OPERA provides additional support for neutrino superluminality

OPERA collaboration has just posted an eprint Measurement of the neutrino velocity with the OPERA detector in the CNGS beam providing further support for the claim that neutrinos move faster than photons. Tommaso Dorigo describes the improved measurements in this blog. I have also discussed in an earlier posting the basic new results reported in OPERA preprint (the rumor was correct at this time!). I attach the abstract of the article.

The OPERA neutrino experiment at the underground Gran Sasso Laboratory has measured the velocity of neutrinos from the CERN CNGS beam over a baseline of about 730 km with much higher accuracy than previous studies conducted with accelerator neutrinos. The measurement is based on high-statistics data taken by OPERA in the years 2009, 2010 and 2011. Dedicated upgrades of the CNGS timing system and of the OPERA detector, as well as a high precision geodesy campaign for the measurement of the neutrino baseline, allowed reaching comparable systematic and statistical accuracies. An early arrival time of CNGS muon neutrinos with respect to the one computed assuming the speed of light in vacuum of (57.8 +/- 7.8 (stat.)+8.3-5.9 (sys.)) ns was measured. This anomaly corresponds to a relative difference of the muon neutrino velocity with respect to the speed of light (v-c)/c = (2.37+/- 0.32 (stat.) (sys.)) ×10-5. The above result, obtained by comparing the time distributions of neutrino interactions and of protons hitting the CNGS target in 10.5 μs long extractions, was confirmed by a test performed using a beam with a short-bunch time-structure allowing to measure the neutrino time of flight at the single interaction level.

The new finding is that there is a jitter in arrival times: the arrival times vary within 50 ms range which corresponds to a distance about 15 m. The shortening of travel times is not however not less than 40 ns from that when neutrinos move with light velocity as the this figure that can be found from the posting of Phil Gibbs demonstrates. Is the determination of the arrival time inaccurate? Or does the neutrino velocity have values above minimum velocity larger than c?

1. In TGD framework this could mean that the space-time sheet along which neutrino arrives would vary from neutrino to neutrino. The simplest possibility is that its length varies and velocity is constant: this does not look totally implausible.

2. Also the state of neutrino inside space-time sheet could vary from neutrino to neutrino. Classical long ranged Z⁰ fields are one of the basic predictions of TGD and in the earlier posting I proposed that neutrino feels classical Z⁰ magnetic field and arrives along cyclotron orbit. This would give a discrete spectrum of arrival velocities as

   v= c_#/(1+ n×hbar× Q_Z(ν)g_ZB_Z/m_ν)^1/2

   with n=0,1,2,... For some value of n the velocity would become sub-luminal. If hbar is large enough, the discrete spectrum could be seen in the arrival times. This spectrum does not however look an attractive explanation for the jitter for which spectrum seems to be above minimum value rather than below maximum value.

As I have explained, TGD explanation is unique in that it requires no tachyons and thus no breaking of causality. The solution is not any ad hoc proposal to explain one particular anomaly but one of the many outcomes of a theory solving a deep conceptual problem plaguing general relativity due to the loss of Poincare invariance. TGD fuses the good aspects of special and general relativities and leads to a unification of fundamental interactions. The basically new thing is the notion sub-manifold gravity: basic principles of special and general relativities remain as such. If effective neutrino super-luminality is real - as it seems to be- it will mean to TGD what Mickelson-Morley meant for special relativity.

TGD based explanation of effective neutrino super-luminality is discussed in the article Are neutrinos super-luminal?.

P.S. There are reasons to suspect that the mightmare of any scientific dissident could be realized. US government could block websites from public and knowing the situation in Big Science it is easy to guess that scientific dissidents like me having also non-standard views about market economy would belong to the first victims. You can prevent this.

Algebraic knots and generalized Feynman diagrams

Witten has been working with knots- also 2-knots - recently (for the latest popular lecture see this) and I think that his interest on these objects is not purely mathematical. Braids are central also for quantum TGD and quite recently I learned about what are called algebraic knots and braids and realized that they might provide a new mathematical building block allowing to sharpen the vision about generalized Feynman diagrams resulting as via the fusion of ordinary Feynman diagrams and braid diagrams.

This strenghens the hopes (or raises the fears?) that a collective concentrated effort could soon transform TGD from art to a mechanical calculation recipes. In the following I tell how braid theory a la TGD differs from standard braid theory, discuss briefly the notion of algebraic knots, and summarize the interpretation of generalized Feynman diagrams as a generalized braid diagrams.

How braid theory in TGD Universe differs from the standard theory?

In TGD framework knots and braids associated with preferred 3-surfaces and possibly also 2-knots and 2-braids defined by string world sheets having braids at their ends appear naturally. This because space-time dimension is D=4. Standard braid theory must be modified to sub-manifold braid theory. Braids reside at 3-surfaces with varying topologies and knot projection must be performed to a preferred 2-surface of M⁴× CP₂. To preferred Minkowski plane M² or sphere S² at light-cone boundary.

What this means from the point of view of braid theory? A typical new situation is the one in which 3-surface is locally a product of higher genus 2-surface and R so that knot strand can wind around the 2-surface: M-theorist would talk about wrapping of branes. This gives rise to what is called non-planar braid diagrams for which projection to plane produces non-standard crossings. How to cope with this kind of situation?

Algebraic knots

The answer to the question emerged as Ulla sent me a link to an article telling about algebraic knots. The introduction of the self intersection of knot - virtual crossing - besides the usual crossing below or above can be applied to non-planar braids appearing in sub-manifold braid theory. Virtual crossing combined with the algebraization of the basic moves for braids leads to completely new and very general mathematical concepts such as kei, quandle, rack, and biquandle applying also to other mathematical structures. The basic algebraic operation is a representation of the "result for x going under y". One example is group endowed with the product a*b= bⁿab^-n for n some integer. The interesting thing is that rack is aset for which the multiplication acts as automorphism. In quantum TGD completely analogous situation occurs: zero energy states define infinitesimal symmetries of S-matrix appearing as building block of M-matrices defining zero energy states.

I see bi-quandle applying to oriented knots as the most interesting structure. It is defined as operation mapping a pair of strand portions before crossing to a pair of strand portions after crossing and satisfying also set theoretic version of Yang-Baxter equation with tensor product replaced with Cartesian product. Note that Cartesian is the classical physics correlate for tensor product used to construct many particle states in quantum physics.

Why I find algebraic knots so interesting?

Why I regard algebraic knots and braids and related mathematical structures as highly interesting notions?

1. All generalized Feynman diagrams are reduced to sub-manifold braid diagrams at microscopic level by bosonic emergence (bosons as pairs of fermionic wormhole throats). Three-vertices appear only for entire braids and are purely topological whereas braid strands carrying quantum numbers are just re-distributed in vertices. No 3-vertices at the really microscopic level! This is an additional nail to the coffin of divergences in TGD Universe.

2. By projecting the braid strands of generalized Feynman diagrams to preferred plane M², one obtains a unified description of non-planar Feynman diagrams and braid diagrams (note that for Feynman diagrams the intersections have purely combinatorial origin coming from representations as 2-D diagrams: for braid diagrams intersections have different origin and non-planarity has different meaning). The necessity to choose preferred plane M² looks strange from QFT point of view but is in TGD forced by the number theoretic vision in which M² represents hyper-complex plane of sub-space of hyper-octonions which is subspace of complexified octonions. It is also forced by the condition that the choice of quantization axes has a geometric correlate both at the level of imbedding space geometry and the geometry of the "world of classical worlds".

3. The obvious conjecture is that Feynman amplitudes are a analogous to knot invariants constructible by gradually reducing non-planar Feynman diagrams to planar ones after which the already existing twistor theoretical machinery of N=4 SYMs would apply (for this conjecture see the earlier posting).

These ideas are not ready to press. I have just started to play with them and I cannot guarantee that the views about what is essential might not change. I am however becoming more and more convinced that quantum TGD as almost topological QFT reduces to the analog of braid theory with topological invariance replaced by symplectic invariance bringing in those aspects of physics for which the notion of length is essential.

For twistorial ideas see the chapter Yangian symmetry, twistors, and TGD of "Towards M-Matrix" and the chapter Knots and TGD of "Physics and Geometry of Infinite-Dimensional Geometry".

OPERA finds neutrinos superluminal even with 2 ns pulse spacing

Lubos informs that OPERA is going to release a new public announcement in two days or so in which they will still describe faster-than-light motion of neutrinos between CERN and Central Italy even though the spacing between the pulses in the new measurements will have been reduced to just 2 nanoseconds.

2 ns spacing between the pulses implies that pulse shape and duration cannot explain the earlier OPERA result as a measurement error. Effectively one studies individual neutrinos. Pulse shape and size has provided for the main stream theorist a cheap and fast way to explain the observation out from his mindscape. Certainly this finding also kills large class of explanations for neutrino super-luminality. Of course, one must still keep mind open for some delicate measurement error. Lubos suggests that there is a systematic error in GPS system, other colleagues have not taken this option seriously.

Sooner or later colleagues might be forced to accept that there is no other alternative than admitting that special and general relativities are somehow wrong. I realized this already towards 1977;-) (and lost my job in Helsinki University within few weeks!). Sub-manifold gravity allows Poincare invariance of special relativity as an exact symmetry unlike general relativity and provides geometrization of known fundamental interactions in terms of sub-manifold geometry for H=M⁴×CP₂.

Sub-manifold gravity also leads to the notion of many-sheeted space-time meaning a revolutionary vision about space-time topology in macroscopic and even astrophysical scales. Maximal signal velocity depends on space-time sheet, has an absolute upper bound, can depend on the distance scale and particle type but not on particle energy in continuous manner, and one can build an argument why it would be higher for neutrinos than for photons. This explanation is not anything tailored to explain OPERA result but is just one particular kinematical consequence of sub-manifold gravity. As a scientist I want to not lose professional skepticism as a basic attitude, but if you do not squeal to colleagues, I can just privately reveal that TGD is it;-)!

For the details of TGD based model of effectively super-luminal neutrinos see the article Are neutrinos super-luminal?.

Anomalous direct CP breaking in D-Dbar system?

Jester has a nice posting about the evidence for CP breaking in D-Dbar system found by LHCb collaboration. I warmly recommend the posting of Jester for any-one interested in details of the experiment.

The finding of LHCb

The basic object of study is the asymmetry for the decay rates of D and Dbar mesons to π⁺π^- and K⁺K^-. One could measure the difference of D and Dbar decay rates divided by their sum to get pure number -call it A_CP - in both channels separately but due to various limitations it is better to measure the difference of these asymmetries called Δ A_CP.

The analysis gives Δ A_CP=-.82+/- .21 (stat).+/- .11 (sys) per cent. The prediction of standard model is of order .01 per cent. 3.5 sigmas inspire questions about new physics due to the new heavy particles possibly appearing in the loops giving rise to the direct CP asymmetry and involving CP breaking phase of CKM matrix in an essential manner. TGD represents new particle of many kinds (squarks of M₈₉ hadron physics and their spartners for instance) but I will not try to say anything but consider to deeper aspects of direct CP breaking.

Arrow of time at single particle level as a deeper reason for direct CP breaking

We have a bad habit to get accustomed with miracles so that they do not look miracles anymore. People busily calculating loop diagrams for CP breaking containing new exotic heavy particles tend to forget the main point. Direct CP breaking - observed aeons ago for K-Kbar system - demonstrates arrow of time at single particle level and as such represents new physics. A possible deviation from standard model predictions in D-Dbar system represents just minor technical details.

Direct CP breaking means arrow of thermodynamics at single particle level: Dbar → D rate and D--→ Dbar rate are not same. The fact is that in standard physics we do not have a slightest idea about how this could happen. CKM matrix is only a parametrization.

What TGD can add is to explain what this mysterious arrow of time at single particle level could mean at the level of first principles. Zero energy ontology is the first principle now and distinguishes between standard physics and TGD.

1. In zero energy ontology quantum states are zero energy states (positive/negative energy part of state initial/final state in ordinary positive energy ontology). Time like entanglement coefficients define what I call M-matrix. Different M-matrices are orthogonal to each other and rows of a unitary U matrix.

2. M-matrix is "square root" of density matrix expressible as a hermitian square root of density matrix and unitary S-matrix. TGD is a square root of thermodynamics in well-defined sense. Thermodynamics and irreversibility enter the game at *single particle level* rather at the level of ensemble. This is new. Arrow of time means that with respect to positive energy states M-matrix involves only prepared states with well defined particle numbers etc. but not with respect to negative energy states (final states).

3. Irreversibility means that the rate for the transformation of D → Dbar is different from that for Dbar → D (for instance). This is just what direct CP breaking is at the level of principle.

What can one say about CKM matrix at the level of first principles?

It is a long way from the irreversibility at single particle level to the calculation of CKM matrix from the first principles, which is the real goal at deeper level. Probably for more than decade ago I worked a model for CKM matrix reducing CKM mixing to topological mixing of quarks (see this).

1. Number theoretical vision suggests that the elements of CKM matrix are rational or at least algebraic numbers in some simple extension of rationals.

2. Physically CKM mixing redues to different mixing of the topologies of quark wormhole throats carrying U and D type quarks. This is of course something totally new.

3. p-Adic mass calculations in turn allow to calculate p-adic mass squared for mixed quark as average of known p-adic mass squared values of non-mixed quarks. Number theoretical constraints are extremely tight since the averages divided by p-adic mass scale squared must be integers.

4. The principle is simple: entropies associated with mixing matrices U and D are maximized subject to these constraints. When I introduced the model I of course had no idea that this analog of second law could correspond to genuine thermodynamics (or its square root) at single quark level. The idea was that since the orbits of partonic 2-surfaces (wormhole throats) are random light-like surfaces, thermodynamics and the analog of second law could make sense. One can reproduce the observed CKM matrix but this is not a real calculation from the first principles.

Concerning the direct CP violation at the level of hadrons, the standard diagrammatic approach using CKM matrix as input probably makes sense and it is easy to imagine candidates for new heavy particles modifying standard model predictions but it is better to leave this for specialists.

Time for time

There are moments when any-one gets deeply frustrated to the situation in what one might call "my own field". For almost two decades ago this kind of deep frustration plus certain personal experiences were the reasons why I started to work with quantum consciousness and quantum biology. For few years ago my attention was directed again to particle physics and basic mathematical challenges of TGD. The last year has been very intense since LHC and Fermilab and also some other experiments have been feeding data directly relevant for TGD. The effective neutrino superluminality was a pleasant surprise which might eventually force even the most bullish colleagues to accept TGD if they want to continue doing funded physics.

The rather recent events - here I mean the really weird censoship in Science2.0 using various dirty tricks that one might expect only a 12 year old computer nerd to use - have however re-created the frustrated feelings again. Is it really true that people calling themselves theoretical physicist are not able to do anything else than rehashing theories which have been dead for decades? Just a look at hep-th in arXiv.org makes me depressed. I can only wonder in what is the world these fellows are living in. Even worse, some colleagues seem to spend their time to silly censoring tricks in blogs! It is really frustrating to see how low the intellectual standards in particle physics theory nowadays are.

For these reasons I was very happy when I discovered that Sean Carroll in Cosmic Variance gave links to really interesting talks in Time conference arranged by fQXI. I have not been too happy for the elitistic nature of these conferences making impossible the communication of really new theoretical ideas. By listening the brilliant talk by neuroscientist David Eagleman, I however learned that this conference made possible communication of extremely interesting experimental findings about the relation of the time of physicist to the subjective time. I sincerely hope that my colleagues would listen this talk and realize that there are fascinating problems to be solved. There is simply no theory and therefore no list of dead theories among which graduate student is allowed to choose as in theoretical physics.

Eagleman together with other neuro scientists make distinction between time and subjective time and the experimental work has revealed that this relationship looks very complex and is poorly understood. One of the key realizations forced by TGD inspired theory of consciousness - in a well-defined sense a generalization of quantum measurement theory - is that geometric time (the time of field equations) and subjective time (experienced time) are two differentnotions. The challenge is to understand how they relate and under what conditions and in what approximation their identification performed routinely my the naive colleagues is possible. This was an excellent reason for continuing listening and I warmly recommend this for the reader. Also the other lectures might be equally rewarding. In the following I just represent TGD based interpretation of the findings and suggest that the reader would not take it too seriously and would try to build his or her own interpretation.

Eagleman talks about what he calls relativity of subjective time. This has of course nothing to do with the relativity of the geometric time. At the basic level subjective time need not even allow any metric measure (as is the case in TGD where subjective time corresponds to a sequence of quantum jumps).

1. Flash-lag effect and its modification

Eagleman tells first about very simple visual illusion known as flash-lag effect. One rotates a small circle around a circular orbit. As the circle passes the horizontal line there is a flash of light in the middle of the circle. If our perception were ideal the flash would be perceived in the middle of the circle. The circle is perceived to be 5 degrees ahead of the flash.

The first explanation to come in mind is that brain anticipates the motion of the flash and represent it to us in a position in which it would be in nearby future. Eagleman decided to test this proposal and studied three different situations. Two of them correspond to a circle rotating in opposite directions and the third one to a situation in which the circle stops at the position of the flash. The theory predicts that the circle is perceived to be ahead in all situations since the perveiver should not know anything about what happens in future. The surprise was that there was no flash-lag when the circle stopped. As if the brain would know what happens in the nearby future.

This kind of observation is not new. I remember more than a decade old experiment studing the galvanic response created by emotionally very provocative picture appearing as an odd-ball in a series of neutral pictures. This kind of response was observed. The mystery was that it was observed before the picture was seen! The result was of course not taken seriously by serious scientists. When a serious scientist associates something with the word "parapsychology" he loses totally ability to rational thinking and begins to rage.

The conclusion is that our moment of subjective time seems to have a finite duration about 80 ms and all events that occur in this time interval are associated with one and same moment of subjective time. This time interval would correspond to 12.5 Hz frequency. In TGD framework the interpretation could be in terms of the time scale assignable to causal diamond (CD) identified as intersection of future and past directed light-cones, which serves as imbedding space-correlate for the moment of consciousness: this time would be the temporal distance between the tips of CD.

The fractal hierarchy of quantum jumps within quantum jumps (identifiable as with a hierarchy of selves withing selves) has the hierarchy of CDs as an imbedding space correlate. For electron the time scale of CD is 100 seconds. What is troubling is that 80 ms corresponds to a time interval which is by 20 per cent shorter. One could of course assign this time scale to some cyclotron frequency in TGD framework but I would be very happy if it would correspond to a time duration of electron's CD.

As Eagleman tells, perception involves gaps. For instance, during saccadic motion necessary for visual consciousness (the explanation in TGD framework is that the conscious experience is associated with nondeterministic change, quantum jump) visual system is not on. We do not however perceive these gaps although we perceive the gaps created by putting lights off. Could it be that the gaps are absent because the 100 ms CDs in the sequences have overlap producing on the average 80 ms intervals without overlap? Could the absence of gaps also tell us that it is retina and various sensory organs which build the fundamental qualia and that brain only constructs a cognitive representation about it decomposing the world to objects with certain properties and names and also builds all kinds of useful associations? This picture applies to all sensory qualia in TGD Universe and one can circumvent various objections against it in terms of TGD view about time.

2. We live in the past: but in what sense?

One surprising fact about consciousness is that we live in the past. The justification for this in terms of standard neuroscience, where brain builds both sensory and cognitive representations of the external world, does not require refined arguments.

Neural communications are extremely slow using light-velocity as the standard. The velocities of nerve pulses are between 1-100 m/s as compared with the light velocity 3× 10⁸ m/s. The communication of the sensory data to brain takes time which can be of order second. The data coming from various sensory organs with varying velocities must be processed and combined to single view about external world at associative cortex. This takes time since it is the slowest signalst that determine the time used for the processing. Eagleman gives a humorous example: tall people should live father in past than the short ones since it takes longer time for neural signals from feet to arrive from cortex to the brain! Different sensory inputs must be also combined together in a realistic manner.

Is the brain really able to meet this enormous challenge? The representation about the external world is not enough: this representation must be also realistic and 80 ms seems to represent the maximum duration of moment of sensory consciousness. Is the velocity of nerve pulses quite too slow to achieve this? And is information processing based on nerve pulse conduction really fast enough?

1. These questions could have been motivation for TGD proposal (or almost-prediction) that sensory organs are seats of primary sensory qualia experienced instantanously.

2. They could have also motivated what proposal that quantum entanglement is needed to bind various parts of the body and brain to form single coherent conscious unit. Quantum entanglement makes possible effective signalling with infinite velocity. Of course, genuine signals are not in question. It is better to speak about macroscopic system behaving like an elementary particle. Dark matter realized as a hierarchy of macroscopic quantum phases with a larger value of Planck constant is what would make this possible.

3. Light velocity is ideal for the communication purposes in the scale of biological body. Could it be that biology might have been stupid enough to miss this kind of an opportunity? Could it be that neuroscientists are the stupid one and simply on a wrong track? In TGD inspired model dark photons with large value of hbar (bio-photons would be dark photons transformed to ordinary photons) define a central element both in the communications from sensory organs to brain and to magnetic body and from magnetic body to biological body. At the level of body the communications would be practically instantaneous.

4. Even in Earth length scale the time taken by EEG photons to travel from biological body to the corresponding layear of the magnetic body would still be be of order .1 seconds and the experiments of Libet demonstrate among other things that our sensory data is a fraction of second old. This has nothing to do with the conduction velocity of nerve pulses. The purpose of nerve pulses would be quite different: they would create fundamental memory representations and the model for this is based on DNA as topological quantum computer vision.

   Explaining this would however require TGD based view about memory as 4-D perception: causal diamonds are 4-D objects and our conscious experience is always about 4-D space-time region. For sensory perception the scale of this region is .1 seconds. For the perceptions that we call memories the scale is often years or even decades. Our conscious experience is 4-dimensional. Also our motor actions are essentially 4-dimensional: moment of consciousness replaces 4-D world (or quantum superpositions of them) with a new one: also our geometric past is changed in every moment of consciousness. This view resolves many puzzles related to memory but time is far from mature for the revolution. My hope is that the talks of Time conference could open the minds of at least some young colleagues.

5. The communications with light velocity make possible feedback from brain to sensory organs making possible the building of standardized mental images by using the virtual sensory input from brain to create a charicature. Our brain would be an artist using primary sensory input as a raw material.

3. Kublai Khan's problem and three more surprises

Eagleman tells about the problem of emperor Kublai Khan. At that time people did not have internet and being a head of an empire of the size of Asia posed many problems. Kublai Khan used emissars travelling around the empire and bringing news about what happened. The problems was the correct integration of these data: the news about ending of some local war somewhere could arrive before the news telling that it had begun! Brain is faced with a similar problem. When the television came, one of the big problems was thought to be the synchronization of pictures and sound. It however turned out that brain takes care of this problem if the picture and sound to be associated with each other are withing 80 milliseconds. The moment of subjective time has this duration.

That we live in past was the first surprise of neuroscience already discussed. Eagleman tells about three more big surprises of neuroscience.

3.1. Time perception recalibrates

The brain must build a logical story about sensory data coming through different sensory channels. To achieve this time perception recalibrates. When one comes from bright sunlight to a dim room, the response function of retina gets slower. This does not however happen at the level of conscious experience. A simple test is a sequence of button clicks causing a flash of light. Experimenter can cheat the subject person by producing the light flash with a delay. Surprisingly, the subject person notices nothing. What is even more surprising that when one adds to the sequence of click-flash pairs an odd-ball for which flash is not delayed, the flash is experienced to take place earlier than clicking! Again a direct evidence for the TGD prediction that our perceptive field is 4-dimensional.

In this kind of situation the natural conclusion of subject person would be that it was not me who did the click. Some other agent caused the flash whereas my own attempt fails. Eagleman suggests that schizophrenia might be a disorder of time perception. Person would attribute his own thoughs sometimes heard as internal voices to some external subjects since the time order is pathological. Maybe. What is known that schizophrenics have very sharp sensory perception which cannot be cheated and that there might be no re-calibration. Eagleman talks about temporal inflexibility. This is of course just a suggestion as Eagleman emphasizes. I am not enthusiastic about this kind of interpretation: the bicameral views of Jaynes fit much better with the idea that magnetic body uses biological body as sensory receptor and motor instrument.

3.2. Time is not one thing

Time perception is much more complex than one might think: it involves many aspects such as duration, simultanety, flicker rate, time ordering. What brain does is the analysis of the sensory imput, and its reconstruction from the resulting small pieces. This is very much what is done in the processing of the raw sound (and also pictures) in movies. This applies also to time perception. In TGD framework also the feedback from brain is essential and basic communications would take place using light. Nerve pulse patterns would serve quite different purpose and are also hopelessly slow for building the percept.

3.3. The rate of time flow correlates with the rate of neural metabolism

There is large number of findings supporting the few that the experienced rate for the flow of subjective time correlates with the rate of neural metabolism and therefore with the intensity of consciousness.

a) Slowing down of the subjective time

Slowing down of subjective time flow is familiar to anyone. This can happen in troublesome situation or in so called flow state. Interestingly, also in very boring situations (say waiting for some-one to come) the same can happen. From my own experience I would say that the slowing down of subjective time characterizes very intense conscious experiences involving intense concentration. But why it would occur when you are bored: perhaps just because you are so intensely conscious about how boring your life is just now. You are not drowsy: you are inpatient and irritated.

Various explanations have been proposed. The proposal that the slowing down of time is analogous to the slowing down of the magnetic tape reducing the frequencies of sounds fails. Another explanation could be in terms of increased time resolution and also I have proposed this explanation. This explanation was tested.

Eagleman did an experiment which could be also seen as a tongue-in-cheek variant of Galileo's famous experiment in which he dropped various objects from the tower or Pisa and measured the time of fall and observed that it does not depend on the weight of the material object. Eagleman dropped subject persons instead of stones!

First of all Eagleman constructed an instrument which he calls perceptive chronometer producing random sequence of digits. In the simplest situation only single digit appeared alternatively as its positive or negative. As the rate of digits exceeds certain critical rate -presumably rather near to 12.5 Hz under normal circumstances- it becomes impossible to distinguish between subsequent digits: one sees only single fuzzy digit. The critical duration for the digit defines a natural unit of subjective time. The idea is to calibrate the rate of the chronometer in such a manner that the subject person is not able to distinguish between digits but that only a small reduction of the digit rate makes this possible. In this kind of situation it is enough to make the person scared and see whether he becomes able to distinguish between subsequent digits.

What Eagleman wanted to test was whether this time resolution increases when a person is really scared. If so, the subjective time measured using this critical unit would be longer in scaring situations. The method of really scaring was ingenious: drop the person from quite high a tower! During the free fall the person first found the critical time resolution of his visual perception which became the time unit used to measure the time of fall. The rate for Person reported his time resolution in two cases: when another person was falling and during own fall. The resolution increased during own fall: the falling time was estimated to be about 36 per cent longer for own falling down using the resolution as a unit.

What does this mean? It seems that the rate of the experienced time flow depends on the level of neural activity. In TGD framework the proper measure of subjective time is single quantum jump (recall that they form fractal hierarchy): this would be the tick of subjective clock. The larger the number of these ticks in a given interval of geometric time, the longer the experienced time duration is. More abstractly: the number of sub-CDs within CD representing mental images of self would provide a measure for the number of ticks during single CD.

Since metabolic energy is the necessary prerequite for the build-up of sensory and cognitive representations (mental images), the prediction is that the rate with which metabolic energy is used by brain correlates directly with the rate of the experienced time flow. When the subject person is falling from a tower, the rate of brain metabolism is higher than normally so that the observations can be understood in terms of the theory. As a matter fact, the correlation of the subjective duration with neural activity is well-known in neuroscience and Eagleman gives a long list of examples.

b) Odd ball effect

In this experiment the subject person perceives a series of figures. The figures are identical apart from some odd-balls between the repeating ones. The duration of odd-ball is experienced to be longer than that of the repeating picture although it is the same. The explanation would be that brain wants to save energy. Less metabolic energy for repeating items and nore metabolic energy for odd-balls, which literally wake-up the partially sleeping brain. The rate of neural metabolism correlating with the intensity of conscious experience (and number of quantum jumps per unit of geometric time/density of sub-CD:s within CD) seems to correlated directly with the experienced slowing down of time.

To sum up, the findings discussed by Eagleman are not easy to understand in the standard conceptual framework of neuroscience. The basic assumptions of TGD inspired theory of consciousness make the explanation trivial. In particular, the hierarchy of quantum jumps containing quantum jumps (of selves having sub-selves with subselves interpreted as mental images of self) and having as an imbedding space correlate the hierarchy of CDs within CDs, explains the correlation of neural metabolic energy consumption with the experienced rate for the flow of subjective time. The higher the density of sub-CDs within CD representing mental images, the higher the intensity of conscious experience,the higher the consumption of metabolic energy to build mental images, and the shorter the average time interval taken by given mental image and serving as a natural unit of subjective time and the longer the experienced duration of time interval.

For background see the chapter About the Nature of Time of "TGD Inspired Theory of Consciousness".

Something badly wrong in Science2.0?

The censorship in Science2.0 has transformed to a farce. I told already in posting about strange "Access denied":s.

After I had tried in vain to answer to a question of Eugen Stefanovich in the blog of Paolo Ciafaloni, I registered to the group as Eugene proposed: Eugene believed that a technical problem was in question.

I was accepted to Science2.0 as a registered member and went to the group only to find that it was not possible to write any comment!! After that I found that my earlier comment and Eugene's response to it had mysteriously disappeared!

It is clear that complete idiots are behind this insanity and they are rapidly spoiling the credibility of Science2.0. From a long experience I can understand quite well the psychology behind this kind of insane activities: jealousy is a horrible disease. This kind of discussion group should be however immune to the actions of people who do not realize that dirty tricks motivated by jealousy are not science.

To give some idea about the level of accepted comments just one example: a fellow who called himself "photon" expressed his thoughts and feelings using language with quite strong anal aroma:

Keep digging your hole. Ignore particle models of light. Ignore extinction theory. Ignore your eyes when V838 Monocerotis blew up. A century wasted on relativity and wave theory is far too long a wrong turn.

It did not become clear to whom his comment was directed since the message did not contain too may bits. If "shit" is some day accepted as an official unit of strongly negatively emotional dis-information then this message - do not forget that it was accepted for publication- managed to conceive at least Mega-shit of dis-information.

Situation is however not so gloomy: some young student expressed his impressions in the following manner: I find it amusing that even individuals with degrees unimaginable to myself, attack each other personally on a science website.

I have no knowledge in the fields of physics as I am just an 18 year old college student, however the comments I read (albeit the technical terms and the majority of theories went right over my head) are amusing considering you are all "professionals" and you are getting discouraged with one another and fighting like little kids.

Just my thoughts.

How quantum arithmetics affects basic TGD and TGD inspired view about life and consciousness?

In previous posting I proposed what I call quantum arithmetics as an answer to the question how real and p-adic physics correspond to each other. What happens is that rationals are replaced with quantum rationals. Same is done also for the algebraic extensions of rationals. One can however get worried and wonder what this means for quantum TGD and TGD inspired theory of consciousness. Is something perhaps lost? I considered this already in some blog comment but realized that the question deserves a separate blog posting. The general conclusion "Calm down!: Nothing is lost but a lot is gained".

The vision about real and p-adic physics as completions of rational physics or physics associated with extensions of rational numbers is central element of number theoretical universality. The physics in the extensions of rationals are assigned with the interaction of real and p-adic worlds.

1. At the level of the world of classical worlds (WCW) the points in the intersection of real and p-adic worlds are 2-surfaces defined by equations making sense both in real and p-adic sense. Rational functions with polynomials having rational (or algebraic coefficients in some extension of rationals) would define the partonic 2-surface. One can of course consider more stringent formulations obtained by replacing 2-surface with certain 3-surfaces or even by 4-surfaces.

2. At the space-time level the intersection of real and p-adic worlds corresponds to rational points common to real partonic 2-surface obeying same equations (the simplest assumption). This conforms with the vision that finite measurement resolution implies discretization at the level of partonic 2-surfaces and replaces light-like 3-surfaces and space-like 3-surfaces at the ends of causal diamonds with braids so that almost topological QFT is the outcome.

How does the replacement of rationals with quantum rationals modify quantum TGD and the TGD inspired vision about quantum biology and consciousness?

What happens to p-adic mass calculations and quantum TGD?

The basic assumption behind the p-adic mass calculations and all applications is that one can assign to a given partonic 2-surface (or even light-like 3-surface) a preferred p-adic prime (or possibly several primes).

The replacement of rationals with quantum rationals in p-adic mass calculations implies effects, which are extremely small since the difference between rationals and quantum rationals is extremely small due to the fact that the primes assignable to elementary particles are so large (M₁₂₇=2¹²⁷-1 for electron). The predictions of p-adic mass calculations remains almost as such in excellent accuracy. The bonus is the uniqueness of the canonical identification making the theory unique.

The problem of the original p-adic mass calculations is that the number of common rationals (plus possible algebraics in some extension of rationals) is same for all primes p. What is the additional criterion selecting the preferred prime assigned to the elementary particle?

Could the preferred prime correspond to the maximization of number theoretic negentropy for a quantum state involved and therefore for the partonic 2-surface by quantum classical correspondence? The solution ansatz for the modified Dirac equation indeed allows this assignment (see this): could this provide the first principle selecting the preferred p-adic prime? Here the replacement of rationals with quantum rationals improves the situation dramatically.

1. Quantum rationals are characterized by a quantum phase q=exp(i2π/p) and thus by prime p (in the most general but not so plausible case by an integer n). The set of points shared by real and p-adic partonic 2-surfaces would be discrete also now but consist of points in the algebraic extension defined by the quantum phase q=exp(i2π/p).

2. What is of crucial importance is that the number of common quantum rational points of partonic 2-surface and its p-adic counterpart would depend on the p-adic prime p. For some primes p would be large and in accordance with the original intuition this suggests that the interaction between p-adic and real partonic 2-surface is stronger. This kind of prime is the natural candidate for the p-adic prime defining effective p-adic topology assignable to the partonic 2-surface and elementary particle. Quantum rationals would thus bring in the preferred prime and perhaps at the deepest possible level that one can imagine.

What happens to TGD inspired theory of consciousness and quantum biology?

The vision about rationals as common to reals and p-adics is central for TGD inspired theory of consciousness and the applications of TGD in biology.

1. One can say that life resides in the intersection of real and p-adic worlds. The basic motivation comes from the observation that number theoretical entanglement entropy can have negative values and has minimum for a unique prime (see this). Negative entanglement entropy has a natural interpretation as a genuine information and this leads to a modification of Negentropy Maximization Principle (NMP) allowing quantum jumps generating negentropic entanglement. This tendency is something completely new: NMP for ordinary entanglement entropy would force always a state function reduction leading to unentangled states and the increase of ensemble entropy.

   What happens at the level of ensemble in TGD Universe is an interesting question. The pessimistic view is that the generation of negentropic entanglement is accompanied by entropic entanglement somewhere else guaranteeing that second law still holds true. Living matter would be bound to pollute its environment if the pessimistic view is correct. I cannot decide whether this is so: this seems like deciding whether Riemann hypothesis is true or not or perhaps unprovable.

2. Replacing rationals with quantum rationals however modifies somewhat the overall vision about what life is. It would be quantum rationals which would be common to real and p-adic variants of the partonic 2-surface. Also now an algebraic extension of rationals would be in question so that the proposal would be only more specific. The notion of number theoretic entropy still makes sense so that the basic vision about quantum biology survives the modification.

3. The large number of common points for some prime would mean that the quantum jump transforming p-adic partonic 2-surface to its real counterpart would take place with a large probability. Using the language of TGD inspired theory of consciousness one would say that the intentional powers are strong for the conscious entity involved. This applies also to the reverse transition generating a cognitive representation if p-adic-real duality induced by the canonical identification is true. This conclusion seems to apply even in the case of elementary particles. Could even elementary particles cognize and intend in some primitive sense? Intriguingly, the secondary p-adic time scale associated with electron defining the size of corresponding CD is .1 seconds defining the fundamental 10 Hz bio-rhythm. Just an accident or something very deep: a direct connection between elementary particle level and biology perhaps?

For details and background see the new chapter Quantum Arithmetics and the Relationship between Real and p-Adic Physics of "Physics as Generalized Number Theory".

Superluminal neutrinos and censorship in Science2.0 again

Paolo Ciafaloni wrote a blog posting with the title "Faster Than Light Neutrinos And Relativity II - A Million Dollar Bet". As a long term unemployed happy to receive even the 100 dollars (not million) promised in the posting, I posted a comment to his blog. Since Science2.0 has already earlier (but strange enough, not before these nasty superluminal neutrinos) censored out my comments, I find it reasonable to publish the comment also in my own blog. May be Paolo sees my comment and sends these 100 dollars. I really need them.

Here is my comment.

-----------------------

All boils down to what one means with maximal signal velocity. I have tried to explain at my blog and also in Science2.0 blogs that the situation changes completely, if one accepts a modification of special and general relativities in which space-time is 4-surface in some higher-D space-time time of form M⁴×S, S internal compact space (fixed to S=CP₂ from the condition that one obtains standard model symmetries). Poincare invariance is not lost and gravitation transforms to sub-manifold geometry.

The point is that light-like geodesics representing orbits of relativistic particles in geometric optics approximation at space-time surface are not light-like geodesics of M⁴×S nor M⁴ in general unless the 4-surface is just the flat canonical imbedding of M⁴. Space-time surface is in general warped and curved and although the motion still takes with light-velocity locally it is not along straight line in M⁴ so that it takes longer time to travel from point A to point B. The maximal signal velocity is reduced its absolute upper bound assignable with a travel along light-like geodesic of M⁴.

Using the terminology of TGD: the maximal signal velocity along neutrino space-time sheets of many-sheeted space-time could be (but need not be) higher than for photons. This velocity could depend on the length of the travel explaining SN1987A case or scale this length. It could also depend on particle species and relativistic electrons would provide a highly interesting test case. The velocity could slightly differ for different neutrinos. Given particle species could even arrive along several different space-time sheets: this could explain two arrival times for SN1987A neutrinos and the problem of two Hubble constants that has caused heated discussions among cosmologists. Needless to say, OPERA could be for TGD what Mickelson-Morley was for special relativity.

See this. this and this.

Matti Pitkanen

To my surprise I managed to get my comment to the Science2.0 and received a question from Eugene Stefanocich. I tried to answer but censors were awake at this time and I got "Access denied" as a responce. Therefore I will answer to Eugene here. I can only hope that Eugene happens to pop up at my blog.

Here is Eugene's question.

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Matti,

what are predictions of your theory for future neutrino experiments? In particular: 1) what will be the time advance if OPERA-type experiment is repeated with a different base length? 2) do you expect to see any difference if tau-neutrinos (which emerge from mu-neutrinos as a result of oscillations) are registered by the OPERA detector? 3) what is your prediction for the MINOS experiment if it is repeated with better accuracy and statistics?

Thanks. Eugene.

And here is my response which failed to pass through the censorhip.

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Eugene,

thank you for good questions. I would be happy if I could answer at precise quantitative level but I cannot. This would require a detailed model for neutrino space-time sheets and this I do not possess. What I have to say about the effective superluminality can be found from this article.

The general predictions and partial answers to some of your questions are here.

1. There is no energy dependence. There is particle and scale dependence. There is an argument suggesting that the velocity is higher for neutrinos than for photon and for photon higher than for relativistic electron. The difference between neutrino families is expected to be small if the proposed mechanism based on electroweak interactions is correct: this because of the universality/flavor independence of electroweak interactions.
2. The dependence on the length scale of the orbit should be via p-adic length scale and therefore piecewise constant. This kind of jump would come at half octaves of basic length scale and might be therefore observable. Increasing or decreasing the distance between CERN and receiver by a factor of sqrt(2) could reveal this effect.
3. The distance between CERN and Gran Sasso is 750 km. If I understood correctly, the distance travelled by neutrinos in MINOS experiment is 734 km (see this). 734 km is slightly above p-adic length scale L(151+2*46)= 2^(46)*L(151)=2^(46)*10^(-8) meters= L(243)=703 km. If I take p-adic length scale hypothesis seriously then the result should be same.
4. In cosmic scales one can estimate maximal signal velocity for photon: a very rough estimate using imbedding of Roberston-Walker cosmology as Lorentz invariant 4-surface is 73 per cent from absolute maximum (for light-like geodesic of M^4). For SN1987A neutrinos and photons the velocity difference would be much smaller than in shorter scales suggesting that the deviation from absolute maximum approaches to zero at very long distance scales.
   1. One possibility is Delta v/c (L_p) propto L_p^-n propto 1/p^-n/2, where L_p propto p^1/2 is the p-adic length scale. By p-adic length scale hypothesis the p-adic prime p satisfies p≈ 2^k. n is an exponent which need not be an integer.
   2. Second suggestive possibility is logarithmic dependence on L_p and therefore on p.

Matti

Addition:

The censorship in Science2.0 has transformed to a farce. I registered to the group as Eugene proposed (he believed that a technical problem was in question). I was accepted to Science2.0 as a registered member and went to the group only to find that it was not possible to write a comment!! After that I found that my earlier comment and Eugene's response to it had mysteriously disappeared! It is clear that complete idiots are behind this insanity and they are rapidly spoiling the credibility of Science2.0. I can understand the psychology behind this kind of insane activities: jealousy is a horrible disease. This kind of discussion group should be however immune to the actions of people who do not realize that dirty tricks are not science.

Cold fusion and serious scientists

Lubos gives again an excellent example of bad science writing. Already the earlier posting about cold fusion serves as a similar sad example about science journalism. What makes Lubos so irritated is that cold fusion seems to be real! So real that it is becoming commercial! This despite the fact that so called serious scientists declare that cold fusion is not possible. The text book nuclear physics simply does not allow it: Coulomb wall!

About serious science

The term "serious" used by a scientist about himself too often condenses to single word attributes like arrogance, intellectual laziness, and profound lack of imagination. Our luck is that there are also not so "serious" theoreticians. People with imagination. For the genuine explorers of the unknown anomalies like cold fusion represent fascinating intellectual challenges. What if the experimentalists are right? How the reality of cold fusion would force to modify nucler physics as it is represented in text books? For these scientists the text book nuclear physics does not represent laws of Moses carved in stone but a product of its own time - something manufactured by ordinary human beings from the restricted data that they had access to. These physicists do not start to rage like a maniac if a theory built for more than half century ago fails to explain all our experimental findings.

It is ironic that many of these "serious" scientists are ready believe even the silliest assertions of the hegemony. For instance, during the last year the claims of the hegemony about what will be seen at LHC have turned out to be wrong one after another. The outlandish predictions assigned to large extra dimensions, to mini black holes, to exotic dark matter particles with weird properties, to the standard view about super symmetry modified to allow baryon or lepton number non-conservation in desperate attempts to explain at least something, etc... have turned out to be wrong. Even the existence of the cherished Higgs is now highly questionable but again the courtly alternatives have been classified and listed: technicolor and non-perturbative efffects in standard model framework.

Another example: the possibility that neutrinos could move faster than photons suggested by the finding of the OPERA group, is dismissed by most colleagues. Again the lack of imagination is the banal reason: "serious" scientist is not able to imagine that the operationally defined maximal signal velocity itself varies if a simple modification of Einstein's theory solving the fundamental problem of General Relativity caused by the loss of Poincare symmetries is accepted. The "energy problem" of General Relativity is one of the dirty family secrets of theoretical physics community about which it is not polite to talk aloud although even second year physics student can understand that something is wrong: general relativity is not the whole story.

It is sad that too many influental bloggers including Tommaso Dorigo - whom I have regarded as a physicist taking more seriously experimental facts than text book theories- has chosen the side of the unimaginative establishment here. I understand that in a small secluded country like Finland those few physicists who have been chosen to act as the touters of the official science know that they must declare to the public that OPERA experimenters made an error. But why also Tommaso?

What if cold fusion is real?

I am happy to regard myself a member of the group of scientists for whom science is not a striking weapon or an instrument of personal career building. For me the anomalies of physics are a source of continual inspiration. There is nothing more stimulating than an unsolved problem and cold fusion is certainly such. This does not mean that I would believe or dis-believe in cold fusion: I am a scientist, not a priest or guru of any kind.

For more than decade ago I started to consider possible explanations for cold fusion in terms of many-sheeted space-time concept. The explanation that I take now most seriously rests on the hierarchy of Planck constants predicted by TGD providing an explanation of dark matter as a phase of ordinary matter with a value of Planck constant coming as integer multiple of the ordinary Planck constant. The scaling of Planck constant implies the upwards scaling of various quantum lengths - in particular the scaling of Compton length - making possible macroscopic quantum phases. The applications to biology are especially interesting.

Also zoomed up nuclei with the size scale of order atomic length scale are possible: this could make possible cold fusion like processes. There are books - written before the first reports about cold fusion - providing empirical and experimental evidence for the claim that cold fusion takes place in living matter (for references and TGD inspired model see this and this).

Needless to say, the reality of cold fusion could boost a profound technological revolution. Not only cheap energy but also the possibility to produce artificially technologically important elements such as metals, whose natural resources are rapidly waning. The alchemistic dream would become true.

To sum up: be very cautious when an aggressive theorists tells that something is theoretically impossible. What he is really expressing is that some theoreticians - quite too often those at the top of the power ladder - possess a very restricted gift of imagination.

Could the value of fine structure vary in cosmological scales?

There has been claims and counter claims about the possible time variation of the fine structure constant. The effect is extremely small. There is also a rather recent claim about the spatial variation of the finite structure constant (thanks to Ulla for the link). The claimed variation of alpha was along certain direction and about Δ α/α≈ 10^-6 for a distance of order of length travelled by light during the age of the Universe if I understood correctly (see this). The claim is based on the study of the atomic spectra of distant galaxies.

The article tells that the spatial variation is along different (how different is not told) directions depending on the method used. This suggests that the reason for observations is not the variation of fine structure constant but something else: most probably a measurement error or with much smaller probability a genuine new physics effect.

The measurements are extremely difficult. One must compare the frequencies of two spectral lines expressible in terms of alpha. These spectral lines should come from same source to eliminate the effect of red shift, one must eliminate the effects of local motions causing red shift, one must eliminate the effects of local magnetic fields, etc... Therefore it is very easy to make some measurement error.

Could the possible variation of alpha relate to coupling constant evolution?

No one claims that the running of gauge coupling could somehow cause the effect and no-one dares to ask why no one does this. Scientists painfully learn to avoid saying anything stupid: when a friendly looking colleague encourages to make stupid questions, the worst thing to do is to really make a stupid question! Shame is an excellent teacher. As a crackpot I can however unashamedly break this rule;-).

The assumption seems in my crackpottish eyes to boil down to the assumption that the natural length scale assignable to electron as its Compton length -and therefore its mass- determines the length scale used in atomic physics. Therefore electron mass would determine the value of the fine structure constant used in atomic physics calculations. Electron mass is simply assumed to have the same value everywhere in the Universe. Therefore also the fine structure constant used by all atomic physicists of the Whole Big Universe would be the same. I might be wrong and miss something important. I would be really happy if I understood this aspect better.

In any case, it is good to try gain some quantitative understanding about the situation.

1. Fine structure constant runs roughly from 1/137 to 1/125 in the mass scale range defined by electron mass and weak boson mass scale. This makes Δα/α∼ 10/137: this makes roughly 5 orders of magnitude giving in linear approximation : Δ α/α (m)= k Δ m_e/m_e with k ≈ 6× 10^-3.

2. If Δ α/α ≈ 10^-6 were due to the running fine structure constant, it would require Δ m_e/m_e∼ 2× 10^-4. The change of electron mass by about 50 eV to be compared with .5 MeV mass of electron and to the ionization energy about 13 eV of hydrogen atom. This is clearly an atomic energy scale. It seems that the relative variation of electron mass of order Δ m_e/m_e ∼ 2× 10^-4 is definitely excluded as too large. Why?

[Note that in TGD framework gauge coupling evolution is replaced with p-adic coupling constant evolution which occurs as jumps at half octaves of the basic mass scale so that this explanation is excluded].

Could the possible variation of alpha be "environmental" effect?

What about the environment of atoms? This is a question that an innocent layman who knows nothing about the rules of the academic theatre might ask.

1. I must confess that I do not understand how the "environment" of atoms could be same at distances of order light age of the Universe in so incredible accuracy. The basic idea behind atomic hypothesis is that the effects of environment on atomic energy levels can be neglected (forgetting of course strong local electric and magnetic fields). But can one be so sure about absence of delicate "environmental" effects not reducing to strong electric and magnetic fields? What one means with "environment"?

2. The absence of "environmental" effects seems to be in a sharp contrast with the observations of Shnoll and others that nuclear decay rates, rates of chemical reactions, etc.. vary with astrophysical periods assignable to solar system. If nuclei, why not atoms? Why also the energy levels could not vary with astrophysical periods and therefore depend on astrophysical environment?

   [For the TGD based model of Shnoll effect see this. For the implications of the model for understanding of real-p-adic correspondence and p-adic length scale hypothesis see this].

Theoreticians, those lucky ones who need not perform the experiments;-), can of course imagine endlessly mechanisms for the variation of fine structure constant. In many-sheeted space-time this exercise is not terribly difficult.

1. For instance, one could ask whether charged particles could leak some of their electric flux to some large space-time sheets so that fine structure constant could be reduced. I indeed did so for few years ago when the news about possible time variation of fine structure constant emerged. Charge quantization does not encourage this idea. Whether the leakage can happen is impossible to tell at this moment.

2. Or could the analog of Shnoll effect predicted to be very general in TGD Universe and reflect real physics- p-adic physics duality (see this) be involved, and cause extremely tiny small spatial and temporal variations on energy levels due to "environment" in cosmic scales?

CMS observes large excess of diphotons

LHC has started to produce data indicating that the new physics required by very general arguments indeed is there. Lubos told yesterday about a preprint by CMS collaboration showing a very large excess of di-photons in proto-proton collisions. This excess is so large that only a rough systematic error can threat its status.

What has been observed?

The following two data bits give strong hints about what might be involved.

1. From the figure in the posting of Lubos one learns that the distribution for the difference Δφ for the difference of the azimutal angles with respect to the beam direction covers rather evenly the span Δφ <2.80 and the production rate is considerably higher than predicted by QCD calculations except near π where the production rate is smaller than the prediction. From momentum conservation one would expect Δφ∼ π in a good approximation in the cm frame of photons. Unless the resonance does not move with a very high velocity, the photons Δ φ≈ π should hold true quite generally. This gives hints about the production mechanism.

2. Figure 3 of the CMS preprint gives the differential cross section with respect to diphoton invariant mass m_γγ as a function of m_γγ. The distribution has a sharp knee between 45-55 GeV. One might be able to see double peak at invariant masses about 50 GeV and 75 GeV and even third peak around 175 GeV. The differential cross section is however anomalous already around 20 GeV which serves as transverse momentum cutoff for photons

   The naive question by a non-professional is whether there could be resonance decaying to two photons with mass in this range. Δ φ∼ π would be however required if the resonance does not move very fast in the cm frame of colliding protons. The cut on transversal momenta is 20 GeV making 40 GeV transversal energy and I am not absolutely sure whether this could cause the shoulder. The experimenters however speak about shoulder and certainly they would not do this if it were due to the cufoff. Therefore I will assume that the shoulder is genuine.

3. If the shoulder located roughly between 45 GeV and 75 GeV is real, it would seem that the two-photon state must be accompanied by a state with opposite momentum and roughly the same energy and thus moving in opposite direction. This suggests two states with mass(es) in the range [90,150] GeV.

What could it be?

The speculation of Lubos is that the decay of Higgs like state with mass around 119 GeV might explain the finding but admits that standard model Higgs should not produce any visible effect. Even worse, the so called little Higgs alternative would predict a reduction of diphoton production rate. There are also exotic explanations involving large dimensions and exotic gravitons but to my opininion these alternatives belong to the realm of bad science fiction and can be safely forgotten.

In my naive mind frame the strong knee around 55 GeV is something which I find very difficult to not interpret as a bump suggesting the presence of a meson like state. On the other hand, the distribution for Δ φ; does not fit with this simplistic picture.

What about the TGD inspired interpretation? The first interpretation that comes into mind relies on the TGD based view about SUSY, which differs considerably from the standard view.

1. As explained in the earlier posting, TGD could allow the realization of SUSY in which quarks and squarks have same p-adic mass scale- perhaps even masses- before the mixing of hadrons and shadrons allowed by R-parity conservation. The mechanism explaining the experimental absence of squarks would be shadronization proceeding faster than the decay of squarks to quark and electroweak gaugino.
   1. In this framework the mysterious X and Y mesons accompanying charmonium states would be their super partners in a good approximation since the mixing would be small. The mixing of mesons and smesons would be however very large near confinement mass scale and make the other mixed state (identified as eigen state of mass squared matrix) tachyonic and eliminate it from the spectrum. The companion of pion would be tachyonic and excluded from spectrum: this would hold true for all smesons containing light quarks and perhaps also those containing only single light squark if the mass scale of the mass squared matrix is determined by the heavier quark and α_s by the lighter quark so that mixing is very large.

   2. A crucial assumption is that the squarks are dark in the sense of having a non-standard value of Planck constant: otherwise the decay widths of electro-weak gauge bosons would be too large. The phase transition changing the value of hbar and having a purely geometric (topological) meaning in TGD framework would accompany also the mixing process being analogous to mass insertions in the lines of Feynman graph.

2. In TGD framework the proposed view about squarks as particles having common p-adic mass scale with quark is suggested to hold true in both the ordinary M₁₀₇- and M₈₉ hadron physics. There is however no need to assume that M₈₉ squarks are dark. The pion of M₈₉ hadron physics could identified as the earlier 144 GeV Higgs candidate, forgotten but mentioned again by Lubos , would have 119 GeV bump as a lighter companion. The two states would be mixtures of pion and spion. The mass values for the bumps assigned to ρ₈₉ and ω₈₉ and to their spartner candidates allow to estimate the mass of the partner of π₈₉. The mass would near to 119 GeV for which there are slight indications.

How the shoulder around 45-55 GeV could be created from the decays of the partner of π₈₉- a (probably strong) micture of pion and spion. Could the two mixtures of M₈₉ pion and its spartner with masses (say) 119 GeV and 144 GeV (one should not take these number too literally) be responsible for the effect as the indications about two peaked structure suggest? Could the spionic parts of the states produce the events diphoton events.

1. The simplest Feynman diagram for the decay of the pion-like state would describe the turn around of squark backwards in time via the emission of two photons. This would produce onlty Δ φ∼ π events and photons with energies around 60 GeV and 72 GeV for the proposed masses 119 GeV and 144 GeV.

   Comment: 144 GeV is the estimate for the mass of π^+/- ₈₉, one obtains 138 GeV for π⁰ ₈₉: I have earlier neglected electromagnetic mass splitting of pions and approximated pion masses with charged pion mass 140 MeV. This scales the second mass to 69 GeV.

2. For a more complex Feynman diagram exchanged squark turning around in time would emit quark and antiquark transforming in this manner to gluino and back to squark. Another possibility is emission of two gluons. This would give photon pair and something which could be just two hadron jets if the emitted quarks and gluons transform to ordinary quarks.

3. The objection is that this model need not explain the strong concentration of diphoton invariant mass to the range 45-75 GeV since in principle 4-particle final states are in question and phase space distribution does not predict anything like this. p-Adic length scale hypothesis however suggests that the resulting quark pairs actually form a p-adically scaled down variant of the pion like state and have therefore mass, which is half of its mass. This would give rise to a resonance like behavior and impy a strong concentration of the events to the invariant masses which are one half of the mass of the mother particle.

   The p-adically scaled up quarks appear even in the TGD based model of light hadrons and produce mass formula replacing Gell-Mann-Nishijina mass formula (see this). As a matter fact, the naive prediction for the mass of M₈₉ pion is just 512 times the mass of the ordinary neutral pion and gives 69.1 GeV!

4. One must also worry about overall parity conservation required if only strong and electromagnetic interactions are involved with the decay process. Pion is pseudoscalar and the decay of pion to two pions with scaled down mass requires parity breaking in the effective action involving the pion fields only unless the vertex contains derivatives but one cannot build a Lorentz invariant involving 4-D permutation symbol from three pion fields. Should one assume that the process breaks parity conservation and involves therefore weak interactions? Or should one assume that second scaled down pion is replaced with two pions with mass equal 1/4 the mass of the decaying pion to give parity invariant effective interaction Lagrangian as assumed in the model of CDF anomaly. This would predict also diphoton pairs with invariant masses scaled down to 22.5-40 GeV. The differential cross section is anomalous down to the 20 GeV cutoff. One should be able to resolve this issue before one can take the model seriously.

A connection with Aleph anomaly

There is an old anomaly known as Aleph anomaly producing 4-jets states with jet-jet invariant mass of 55 GeV. According to the reference, the anomaly did not survive improved statistics. Delphi and L3 also observed 4-jet anomaly with dijet invariant mass about 68 GeV: this not too far from the mass for p-adically scaled down mass of π₈₉ equal to 69.1 GeV! Remarkably, according to the above reference L3 observation survived the improvement of the statistics!

1. For more than decade ago I proposed an explanation of Aleph anomaly in terms of a meson-like state formed by p-adically scaled up variants of b quark and its antiquark (see this ). The mass of the resonance was predicted correctly using p-adic length scale hypothesis predicting that the mass of scaled up b quark is half octave of the mass of b quark.

2. The model could be generalized by replacing b quark with its super-partner if one assumes that SUSY breaking means only different p-adic mass scale. There is however an aesthetic problem (I take aesthetic arguments very seriously). The model for X and Y mesons assumed that the p-adic mass scale is same: now one should give up this assumption for b quark. The reader has probably already asked whether Aleph anomaly and the recent CMS anomaly could correspond to the same meson like state. 4-jets could be produced when sb and sbbar decay to bbbar pair by emission of gluinos which then exchange quark to produce quark pair or gluon pair. In the decays of X and Y mesons the resulting quark pair would form pion or some other meson. Now two quark or gluon jets by exchanged gluinos would be produced giving altogether four jets.

3. CMS anomaly suggests a different interpretation. Perhaps the 4-jets with di-jet energies around 55 GeV and 68 GeV are produced by the decays of the mixtures of M₈₉ pion and spion with masses around 110 GeV and 144 GeV producing as intermediate state the 2-adically scaled down pions with half of their original masses.

   The same mechanism is assumed also in the model of CDF anomaly discovered for three years ago but already forgotten. Political memory is short! The mechanism would be a modification of that producing the diphoton excess. Squark and anti-squark would transform to quark-antiquark pair giving rise to intermediate scaled down pionlike state decaying to two jets with invariant mass concentrated around the mass of pion-like state. The exchanged gluino emits quark and antiquark or two gluons. Quark antiquark state could also form a scaled down M₈₉ pion before the decay to two jets. The outcome would be four jets with concentration to preferred invariant masses.

For details and background see the chapter New particle physics predicted by TGD: part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".

Quantum Arithmetics and the Relationship between Real and p-Adic Physics

p-Adic physics involves two only partially understood questions.

1. Is there a duality between real and p-adic physics? What is its precice mathematic formulation? In particular, what is the concrete map p-adic physics in long scales (in real sense) to real physics in short scales? Can one find a rigorous mathematical formulation of canonical identification induced by the map p→ 1/p in pinary expansion of p-adic number such that it is both continuous and respects symmetries.

2. What is the origin of the p-adic length scale hypothesis suggesting that primes near power of two are physically preferred? Why Mersenne primes are especially important?

A possible answer to these questions relies on the following ideas inspired by the model of Shnoll effect. The first piece of the puzzle is the notion of quantum arithmetics formulated in non-rigorous manner already in the model of Shnoll effect.

1. Quantum arithmetics is induced by the map of primes to quantum primes by the standard formula. Quantum integer is obtained by mapping the primes in the prime decomposition of integer to quantum primes. Quantum sum is induced by the ordinary sum by requiring that also sum commutes with the quantization.

2. The construction is especially interesting if the integer defining the quantum phase is prime. One can introduce the notion of quantum rational defined as series in powers of the preferred prime defining quantum phase. The coefficients of the series are quantum rationals for which neither numerator and denominator is divisible by the preferred prime.

3. p-Adic--real duality can be identified as the analog of canonical identification induced by the map p→ 1/p in the pinary expansion of quantum rational. This maps maps p-adic and real physics to each other and real long distances to short ones and vice versa. This map is especially interesting as a map defining cognitive representations.

Quantum arithmetics inspires the notion of quantum matrix group as counterpart of quantum group for which matrix elements are ordinary numbers. Quantum classical correspondence and the notion of finite measurement resolution realized at classical level in terms of discretization suggest that these two views about quantum groups are closely related. The preferred prime p defining the quantum matrix group is identified as p-adic prime and canonical identification p→ 1/p is group homomorphism so that symmetries are respected.

1. The quantum counterparts of special linear groups SL(n,F) exists always. For the covering group SL(2,C) of SO(3,1) this is the case so that 4-dimensional Minkowski space is in a very special position. For orthogonal, unitary, and orthogonal groups the quantum counterpart exists only if quantum arithmetics is characterized by a prime rather than general integer and when the number of powers of p for the generating elements of the quantum matrix group satisfies an upper bound characterizing the matrix group.

2. For the quantum counterparts of SO(3) (SU(2)/ SU(3)) the orthogonality conditions state that at least some multiples of the prime characterizing quantum arithmetics is sum of three (four/six) squares. For SO(3) this condition is strongest and satisfied for all integers, which are not of form n= 2^2r(8k+7)). The number r₃(n) of representations as sum of squares is known and r₃(n) is invariant under the scalings n→ 2^2rn. This means scaling by 2 for the integers appearing in the square sum representation.

3. r₃(n) is proportional to the so called class number function h(-n) telling how many non-equivalent decompositions algebraic integers have in the quadratic algebraic extension generated by (-n)^1/2.

The findings about quantum SO(3) suggest a possible explanation for p-adic length scale hypothesis and preferred p-adic primes.

1. The basic idea is that the quantum matrix group which is discrete is very large for preferred p-adic primes. If cognitive representations correspond to the representations of quantum matrix group, the representational capacity of cognitive representations is high and this kind of primes are survivors‍ in the algebraic evolution leading to algebraic extensions with increasing dimension.

2. The preferred primes correspond to a large value of r₃(n). It is enough that some of their multiples do so (the 2^2r multiples of these do so automatically). Indeed, for Mersenne primes and integers one has r₃(n)=0, which was in conflict with the original expectations. For integers n=2M_m however r₃(n) is a local maximum at least for the small integers studied numerically.

3. The requirement that the notion of quantum integer applies also to algebraic integers in quadratic extensions of rationals requires that the preferred primes (p-adic primes) satisfy p=8k+7. Quite generally, for the integers n=2^2r(8k+7) not representable as sum of three integers the decomposition of ordinary integers to algebraic primes in the quadratic extensions defined by (-n)^1/2 is unique. Therefore also the corresponding quantum algebraic integers are unique for preferred ordinary prime if it is prime also in the algebraic extension. If this were not the case two different decompositions of one and same integer would be mapped to different quantum integers. Therefore the generalization of quantum arithmetics defined by any preferred ordinary prime, which does not split to a product of algebraic primes, is well-defined for p=2^2r(8k+7).

4. This argument was for quadratic extensions but also more complex extensions defined by higher polynomials exist. The allowed extensions should allow unique decomposition of integers to algebraic primes. The prime defining the quantum arithmetics should not decompose to algebraic primes. If the algebraic evolution leadis to algebraic extensions of increasing dimension it gradually selects preferred primes as survivors.

For details and background see the new chapter >Quantum Arithmetics and the Relationship between Real and p-Adic Physics of "Physics as Generalized Number Theory".

More about strange charged trilepton events

I already told about indications for strange charged tri-lepton events at CMS. The inspiration came from a posting CMS sees SUSY-like tri-lepton excesses of Lubos.

Only a few days later both Tommaso and Lubos discussed a quite recent paper telling about charged tri-lepton events observed at CMS.

1. From Tommaso's posting one learns that three charged leptons with total mass near to Z⁰ mass have been observed. Charge conservation of course requires fourth charged lepton if the particles originate in the decay of Z⁰ as assumed and Tommaso argues that this lepton has so low energy that it is not detected. This kind of lepton could results in an energy asymmetric decay of photon. The assumption that Z⁰ is the decaying particle might be however un-necessarily strong: it could be quite well W with almost the same mass. In this case charge conservation allows genuine charged tri-lepton event. The discussion of my earlier posting suggests the decay W→ sW+sZ to be the source of charged tri-lepton events.

2. The authors of the paper propose that the reaction could be initiated by a decay of squark or gluino and necessarily involving R-parity breaking. There are two possibile options for R-parity breaking allowed by proton stability depending on whether it conserves lepton or baryon number. For lepton number violating option intermediate particle is neutralino (lightest sparticle which is stable in R-parity breaking scenarios ) and for baryon number violating scenatior bino or higgsino. The R-parity violating decay of lightest spartner (neutral) would yield slepton-lepton pair and the R-parity violating decay of slepton a lepton pair plus neutrino. This would produce instead single observed lepton charged tri-lepton state. The authors do not give enough details to make possible for a non-professional to deduce what the detailed model for the process really is.

It is interesting to consider the situation in TGD framework in light of the crucial additional data (the three charged leptons have mass rather near to that of Z⁰ and therefore to that of W).

1. The decay of W → sW +sZ with the decays sW and sZ proceeding in either of the two manners discussed in the previous posting would predict that the total mass of all particles produced is near to W mass (and therefore Z mass) and also why one obtains genuine charged tri-lepton states. The problem is that missing energy in the form of neutrinos and neutral sparticles is present and it is not at all clear why this energy should be small.

2. An option not discussed discussed in the previous posting is the decay W→ sν+L followed by the decay sν→ L+sW followed by sW→ L+sν would not break R-parity and would produce sν. Total energy would correspond to W mass but it is not clear why the missing energy assigned with sν should be small.

3. R-parity violation predicted by TGD however allows also to consider the direct decay sνrarr; L⁺+L^- so that there would be no missing energy. One could say that the decay is the reversal of a process in which L⁺+L^- annihilates to a sν identifiable as a pair of neutrino and right-handed neutrino at microscopic level. All standard model quantum numbers would be conserved.

In TGD framework R-parity violation is a prediction of the theory and it would not violate either baryon or lepton number conservation. There is no need to assume undetected charged lepton since charge conservation allows charged tri-lepton final state as such without any missing energy. Obviously the TGD based model is by several orders of magnitude simpler than the model based on standard SUSY.

For details and background see the chapter New particle physics predicted by TGD: part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".

3-jet and 9-jet events as a further evidence for M89 hadron physics?

Lubos Motl told about slight 3-jet and 9-jet excesses seen by CMS collaboration in LHC data. There is an article about 3-jet excess titled Search for Three-Jet Resonances in pp Collisions at s^1/2 = 7 TeV by CMS collaboration. Figure 3 of the article and also the figure of Lubos blog posting shows what has been found. In 3-jet case the effects exceeds 3-sigma level between 350 GeV and 410 GeV and the center is around 380-390 GeV.

Experimenters see 3-jets as 1.9 sigma evidence for SUSY. It is probably needless to tell that 1.9 sigma evidences come and go and should not be taken seriously. Gluino pair would be produced and each gluino with mass around 385 GeV would decay to three quarks producing three jets. In tri-jet case altogether 3+3=6 jets would be produced in the decays of gluinos. The problem is that there is no missing energy predicted by MSSM scenario without R-parity breaking. Therefore the straightforward proposal of CMS collaboration is that R-parity is broken by a coupling of gluino to 3 quark state so that gluino would effectively have quark number three and gluino can decay to 3 light quarks- say uds.

The basic objection against this idea is that the distribution of 3-jet masses is very wide extending from 75 GeV (slightly below 100 GeV for selected events) to about 700 GeV as one learns from figure 1 of the CMS preprint. Resonance interpretation does not look convincing to me and to my humble opinion this is a noble but desperate attempt to save the standard view about SUSY. After proposing the explanation which follows I realized to my surprise that I had already earlier tried to explain the 390 GeV bump in terms of M₈₉ baryon but found that this explanation failssince the mass is too low to allow this interpretation (see this).

There is also an article about nona-jets titled Has SUSY Gone Undetected in 9-jet Events? A Ten-Fold Enhancement in the LHC Signal Efficiency but I will not discuss this except by noticing that nona-jet events would serve as a unique signature of M₈₉ baryon decays in TGD framework if the proposed model for tri-jets is correct.

Before continuing I want to make clear my motivations for spending time with thinking about this kind events which are probably statistical fluctuations. If I were an opportunist I would concentrate all my efforts to make a maximum noise about the successes of TGD. I am however an explorer rather than career builder and physics is to me a passion- something much more inspiring than personal fame. My urge is to learn what TGD SUSY is and what it predicts and this kind of activity is the best manner to do it.

1. Could one interpret the 3-jet events in terms of TGD SUSY without R-parity breaking?

I already mentioned the very wide range of 3-jet distribution as a basic objection against gluino pair interpretation. But just for curiosity one can also consider a possible interpretation in the framework provided by TGD SUSY.

As I have explained in the article, one could understand the apparent absence of squarks and gluinos in TGD framework in terms of shadronization which would be faster process than the selectro-weak decays of squarks so that the standard signatures of SUSY (jest plus missing energy) would not be produced. The mass scales and even masses of quark and squark could be identical part from a splitting caused by mixing. The decay widths of weak bosons do not however allow light exotic fermions coupling to them and this in the case of ordinary hadron physics this requires that squarks are dark having therefore non-standard value of Planck constant coming as an integer multiple of the ordinary Planck constant (see this). For M₈₉ hadron physics this constraint is not necessary.

One can indeed imagine an explanation for 3-jets in terms of decays of gluino pair in TGD framework without R-parity breaking.

1. Both gluinos would decay as sg→ sq+q^* (or charge conjugate of this) and squark in turn decays as sq → q+ sg. This would give quark pair and two virtual gluinos. Virtual gluinos would transform to a quark pair by an exchange of virtual squark: sg→ q+sq^*. This would give 3 quark jets and 3 anti-quark jets.

2. Why this option possible also in MSSM is not considered by CMS collaboration? Do the bounds on squark masses make the rate quite too low? The very strong lower bounds on squark masses in MSSM type SUSY were indeed known towards the end of August when the article was published. In TGD framework these bounds are not present since squarks could appear with masses of ordinary quarks if they are dark in TGD sense. Gluinos would be however dark and the amplitude for the phase transition transforming gluon to its dark variant decaying to a gluino pair could make the rate too low.

3. If one takes the estimate for the M₈₉ gluino mass seriously and scales to a very naive mass estimate for M₁₀₇ gluino by a factor 1/512, one obtains m(sg₁₀₇)=752 MeV.

As already noticed, I do not take this explanation too seriously: the tri-jet distribution is quite too wide.

2. Could tri-jets be interpreted in terms of decays of M₈₉ quarks to three ordinary quarks?

3+3 jets are observed and they correspond to 3 quarks and antiquarks. If one takes 3-jet excess seriously it seems that one has to assume a fermion decaying to 3 quarks or two quarks and antiquark. All these quarks could be light (u,d,s type quarks).

Could M₈₉ quarks decaying to three M₁₀₇ (ordinary) quarks (q₈₉→ q₁₀₇q₁₀₇q^*₁₀₇) be in question? If this were the case the 9-jets might allow interpretation as decays of M₈₉ proton or neutron with mass which from naive scaling would be 512× .94 GeV ≈ 481 GeV resulting when each quark the nucleon decays to three ordinary quarks. Nona-jets would serve as a unique signature for the production of M₈₉ baryons!

M₈₉ quarks must decay somehow to ordinary quarks.

1. The simplest guess is that the transformation q₈₉ → q₁₀₇q₁₀₇q^*₁₀₇ begins with the decay q₈₉→ q₁₀₇ + g₈₉. Here g₈₉ can be virtual.

2. This would be followed by g₈₉→ q₁₀₇+q^*₁₀₇. The final state would consist of two quarks and one antiquark giving rise to tri-jet. The decay of M₈₉ gluon could produce all quark families democratically apart from phase space factors larger for light quarks. This would produce 3+3 jets with a slight dominance of light quark 3-jets.

There are two options to consider. The first option corresponds to a production of a pair of on mass shell M₈₉ quarks with mass around 385 GeV (resonance option) and second option to a production of a pair of virtual M₈₉ quarks suggested by the wide distribution of tri-jets.

1. Could the resonance interpretation make sense? Can the average 3-jet mass about 385 GeV correspond to the mass of M₈₉ quark? The formulas m(π₈₉)= 2^1/2m(u₈₉) (mass squared is additive) together with m(π₈₉)= 144 GeV would give m(u₈₉) ≈ 101.8 GeV. Unfortunately the mass proposed for the gluino is almost 4 times higher. The naive scaling by factor 512 for charmed quark mass m(c₁₀₇)= 1.29 GeV would give 660.5 GeV, which is quite too high. It seems very difficult to find any reasonable interpretation in terms of decays of on mass shell M₈₉ quarks with mass around 385 GeV.

2. One can however consider completely different interpretation. From figure 1 of the CMS preprint one learns that the distribution of 3-jet masses is very wide beginning around 75 GeV (certainly consistent with 72 GeV, which is one half of the predicted mass 144 GeV of M₈₉ pion) for all triplets and slightly below 100 GeV for selected triplets.

   Could one interpret the situation without selection by assuming that a pair of M₈₉ quarks forming a virtual M₈₉ pion is produced just as the naive expectation that the old-fashioned proton-pion picture could make sense at "low" energies (using of course M₈₉ QCD Λ as a natural mass scale) also for M₈₉ physics. The total mass of M₈₉ quark pair would be above 144 GeV and its decay to virtual M₈₉ quark pair would give quark pair with quark masses above 72 GeV. Could the selected events with total 3-jet mass above 100 GeV correspond to the production of a virtual M₈₉ quark pair?

To sum up, if one takes the indications for 3-jets seriously, the interpretation in terms of M₈₉ hadron physics is the most plausible TGD option. I am unable to say anything about the 9-jet article but 9-jets would serve as a unique and very dramatic signature of M₈₉ baryons: the naive prediction for the mass of M₈₉ nucleon is 481 GeV.

For details and background see the article Is the new boson reported by CDF pion of scaled up variant of hadron physics? and the chapter New particle physics predicted by TGD: part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".