 3-space in cosmology since 3-D curvature scalar cannot vanish for Robertson-Walker cosmology imbeddable as a minimal surface except at the limit of infinitely large causal diamond (CD) implying that cosmological constant, which is proportional to the inverse of the p-adic length scale squared, vanishes at this limit. Note that the dependence Λ∝ 1/p, p p-adic prime, allows to solve the problem caused by the large value of cosmological constant in very early cosmology. Quite generally, volume term would describe finite volume effects analogous to those encountered in thermodynamics.
   

The argument against gravitation as entropic force can be circumvented in zero energy ontology

Could TGD allow to resolve the basic objection against gravitation as entropic force or generalize this notion?

1. In Zero Energy Ontology quantum theory can be interpreted as "complex square root of thermodynamics". Vacuum functional is an exponent of the action determining preferred extremals - Kähler action plus volume term present for twistor lift. This brings in gravitational constant G and cosmological Λ constant as fundamental constants besides CP₂ size scale R and Kähler coupling strength α_K (see this). Vacuum functional would be analogous to an exponent of E_c/2, where E_c is complexified energy. I have also considered the possibility that vacuum functional is analogous to the exponent of free energy but following argument favors the interpretation as exponent of energy.
   
   
2. The variation of Kähler action would give rise to the analog of TdS term and the variation of cosmological constant term to the analog of -pdV term in dE= TdS- pdV. Both T and p would be complex and would receive contributions from both Minkowskian and Euclidian regions. The contributions of Minkowskian and Euclidian regions to the action would differ by a multiplication with imaginary unit and it is possible that Kähler coupling strength is complex as suggested in (see this).
   

   If the inverse of the Kähler coupling is strength is proportional to the zero of Riemann zeta at critical line, it is complex and the coefficient of volume term must have the same phase: otherwise space-time surfaces are extremals of Kähler action and minimal surfaces simultaneously. In fact, the known non-vacuum extremals of Kähler action are surfaces of this kind, and one cannot exclude the possibility that preferred extremals have quite generally this property.
   
   

3. Suppose that both terms in the action are proportional to the same phase factor. The part of the variation of the Kähler action with respect to the imbedding space coordinates giving the analog of TdS term would give the analog of entropic force. Since the variation of the entire action vanishes this contribution would be equal to the negative of the variation of the volume term with respect to the induced metric given by -pdV. Since the variations of Kähler action and volume term cancel each other, the entropic force would be non-vanishing only for the extremals for which Kähler action density is non-vanishing. The variation of Kähler action contains variation with respect to the induced metric and induced Kähler form so that the sum of gravitational and U(1) force would be equal to the analog of entropic force and Verlinde's proposal would not generalize as such.
   

   The variation of the volume term gives rise to a term proportional to the trace of the second fundamental form, which is 4-D generalization of ordinary force and vanishes for the vacuum extremals of Kähler action in which case one has analog of geodesic line. More generally, Kähler action gives rise to the generalization of U(1) force so that the field equations give a 4-D generalization of equations of motion for a point like particle in U(1) force having also interpretation as a generalization of entropic force.
   
   

4. There however an objection against this picture. All known extremals of Kähler action are minimal surfaces and there are excellent number theoretical arguments suggesting that all preferred extremals of Kähler action are also minimal surfaces so that the original picture would be surprisingly near to the truth. The separate vanishing of variation implies that the solutions do not depend at all on coupling parameters as suggested by number theoretical universality and universality of the dynamics at quantum criticality. The discrete coupling constant evolution makes it however visible via boundary conditions classically. This would however predicts that the analogs to TdS and pdV vanish identically in space-time interior.
   

   The variations however involve also boundary terms, which need not vanish separately since the actions in Euclidian and Minkowskian regions differ by multiplication with (-1)^1/2! The variations reduce to terms proportional to the normal component of the canonical momentum current contracted with the deformation at light-like 3-surfaces bounding Euclidian and Minkowskian space-time regions. These must vanish. If Kähler coupling strength is real, this implies decoupling of the dynamics due to the volume term and Kähler action also at light-like 3-surfaces and therefore also exchange of charges - in particular four-momentum - becomes impossible. This would be a catastrophe.
   

   If α_K is complex as quantum TGD as a square root of thermodynamics and the proposal that the spectrum of 1/α_K corresponds to the spectrum of zeros of zeta require, the normal component of the canonical momentum current for Kähler action equals to that for the volume term at the other side of the bounding surface. The analog of dE=TdS-pdV=0 would hold true in the non-trivial sense at light-like 3-surfaces and thermodynamical analogy holds true (note that energy is replaced with action). The reduction of variations to boundary terms would also conform with holography. Strong form of holography would even suggest that the 3-D boundary term in turn reduces to 2-D boundary terms.
   

   A possible problem is caused by the variation of volume term: g₄^1/2 vanishes at the boundary and gⁿⁿ diverges. The overall result should be finite and should be achieved by proper boundary conditions. What I have called weak form of electric-magnetic duality allows to avoid similar problems for Kähler action, and implies self-duality of the induced Kähler form at the boundary. A weaker form of boundary conditions would state that the sum of the variations of Kähler action and volume term is finite.
   
   

Physically this picture is very attractive and makes cosmological constant term emerging from the twistorial lift rather compelling. What is nice that this picture follows from the field equations of TGD rather than from mere heuristic arguments without underlying mathematical theory.

See the article Emergent gravity and dark Universe or the chapter TGD and GRT of "Physics in Many-Sheeted Space-time".

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Muon surplus in high energy cosmic ray showers as an indication for new hadron physics

According to the article "Viewpoint: Cosmic-Ray Showers Reveal Muon Mystery in APS Physics (see this) Pierre Auger Observatory reports that there is 30 per cent muon surplus in cosmic rays at ultrahigh energy around 10¹⁹ eV (see this). These events are at the knee of cosmic ray energy distribution: at higher energies the flux of cosmic rays should be reduced due to the loss of energy with cosmic microwave background. There are actually indications that this does not take place but this is not the point now. This article tells about how these showers are detected and also provides a simple model for the showers.

This energy is estimated in the rest system of Earth and corresponds to the energy of 130 TeV in cm mass system for a collision with nucleon. This is roughly 10 times the cm energy of 14 TeV at LHC. The shower produced by the cosmic ray is a cascade in which high energy cosmic ray gradually loses its energy via hadron production. The muons are relatively low energy muons resulting in hadronic decays, mostly pion decays, since most of the energy ends up to charged pions producing muons and electrons and neutral pions decaying rapidly to gamma pairs. The electron-positron pairs produced in the electromagnetic showers from neutral pions mask the electrons produced in neutral pion decay to electrons so that the possible surplus can be detected only for muons.

Since cosmic rays are mostly protons and nuclei the primary collisions should involve a primary collision of cosmic ray particle with a nucleon of atmosphere. The anomalously large muon yield suggests an anomalous yield of proton-antiproton pairs produced in the first few collisions. Protons and antiprotons would then collide with nuclei of atmosphere and lose their energy and give rise to anomalously large number of pions and eventually muons.

Unless the models for the production (constrained by LHC data) underestimate muon yield, new physics is required to explain the source of proton-antiproton pairs is needed.

In TGD framework one can consider two scaled up variants of hadron physics as candidates for the new physics.

1. The first candidate corresponds to M₈₉ hadron physics for which hadron masses would be obtained by a scaling with factor 512 from the masses of ordinary hadrons characterized by Mersenne prime M₁₀₇= 2¹⁰⁷-1. There are several bumps bumps identifiable as pseudo-scalar mesons with predicted masses also some bumps identifiable as some scaled up vector mesons (see this). Also the unexpected properties of what was expected to be quark gluon plasma suggest M₈₉ hadron physics. In particular, the evidence for string like states suggests M₈₉ mesons. If the situation is quantum critical, M₈₉ have scaled up Compton length. The natural guess is that it corresponds to the size of ordinary hadrons.
   

   The proton of M₈₉(=2⁸⁹-1) hadron physics would have mass of 512 GeV so that the production of M₈₉ hadrons could take place at energies, which for ordinary hadrons would correspond to 260 GeV meaning that perturbative M₈₉ QCD could be used. The quarks of this hadron physics would hadronize either directly to ordinary M₁₀₇ or to M₈₉ hadrons. In both cases a phase transition like process would lead from M₈₉ hadrons or to M₁₀₇ hadrons and produce a surplus of protons and antiprotons whose collisions with the nuclei of atmosphere would produce a surplus of pions.
   
   

2. One can also consider M₇₉ hadron physics, where M_G,79 corresponds to Gaussian Mersenne (1+i)⁷⁹-1. The mass scale would be 32 times higher than that for M₈₉ hadron physics and correspond to 8 GeV for ordinary hadron collisions. Also now perturbative QCD would apply.
   
   

One can argue that M₈₉ or M_G,79 hadron physics comes in play for collisions with small enough impact parameter and gives an additive contribution to the total rate of protons and antiproton production. The additional contribution would be of the same order of magnitude as that from M₁₀₇ hadron physics.

Could quantum criticality play some role now?

1. What is the situation is quantum critical with h_eff/h>1? The first naive guess is that at the level of tree diagrams corresponding to classical theory the production rate has has no dependence on Planck constant so that nothing happens. A less naive guess is that something similar to that possibly taking place at LHC and RHIC happens. Quantum critical collisions in which protons just pass by each other could yield dark pseudo-scalar mesons.
   
   
2. If quantum criticality corresponds to peripheral collisions, the rate for pseudo-scalar production would be large unlike for central collisions. The instanton action determined to a high degree by anomaly considerations would be determined the rate of production for pseudo-scalar mesons. Vector boson dominance would allow to estimate the rate for the production of vector bosons. Peripherality could make the observation of these collisions difficult: especially so if the peripheral collisions are rejected because they are not expected to involve strong interactions and be therefore uninteresting. This might explain the disappearance of 750 GeV bump.
   
   
3. Suppose that quantum criticality for peripheral collisions at LHC and RHIC enters into game above the mass scale of M₈₉ pion with mass about 65 m_p∼ 65 GeV and leads to creation of M₈₉ mesons. By a simple scaling argument the same would happen in the case of M_G,79 hadron physics above 65 m_p(89)= 3.3 × 10⁴ TeV to be compared with the collision energy of ultrahigh energy cosmic rays about 13× 10⁴ TeV.
   
   

See the article M₈₉ Hadron Physics and Quantum Criticality or the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic Physics".

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Induction coils in many-sheeted space-time

I have been trying to concretize many-sheeted space-time by thinking what simple systems involving electric and magnetic fields would look like in many-sheeted space-time. The challenge is highly non-trivial since the basic difference between Maxwell's theory and TGD is that allows extremely limited repertoire of preferred extremals and there is no linear superposition.

1. By general coordinate invariance only 4 field like variables (say CP₂ coordinates) are possible meaning that all classical fields identified as induced fields are expressible in terms of only four field like variables at at given sheet. This has several implications.
   

   The classical field equations determining the space-time surface theory is extremely non-linear although they have simple interpretation as expression for local conservation laws of Poincare charges and color charges. Linear superposition of Maxwell's equations is lost.
   

   Only for so called topological light rays ("massless extremals"), MEs) the linear superposition holds true but in extremely limited sense: for the analogous of plane waves travelling in either direction along ME. One has pulses of arbitrary shape preserving their shape and propagating in single direction only with maximal signal velocity.
   
   

2. Strong form of holography (SH) implies that 2-dimensional data at string world sheets and partonic 2-surfaces fix the space-time surfaces. 2-D data include also the tangent spaces of partonic 2-surfaces so that the situation is only effectively 2-D and TGD does not reduce to any kind of string model.
   

   It is possible that the light-like 3-surfaces defining parton orbits as the boundaries of Minkowskian and Euclidian space-time regions possess dynamical degrees of freedom as conformal equivalence classes. Kac-Moody type transformations trivial at the ends of partonic orbit at boundaries of causal diamond (CD) would generate physically equivalent partonic orbits. There would be n conformal equivalence classes, where n would correspond to the value of Planck constant h_eff=n× h. At the ends of orbit all these n sheets of the singular covering would co-incide. Possible additional degrees of freedom making partonic 2-surfaces somewhat 3-D would be therefore discrete and make possible dark matter in TGD sense.
   
   

What is clear that single space-time sheet is very simple entity, and one can assign to it only extremely limited set of say solutions of Maxwell's equations. More complex solutions must correspond to many-sheeted space-time surfaces approximated as slightly curved pieces of Minkowski space at the GRT-QFT limit of TGD.

This limit is discovered by noticing that a test particle touches all sheets of the space-time surface in a given region of Minkowski space - they are extremely near to each other. Test particle experiences sums for the induced gauge potentials and gravitational fields defined is deviations of the induced metric from flat Minkowski metric. These sums corresponds naturally to the gauge potentials and gravitational fields assignable to the GRT-QFT limit. One obtains GRT plus standard model.

The challenge is to look whether one can indeed construct typical Maxwellian field configurations as sums of electromagnetic gauge potentials represented as induced gauge potentials at various sheets. The simplest configurations would be realizable using only two sheets.

I have already considered the realization of standing waves not possible as single sheeted structures as ≥ 2-sheeted structures carrying the analogs of sinusoidal waves (see this).

1. The proposal is that magnetic bodies (MBs) use this kind of standing wave patters to generate biological structures: charged biomolecules would end up the nodal surfaces of the standing wave and become stationary structures. Of course, also time varying nodes are possible.
   
   
2. MB could use the MEs parallel to flux tubes connected to a given node of tensor network to generate biological structures at the node. Note that the interference patter would be completely analogous to that of a hologram but allowing more than two waves. As a matter of fact, I considered a vision about living systems as conscious holograms for decades ago (see this) but was not able to invent a concrete model at that time. This Chladni mechanism - as one might call it - could be a general mechanism of morphogenesis and morphostasis.
   
   

Second challenge - raised by discussions with my friend Samppa - is provided by the field patterns of an inductance coil with AC current flowing around the boundary of cylinder.

1. The current is typically AC current. Oscillating magnetic field has direction parallel or opposite to the cylinder and electric field field lines rotate around the cylinder. That the geometry of field pattern is this is easy to understand by looking just the general form of the solutions of the Maxwell's equations in question.
   
   
2. What is essential is that one has standing wave type field pattern meaning that the fields at all points of the cylinder oscillates in the same phase. The temporal and spatial dependences of the magnetic field separate into product of sinusoidal function and spatial function, which in the simplest situation is constant. One might even regard the standing wave property as a signal of quantum coherence.
   
   

Could one use MEs as building bricks to construct the field pattern associated with the coil?

1. MEs define an extremely general set of (hopefully preferred) extremals of Kähler action. Basic type of ME corresponds to cylindrical regions inside which pulses propagate in the same direction along the cylinder. It is also possible to have waves propagating radially: either inwards or outwards. The ansatz for ME is following. Restrict the consideration to a geodecic sphere S² of CP₂, assume that S² coordinates (Θ,Φ) have dependence [sin(Θ)=sin(ω (t+/- ρ),Φ=nφ ], where [ρ,φ] are cylindrical radial and angle coordinates. The resulting magnetic field is in z-direction and the lines of the electric field rotate around the cylinder. The sum of these fields is a standing wave in radial direction representing just right kind of magnetic and electric fields.
   
   
2. What is amusing that the field experienced by the test particle would be expressible as sum of the two modes of TGD counterpart of radiation field. If the AC frequency is 50 Hz, the period of radial cylindrical wave characterized by wave vector k=ω (c=1) is of order wave length λ=2π/k, which is of order 10⁷ meters, order of magnitude of Earth radius! Hence the longitudinal magnetic field is essentially constant for the coils encountered in practical situation.
   
   
3. The boundary of the cylinder carries the AC current. The description of this current is a further challenge to TGD
   and will not be considered here.
   
   

One can of course have more general currents generating much more general waves, not necessary standing waves.

1. The general recipe would be simple. These fields can be expressed as a Fourier decomposition of simple sinusoidal field patters. Assign to each sinusoidal field pattern a space-time sheet in the proposed manner so that superposition for modes is replaced with union of space-time surfaces.
   
   
2. The more terms in the Fourier expansion, the larger the number of sheets for the many-sheeted space-time is. The number of space-time sheets gives a measure for the complexity of the system. For instance, a current with form of square pulse is an interesting challenge. Should one approximate the square pulse as a superposition of space-time sheets of its Fourier components?
   
   

See the chapter TGD Based View about Classical Fields in Relation to Consciousness Theory and Quantum Biology of "TGD and EEG".

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.