Wikipedia: “v > c is possible for cosmological red-shifts because the space which separates the objects (– for example, a quasar from the Earth) can expand faster than the speed of light ”

The fallout of the Schwarzschild radius as a physical delimiting parameter
The “fallout” that the Schwarzschild Radius is, as a physical delimiting parameter.

Yesterday night (– this article written on November 28, 2011), I hit upon, accidentally, on an article in the internet, that had in 2009 exposited on something exactly in my line of thinking, which I have been occupied with only in the last week. (– This article linked at the bottom can’t be found as its missing.)

The Pioneer Anomaly is something I haven’t studied yet, in detail, except my Flyby Anomaly Analysis results tell me the Schwarzschild Radius is a physical parameter, contrary to Weinberg’s exposition on this where he tells us despite its lack of physical meaning its a moral lesson anyway and the radius changes with coordinate system transformations. While that is correct, my insight is new. … The Schwarzschild radius explains the flyby speed increment as a ratio of the Schwarzschild radius ( hence forth S-radii) and the separation from source of mass of primary. The speed increment therefore drops rapidly as an inverse of separation {– or higher power radial?}.

SO, that is the physical meaning of S-radii, if this S-radii is an actual radius as in case of a black-hole, this means the speed increment or speed fallout or “speed error” permitted by theory (– of Relativity, namely: General Theory of Relativity which is a theory of gravity by Albert Einstein)  is vast. But for cosmological objects whose actual radius is far larger than S-radii, — such as planet earth,we happily roam around on the surface of such objects. When this surface, eg in the case of a satellite that is escaping such surfaces or bodies, and the separation is even much larger than actual surface radius, the speed increment decreases, maintaining a ratio with the S-radii.

The fact that the speed-fallout depends on S-radii is therefore a physical attribute of the S-radii. The S-radii is an edge in the space-time which even light can not escape (– not just for black-holes but for any kind of gravitational objects that can sufficiently modify space-time) and how much light can not escape is given by how close light is placed to the source of potential. eg for black-holes light does not escape at-all in addition to Quantum Mechanical uncertainties known as Hawking Radiation, but for other massive gravitational objects by certain amount the light suffers in its motion.

eg for our sun the S-radii is about 3 kms hence in its motion light will suffer uncertainties of the order of 3 km/second in its speed of 3,00,000 km/second close to Sun’s surface and gradually lesser, away from the surface. But for earth, light suffers about 1 cm / second if light passes close to earth surface, and lesser and lesser away from the surface. The exact anomaly that light will suffer will be lesser than S-radii, the exact value of S-radii of earth is closer to 9 mm, and we are never in the center of earth and in the center of earth there is not enough mass, so it only makes sense that light will suffer on the surface of earth a few mm/second anomaly, which is what flyby anomalies are.

Extending this to the Pioneer Anomaly last night I calculated that the Pioneer-10/11 escape the Sun-potential with a speed fallout to the order of 622 kms/year, or depending on how you factor in the speed, in my calculation, this can be half that value as well, 311 kms/yr. This is “exactly” what is observed in case of Pioneer Satellite, ~400 km/year fallout. So Schwarzschild solution of theory-of-relativity indeed explains Pioneer Anomaly. These solutions are basics and how did it even escape for decades? It happens when we ignore basic ideas which can be done back of the mail and we jump onto complicated ideas first.

The article I mentioned above {– linked below, but target does not exist anymore} I arrived at accidentally, also did the same conclusion, in 2009. It brought in escape velocity as the observed fallout speed and the Hubble recession. Hubble recession gives an additional speed to objects placed at that radial point because space is expanding, hence a minus sign from the fallout speed. Fallout is what you call Pioneer or flyby anomaly, a puzzling speed increment. I make an additional note enlightened by Weinberg: the Hubble constant here is actually in the order of the angular velocity of the receding object coming from the potential which it is trying to escape.

Check the beautiful beautiful text of Weinberg, my money has turned worth of spending on this text, angular velocity in orders of negligible 2nd orders which is what it is when you are far far away from source of potential, is a power of 3/2 of inverse radial separation. v=wr, velocity-squared is thus “one” inverse radial separation, velocity squared is what is in order of potential and order of time dilation/contraction.

SO the actual potential, the angular motion of Sun hence the receding Pioneer and Hubble adjustment are perhaps enough, at-least fittingly, to explain the pioneer anomaly.

The Schwarzschild has already explained the Flyby although that is not how I proceeded to explain this, it turned out that it had such a simpler explanation, basic Relativity Theory. Needless to say as I have mentioned elsewhere it all came to my notice because I was studying the OPERA anomaly in terms of gravitational effect on the GPS satellites and I was solving for it’s trajectory.

You can expect me to publish all these results soon, but I am bounded by my own resources.

SO you hear people telling you the pioneer anomaly acceleration matches a -c.H, note that this is same as -cw, where w=angular recession speed as I just explained above, which is to be subtracted from the fallout speed. So without a Hubble constant expansion my Flyby analysis is exactly same as Pioneer anomaly and as I had noted in another article perhaps, the radars are placed ON EARTH for both cases, a difference that should not bother you, it just gives you an angular deflection because WE (earth) are perhaps “equally” away from the Pioneer as the Sun.

The pioneer is a real pioneer, it has escaped the solar system which is at-least 1 AU. And I did another 1 AU calculation yesterday which gives why the Solar orbit motion of the GPS-satellite and EARTH together means it is the differential effect of this motion which goes towards a 10^-16 order and is not a cause to worry regarding the OPERA anomaly.

Just the basic celestial mechanics explains these anomaly (Pioneer and Flybys) for almost all parts of the effect. And in case of OPERA Anomaly the basics explain that the anomaly is NOT coming from Gravity related effects ** . One more note: like the Hubble expansion correlation in case of Pioneer, in case of flyby, Anderson had given a 2.w.R * (deflection_initial – deflection_final). That’s nothing but the total angular deflection I had given from basic considerations, recently. I gave for photons, in-case of satellite one needs to factor in the small velocity of satellite into the trajectory and its mass, photons travel at c=1, but satellites at non-relativistic speeds. But this is basic general relativity as given in Weinberg’s Text, referred above. SO, in both cases, flyby and pioneer, basic Physics explains the anomaly and in case of OPERA we have to look elsewhere.

** As an update, while OPERA experiment claims that their wire was not in place, their paper must give a Physics reason, the Physics reason has been pointed out by me 2 years ago, namely Heisenberg Uncertainty Relation gives a stringent condition as to what will be the uncertainty on photon speed given an uncertainty on its energy, Photon being a mass-less particle Energy-time uncertainty translates as speed-time uncertainty, hence a few MB or KeV error in the experiment detector which is a very common thing in particle detectors, I worked in the Belle Detector in Japan that measures neutrinos among other things, would easily give a 7.5 km/second error of light speed, which is what the neutrino is traveling above speed-of-light, this was not considered in their paper. Even if the wire was in place such a result has to be considered a theoretical uncertainty mixed with systematics of detector rather than a technical or electronics glitch.

Note: (The following note is redundant now except shows some science in action: what I suggested Vs how I myself arrived at an answer, the answer being the above update) One of the strongest candidates that need to be studied is the “Optical” nuclear potentials affecting the neutrino’s motion along the baseline, just in case. Although the neutrino’s excess sounds to be too much to digest, if true, astounding Physics is knocking at the door, if not we have real time lesson, how to do science. Not that we have not had these kind of lessons plenty of times in the history of scientific investigations but they are not popularized. What is popularized more is warped dimension and multiverse. Just in itself it is not a bad idea, the later. But our efforts should span in a comprehensive way so that we make actual progress in the education of science.

From Anderson’s flyby formula (as written above: 2.w.R * (deflection_initial – deflection_final) ), empirical they called it but it was basic physics, because thats exactly what the Relativity Theory predicts for trajectories of particles in cosmos. (Refer to Weinberg’s Text in Gravity again) This should have been clear as soon as these correlations were known or as soon as we notice that flyby is millimeter range and Earth S-radii is millimeter range.  The last blocked statement is not due to  Anderson, but it was never noticed, you can duly credit this to me. :)

For Pioneer Anomaly one could immediately see that Sun’s surface potential is 1000 times stronger than earth’s hence the 3 km S-radii of Sun drops to millimeter again, as observed for Pioneer, towards a distance of 1 AU, a few millimeter per second is 400 kms/year.

One more note, in case of Flyby our radar is placed on earth but in case of Pioneer our radars are not placed on Sun but on earth, all that matters is we have to slightly adjust our coordinate systems origin. The 622 kms/year I gave is for 1 AU separation from Sun, so this will go further and further down as Pioneer satellite recede completely out of Solar system range, very good names though, Pioneer. Send Jimmy on one of these satellites. He once claimed to me he is a pioneer while driving me in his car towards Tsuchiura and took his hands off the wheel for a couple sec, I said that’s fine but first restore your driving control.

The following link has lost its target I don’t know why Sesselman removed his website. If you get hold of him ask him, there was some cool physics there.

Click on the link: to read Steven Sesselmann’s musings about Pioneer anomaly, note of caution he is playing his mind around fictitious theories like where he thinks force is needed to be disregarded but not potential, such things have no meaning and you need not give him more peanuts than he is asking, argue with him.

— The link might have changed, I do not pursue anyone though to have a compulsive voyage to find out the exact article. It was mentioned in jest only.  

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