The Problem with Fields .
21 Dec 2008
A sad tale of Hidden Assumptions and Fictitious Forces .
Our story begins with Isaac Newton about 400 years ago . He proved that radially symmetric bodies (like balls) can be treated as a point-mass from a gravitational viewpoint as long as f=G*m(1)*m(2)/ (R^2) holds . This is his famous Law of Gravitation .
Fast forward to the Twentieth Century . Space probes were measured to have accelerations not predicted by expected theory . (See New Scientist 20 Sept 2008 p38 "Fly-by Fright." )
Fright indeed . Physical laws were under threat .
It was first noticed with the Pioneer probes and stimulated the MOND (Google it) modification to Newton's Law .
But the effect was small and controversial .
But then even a bigger shock came . Probes doing slingshots around the Earth (like Gallileo in 1992 , Near Shoemaker in 1998 ) showed such large divergences from expected velocities after the slingshot that the matter could not be swept under the carpet anymore . (The favourite human response.)
Is our understanding of physics wrong ?
What is going on ?
They treated planets as point sources in their programs .
(Remember , these are the guys that mixed up newtons and poundals on the Mars probe) .
The Earth-Moon illustration .
The system orbits around a common center of gravity which lies inside the Earth .
Even school atlases' state this .
You can treat the Earth as a gravity point-source , but then you must include the Moon as well (and other bodies , but their effect is very small) .
The velocity change during the slingshot maneuver is dependant on the Earth's rotation around the common center of gravity . The Earth-Moon rotational plane coincides roughly with the Earths equator . Hence the observational datum that the velocity change is proportional the difference in the angles incoming and outgoing with reference to the equatorial plane .
What is happening ?
Are conservation laws being violated ?
Internal Slingshot .
It is simply a slingshot maneuver around a virtual mass .
The Earth-Moon rotating system is not radially symmetric . It is lumpy . The velocity change is dependant on a large number of factors , but can be calculated .
The energy comes from the weak coupling between angular momentum and linear momentum .
From a really basic viewpoint , this can be easiest seen as the difference between a straight line touching a circle and the continuation of the circle . (Newton's laws measure forces by disturbances from a straight line .)
Another way of looking at it :
The gravitational attractions on an outside probe of masses rotating around each other and about a common center of gravity do not cancel out . A small vector-residue is left .
This is a dynamical effect . Movements only need apply .
This can be calculated ,
But will vary in every instance .
(A software-computer (General Theory) is not possible .) This is because there are three bodies involved :
Earth , Moon and Probe .
The Three-body Problem has no general solution . This is well known in mathematics Now are you happy ?
Calculating this gravitational difference gives rise to a disturbing effect : the mathematical terms for the field probe does not vanish .
In hindsight , a necessary effect because of the general insolubility of the Three-Body problem . But not obvious beforehand .
This is simply restating there is no general solution of the Three-body Problem .
Two bodies plus a probe makes a three-body problem . Every case will be different . Use Chaos theory .
This will be true for any body in the solar System (ie Pioneer probes) , as well as any rotating set of bodies in this Universe .
The Field Assumption .
Beloved of theoretical physicists , mainly because they are too lazy to do it properly .
The Classical definition is a probe mass , charge or whatever examined near the identifiable object . The forces the probe experience are defined as the Field . The Probe is then ignored .
This has the hidden assumption that the effect of the probe can be cancelled out .
(Ie that it is really a Two-body Problem).
In most radially symmetric objects like balls or charges this can be done .
But , alas , it breaks down if the objects are lumpy . Then the pesky mathematical terms denoting the probe just won't go away .
Without the hidden assumptions about symmetry , error margins have to be specified .
We cannot use our software computer (ie theory) to cancel out the interference of our test-probe .
This is analogous to Heisenberg's Uncertainty Principle , but not similar .
You have to understand levels of Randomness
(See http://andreswhy.blogspot.com "NewTools " )
Error-margins at Beth(x+1) level for Beth(x) levels can be made arbitrarily small (although maybe not zero) .
General Relativity and Tensors .
This effect can be clearly seen if you use Ricci's Tensors to denote gravitational fields. This is the really general granddaddy of fields .
Tensor theory very clearly requires that tensors are only defined in continuous and differentiable spaces . (Rather amusing , since this takes place before any metric is assigned . Sub-Space !) Hence the problems with quantum gravity . A quantal system is by definition discontinuous . Trying to describe it by continuous methods is futile .
Or Bio-fields . Things are just too idiosyncratic for meaningful abstractions using fields .
Fictitious Forces .
The major culprit is centripetal force (also known as centrifugal force ) . This is a fictitional force to balance the theory's bookkeeping .
From the above you can see that a large composite body like a galaxy composed of many objects rotating around each other and all around a center will have a nett attraction either larger or smaller than by gravity alone .
If larger , objects that we observe to fall around it in orbit will have a higher speed than required by the fictitious centripetal force of purely gravitational attraction .
Dark matter , anyone ?
If smaller , things fly apart .
Negative Dark matter , anyone ?
If you look at the maths , being exactly the same will smack of design (The probability of this is very small for Beth(0) randomness ) .
Stellar engineering on Beth(2) or Beth(3) scale .
Does this sound familiar ?
Dark Matter .
Phlogiston , ahoy! Your buddy Dark Matter is coming .
You can then dance the Ptolemaic Gavotte .
Can Fields be salvaged ?
But then horrible contortions are necessary .
Dimensions writhe in semi-being . As a last resort , a marriage counselor might have to be called in .
But why bother ? There are better ways .
If you have to , assign error margins to every field-point and interact the error-margins . This will automatically result in spiky discontinuities . Gauss would have loved them , but unless you are as expert as he was, try the simpler route .
Once again , why bother ? Use Beth(x) systems .
And if you are feeling adventurous , try numbers that only exist at different Beth(x>1) levels .
Guaranteed to lose weight .