Full Neutrino Article

Do we live in a Brane Lensed Region By: Paul Karl Hoiland Abstract: I will offer a possible solution to the Neutrino Oscillation Problem where the KK series neutrino’s shed their energy in local brane lensing. This idea could explain both the Pioneer Probe slowdown and other observation evidence that suggests C is a variable. A 5-dimensional fermion Ψ can be decomposed into two Weyl fermions, Ψl and Ψr. The action of the model is given by

Where are the five dimensional Dirac Matrices. We then introduce dimensionlessYukawa couplings via

We will assume that

are of the order one.

We can then decompose the five dimensional fermions int states,

into a tower of KK

We then find that a certain linear combination of KK states are not coupled to left hand states. The ones that do are

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It is these other KK states that since they do not couple may be of primary import here. However, the lack of observational evidence supporting a major contribution to neutrino evolution tends to suggest the above forms could also play a factor in local and global brane lensing at least partially. In this context their resulting mass terms are

And the Dirac Mass Matrix is

With

we would use

. If

then we find the scale is far below that of the electro-weak symmetry breaking scale. If

And

These masses would fit well with those required of solar system observation data at present.

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Now the probability for say

to oscillate into sterile neutrinos is given by

Where

And

The current observation evidence shows the neutrino flux far below SM predictions and best alternative is some form of oscillation is going on. The actual data shows only a fraction get converted to sterile forms. It is this fraction I find most suspect considering the C velocity difference internal to external system is 8 meters per second which in itself suggests something of a fractural nature. Large fluxes of anti-electron neutrinos are produced at nuclear power reactors. If the flux can be either predicted accurately or measured by a nearby detector, measuring the flux at a certain distance L from the reactor gives the electron neutrino survival probability as

The results of current experiments are consistent with no oscillation hypothesis, that is,

The electron neutrino survival probability is determined by

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For

and the values chosen for the

The implication of test data so far is

Thus, I see our focus should be on those neutrino’s that should contribute and do not. That leads us back to the following states.

If we treat this Lensing along lines utilized in BH’s in the Bulk then we could utilize the model used by Whisker which is an RS model type II with a Reissner-Nordstrom black hole . The metric I will ignore for the moment since it can be found in several articles. The important issue is the charge has two effects: 1.) The tidal charge parameter Q comes from the projection on the brane of free gravitational field effects in the bulk, and it can be positive or negative. When Q is positive, it weakens the gravitational field, 2.) And if it is negative the bulk effects strengthen the gravitational field,(see Authors notes on this.) The horizon radius is given by

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And the radius of the Photon Sphere by

The near horizon metric would be

This is a modified version of the normal Schwarzschild one. We could utilize the above equations with the neutrino mass/energy to get a picture of the lensing effect. It would have to be assumed that since we have one local velocity of light in system and another external that these lensing neutrinos shed energy into brane lensing along their path from the Sun outward. We can then look at the following idea proposed by Fernando Loup. In a more generalized form, considering the metric

It follows,

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We observe that k is large for Brane Lensing. In turn, H doesn’t need to be large and It follows that

And

Manipulating this we get

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Consider then

Where g00=1 we have

So that

We then find that

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From which we find

When

is always positive. With the limit case we get

When where k is the coefficient for the Chung-Freese Brane Lensing. The total energy needed for local brane lensing is given by

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it follows that for dV to account for the Universe and Hyperspace dimensions, we must have

What one needs to get a proper picture here is to return to the older Dirac lattice idea on the Planck scale. Each Planck unit is seen as a miniature BH. If we consider these BH’s as mini-in-Bulk Blackholes then every particle has a Bulk BH inside it. While some particles stay on Brane and some travel off brane these specific Neutrinos lack of altering normal neutrino’s may be explained as their energy transforms the local brane lensing and in the process alters our in system velocity of light instead of the other. The external to local difference in C is only 8 meters per second based upon the Pioneer Probes signal difference which I suspect is evidence of just such a case. The total flux of neutrinos from the sun ought to be some 200 000 000 000 000 000 000 000 000 000 000 000 000 per second, corresponding to a flux of about 6.5 × 1010 neutrinos per square centimeter per second hitting the earth. The flux of neutrinos observed in Super-Kamiokande is less than 40% of that predicted from standard solar models (Fukuda et al 1998c). No significant variations with either day/night or season have been observed. The energy spectrum of the neutrinos is not significantly different from expectations, though there is a hint of a surplus (or smaller deficit, rather) at the highest energies (Fukuda et al 1998e; Normile 1998a). Neutrinos of different mass will behave in the same way as K0 mesons. The SNO has confirmed that the other 60% do indeed exist as other flavors of neutrinos. This has given further weight to the KK based modeling. A small mass difference and a high energy translates to a very long oscillation distance. With the other evidence of little or no oscillations and the fact that the KK series does exist at least in part there is further evidence for this theory and its long range effect out to the bounds of our Solar system would be well supported.

Reference: 1.) R. Whisker, Phys. Rev. D 71, 064004 (2005) 2.) Fernando Loup, Paulo Alexandre Santos, Dorabella Martins da Silva Santos, Hyperdrive A Go Go-The Star Wars Hyperdrive September 24, 2003 AUTHORS NOTES:

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The control of the Israel condition on the brane, at least the part that we can control is the pressure P and the energy density p associated with matter confined on the brane. Any increase here increases the warp factor. The actual equation used in general form is: -6δuα=κ25(1/2P + 1/3p) (* if we could generate negative energy then in essence we’d be doing the opposite and increasing the volume by lowering the local warp factor) In a normal condition this is assumed as a constant where p=-3/2P. For Neutrinos, depending upon how they appear in the Bulk and their associated tidal charge parameter Q from the equations in this article they could simulate or create either an increase or a decrease in local brane lensing. As mention more than the three KK series may be involved here and the resulting 8 meters per second velocity difference in system to external of our system could be a combined effect where different tidal charge parameters are mixed. It was the Sunward pointing vector in this problem that suggested to me to look for properties the Sun has which led to what type of particles it puts out. One can ignore both photons for lack of evidence there and exotic particles of heavy mass since their effect would be short range in nature. The only missing element under the SM is the neutrinos themselves. The Sunward direction suggests a vector quality not a scalar one in and of itself. The major reason I ignored them for the sake of this article is the other KK series neutrinos should travel off bulk with little effect to our brane and it is the three KK series neutrinos which should be contributing to neutrino oscillation and do not. This begs the question what do they do? When you combine this with apparent observation evidence from the Pioneer Probe of a sunward directed slowdown and consider the properties our Sun has their lack of contribution in one area tends to suggest they may contribute in another area. While I agree this is all speculative at best. Since we only have the data from one Probe to look at the alternative is to suggest that something is wrong with Einstein’s General Relativity. I would also suggest this could go a long way to solving some of the other observational evidence that seems to suggest C could be a variable that has called into question Einstein’s Special Relativity. If one remembers his C as a constant depends upon certain vacuum conditions then the idea of C being able to vary across space-time and cosmic history begins to become possible without a major violation of SR. In the context of general relativity, gravity is interpreted as the curvature of a 4dimensional space-time. The fundamental equations of general relativity are the Einstein’s Field Equations:

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Where

Is the Einstein Tensor

And

the energy-momentum tensor of matter. Given that general relativity is the theory that best fits available data at solar system scale and beyond, with the noted observation evidence that C could vary I find no reason to suggest GR is wrong. However, as a slight modification to GR brane lensing does offer a middle of the ground approach that preserves GR intact. As I have also mention this suggests a picture of the space-time consisting of discrete Planck lattice at the fundamental level. When the gravitational effect becomes important, there emerges an absolute limit on the smallest scale one can resolve. The reason is that with high enough energy stored in a local region, one creates a black hole instead of digging further into shorter distance. We can formulate this statement in a mathematically precise way. As is well known, the mass of a Schwarzschild black hole is proportional to its radius Newton’s constant can be translated into a length scale

And in D-Dimensional space-time as

By the uncertainty principle, the smallest length scale associated with

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where

Combining the black hole formula with this minimum uncertainty relation, we get

Since the event horizon hides all the information inside the black hole, it forbids further exploration on scale smaller than the black hole radius given by

This gives us

Thus the Planck length sets the limit on our ability to study the microscopic world. However our Planck lattice is not fixed, but can grow with increasing energy. This is the so-called UV-IR connection which can be expressed as

Now consider an ordinary matter system of energy E and size R.. If we drop this system into a single Planck unit the lost matter entropy must be compensated by the Planck unit’s entropy

This also applies to energy transfer into the Planck scale. Thus, the Bekenstein bound

holds even here. The area A is measured in units of

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Quantum Lattice at low energy

Lattice at high energy

We could also picture this along string coupling. The string coupling would be

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This leads to the black hole entropy

With

There would only be a weak coupling and since these neutrino KK states have small mass the range would be limited which is exactly what the observational evidence suggest. The governing of curvature is determined by the Israel Condition ΔKαβ = 8Π[Tαβ -1/3hαβT] Where Tαβ includes both the brane tension and the fields living on the brane. The brane tension is governed by the discontinuity in the slope of the warp factor of the brane. ds2 = e-2μyημνdxμdxν + dy2 is the usual five dimensional metric when Tαβ = 0. If one follows the double brane approach our brane has negative tension and the hidden brane has positive tension. In the single brane approach you vary gravity by varying the single brane tension which varies the volume of AdS hyperspace and Bulk space-time in an opposite fashion also. So assuming we have no energy condition violations to account for and all energy is positive in our space-time the way to alter the brane tension of our single brane is to increase or decrease the energy present. If positive energy works to compact the volume then reducing the energy should work to increase the volume. The only usable way to achieve this that does not involve weak energy condition violations requires either a carrier particle that affects at least locally the Israel condition or a process to shift energy into the Planck scale. Nature seems to use both a carrier and a reduction in local mass/energy density with the later not involving weak energy condition violations. As far as the hyperdrive idea proposed by Fernando Loup goes we can only reproduce the first and possibly simulate the second with something akin to the Woodward effect focused at the Planck scale.

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