The result of course does not mean that there would be no dark matter. It only says that the main stream of particle physics community has been at completely wrong track concerning the nature of dark matter. As I have patiently explained year after year in this blog, dark matter is not some exotic particle this or that. Dark matter is something much deeper and its understanding requires a generalization of quantum theory to include hierarchy of Planck constants. This requires also a profound generalization of the notion of space-time time.
In particular, all standard particles can be in dark phase characterized by the value of Planck constant, and the main applications are TGD inspired quantum biology and consciousness theory since dark matter with large value of Planck constant can form macroscopic quantum phases. Also dark energy in TGD sense is something very different from the standard dark energy. Dark energy in TGD Universe corresponds to Kähler magnetic energy assignable to magnetic flux tubes carrying monopole flux. These magnetic fields need no currents to generate them, which explains why cosmos can full of magnetic fields. Superconductors at the verge of breakdown of superconductivity and even ordinary ferromagnets might carry these Kähler monopole fluxes although monopoles themselves do not exist.
The result of LUX was expected from TGD point of view and does not exclude particles dark in TGD sense. Even dark particles at the mass scale of tau lepton and even at mass scale of 7-8 GeV can be considered and the CDF anomaly reported few years ago could have explanation in terms of dark variant of tau-pion identifiable as pion like bound state of colored tau leptons: also for other leptons analogous states have been reported (see this). The experimental signatures of this kind of particles are however very different from the dark particles that LUX was searching for and could explain some reports about evidence for dark matter in ordinary sense.
The lesson to learn is that one can find only what one is searching for in recent day particle physics. Particle phenomenologists should return to the roots. Challenging the cherished beliefs - even the beliefs about what QCD color is - is painful but is the only way to make progress.
15 comments:
Very well, the news is promising:).
Dear Hamed,
I should have said N=1 SUSY;-) or even MSSM. Many other SUSYs waiting to be studied;-).
By the way, there is an excellent article about bi-spinors, twistors, N=4 SUSY, BCFW, twistors and all that at http://arxiv.org/pdf/1308.1697v1.pdf. You might find it interesting.
Dear Matti,
Yes this is a good article for me to learn.
In classical TGD, what does it cause that a 3-suface has some determined components of induced metric and induced kahler form? Or what are the things that make a 3-surface this induced metric or kahler form and not another possibilities? Also in another words, how one can change the induced metric or induced kahler form of an object? Maybe when we warm the object, it’s induced metric changes?
Dear Hamed,
induced metric, Kahler form, spinor connection, etc.. are known once the surface is known. These tensors are just projections of the imbedding space tensor quantities (metric, Kahler form,...) to space-time surface obtained by contracting with the gradients of imbedding space coordinates.
This is the content of geometrization of physics at classical level in TGD framework. It gives extremely powerful constraints since only four field like variables remain and one has not only extremals but preferred extremals of Kahler action. What allows to avoid contradictions is the notion of many-sheeted space-time allowing to get the counterpart of superposition for fields in terms of union of space-time sheets: effects are superposed, not fields.
About your example: when we warm the object, its induced metric certainly changes a little bit since the space-time surface representing the object is deformed. When you raise your hand, the space-time surface representing your hand, is deformed.
Here we must of course be cautious: quantum level one has only quantum superposition of space-time surfaces, quantum state idealised as single space-time surface is indeed an idealization. One can assign to quantum state single space-time surface only modulo measurement resolution: as quantum fuzzy geometry and topology.
In string models using Polyakov formulation one introduces metric to string world sheet as independent dynamical degrees of freedom rather than as induced metric as in TGD and then eliminates it using conformal invariance and Weyl invariance. What remains are imbedding space coordinates in some preferred metric for world sheet (gauge choice) plus Faddeev-Popov ghosts. In TGD one replaces the notion of path integral approach with that of WCW geometry.
Dear Matti,
Thanks, I have presumptions on GRT and this leads to misunderstanding about TGD. Therefore I try to ask about superposition of effects to understand better about it:
Suppose there is a test particle on a space time sheet. Now the test particle moving along the geodesics in the effective metric. This effective metric is sum over deviations of induced metrics from flat M4 metric at various space-time sheets.
Let create a new object on the same space time sheet that the test particle was on it. The induced metrics of the various space time sheets(also at other regions outside of the object) are changed by the object. Hence the object influence on the test particle by changing the metrics of various space-time sheets.
In GRT, one can say the new object only influence on the space time(that is one) but here it influence on the various space-time sheets.
But how can calculate that what is the amount of the influences on each of space-time sheets? For example sun because of it’s mass, influence on the space time sheets of solar system and the milky way galaxy. In other words, can one calculate counterpart of Sun to metrics of space-time sheets of solar system and of Milky Way galaxy at every points.
Dear Hamed,
quite a challenge! Thinking in terms of preferred externals it is clear, that the formation of wormhole contact (touching) between test particle and various space-time sheets assignable to massive bodies certainly affects the space-time sheets of the massive objects. The challenge is how to calculate this.
The approach that I take serious is QFT/string inspired. It assumes at fundamental level quantum superpositions of space-time sheets but does not deal explicitly with them. The outcome is essentially stringy description at the level of imbedding space. Getting rid of details is possible thanks to the gigantic symmetries involved.
*If one can construct QFT approach allowing to describe also graviton scattering, one can argue that one one forget all the details and apply the results even in astrophysical context. Since particles are space-time sheets at fundamental level, it would seem to me that Feynman diagrammatic approach is the only approach that can be practical.
*This gives amplitudes and by very general arguments the result must be same as those resulting from general assumption such as spin 2 character of graviton: twistor Grassmann approach would allow to skip over all details involved and approximate the situation by stringy variants of twistor diagrams in M^4xCP_2. It is quite essential that string world sheets connecting wormhole contacts are involved even in the description of ordinary physical particles: wormhole contacts itself are building bricks: without the presence of another contact one would have single Kahler magnetic monopole not allowed by field equations.
The beauty of this approach is that it automatically takes into account momentum conservation and the reaction of test particle to the motion of particle. To me this looks the most realistic approach as far as the response of central mass to test particle is considered at the level of momentum balance.
To be continued....
Continuation....
How to translate this picture to space-time geometry? *Suppose* that approximating of system with single space-time sheet makes sense with a finite measurement resolution [The objection that colour quantum numbers require superposition in CP_2 cm degrees of freedom can be circumvented.]
Does classical approach really work? Or should one consider motion as sequence of quantum jumps in which classical space-time surface assignable with the central mass or test particle is replaced by a new one and defines "instantaneous eternity" moving in M^4?
For "isntantaneous eternity" option the proper time coordinate along orbit would define a sequence of "instantaneous eternities" [in the approximation that the duration assignable to quantum jump vanishes.]. This option seems more attractive to me. With these assumptions the origins of space-time sheets with asymptotic Schwarschild metrics would move along the orbits of central mass and test particle in M^4.
One should also say something more concrete about these "instantaneous eternities". What it really means when "test particle is on a space-time sheet". Particle has wormhole contact connections to several space-time sheets. This question is also encountered in approach A leading to stringy amplitudes.
a) The most fundamental wormhole contacts correspond to the structure of particle itself and there is Kaehler magnetic monopole flux through them stabilising the contacts. One might call these two space-time sheets the fundamental ones and they are expected to be glued along their boundaries to form single two-sheeted structure - say in the scale of Compton length (it seems difficult to satisfy boundary conditions if one allows real boundaries). Then there are also the sheets, which particle just touches: these wormhole contacts are unstable. In this sense particle can reside at several space-time sheets simultaneously and experience the superposition of effects. Particle exists at space-time sheet when it has Kahler magnetically charged wormhole contact to it: this looks good.
b) Schwartschild metric allows imbedding as vacuum extremal and non-vacuum extremals could be small deformations of Schwartschild metric asymptotically. In the zeroth approximation only that of test particle. In the next approximation the M^4 positions of also central mass would change quantum jump by quantum jump. M^4 momentum conservation - not available in GRT - should help to evaluate this motion. The projection of the orbits to M^4 would be an essential part of description lacking from GRT description and give the Newtonian description in terms of forces.
Dear Matti,
So Thanks. it is some difficult for me to deduce the answer from your comments. So i need more time.
I ask another question:
One can say there are two Hamiltonians. One for vibrational degrees of freedom of the 3-surface in space of simplectic orbits of the 3 surface and another for cm degrees of freedom of the 3 surface. Sum of the two Hamiltonians are the total Hamiltonian. Is that a correct picture?
Dear Hamed,
the key idea is that scattering amplitudes for graviton exchanges at the level of imbedding space is the correct approach to gravitation.
This gives automatically rise to scattering with reaction from momentum conservation whereas in the approach of general relativity (geodesic lines) based on abstract space-time geometry one loses four-momentum and can speak only about acceleration.
The use of single space-time surface to describe the entire scattering is perhaps too strong and idealisation. "Instantaneous eternity" would replace single space-time with a sequence of them parametrized by proper time coordinate. The best approach is perhaps to accept WCW picture from the beginning since it is indeed used to deduce scattering amplitudes.
I will answer your question separately.
Dear Hamed,
thank you or nice questions.
You talk about Hamiltonians in the sense of classical field theory - essentially as generators of time evolution for 3-surface in WCW or rather - phase space associated with it. I am skeptic about the usefulness and even existence of this kind of description in TGD framework. Just this skepticism led to the notion of WCW and to geometrization of quantum theory.
a) In the usual classical QFT one can introduce formally Hamiltonian formalism once one has Lagrangian. This requires extension of the configuration space of fields at time=constant slice (analog of WCW) by introducing canonical momentum densities so that one obtains phase space as symplectic manifold: that is analogs of q, and p in wave mechanics.
Conserved energy for fields gives Hamiltonian acting in phase space, and one can formulate time evolution in terms of this Hamiltonian and also perform quantisation by the usual rules extended to infinite-D context. Of course, the usual problems emerge: normal ordering difficulties and infinities in perturbation theory due to squares of delta function. The approach works only formally since the replacement of Kronecker delta by Dirac delta does not work.
This problem relates deeply to three different algebraizations of quantum theory proposed by von Neumann: the use of factors of type III correspond to the naive replacement of Kronecker by Dirac. Hyperfinite factors of type II does not perform this replacement: finite measurement resolution is the key notion expressed in terms of inclusions of HFFs and it effectively keeps Kronecker deltas since finite measurement resolution implies discretization at space-time and imbedding space level.
b) In TGD framework this naive field theory approach fails. One can define canonical momentum densities but cannot solve time derivatives of imbedding space co-ordinates as single valued functions. The basic reason is that action principle becomes extremely degenerate at space-time surface defined by canonical imbedding of the empty Minkowski space. In lowest order the action is fourth order in gradients around M^4 so that one cannot defined propagator in terms of kinetic term quadratic in gradients. Perturbation theory fails completely because one cannot define propagator for small deformations of M^4. One could even define Hamiltonian as conserved energy formally but one cannot define the phase space so that it does not help much.
To be continued….
Continuation....
To sum up, Hamiltonian cannot define time evolution of space-time surface in TGD framework.
Hamiltonians appear in TGD (or my vision about TGD!) in completely different manner - as representations for Lie-algebra of the infinite-dimensional space of 3-surfaces. More precisely: the action is on partonic 2-surfaces at boundaries of CDs and field equations for preferred externals allow to continue its action to partonic 2-surface to that on entire 4-surface. This is delicacy but an important one.
a) WCW - or rather that part of WCW, which corresponds to quantum fluctuating degrees of freedom which by definition are those contributing to the line element of the metric of WCW - can be regarded as infinite-D symplectic group possessing a unique metric invariant under the group action. Here one can consider also coset spaces (finite measurement resolution and conformal symmetries) but this is technical detail.
b) The exponentiation of these Hamiltonians generates one-parameter subgroups of this symplectic group. These orbits are analogs of particle orbits with Hamiltonian dynamics but I believe that one cannot chose any specific Hamiltonian as "THE Hamiltonian": this for the reasons that became already clear.
c) These Hamiltonians define isometries of WCW (but not of imbedding space in general). This is important since it means that WCW has infinite-D isometry group. Without this there is no hope about well-defined Riemann connection in WCW as became clear already in the case of loop spaces.
d) These Hamiltonians can be taken to be function basis for delta M^4xCP_2 and they can be labelled by colour quantum numbers, angular momentum, integer n labelling the dependence on power of light-like radial coordinate.
Your decomposition to vibrational and cm degrees of freedom but Hamiltonian interpreted in terms of time evolution of TGD does not make sense in TGD framework but does have analog in this picture. Those Hamiltonians of CP_2 that represent isometries indeed act on CP_2 cm degrees of freedom of 3-surface. In delta M^4_+ the Hamiltonians representing rotation of delta M^4_+ (r=constant sphere S^2) are also isometries. M^4 translations do not allow representation as WCW Hamiltonians since they lead out of delta M^4_+. But this is another problem.
Dear Hamed,
what probably makes it difficult to understand TGD, are the thinking habits from general relativity and from classical field theory.
a) In GRT one thinks in terms of abstract 4-geometries: no forces, just geodesic motion. In TGD framework in terms of 4-D surfaces so that 4-momentum conservation and description of gravitational scattering in imbedding space M^4xS replace pure space-time description (forces as momentum exchanges make a comeback!).
This is what happens already in string models formulated in M^10: of course, this is unphysical option. This fantastic outcome was however lost since people wanted to get space-time out of the theory describing physics of 2-D space-times either by spontaneous compactification or by introducing branes. The introduction of stringy landscape probably is (and hopefully remains) the silliest sidetrack in the history of theoretical physics.
In TGD the fundamental approach relies on WCW: one gives up the notion about unique space-time and replaces it with quantum superposition of space-times. One can of course hope that unique space-time could emerge as a reasonable approximation made possible by finite measurement resolution.
b) Standard canonical quantization and path integral formalism fail in TGD even at formal level. Actually they fail also in QFT as the problems with infinities demonstrate.
The solution is geometrization of quantum physics by introducing WCW and represents something completely new having not counterpart in officially existing theoretical physics. WCW is the counterpart of configuration space. No counterpart of phase space is introduced since this is not possible. Finite measurement resolution (no replacement of Kronecker by Dirac) meaning use of hyperfinite factors of type II_1 is the mathematical counterpart for this approach.
Dear Matti,
Thanks a lot.
I participated yesterday and also today at conference on fundamental physics.
I ask my questions about your comments after that. Maybe tomorrow.
Dear Matti,
I can't go further. I must enough learn infinite dimensional lie algebras and after it, learn TGD. I try.
A non-related question to before:
The scale of atoms are very near to the scale of molecules. Hence it seems that there isn't any cutoff for the states of atoms at the resolution of molecules?
Dear Hamed,
the natural UV cutoff for object of given size is smaller than the object if one wants to say something about its structure, say the energy levels and electronic structure of atom.
In the case of hydrogen atom the UV cutoff should be below electron Compton length. For molecules one could treat atoms as point like: cutoff would be atomic size scale.
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