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The CERN-SPS accelerator has been briefly operated in a new, lower intensity neutrino mode with about 10 ^{12} p.o.t. /pulse and with a beam structure made of four LHC-like extractions, each with a narrow width of about 3 ns, separated by 524 ns. This very tightly bunched beam structure represents a substantial progress with respect to the ordinary operation of the CNGS beam, since it allows a very accurate time-of-flight measurement of neutrinos from CERN to LNGS on an event-to-event basis. The ICARUS T600 detector has collected 7 beam-associated events, consistent with the CNGS delivered neutrino flux of 2.2× 10^{16} p.o.t. and in agreement with the well known characteristics of neutrino events in the LAr-TPC. The time of flight difference between the speed of light and the arriving neutrino LAr-TPC events has been analyzed. The result is compatible with the simultaneous arrival of all events with equal speed, the one of light. This is in a striking difference with the reported result of OPERA that claimed that high energy neutrinos from CERN should arrive at LNGS about 60 ns earlier than expected from luminal speed.
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The TGD based explanation for the anomaly would not have been super-luminality but the dependence of the maximal signal velocity on space-time sheet (see this): the geodesics in induced metric are not geodesics of the 8-D imbedding space. In principle the time taken to move from A (say CERN) to point B (say Gran Sasso) depends on space-time sheets involved. One of these space-time sheets would be that assignable to particle beam - a good guess is "massless extremal": along this the velocity is in in the simplest case (cylindrical "massless extremals") the maximal signal velocity in M^{4}×CP_{2}.

Other space-space-time sheets involved can be assigned to various systems such as Earth, Sun, Galaxy and they contribute to the effect (see this). It is important to understand how the physics of test particle depends on the presence of parallel space-times sheets. Simultaneous topological condensation to all the sheets is extremely probable so that at classical level forces are summed. Same happens at quantum level. The superposition of various fields assignable to parallel space-time sheets is not possible in TGD framework and is replaced with the superposition of their effects. This allows to resolve one of the strongest objections against the notion induced gauge field.

The outcome of ICARUS experiment is not able to kill this prediction since at this moment I am not able to fix the magnitude of the effect. It is really a pity that such a fantastic possibility to wake up the sleeping colleagues is lost. I feel like a parent in a nightmare seeing his child to drown and being unable to do anything.

There are other well-established effects in which the dependence of maximal signal velocity on space-time sheet is visible: one such effect is the observed slow increase of the time spend by light ray to propagate moon and back. The explanation is that the effect is not real but due to the change of the unit for velocity defined by the light-velocity assignable to the distant stars. The maximal signal velocity is for Robertson-Walker cosmology gradually increasing and the anomaly emerges as an apparent anomaly when one assumes that the natural coordinate system assignable to the solar system (Minkowski coordinates) is the natural coordinate system in cosmological scales. The size of the effect is predicted correctly. Since the cosmic signal velocity defining the unit increases, the local maximal signal velocity which is constant seems to be reducing and the measured distance to the Moon seems to be increasing.

## 13 comments:

Dear Matti,

-I learned the basic notions of Riemannian geometry like geodesics, Riemann tensor and … but I am skeptic about the basic notions of the manifold. For example one can assigns to each point of a manifold a tangent and a cotangent vector space but I don’t think in TGD a 3-surface composes of points? Does in TGD Classical space-time points would be replaced by regions of the space-time as like the viewpoint of C. J. Isham? Then it should be reconsideration in basic notions of manifold.

-Another question:

I have “The philosophy of Quantum mechanics” in the academic term. My teacher said:

“In Bohm quantum theory, one can decomposes psi(wave function) as Psi=R * exp(i*s/h). and the principle: v=grad(s)/m,

v is the classical velocity of the electron.

Therefore in Bohm theory one can assigns to a particle both a wave function psi and particle positions(as classical). (some weak similarity with TGD!)

Bohm theory is very richer than Bohr model for describing the orbitals of hydrogen’s atom “

Is there any relation between the classical position of a particle in Bohm theory and classical space-time x4(x3)?

In TGD Psi replaced with M-matrix and exp(i*s/h) is Generalized to S-matrix, then what does it means v=grad(s)/m in this generalization?

Dear Hamed,

I will answer your questionS after I have returned to home. I am not at summer cottage of my friend and computer is unfamiliar to me and even typing is very difficult!

No problem, Thanks Matti. I will wait for that.

http://arxiv.org/pdf/1102.5002.pdf a book with link to quantum geometrodynamics from 2011

Ulla,

I hope Matti can check out the link at my last post containing comments to you- I need to learn more of how to use the computer, old bad habits are catching up with me like not typing the numbers by touch or using only one side of the shift keys.

hammed,

you seem interested, I have posted some fundamental things on the nature of Riemann manifolds in the continuous and discrete worlds.

ThePeSla pesla.blogspot. com

Matti,

You are right of course that the velocities depend on the spacetime sheets, 8D or otherwise. But in the simple model I just suggested for hammed it may not be in principle that these can be observed in the actual measure and it s range as a real physical path after the fact of it for analysis. But this does not make the reality of the symmetries and levels there something fanciful and unreal.

Matti,

a challenge for TGD relating to three recent science daily articles if you want to play, a thought experiment in the testing of the measure of total theories and their range and unity. Called Evidence

ThePeSla

Dear Hamed,

Your first question was following:

"I learned the basic notions of Riemannian geometry like geodesics, Riemann tensor and … but I am skeptic about the basic notions of the manifold. For example one can assigns to each point of a manifold a tangent and a cotangent vector space but I don’t think in TGD a 3-surface composes of points? Does in TGD Classical space-time points would be replaced by regions of the space-time as like the viewpoint of C. J. Isham? Then it should be reconsideration in basic notions of manifold."

I am not quite sure what you mean! 3-surface is locally a manifold and decomposes to points: in other words it is chartable and therefore can be represented by 3-D maps with each page of the map 3-D Euclidian space E^3 and there are chart maps identifying the images of same point at different pages. Chart book about the surface of our planet is an example about what I mean! There are diffeomorphisms between different pages of the book.

One can assign to it tangent and co-tangent spaces and their tensor products and powers and this is necessary in order to define forms and vector fields. For instance, induced metric can be interpreted in terms of induced tangent bundle.

There are of course some delicacies. Local manifold property can fail for surfaces and it does so for the "lines" of generalized Feynman diagrams at vertices in the same manner as it fails for ordinary Feynman diagrams at vertices due to the fact that the topology of "Y" is not topology of "I".

There is also the notion of finite measurement resolution which could be also understand as discretization obtained b y replacing space-time regions with points. Consider as an concrete example all space-time points for which coordinates have same first N decimal digits. This defines certain space-time region replaced with single point.

About Isham's view point I do not know enough to say anything.

Dear Hamed,

you second question.

"I have “The philosophy of Quantum mechanics” in the academic term. My teacher said:

“In Bohm quantum theory, one can decomposes psi(wave function) as Psi=R * exp(i*s/h). and the principle: v=grad(s)/m, v is the classical velocity of the electron. Therefore in Bohm theory one can assigns to a particle both a wave function psi and particle positions(as classical). (some weak similarity with TGD!) Bohm theory is very richer than Bohr model for describing the orbitals of hydrogen’s atom.

Is there any relation between the classical position of a particle in Bohm theory and classical space-time x4(x3)?

In TGD Psi replaced with M-matrix and exp(i*s/h) is Generalized to S-matrix, then what does it means v=grad(s)/m in this generalization? "

I try first to summarize what I have understood about Bohm theory.

a) I think that the original motivation was to keep theory deterministic and classical by introducing the hydrodynamical interpretation. The first ad hoc postulate is Guiding equation is that some points representing classical particles are "active" and entire solution of Schroedinger equations serves as guide wave defining particle orbit as a flow line of a hydrodynamical flow so that one would have a kind of hydrodynamical interpretation. This implies non-locality of the theory since the Schrodinger amplitude induced "quantum force" acting on the classical particle.

Particle motion is determined by the identification of velocity as given by above formula: Newton's equation is replaced with first order differential equation for a flow. This is quite a big difference from second order differential equations in Newtonian framework. I think that one obtains Newton's equations at semiclassical limit.

See http://en.wikipedia.org/wiki/Bohm_interpretation#Guiding_equation

b) I do not understand how one could obtain state function reduction from this picture as a prediction. The reason is that the theory is deterministic and Quantum equilibrium hypothesis - second ad hoc postulate - stating Born rule is introduced but according to Wikipedia it has not been shown that it follows as asymptotic property of

solutions of Schrodinger equation.

c) At the level of formulas Bohm theory makes sense in wave mechanics. In QFT it ceases to do so since the highly non-linear formulas cease to make sense infinite-D context. For fermions described by Grassmannian variables classically this idea fails.

d) The weakness of the Bohm theory is that if you want to apply it, you must do the practical calculations using ordinary wave mechanics and then introduce Bohm theory. Just a complex re-interpretation with two questionable hypothesis is in question state function remains a mystery.

Dear Hamed,

You wondered about similarities between Bohm and TGD. I shall first list the differences between Bohm's theory and TGD.

a) In TGD one assumes state function reduction governed by Born rule plus Negentropy Maximization Principle. No analog of quantum equilibrium hypothesis is introduced.

b) Dynamics of space-time surfaces is dictated by Kahler action plus preferred extremal property rather than by guiding equation.

c) No selection of "active" space-time surfaces is made and the field equations defining space-time surface are defined by Kahler action rather than wave functional.

There are also similarities.

a) Also TGD is very classical. At WCW level one has only classical spinor fields. At space-time level classical physics, which fails to be strictly deterministic except locally - is exact part of quantum theory and even WCW geometry: space-time surfaces are analogous to Bohr orbits. This translates to holography in 3-D and even 2-D sense as effective 2-dimensionality: partonic 2-surfaces plus 4-D tangent space data. Path integral over 4-surfaces is replaced with functional integral over 3-surfaces (or 2-surfaces with these data).

b) Quantum classical correspondence - more or less equivalent with holography - requires that the quantum numbers of quantum state must be coded into the geometry of the preferred extremals: this is highly non-trivial condition and I have discussed a detailed proposal for how this is achieved. Guiding equation is therefore replaced with much weaker condition.

I cannot imagine any interpretation for v=grad(S)/m since S is not a function in WCW but matrix between positive and negative energy parts of zero energy states.

You talk of the 3-surface as lightlike or Euclidean, sometimes use the massless extremals analogy.

A wormhole has these charachters. How is a wormhole done?

Can this be understood as space without gravity and time too?

Then here would be FTL conditions, as a giant plasmoid/particle?

Massless extremals are 4-D surfaces: correlates for radiation. I would compare them to laser beams.

Wormhole contacts are formed unavoidably if you have two space-time sheets whose projections are in same region of Minkowski spaces. These surfaces are with distance about 10^4 Planck lengths and unavoidably touch here and there and form wormhole contacts.

Dear Hamed,

As the course has to word "Philosophy" in it, David Bohm is excellent choice. Bohm tells himself that his own interpretation was not meant as final word of interpretations of QM, but primarily to reestablish dialogue in science after the Einstein-Bohr communication breaddown. Also the word and concept of no-collapse decoherence was originated by Bohm.

In my youth Bohm's philosophical ideas about order of orders (deterministic-chaotic continuum, generative, implicate and holomovement orders) was an eye-opener and 'Science, Order and Creativity' is one of the best books I've read.

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