The article says that Pioneer anomaly is understood. I am not at all convinced about the solution of Pioneer anomaly. Several "no new physics" solutions have been tailored during years but later it has been found that they do not work.

Suppose that dark matter is at the surface of sphere so that by a well-known text book theorem it does not create gravitational force inside it. This is an overall important fact, which I did not use earlier. The model explains both anomalies and also allow to calculate the total amount of dark matter at the sphere.

- Consider first Pioneer anomaly.

- Inside the dark matter sphere with radius of Jupiter's orbit the gravitational force caused by dark matter vanishes. Outside the sphere also dark matter contributes to the gravitational attraction and Pioneer's acceleration becomes a little bit smaller since the dark matter at the sphere containing the orbit radius of Jupiter or Saturn also attracts the space-craft after the passby. A simple test for spherical model is the prediction that the mass of Jupiter effectively increases by the amount of dark matter at the sphere after passby.

- The magnitude of the Pioneer anomaly is about Δa/a=1.3× 10
^{-4}and translates to M_{dark}/M≈ 1.3× 10^{-4}. What is highly non-trivial is that the anomalous acceleration is given by Hubble constant suggesting that there is a connection with cosmology fixing the value of dark mass once the area of the sphere containing it is fixed. This follows as a prediction if the surface mass density is universal and proportional to the Hubble constant. The value of acceleration is a=.8× 10^{-10}× g, g=9.81 m/s^{2}whereas the MOND model () finds optimal value for the postulated minimal gravitational acceleration to be a_{0}=1.2× 10^{-10}m/s^{2}. In TGD framework it would be assignable to the traversal through a dark matter shell. The ratio of the two accelerations is a/a_{0}=6.54.

Could one interpret the equality of the two accelerations as an equilibrium condition? The Hubble acceleration associated with the cosmic expansion (expansion velocity increases with distance) would be compensated by the acceleration due to the gravitational force of dark matter? Could one interpret the equality of the two accelerations as an equilibrium condition? The Hubble acceleration H associated with the cosmic expansion (expansion velocity increases with distance) would be compensated by the acceleration due to the gravitational force of dark matter. The formula for surface density of dark matter is from Newton's law GM

_{dark}/R_{2}= H given by σ_{dark}= H/4π G. The approximate value of dark matter surface density is from Hc=6.7 × 10^{-10}m/s^{2}equal to σ =.8 kg/m^{2}and surprisingly large.

- TGD inspired quantum biology requiring that the universal cyclotron energy spectrum of dark photons h
_{eff}=h_{gr}transforming to bio-photons is in visible and UV range for charged particles gives the estimate M_{dark}/M_{E}≈ 2× 10^{-4}and is of the same order of magnitude smaller than for Jupiter. The minimum value of the magnetic field at flux tubes has been assumed to be B_{E}=.2 Gauss, which is the value of endogenous magnetic field explaining the effects of ELF em radiation on vertebrate brain. The two estimates are clearly consistent.

- Inside the dark matter sphere with radius of Jupiter's orbit the gravitational force caused by dark matter vanishes. Outside the sphere also dark matter contributes to the gravitational attraction and Pioneer's acceleration becomes a little bit smaller since the dark matter at the sphere containing the orbit radius of Jupiter or Saturn also attracts the space-craft after the passby. A simple test for spherical model is the prediction that the mass of Jupiter effectively increases by the amount of dark matter at the sphere after passby.
- In Flyby anomaly spacecraft goes past Earth to gain momentum (Earth acts as a sling) for its travel towards Jupiter. During flyby a sudden acceleration occurs but this force is on only during the flyby but not before or after that. The basic point is that the spacecraft visits near Earth, and this is enough to explain the anomaly.

The space-craft enters from a region outside the orbit of Earth containing dark matter and thus experiences also the dark force created by the sphere. After that the space craft enters inside the dark matter region, and sees a weaker gravitational force since the dark matter sphere is outside it and does not contribute. This causes a change in its velocity. After flyby the spacecraft experiences the forces caused by both Earth and dark matter sphere and the situation is the same as before flyby. The net effect is a change in the velocity as observed. From this the total amount of dark matter can be estimated. Also biology based argument gives an estimate for the fraction of dark matter in Earth.

A simple TGD model for the sphere containing dark matter could be in terms of boundary defined by gigantic wormhole contact (at its space-time sheet representing "line of generalized Feynman diagram" one has deformation of CP_{2} type vacuum extremal with Euclidian signature of induced metric) with radius given by the radius of Bohr orbit with gravitational Planck constant equal to h_{gr} =GMm/v_{0}. This radius does not depend on the mass of the particle involved and is given by r_{n}= GM/v_{0}^{3} where 2GM is Schwartschild radius equal to 3 km for Sun. One has v_{0}/c≈ 2^{-11}.

An interesting possibility is that also Earth-Moon system contains a spherical shell of dark matter at distance given by the radius of Moon's orbit (about 60 Earth's radii). If so the analogs of the two effects could be observed also in Earth Moon system and the testing of the effects would become much easier. This would also mean understanding of the formation of Moon. Also interior of Earth (and also Sun) could contain spherical shells containing dark matter as the TGD inspired model for the spherically symmetric orbit constructed for more than two decades ago suggests. One can raise interesting questions. Could also the matter in mass scale systems be accompanied by dark matter shells at radii equal to Bohr radii in the first approximation and could these effects be tested? Note that a universal surface density for dark matter predicts that the change of acceleration universally be given by Hubble constant H.

For background and details see the chapter TGD and Astrophysics of "Physics in Many-Sheeted Space-time" or the article Pioneer and Flyby anomalies for almost ten years later.

## 17 comments:

Martin,

Now you are making deeper connections to foundational theory looking for the Big Picture. I am lately calling this Praeternatural Mathematical Physics.

Signs are important. This question of what we mean by speculative dark matter or multiverse concepts seems to be the source of many new papers.

Perhaps it is not so crazy for me to read negative 11 as a power of two or three in binary. I just do not see why physicists di not take p-adic math or surrealistic calculus more seriously.

Your synthetic intuitions are strong and carefully considered. You may have been ignored, marginalized, but it must be some consolation that you have been on the forefront of our dancing anew.

Matti (spell check error)...

I am also fighting against these spell check errors with my age vision! It is amusing that I get almost every day a link to a new anomaly and the solution as a rule is in terms of the few basic concepts provided by TGD. It is marvellous to collect the fruits of the work of 37 years and they hang rather low in the trees! Unfortunately my colleagues refuse to see (neither) the trees (nor the wood;-). What can I do? Buy them eyeglasses or what?

It is really a pity that my theoretical colleagues have missed the boat so totally. I have not saved my efforts in my attempts to communicate. After ten years of fruitless efforts I characterised their attitude as ordinary simple stupidity (collective, nothing personal). Decade later extraordinary stupidity looked more to the point. Now I remain just speechless as I read that super string people are trying to produce small cosmological constant and report at the end of the article a small might-be technical difficulty: the flux density (density, yes!) is infinite!

This makes me smile :)

The biggest anomaly of all are the constants. It must have been a hard nut for Einstein to swallow, the reintroduction of the dimensionless cosmological constant.

Still he held the clue to it, a small variation in the speed of light...

Cosmological constant is only a parameter, which appears at the GRT limit of TGD when the sheets of many-sheeted space-time are replaced with single slightly curved piece of Minkowski space: I have described the details many times and will not go to this.

At the level of many-sheeted space-time cosmological constant is not needed. The basic vacuum extremals providing rough long length scale description involve automatically accelerated expansion. Magnetic flux tubes carrying dark energy as magnetic energy and negative magnetic tension as counterpart of mysterious negative pressure provide more microscopic description. In the very early cosmology magnetic flux tube become cosmic strings and one has gas of string like objects.

Matti, what is the reason that the dark matter sphere should be located outside the earth? And not inside?

It is only necessary that the sphere and orbit have roughly same radii as becomes clear on thinks what happens in sling mechanism. Maybe I have formulated it too strongly. One can imagine that Earth was formed when dark matter first transformed to ordinary one at flux tube and the this flux tube contracted to Earth. The really nice prediction would be that the density of dark matter is universally .3 kg/m^2 and change of acceleration equals to Hubble acceleration. At least one could check this by spacecraft going through the sphere associated with Moon.

To place the dm sphere inside the earth has asecond advantage, that it coul explain the "growing earth hypothesis"

Yes. This is true at least if one identifies growing Earth hypothesis in terms of relatively rapid scalings of Earth radius by a power of 2 (p-adic length scale hypothesis) - say just factor of 2- and realising cosmic expansion in quantized manner at the level of astrophysical objects in general. This model would give connections also with Cambrian explosion in which highly developed life forms emerged from "nowhere" (actuality from underground seas in the proposed model as an outcome of rapid expansion causing fractures), the emergence of gigantic animals (as gravitation diminished by a factor 1/4), and also with climate evolution when oceans were formed.

The localisation of matter on sphere is of course an approximation. Spherical cell of radius given by Earth's orbital radius and of some thickness, say that given by Earth's diameter looks more realistic assumption. Instead of sphere one would have still 2-D surface but with very complex topology having a lot of handles and looking like a spherical shell of finite thickness.

Interestingly the gravitational Compton length calculated from gravitational Planck constant h_gr= GMm/v_0 does not depend on particle mass m and equals to the radius of Earth in good approximation. It would give estimate for the thickness of the shell.

An interesting question is whether this kind of rapid expansions have occurred also for solar system scaling up planetary radii by two and whether this could relate to Titius-Bode law.

Matti, I made a little sketch for the dark matter sphere inside the earth.

As a surprize even the so called P-wave anomaly could be explained. see:

https://www.flickr.com/photos/93308747@N05/15553800153/

Hi,

thanks for a very interesting comment.

In to remove possible misunderstandings I just re-state that in the case of Pioneer and Flyby anomalies is around Sun and has radius which is in good approximation the orbital radius of Jupiter/Earth.

It becomes clear from the illustration that you talk about sphere centered around Earth. This kind of sphere with radius equal to the orbital radius of Moon could be there and if the universality holds true the acceleration anomaly would be same as for Jupiter so that this is testable by using only satellites going farther than Moon. The special feature is that the anomaly would be same in very direction!

One can quite well consider also dark matter shells inside Earth. I have proposed that all astrophysical objects could have this kind of onion like structure. For the first time I proposed this with inspiration coming from an ansatz for an extremal of Kahler action: the mass density was localised to a shell. p-Adic length scale hypothesis would suggest onion like structure radii coming as powers of two multiples of basic radius. When many-sheeted space-time is

approximated by collapsing the sheets to single region of slightly deformed Minkowski space, this onion like structure is of course blurred.

I saw few days ago in Thinking Allowed Original:

https://www.facebook.com/groups/thinkallowed/

a link telling that Earth is claimed to have a kind of inner Earth. Maybe it could correspond to this kind of structure consisting of dark matter.

The onion like structure would at the level of dark matter with huge gravitational Planck constant h_gr= GM_Dm/v_0. M_D the dark matter mass for Earth or its part and m mass of elementary particle. What comes in mind is an analogy with atomic nuclei as a model for dark part of planets and also Sun. Nuclear physics suggests harmonic oscillator model as the first guess: in this case the radii of the shells would come as sort(n), n the diagonal quantum number. By equivalence principle the radii would not depend on m.

I have sometimes heard about P-wave anomaly but do not remember any details. It might well relate to this kind of macroscopically quantum gravitational onion like structure.

Fascinating!

Thank you for your reaction Matti.

Pioneer anomaly should be not influenced by this earth related phenomenon , i think.

Cool.

Oort cloud should be kind of such structure "in good approximation the orbital radius of Jupiter/Earth."

And it seems linked to dark matter http://physicsworld.com/cws/article/news/2014/mar/11/did-dark-matter-help-kill-off-the-dinosaurs :) (There are so many theories about this, but really...)

Modified Newtonian dynamics (MOND)[47][48] suggests that at their distances from the Sun, the objects comprising the Oort cloud should experience accelerations of the order of 10−10 m/s2, and thus should be within the realms at which deviations from Newtonian predictions come into effect. According to this hypothesis, which was proposed to account for the discrepancies in the galaxy rotation curve, which are more commonly attributed to dark matter, acceleration ceases to be linearly proportional to force at very low accelerations.[47] If correct, this would have significant implications regarding the formation and structure of the Oort cloud. However, the majority of cosmologists do not consider MOND a valid hypothesis.[49] http://en.wikipedia.org/wiki/Oort_cloud

Also around Milky Way is this same structure. Probably around every star and galaxy then.

What about the Allen belt?

Dark matter can of course be in two places, both at center and at surface boundaries. In galaxies it is seen more at the boundaries, I think? In biology it can very well be both.

http://arxiv.org/abs/1403.0576

Ulla: Indeed dark matter Black Hole point sources I suggest can be present as sunspots but also as galaxy anchor BHs. see perhaps:

images: 219, 221, 222, 225, 226, 229. of

https://www.flickr.com/photos/93308747@N05/?details=1

Everything is related calls "dark" not proven anything, nor can it be measured and counted. It is an attempt to cheaply can insert "a higher level" of science. But a major obstacle in the fact that no one has heard anything about what science calls "dark" as energy and matter. This "dark" is neither matter nor energy, because it is the ether that has no properties not matter or energy, for which there is no known almost nothing. Why? Because the ether substance that fills the infinite sphere of the universe, and belongs to the spiritual entity of the universe (SEU), which is under the command of the Absolute consciousness of the universe (ACU). It's just unfathomable power of creation. From the ether under the command ACU formed part of the manifested universe-COSMOS, which is visible, measurable, and of matter and energy. Anyone who tries to deceive others that he knows what is "dark" are just hallucinations reinforced the desire to achieve reputation in science based on the fact that empty no relationship with natural laws.

All of the materials and various energy "submerged" in the ether. And the tiniest subatomic particles (quarks and strings) are filled with ether, as our planet, ourselves and each cell in us.Kada man to be scientifically studied and began to believe SEU, and ACU. USING INTUITION, Then will open up vistas for observing what science calls DARK ".

I just finisht a combined aticle on plasma production and gravity effect for flyby:

https://www.academia.edu/10016801/Evidence_for_Dark_Matter_based_plasma_dust_and_ice_production_inside_Comets_like_67P_C-G._and_the_growing_Earth

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