Requiem for Relativity

For those people not too clued up on maths but who would like to take a look at a nice explanation, here's a link. Worth taking a look just to see the wonderful Ulam's prime number spiral.

plus.maths.org/issue25/features/whirlpool/index.html

Of note also is the families of simple quadratics of prime numbers, and that number b = 14 point something or other. When I was talking to Cosmicsurfer about this I did mention that 8 would be an interesting quantum number, as it's 2*2*2 a cube and the other two roots are going to be complex. I wonder if we can build models of possible solar systems?

I wonder what happens if nature uses some other system than you guys use in your models? Currently we humans are stuck on the modern numbering system but in the old days other humans used other systems to organize their observations of nature. Why assume the modern system is any better or nearer to being able to understand the nature of things? Maybe prime numbers mean nothing to nature and why should they mean anything? I don't get it but want to.

Hi Jim, it's not the case that there's the universe and then there is us. The universe by definition is all that there is. Life is a part of it, and life, if it's to survive, needs to learn any possible rules. Actually those rules are embodied in life itself.

A chimp might pick up a twig and get ants from a log, tool use. An aardvark does the same but with its tongue, and that's obviously not tool use. Use of a tool calls for abstract thought but the actual tool is still something from the environment.

The next step up, something emerging from complex biological structures, is the abstract tool. One to one correspondence. In effect our chimp says to its apprentice chips, get your own twig! Getting chimps to understand that the first twig is not some magic twig, takes a long time. The first chimp hasn't thought, oh I can use any similar twig, it probably thinks that it has the one and only magic twig. It's theirs though, and it's not going to part with it.

Lots of quite vicious fights at first but eventually the group learn the new technique and the survivability of the group gives them an advantage. Our clever chimp then learns a new trick. As a teacher its group status has risen. It gestures at a hole in an ant hill and another chimp does the work of getting the ants out. That's a tool, it's as much of a tool as a shifting spanner. This group of chimps have become a society of chimps. Cultural pressure, as an abstract tool, forces the dependance of the group into ever more complex tool use. I suppose we will have to divide thing up into abstract and concrete tool use, and further into implicit and explicit conceptual use. The first machine is the new dynamic of a learnt and shared co-operative survival strategy.

Jump forward in time, next to flint quarries are found balls of indented clay. Inside of them are found other balls of clay. These are contracts! The concept of one to one correspondence has made giant leaps forward. These people are as clever as we are. It can't be said however, that as yet, they have a number concept but they are well on the way to inventing one.

To cut a long story short, our mathematical number concepts are far more explicit than the people's of the past but its the same maths. A maths firmly rooted in sheer survival value. A maths furthermore that's rooted in cultural pressure. The upshot of that is, we get calculus when society has a pressing need for it and not before. We get new theories whenever there's a cultural paradigm shift. We are members of a society first and scientists/mathematicians second. Einstein lived in an epoch of cultural relativistic crisis, emerging global players needed a new concept of international law.

Back to the maths. Hop in a time machine and show Newton the lorentzian. He would recognise it as the equation of an ellipse. If you had written it as 1 - 1 / eta with eta being a very large number, he might have said, oh let's think of that as an exponential compound interest problem. He believed that the speed of gravity was instantaneous, he solves the problem of true compound interest being e, yet he cannot connect the dots.

As soon as we allow for the idea that gravity is faster than light and that we can have such a thing as negative refractive index, then the lorentzian looks as though it bears some relationship to the zeta functions of Riemann. We have a phase transition at the speed of light with a wave that can take on a neg r.i. The phase velocity; which could always go faster than light; suddenly switches into a group velocity and vis versa. We get two anti parallel waves, one goes leftwards slowly the other goes rightwards quickly, and vis versa.

Can we think of Le Sage shadows as wave guides? For the Earth and the Sun, we have a tapered tube which is tiny at the Shwartzchild radius of the earth and comparatively tiny at the centre of the sun. Can such a thing carry a wave that carries information? I would argue that it can. A decoherent signal can be reconstituted.

An exponential gravitational wave then, that carries the electromagnetic wave with it. Would the Riemann harmonics, which carry quantum information, be the factor that decodes such a wave? Our exponential curve now has steps in it. The steps become more and more accurate in terms of Gauss' dice the further we go along the line. A pattern of prime numbers, billions of light years distant, can then influence local quantum states. Pretty wild but I dont see anything wrong with the logic as yet.

The asteroid belt lies mainly between 2.1 & 3.3 AU. These radii correspond to the 4:1 and 2:1 orbital resonances with Jupiter. The 2:1 resonance seems a likely explanation for the outer, 3.3 AU, boundary. On the other hand, it's not obvious that the 4:1 resonance (rather than the 5:2, 3:1, or 5:1) should be the inner boundary.

Barbarossa's existence, combined with an ether theory, would give an alternative explanation, for the inner asteroid belt boundary at approx. 2.1 AU. With my estimates of approx. 0.0105 solar mass for the Barbarossa system at approx. 200 AU distance, the c.o.m. of the solar system lies approx. 2.1 AU from the sun.

A vortex of force at the solar system's c.o.m., significant for small objects, might have prevented planetary condensation in the asteroid belt (Bode's law --> planet at 2.8 AU). It might also be favorable for the orbits of small objects to have the solar system c.o.m. in their interior (positive "winding number").

In the 19th century, the Astronomical Journal published many asteroid observations, often with ~10 data points for one asteroid. Mostly these are northerly oppositions; most of the long series are from before the U. S. Civil War (War Between the States). The Astronomische Nachrichten published many long series of asteroid observations too, often from South America; most of these are from before World War I.

At Drake Univ. in Des Moines, I found two sets of observations of (9)Metis in 1851, 21 by Graham (who discovered Metis in 1848) and 22 by Ferguson of the USNO (AJ 2:12-13, 2:43-44). Ferguson says he corrected for parallax (i.e., his positions are geocentric) and for atmospheric refraction. Graham also says he corrected for parallax. Presumably Graham corrected for refraction (considering his precision). Graham gives Observed minus Calculated values too.

In these observations, Metis' longitude is near Barbarossa's. Metis and Earth had equal heliocentric longitude (Metis' fastest retrograde motion in geocentric RA) in early February. Barbarossa and Metis would have had equal heliocentric longitude in March.

Metis' perihelion is 2.10 AU, at longitude 74. Its eccentricity is only 0.12; and its inclination only 5.6deg.

Graham's Obs. minus Calc., in both RA and Decl, show Metis lagged significantly in geocentric ecliptic longitude (ecliptic latitude was unaffected) in March. Ferguson's data corroborate this.

Ferguson's March 1 & 2 points are invalid, because his article contradicts itself, regarding the catalog number of the comparison star. The Declination is 15 or 30 arcseconds off, for these two; maybe the wrong comparison star was chosen because its RA (but not Decl) equalled that of the correct star.

Comparing 3rd and 4th degree Lagrangian interpolation, I'm confident that I know Graham's "Calculated" accurately for five of Ferguson's points. For three other Ferguson points, there was enough difference between the 3rd & 4th degree interpolations in RA and/or Decl, to make the 4th degree interpolation doubtful; one of these was an extrapolation.

Ferguson's remaining five useful points within the interval of Graham's observations, show a consistently greater ecliptic longitude than Graham's. However, these points of Ferguson's, do corroborate the March lag in Metis' longitude.

I added a constant adjustment to Ferguson's RA and Decl, so that his five useful points would have, on average, the same Obs-Calc as the immediately following or preceding Graham points. I also added small corrections (<1%) for perspective, to all Obs-Calc values.

Then I found the vertex time, for the parabola in time, correlating best with any linear combination of RA & Decl Obs-Calc for the 21+5=26 time points. The best correlation was 0.49, i.e. 2.57 sigma, p=1.0% 2-tailed. Metis' orbit is inclined approx. 15.25deg counterclockwise (ccl) to the positive celestial equator in the observed region; the best correlation is a lag away from the direction 8.3deg ccl to the celestial equator. The maximum lag is March 24.2 (counting March 24.0 as noon), which happens to be the time of Metis' stationarity.

A kind of 90% confidence point, occurs 31 days retrograde (equivalent to 8deg of Metis' orbit) where the statistical significance of the correlation coefficient is p=10%. There was essentially no confidence point prograde, because the correlation coefficient decreased only slightly.

By Lagrange polynomial, I extrapolated the coordinates of the Barbarossa system's c.o.m., from the 1954, 1986, and 2007 photos. Remarkably, Metis' ecliptic longitude at the best-correlated time vertex, differs only 0.15deg from Metis' longitude at closest approach to the solar system's c.o.m. point, assumed to be 2.1 AU from the sun and with the same heliocentric coordinates as Barbarossa. My calculations considered orbital eccentricities and inclinations, to first order or better. Jupiter can alter this c.o.m. longitude as much as 0.14deg, but considering their positions, Jupiter & Saturn affected the c.o.m. longitude by + and - 0.07deg, resp.

So, there was an anomalous apparent rearward displacement of Metis, by a few arcsec (i.e., a few thousand miles) when Metis passed just outside the solar system's center of gravity (assuming Barbarossa's existence). The time of maximum displacement corresponded to a longitude only 0.15deg from Metis' closest approach to the solar system's center of mass.

The Astronomische Nachrichten 186(4450):147,152 at Drake Univ., contain analogous 1910 South American data for (71)Niobe, but for only three weeks, vs. four months for Metis. For Niobe's displacement, the correlation with a parabola in time, is much more significant statistically, but the direction is perpendicular to the orbit, and the longitude of maximum displacement differs 10deg from Barbarossa's. Niobe's time of maximum displacement lies in a statistical interval of only a few days, near Niobe's opposition to Earth.

Niobe passed well behind the theoretical solar system center of mass. Metis passed slightly behind the c.o.m. but well above.

Hi Joe, I've been thinking about Bode's "law "as well. Is it the case that our solar system is quantised? Let's say that we have an exponential aether that has these odd Riemann bites taken out of it. Then it makes some sort of sense, to me, to think of Bode's "law "as being somehow related to 1 /2 + b i

Now I don't think anybody likes that n = minus infinity for Mercury, let's face it it's a little bit of a cheat. So I thought Id say 1 /2 + 1/ 2 i for the Earth.
sqrt(0.5^2 + 0.5^2) = 0.7071 and the angle is obviously 45 degrees.

The first Riemann harmonic is 14.134725 approximately.
sqrt(025 + 14.134725^2) = 1.41435657041E 01
Now multiply that by 0.707 to get 1.00010112195E 01 Well the Earths orbit isn't one a.u. all the time, so lets call it ten. 10 angle 85.9 degrees.

Hi Stoat, excellent post on gravitational shadowing. I totally agree that the effect certainly casts more than a shadow but allows electromagnetic monitoring of graviton radiations. This is far different than looking for gravity waves, I am talking about an instant communications causing local electromagnetic/radio wave interference and this effect registers with in low frequency electronic devices as white noise. I submit that graviton energy is the cause for CMB radiation and that all background noise is instantaneously influenced by the higher spectrum graviton waves that could be heard for instance from a super nova way before the light waves from the explosion ever reached Earth. John