## Mercury, Lagrange, Einstein, Solar Dynamics

I was thinking about the Solar Barycenter motion and how General Relativity might account for some of the stellar changes as the sun changes orbital positions (and not getting very far). Partly because I’d been good at Newtonian mechanics and it was pretty well built into my brain when I ran headlong into relativity and just didn’t want to let go of what was already built in. A very similar problem happened with my exposure to Hamiltonian and Lagrangian math / physics. At that point, I had enough Physics to graduate, so just decided I didn’t ‘need to go there’. And set it aside.

That was a decent choice, really, as I’ve not missed ‘a good skill level’ in relativity and non-Newtonian mechanics. It just doesn’t come up much in life. ( Mostly it’s just good for understanding what theoretical is used in some Science Fiction and the occasional interesting bit of ‘news’ in the realm of real science. Knowing about them is as useful as knowing them for day to day pondering.

But every so often, I have had some regrets. Especially when I see something really really interesting to think about, and realize I don’t have the tools with which to do it. This is one of those moments.

So I’d originally thought that a ‘brush up’ on relativity might be enough. My general idea was that frame dragging might be involved with the solar changes as it wobbles around the barycenter. We have some evidence that objects as small as the Earth have a significant frame dragging:

http://www.nasa.gov/vision/earth/lookingatearth/earth_drag.html

The wiki gives an idea what kind of things happen due to frame dragging (and why I was interested in it, as it could induce some unexplained movements into solar matter as it is in a very high gravity field AND is rotating about the solar axis fairly rapidly AND the entire sun gets moved a solar diameter or so back and forth by the planetary gravity shifts. So with all that going on, some of these effects just looked like “they might matter”:

Frame dragging effects

Rotational frame-dragging (the Lense–Thirring effect) appears in the general principle of relativity and similar theories in the vicinity of rotating massive objects. Under the Lense–Thirring effect, the frame of reference in which a clock ticks the fastest is one which is revolving around the object as viewed by a distant observer. This also means that light traveling in the direction of rotation of the object will move past the massive object faster than light moving against the rotation, as seen by a distant observer. It is now the best-known effect, partly thanks to the Gravity Probe B experiment. Qualitatively, frame-dragging can be viewed as the gravitational analog of electromagnetic induction.

Also, an inner region is dragged more than an outer region. This produces interesting locally-rotating frames. For example, imagine that an ice skater, in orbit over the equator of a black hole and rotationally at rest with respect to the stars, extends her arms. The arm extended toward the black hole will be torqued spinward. The arm extended away from the black hole will be torqued anti-spinward. She will therefore be rotationally sped up, in a counter-rotating sense to the black hole. This is the opposite of what happens in everyday experience. If she is already rotating at some speed when she extends her arms, inertial effects and frame-dragging effects will balance and her spin will not change. Due to the Principle of Equivalence gravitational effects are locally indistinguishable from inertial effects, so this rotation rate, at which when she extends her arms nothing happens, is her local reference for non-rotation. This frame is rotating with respect to the fixed stars and counter-rotating with respect to the black hole. A useful metaphor is a planetary gear system with the black hole being the sun gear, the ice skater being a planetary gear and the outside universe being the ring gear. See Mach’s principle.

Another interesting consequence is that, for an object constrained in an equatorial orbit, but not in freefall, it weighs more if orbiting anti-spinward, and less if orbiting spinward. For example, in a suspended equatorial bowling alley, a bowling ball rolled anti-spinward would weigh more than the same ball rolled in a spinward direction. Note, frame dragging will neither accelerate or slow down the bowling ball in either direction. It is not a “viscosity”. Similarly, a stationary plumb-bob suspended over the rotating object will not list. It will hang vertically. If it starts to fall, induction will push it in the spinward direction.

Linear frame dragging is the similarly inevitable result of the general principle of relativity, applied to linear momentum. Although it arguably has equal theoretical legitimacy to the “rotational” effect, the difficulty of obtaining an experimental verification of the effect means that it receives much less discussion and is often omitted from articles on frame-dragging (but see Einstein, 1921).

Static mass increase is a third effect noted by Einstein in the same paper. The effect is an increase in inertia of a body when other masses are placed nearby. While not strictly a frame dragging effect (the term frame dragging is not used by Einstein), it is demonstrated by Einstein that it derives from the same equation of general relativity. It is also a tiny effect that is difficult to confirm experimentally.

Changes in time are likely too small to make much difference, but a sudden shift in what is ‘spinward’ or not, as the barycenter area is inside vs outside the sun, changing relative spin rates and masses, well, that has potential (IMHO).

So off I went to see if it was ‘worth it’ to spend weeks (months? years?) getting the skill level up on relativity and non-Newtonian mechanics. For an example of what it’s like, here’s the wiki:

https://en.wikipedia.org/wiki/Lagrangian_mechanics

https://en.wikipedia.org/wiki/Hamiltonian_mechanics

The Lagrangian math isn’t all that hard. But it still just looks like ‘mostly a bother’ to my Newtonian biased mind. I’m also prone to ‘over exploration’ and need to actively limit what things I go chasing after, lest nothing ever reach an end. Knowing how to ‘edit future time expenses’ is important; and this would take a LOT of time.

I’d started looking at Mercury, and how the orbit precession is a bit out of kilter for Newtonian mechanics and needs General Relativity to explain it. Figured it ought to have an example explanation or two somewhere; and if I wrapped my head around one body in an orbit I could likely make progress toward roiling fluids in an intense magnetic field in a ‘trefoil’ orbit of the barycenter. (Hoping mostly for just enough ‘clue’ to be able to make a ‘possible vs unlikely’ determination).

Along the way I ran into a striking paper. It claims to be ‘scheduled for publication 2013’, but doesn’t say where.

http://toe.sytes.net:65333/planetary%20precession.pdf

Scheduled for publication in early 2013

GALILEAN ELECTRODYNAMICS

Orbital Precession without GRT
David Barwacz

The anomalous precession of the planet Mercury’s orbit puzzled scientist for decades. Einstein developed a curved space model of gravitation (General Relativity) and showed that the precession of the planets could be explained very accurately with this model. This fact combined with the prediction and subsequent observation of the gravitational bending of light rays, made GR one of, if not the most, highly accepted theories in science. In this paper I will show that the precession of the planets can be explained with nothing more then Special Relativity, Newtonian derived formulas and simple mathematical relationships. The result is extremely accurate.

Keywords: Planetary Precession, General Relativity, Orbital Precession of mercury, Flat Space, Lagrangian

On the one hand, part of my brain is just refusing to accept that General Relativity might be wrong. Yet, Despite reading the paper over fairly closely, I can’t see where it is wrong.

There’s one place with a bit of handwaving on ignoring a very small term, yet that’s a frequently done technique. There’s some other places where I’m not good enough at Lagrange formulas to say for sure if he’s done the math substitutions right. (Sometimes in math problems, there are things that “look good” but are not allowed or lead to bogus results.)

So I’m “stuck” at this point. It’s a very interesting paper, with some rather dramatic implications if shown right. Yet I can’t “Vest” in it, as I can’t properly judge it.

### With that caveat

To give an idea of the implications ( or possible implications) we need to skip down to the bottom of the paper.

Conclusions

The precession observed in the orbit of Mercury can be explained with nothing more than well-accepted physical formulas, mathematical identities, and relatively simple mathematics.

No assumptions about the nature of the gravitational field are required and space is treated as ‘flat’. Although the above discussion is based on approximations, the small relativistic components should and do make it very accurate. One could infer from the above discussion that gravity acts on an objects total energy and not just rest mass. The additional energy is then treated as additional kinetic energy. No alterations of Newtonian gravity are required.

In this paper the Lagrangian operators were used to develop mathematical identities. It is clear that a modification of the Lagrangian method was required based on the functional form of energy equations. One can only wonder what other problems in physics may benefit from a reevaluation of the application of the Lagrangian method to non-Newtonian energy functions.

In the calculations there appears a curious term that deserves some exploration. The k term is orbital-path related. It skews the gravitational constant and this skewing can be positive or negative or zero depending on the eccentricity of the orbit. For the Pioneer space probe ε = 1.7372 and k is positive resulting in an increase in the gravitational force. Prior to being subjected to the ‘sling shot effect’, its eccentricity was most likely much smaller. This would have resulted in an effective increase in G after it reached its escape velocity, and may be at least partially responsible for the pioneer anomaly.

By including the k term in the calculation, one would expect slight variations from predicted orbits. NASA often uses the sling-shot effect to accelerate space craft. It is common to flyby a planet in a particular orbital path in order to change the orbit relative to the Sun (often substantially increasing velocity relative to the solar system Barycenter) and substantially changing the eccentricity of the crafts solar orbit. NASA has in fact measured small anomalies in the majority of Earth Flybys. Based on the formula developed here, one would expect small anomalies in the resulting solar orbit. Although a substantial amount of orbital data relative to the Earth has been published, there appears to be no data published relative to the change in the solar orbit. Such data would be necessary in order to determine if the method used here could shed some light on the anomalies. This author is preparing further papers to show that both the bending of light and the gravitational red shift can be explained using reasoning similar to that described here.

So at that point, light itself would be subject to gravity. Having very low energy per photon, it will not have a dramatic effect, but perhaps enough. Photons can take hundreds of thousands of years to get to the surface of the sun. During that time, being ‘slopped’ back and forth a bit by gravitational stirring could easily change surface dynamics in subtle ways. Similarly, areas of excess energy would be pulled down a bit more than those of lower energy. The potential for various feedbacks and rotational deflections of matter on the Sun increases.

But there’s even a bit more…

If gravity works on the total energy, not just rest mass, then various kinds of pulsating can be self driven. More energy build up leading to greater gravitational squeeze that makes even more fusion energy; until the heat builds enough to push the matter outward enough to decrease heat and lower gravitational pressures. We get something of a potential explanation for pulsars and related. (Yes, similar effects happen in Newtonian mechanics suns. This is a small quantitative change, not qualitative).

This could also be used as a mechanism for my notion of “photons orbiting each other” as the basis for matter. As gravity is an inverse square function of Radius, IFF it works on total energy, not just rest mass, all that is required is a very very very small Radius and those two packets of ‘total energy’ could exert enough gravitational force on each other to become stuck. At that point, all you need is angular momentum to linear momentum translations (and conservation) along with conservation of energy. Matter just becomes ‘condensed energy’ and the fundamental particle becomes the photon.

Unfortunately, that’s as far as I can get in the time I’ve put on it.
(Or am likely to put on it).

Rather than getting a better handle on how to “do the math” of General Relativity and a rotating wobbling sun, I’m further now than ever from an answer. While it’s interesting to contemplate a world with gravity acting on total energy, it adds rather than removing, complications.

With that, I’m going to step away from relativity for a while and go back to some money topics and ‘take a break’ from the harder stuff. Time for morning coffee… There’s nothing like setting out to simplify something, and having it become less sure and more complicated, to raise a thirst for more coffee ;-)

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
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### 8 Responses to Mercury, Lagrange, Einstein, Solar Dynamics

1. Jason Calley says:

The only way that frame dragging makes common sense to me is to invoke Mach’s Principle that inertia is the result of acceleration with respect to all the other matter in the universe. The very concept of inertia does not even make sense in a universe with one object. Hypothetically, in a universe with two very tiny objects located very far apart, inertia would be close to zero. Similarly, if you are orbiting near a massive body, then the massive nearby object tends to overwhelm the universal frame and your unaccelerated motion “falls in synch” with the huge neighbor. Maybe not the best phrasing on my part, but it makes at least a little sense to me!

One interesting aspect of the warped space-time near massive objects is that at some point the outward centrifugal force of orbiting bodies is reversed and becomes an inward pointing force that makes stable orbits unachievable.
http://www.npl.washington.edu/av/altvw55.html
This reversed force is not due to frame dragging but rather to the fact that the geodesics in the area are so very curved.

2. J Martin says:

…gravitational red shift…

Goodbye the expanding universe theory ? goodbye dark matter / energy ?

If so then the next paper from David Barwacz could be a humdinger.

3. EM – it’s something I’ve been working on since I first learned it around 40 years ago. General Relativity is not compatible with Quantum Mechanics, and they can’t both be correct, but we find that in practice they give the right answers. My attempt at this Gordian knot is to say that whereas QM tells you what is, GR tell you what you will measure, and what you measure is riddled through with speed-of-light problems, since that is what we use as our yardstick. Maths in GR gets somewhat tricky, and above what I can deal with.

Gravitational potential energy has to be stored somewhere. The most logical place for it would be extra mass in the objects, and that means that the inertial mass of something would increase the more gravitational potential it had. But then you look at a distant star and say something like “but this apple in my hand has a lot of gravitational energy to that star, and that one…” and the thing has to be turned round so that, as you get into a gravitational field, the inertial mass must actually decrease the deeper you go.

Logically, from QM, gravity cannot be mediated by speed-of-light-limited gravitons, since that makes the maths far too difficult for a particle to know what it is supposed to do. Since by QM any particle has a calculable probability of being somewhere else (say Alpha Centauri) at this moment of time, then the idea of gravitons and a localised particle gets a bit difficult to sustain. Since the inertial mass has to decrease as you bring two particles together, then we’re really looking at a “field” of spread-out matter probability. Noting that time slows in a gravitational field, I also turn this round and think that a matter-field must slow down time, and that the amount of slowing of time should be related to the probability density of the matter. Since matter-probability-fields must obviously overlap, where they overlap they must have a higher probability of some matter being there. If that is so, then time would go slower in that overlap. With slower time, the matter would have less energy, so the matter moves to the configuration where it has lowest energy – this looks like a gravitational field. So the gravitational field is only the result of time slowing in a matter-probability field.

OK, I’ve turned a few theories on their heads there. When I’ve finished the current projects I’ll go back to getting some maths behind it. More fun than watching football, anyway….

Once upon a time, back in the beginnings of the 21st. century, some people still believed that the universe was made of round, cold and dead stones orbiting all of them around hot furnaces fueled with hydrogen…and everything caused by (they called it a LAW) “gravity”. Such a “gravity” of them was really a very grave distortion of perception…That was back then….before the “fiscal cliff” happened :-)

5. R. Shearer says:

Please get back to it before the world ends. :)

6. p.g.sharrow says:

Inertia is the resistance to change in motion, relative to everything else. Relativity is measurements based on a point of reference. Mass is an indication of inertia under local conditions.Everything has some amount of inertia and therefor mass. Charge in motion. pg