BaryCenter Update I
Andre Willers
6 Nov 2014
Synopsis :
BaryCenters are essential in understanding the identity of anything . You , and the particles that compose you . A way of looking at fractals .
Discussion :
1.Pulling together some threads .
See the Appendices below . After SupSup Appendix there is a separate numbering system , but don’t pay too much attention to it .
2. I have not included the structure of the AI(x) minds (like humans ) . It is self-evident , and can be found elsewhere in the Blog “Andre’s Why”
3. I have not included genetic structures or barycenters of virtual genome constructs . Too much .
4. The dear reader must fill in themselves the latest work on MOND . They’re still dancing on the heads of pins there .
5. No attempt has been made to correlate crumpled space-time with quantum effects or rogue swan effects
Just swim through it and have fun !
Adding a finite number of tangential universes actually makes many problems in barycenters solve themselves .
It also makes a workable momentum tap theoretically possible .
Spindizzily Yours
Andre
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Appendix I
Barycenters , Stellar- and Proton Stability
Andre Willers
7 May 2011
Synopsis :
A Barycenter inside an object's defined delineation radius destabilizes it .
Discussion :
Suns :
Our sun has a barycenter just outside it's surface , mainly due to Jupiter .
What does this mean ?
It means that Sol is not prone to massive eruptions that will sterilize the planets .
The same will be true for other Solar systems .
A barycenter inside the Sun will impart massive momentum surges to the normal stellar processes , resulting in large EMP and particulate fluxes due to fusion in extra-solar environments (loops) . This would sterilize any life processes on planets .
Earth-Moon has a barycenter inside the earth . This means very large tides as well as active tectonics .Basically , the generation of life . Just enough destabilization .
Protons :
Proton size has to be smaller than the barycenter distance from the proton's center .
If it is greater , it will decay .
If it doesn't , it's boundary is forever teasing the edges of instability . The half-life of protons can be calculated from this .
Substituting muons for electrons (see "NewScientist" 26 Mar 2011 p50 "Nuclear bad boys" ) led to a factor of about 4% reduction in the size of the proton .As expected . They did not mention decay products from proton breakdown .
This is actually a planar explosive
(energy release along general proton spin axes) .
About 4% conversion of mass into energy .
It also means that a chain reaction is possible .
A really large bomb .
But , also , a space drive .
Spindizzy . Dirac equations apply .
What will Humans choose ?
Andre
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Appendix II
Barycenters II :Spindizzy Matter-conversion Pulse-rocket .
Andre Willers
12 May 2011
Synopsis:
Energy release from decrease in proton size is channeled partly into chain reaction , and partly into intensification of magnetic field . Once this grows over 10^16 Tesla , charged particles start forming out of the vacuum (starting with rho-mesons) . These short-lived particles are usually more massive than electrons . So we have a short , intense positive-feedback pulse where energy comes from proton and neutron decay , as well as vacuum energy as created particles are separated by the really intense magnetic forces .
Discussion :
References :
2. "NewScientist" 9 Apr 2011 "Magnets pluck current from void"
The Plan :
1.Wrap a number of small packets of hydrogen(protons) in fine copper wire .
2.Pack them in-line in a tube with a heavy duty conductor wrapped around them for the proton-axis alignment .
3.In between them , put a doped layer of matter that decays into muons .
4.Pulse one end of the tube heavily with muons , while pulsing a heavy current through the big outer winding to align the protons .
Mass will be expelled at the other end (your jet)
5.Repeat . (Pulse)
6.Stand back far away . (Do not try this at home)
Negative EMP:
A theoretical possibility .
All EMP pulses are flattened ("sucked up") into the formation of vacuum-particles .
Think matter rectifiers and matter transistors .
This will lead to ultra-collapsed matter . (Not neutronium , black hole or any squashed matter . Pure matter without any charge in stable configurations.)
Even a catalysis under certain conditions .
The radiation signature might be much smaller than supposed .
Properly balanced , it will be zero .
But when is the universe ever properly balanced ?
It is much more likely that Negative-EMP dominates .Which means a leaching effect on EM waves . It would seem as if wavelengths are growing longer as time goes on .
Sounds familiar ? (Hubble effect , universe expansion)
A neat twist on the Hoyle-Chandrasekhar Steady-State Universe . Instead of matter being continuously created , EM is being continously destroyed and transformed .
Conservation Principles :
This set of Universes are characterized by Delineation : Delineation , by definition , creates a Paired Principle: any delineated change is associated with another delineated change . Also known as Laws of Conservation of Energy , Mass , Information ,etc .
Trans-luminal effects :
What happens to the information encoded in EM which is zeroized by Negative EMP?
The new home (a small particle-pair) has insufficient capacity to store much (order of 256 bits) , whereas the EM has potentially very large information content .
So , the information pops up somewhere else in this universe . And it is not limited by EM speed , by definition .
Hyperdrive :
So , we only need to keep the information packets together . Which is an engineering problem .
Enclosing the spaceship in a shell of magnetic fields exceeding 10^16 Tesla will isolate it from the local space-time , enabling it to pop up at some other space-time coordinate . Sounds simple , but remember conservation of information .
The KISS principle applies with a vengeance .
Hyperdrive pilots will have to have a simplicity . Everybody will get lost in multiplicity .
Quantum Laundering :
The problem is isolating the observer from quantum observer effects before and after the experiment .
Remember , it is time-independent , but complexity dependant .
We know the complexity of this set of universes is of the order of
1/dx * 1/dmv <= 2pi/h ….from Heisenberg uncertainty principle
<= 9.482514 * 10^33
This is the measure of Complexity of the Beth(0) Universe we find ourselves in .
Our problem is to find a sufficiently complex procedure that is simple to execute in a repetitive fashion . Luckily this has already been done .
This is the Laundering Procedure :
It usually follows entropy , but this can be reversed (time travel)
An ordinary bridge card game (52 cards) where every card comes into play , has a maximum complexity of the order of 10^14 .
But add a joker or two , and the complexity rises to the order of 10^41 , bigger than the complexity of the underlying substrate Beth(0) universe .
Tarot cards are even higher .
Delicious !
If the experimenters played any poker with jokers , before or after the quantum experiment , it would affect the result .
Especially after the experiment .
Cold fusion is a case in point .
CERN should do this . But they only pay lip-service to the idea that the observer is an integral part of the process , never mind that the effect of the observer can be isolated by complexity protocols .
Hyperdrive Captains will have to be players of jokers or tarot .if they want to arrive at their advertised destinations .
Las Vegas Starport , anyone ?
Andre
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Appendix III
Barycenters III : Spindizzy Theory
Andre Willers
14 May 2011
Synopsis :
Asymmetric orbitals around barycenters leads to lags between magnetic momentum and angular momentum of mass . This generates fluctuations in G . The effect gets very pronounced if the barycenter is inside the definition horizon one of the particles involved .
Macro-asymmetric effects can be engineered (ie a space-drive)
Discussion :
The relevant equation is the Locke derivation of the Dirac-Brackett equation :
G = (2*c/b) ^2 * (P/U)^2
Where
G=Gravitational Interaction between particles
C is lightspeed , b~0.25 , P is magnetic moment , U is Angular Momentum .
The Trick :
1.P and U are divorced (lagged) in Barycenter descriptions .
The centers do not coincide .
2.G then varies . This averages out unless some rectifying element is applied .
Usually , this is simply dipping the barycenter below the definition horizon of a particle .
3.But you can apply precise EM lasers at beat frequencies to increase the lag .
This will biase G in the direction of the lasers .
In other words , a reactionless mass space drive .
Testing :
This can be tested on university desk-top systems .
Tribute to James Blish .
We don't need a Bridge on Jupiter .
But he was the Bridge .
May we see Cities in Flight .
Andre
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Appendix IV
Barycenter IV
Andre Willers
21 May 2011
Synopsis:
Measurements of Big G (Newton's Gravitational Constant) have been warped by the hidden assumption that small g (Earth's gravitational attraction at the surface) remains constant . But it fluctuates depending on the barycenter .
Discussion :
Measurement techniques :
Torsion Balance or Free-hanging pendulums .
See NewScientist 23 Apr 2011 p45
Both require the hidden assumption that the rate of change of g in two horizontal dimensions is zero .
But it is not .
The experimental apparatus is orbiting around the barycenter , changing the g vectors
And they did not compensate for this . After two centuries .
GRRR !
We expected better .
The order of G error (10^-4 ) fits the barycenter discrepancy .
Humans will have to do better than this if they expect to survive .
You get a big fat D minus .
Andre
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Appendix V
Dark Matter Update .
Andre Willers
28 Jun 2012
Synopsis :
Dark matter and energy are fictitious , but crumpled branes seem to be real . This adds significantly to complexity . This reallity might not be a simulated locale .
Discussion :
Briefly , slingshot-effects are sufficient to explain supposed gravitational anomalies . They simply exchange energy between rotating masses and linear kinetic energy . The momentum transfer is called the slingshot effect . It also means that a significant percentage of the energy in the system is “in transit” , as it were . We are talking interstellar distances . It is a dynamical system . The observed effect is either an overmass or an undermass , depending on the dynamics of the in-transit momentum transferring masses .
The Crumpling of space-time from brane collisions actually increases the complexity of possible paths . Luckily , we can compute this from general theory (See Appendix I) . This is because of one of the few Hyperdimensional Theorems we know to be true : We can always find a set of dimensions , so that the distance R from the center of random Beth(0) movements is R=d*Square root of(n) , where d is a step and n is the number of steps .
This seems contradictory . But remember , these are deterministic systems . They only become random because of random constraints . Thus , constraints increase randomness by the same order that the constraints are random . If the space-time crumpling is beyond our understanding , it is ,by definition , random . Then we can use the Crumpled Paper Algorithm . See Appendix I .
See Appendix III for some Randomness .
Are we in a simulation ?
In Appendix I we derive mu=2.1773242 * 10^ (-4) , meaning ratio of volume-of-mass to volume in a Planck Universe that is crumpled .
This is another way of saying that the possible number of crumplings (N) is
N=2^ (1/mu) (from Binomial distribution .)
The degrees of randomness in the crumpling .
Also a measure of the degree of complexity .
N = 2^4592.7933 . A large number .
In Appendix II we derive a measure of complexity from observed Planck quantities and found it wanting in the complexity stakes .
1/dx * 1/dmv <= 2pi/h ….from Heisenberg uncertainty principle
<= 9.482514 * 10^33
But , the complexity of the crumpling completely overshadows the planck complexity .
Thus , if we are in a simulation , N will have to be drastically lower . In other words few and major folds in the space-time crumpling . These should be detectable . One thinks of black-holes . In an artificial locale , the number of black-holes per cubic parsec should give an indication . A nice little problem for the Dear Reader .
More likely , the number of singularities simply balance the values of the Planck values . Not cause , but in a dynamic balance .
What use is this argument , one might ask .
Well , you can make a super-battery . Spin a particle in a capacitor field . Very high energy densities can be achieved . Store energy in spin .
The Karma of Constraints .
Andre
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SupSup Appendix .
Appendix I
Crumpling Paper and Space-Time
Andre Willers
23 Feb 2012
“The moving finger writes , and having writ , crumples it in random ruins.”
With apologies to Omar Khayyam .
Synopsis:
Crumpled paper gives a good approximation of spacetime as a membrane with clumpy masses .
“Empty” spaces not occupied by the membrane gives an impression of dark matter .
We derive an expression to give this ratio using Infinite Descent and Beth(0) Random Walk .
Discussion :
1.The Crumpled paper :
Consider a paper disk of radius r and thickness d .
It's volume is then Vp=pi * r^2 * d
Draw a line from the center to the edge , in steps of length d , over the edge , then back to the center Let nu=r/d , a measure of the thickness of the paper . Note that it is a pure number .
The number of steps in the line is then n0=(2r/d)+1
But the number of steps to the edge of the original paper disk is n1=r/d=(n0-1)/2
r=d*(n0-1)/2
n0=2*nu+1
Vp=(pi*d^3*(n0-1)^2 )/4
Crumple it up in a way that is as random as flipping a coin (ie Beth(0) )
The Trick : The line we have drawn up above breaks up into random vectors by rotating through a third dimension = crumpling into a ball .
We thus have a continuous line of random steps of known number of steps .
In 3 dimensions , the mean square distance from the center then is known
R = d * (n0)^0.5 …. See true for all dimensions as long as all are of Beth(0) order of randomness.
Volume of crumpled ball Vb=4/3*pi*R^3
The Ratio Vb/Vp = mu then gives the ratio of crumpled ball space to volume of paper mass .
Mu={4/3*pi*d^3 *n0^(3/2)} / (pi*d^3*(n0-1)^2 )/4
Notice the d^3 term and pi cancels out . This has profound physical implications .
This simplifies to
Mu=4*4/3*(n0^3/2/(n0-1)^2)
Expressed as thickness of paper , nu , which is a pure number independent of metric chosen .
mu=4*4/3(2*nu+1)^3/2 / (2*nu)^2
mu=4/3*(2nu+1)^3/2 / nu^2
This gives a quartic equation in nu , which can be solved exactly algebraically .
(mu)^2*(nu)*4 – 2^7/3^2 *(nu)^3 – 2^6/3^2(nu)^2 – 2^5/3^2 * (nu)^1 - 2^4/3^2 =0
Test it on A4 paper:
A4 paper has thickness d~0,1 mm and r~150 mm
nu=150/0,1
nu=1500
mu=4/3*(3001^3/2)/(1500^2)
mu=0.097421589
mu= 1- 0.90257841
This means that the crumpled A4 paper ball encloses about 90% empty space .
This agrees with experimental results . See NewScientist.
Note that the force applied does not matter . As long as the paper is untorn , mu will be the same .
How many times can it be folded ?
Solving the above (see below) gives mu=1 for about nu=14.7 to 14.8 .
This means there are no empty spaces left to fold into .
This can get complicated , so I will keep it simple .
Take a piece of paper and fold it . You then have a new piece of paper .The test-circle of same r will have double the thickness .
Ie , nu will double .
Between 7 and 8 folds , nu will hit the ceiling of mu=1 , regardless of the starting value of nu .
This is the maximum number of paper folds , as confirmed from other sources .
Physical interpretations :
Take an m-dimensional space . Randomness of order Beth(0) applies equally to all . The underlying equalizer . Collapse it to three dimensions and let the third one approach single Planck lengths .
Then we can use the above paper approximation . Notice how d cancels out except for an addition of 1 in final ratio .
What does it mean ?
See the physical universe as a brane (ie sheet of paper) in a multiverse . Crumpling it means it has mass and singularities . Both are aspects of the same thing .
An estimate of the number of singularities can be made from edges and points in crumpled paper .
Can we crumple the paper to a ball that is just paper ?
That is a particle .
The answer is “Yes” .
Such crumpling means that mu=1 (no empty space in any dimension )
This gives an quartic equation in nu that solves to four values , other dimensions than three denoted by i=(-1)^0.5
nu1= 14.722181 (this makes the physical particle universe possible . Mass .
Nu2= - 0.004167 + i*0.49558 (Rotation :Spin :charge and magnetism)
nu3 = - 0.004167 - i*0.49558 (Rotation :Spin :charge and magnetism) notice the minus sign .
Nu4= - 0.49164542 (quantum effects as the particles dither. Inertia?)
What does a negative nu mean ?
nu=r/d . A negative nu means one of r or d must be negative .
1.If r is negative , it can be interpreted as curled up dimensions , inside the “outside” dimensions as defined by i . See
http:andreswhy.blogspot.com“ The inside of zero” Aug 2009
2.If d is negative , it can be interpreted as quantum effects . A particle does not “occupy” all the space . Likes hopscotch .
3.But notice the the two are interrelated .The notorious observer effect . Where we place the minus sign between r or d .
There should be relationships between nu2 , nu3 and nu4 . Various rotations between macro- and micro dimensions .
This means the contraption is not symmetrical But we already know that ,
Physical constants :
Things like charge , mass , etc should be derivable from these basics . Hint:use lots of crumpled paper .
There is hope . The fact that it is quartic equation , which is always solvable , means that the Universe can be understood . Complicated and perverse , but as long as you stick to Beth(0) randomness , it can be understood . For higher orders of randomness , good luck .
Dark Matter :
I nearly forgot . Using Planck units , we can define the ratio of thickness of the brane as
nu=c*PlanckTime/(1*Planck Time)
nu=c = 3*10^8
This gives a
Mu=4/3*(2c+1)^3/2 / c^2
Simplifying (c is very large) . This gives the approximation
mu=4/3* 2^1.5 / c^0.5
mu=2.1773242 * 10^ (-4)
mu = 1-0.999783357
This means that 99.9783357 % of the universe can be interpreted as being “Dark Matter”.
Ie with attractive and repulsive qualities . Basically empty space .
May you have joy of that .
An interesting aside :Creative artists .
How many pieces of paper does an artist need to crumple up and throw away before he finds something acceptable ?
Something acceptable would translate to mu=1 . Thus , we can say 7-8 truly random foldings should give a result .
The same holds for cryptanalysis or any attempt to find an unknown .
Algorithm :
Try 8 times , crumple , then put it aside and try again later .
There is a quantum connection , strange as it might seem .
And what about a nice little Crumpling App for smartphones ?
But the randomness should be from truly random tables , not pseudo-random generators .
Randomly yours.
Andre
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Appendix II
Slingshots , Dark Matter and Dark Energy.
Andre Willers
17 Apr 2011
Synopsis :
Dark matter and Dark energy are misinterpretations of slingshot effects where the probe-mass is not infinitesimal .
In other words , they are observational artifacts .
Discussion .
Reproduced in Appendix A for ease of reference .
Field Theory assumes that Probe Masses can be infinitesimal . Yet , if we combine finite probe masses with SlingShot theory , a better fit to explain astrophysical anomalies is obtained . Also meson interactions .
Why Slingshot ?
1. Because we do not have a theory of three interacting masses . But we can do it for two masses . But everything rotates and orbits . So , we can describe all moving delineated masses as interactions of two masses slingshotting .
2. It is a valid mechanism for converting angular momentum into linear momentum .
See Penrose Process (http://en.wikipedia.org/wiki/Penrose_process )
And vice-versa .
The alert reader will notice reactionless drives and high-energy storage devices lurking in these seeming innocuous statements .
An Example :
A simple slingshot , though the principles hold for more complex cases .
V2={(1-m/M)v1+2U1} / {1+m/M}
We choose not to let m be small relative to M .
But we are also too lazy , ignorant and old to count every particle in a universe .
So we cheat and say : let x = m/M , then integrate v2 for 0 <= x =<1 span="" style="mso-spacerun: yes;"> 1>.
This means that the probe mass m takes on finite values from zero to our major mass M . This then includes subatomic and atomic and any other particles .
This gives values
Integral (v2) dx (from x= 0 to 1) = 2*ln(2)*(v1+u1) ………(1)
Integral {(v2)^2} dx (from x= 0 to 1) = 2*(v1+u1)^2 – 4*ln(2)*v1*u1 + 1 ……(2)
Equation (1) tells you how to make an inertialess drive .
The Spindizzy strikes again !
Equation (2) is an Energy equation and is responsible for all those horrible contortions of Mond (especially the last term of +1) .
It also tells you how to make stable , high , density energy storage devices .
Remember , magnetism is spin . If there is spin , there are Slingshots .
Galaxies seeming to orbit too close and fast/slow are simply exchanging slingshot masses (cf mesons)
Bits and pieces of the universe keep on flying around , creating space-time as they go.
It depends on their entanglements . The present universe looks more like an amoeba , with tentacles shooting out . The extent of space and time depends on where you look.
Vacuoles ?
Mini-universes created by tendrils of slingshot masses enclosing . Interesting spin effects as different tendrils have different velocities .
These should be able to be created in the laboratory .
Complexity :
Invert the Heisenberg Principle to define the Complexity of a Beth(0) Universe .
dx*dmv >= h/2pi ….Heisenberg uncertainty principle
Let 1/dx be all the possible values of x (ie the complexity of space)
Let 1/dmv be all the possible values of momentum . (ie complexity of time)
1/dx * 1/dmv <= 2pi/h ….from Heisenberg uncertainty principle
<= 9.482514 * 10^33
This is the measure of Complexity of the Beth(0) Universe we find ourselves in .
This almost certainly means that we are in a simulation .
The Complexity of Beth(0) is too small .
But is it sufficient for open-ended complexity of Beth(>0) ?
I can intuit that there is a threshold .
Bah .
I can also intuit that we are probably on a chaotic boundary threshold .
Go one way , and you recycle (Karma concept)
Go another way , advance .
And it was designed this way .
Storming Heaven .
Shooting tendrils of space-time into the multiverse will decrease the Heisenberg constant , thereby increasing the complexity past the threshold of recycling .
The Poor Civilization's Singularity .
The mass of the soul .
This can now be calculated from first principles from the complexity of momentum .
It is about 4! gm = 24 gm relative to the surrounding universe simulation .
And may you have joy of that .
May God have Mercy .
Andre
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Appendix A
The Problem with Fields .
Andre Willers
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 ?
No .
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 ?
No .
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
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 ?
Maybe .
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 .
Andre .
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Appendix III
Orders of Randomness 2
Andre Willers
15 Aug 2008
I have been requested to expand a little on orders of Randomness and what it means .
Please note that human endeavours at this date use only randomness of the order of flipping a coin ( Beth(0) )
Aleph is the first letter of the Hebrew Alphabet . It was used by Cantor to denote
Classes of Infinity (ie Aleph(0) for Rational numbers , Aleph(1) for Irrational Numbers , etc
Beth is the second letter of the Hebrew Alfabet . It means “House”
I will first repeat the derivation of Orders of Randomness from http://andreswhy.blogspot.com : “Orders of Randomness” because it is so important .
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Start Quote:
First , simple Randomness .
Flip of a coin .
Heads or Tails . 0 or 1
Flip an unbiased coin an infinite number of times ,write it down below each other and do it again .
All possible 0 and 1’s
An example : Beth(0)
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Flips(1) 0,1,1,1,1,… etc
Flips(2) 0,1,1,1,0,… etc
.
Flips(infinity) 0,0,0,0,0,0,…etc
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This describes all possible states in a delineated binary universe .
“delineated binary” means a two sided coin which cannot land on it’s side .
Now draw a diagonal line from the top left of Flips(1) to Flips(infinity) .
At every intersection of this diagonal line with a horizontal line , change the value .
The Diagonal Line of (0,1)’s is then not in the collection of all possible random
Horizontal coin-Flips(x) .
This means the Diagonal Line is of a stronger order of randomness .
This is also the standard proof of an Irrational Number .
This is the standard proof of aleph numbers .
Irrational numbers ,etc
Since any number can be written in binary (0,1) , we can infer that the order of randomness is the same as aleph numbers .
This means we can use number theory in Randomness systems .
Very important .
Google Cantor (or Kantor)
Define coin-flip Randomness as Beth(0) , analogous to Aleph(0)
Then we have at least Beth(1) , randomness an order stronger than flipping a coin .
Then we can theorize Beth(Omega) <->Aleph(Omega) .->
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Cardinal Numbers .
The cardinal number is the index x of Aleph(x) .
Cantor proved that
Aleph(n+1) = 2 ^ Aleph( n )
Where n is the cardinal number of the infinity .
Tying them together :
He also proved that
P(A) = 2^ n
Where A is any set , P(A) is the PowerSet of A and n is the cardinal number of set A
Thus , Cardinal Number of P(A) =(n+1)
The PowerSet of A = the Set of all subsets of A .
This sounds fancy , but it is simply all the different ways you can combine the elements of set A . All the ways you can chop up A .
You can see it easily in a finite binomial expansion (1+1)^n = P(A) = 2^n
There we also chop and dice , using infinite series .
Can you see how it all ties together ?
Why 2 ?
This derives from the Delineation Axiom . Remember , we can only talk about something if it is distinct and identifiable from something else . This gives a minimum of 2 states : part or non-part .
That is why the Zeta-function below is described on a 2-dimensional plane , or pesky problems like Primes always boil down to 2 dimensions of some sort .
This is why the irrational numbers play such an important part in physics .
Z=a+ib describes a 2-dimensional plane useful for delineated systems without feedback systems
Its in the axiom of Delineation , dummy .
But we know that Russell proved that A+~A
The difference can be described as the Beth sequences . Since they are derivatives of summation-sequences(see below) , they define arrows usually seen as the time-arrows .
These need not to be described a-la-dunne’s serial time , as different Beth levels address the problem adequately without multiplying hypotheses .
Self-referencing systems and Beth sequences .
A Proper Self-referencing system is of one cardinal Beth number higher than the system it derives from .
Self-referencing systems (feedback systems) can always be described as sequences of Beth systems . Ie as Beth(x) <-> Beth(y) . The formal proof is a bit long for inclusion here .->
The easiest way to see it is in Bayesian systems . If Beth(x) systems are included , Bayesian systems become orders of magnitude more effective .
Life , civilization and markets are such . See below .
Conservation Laws :
By definition , these can always be written in a form of
SomeExpression = 0
Random (Beth(0) Walk in Euclidean 2-dimensions
This is a powerful unifying principle derived from the Delineation Axiom .
In Random Walk the Distance from the Center is = d * (n)^0.5 . This is a property of Euclidean systems .
(Where d = step , n=number of random beth(0) steps)
Immediately we can say that the only hope of the Walker returning to the center after an infinity of Beth(0) steps is if d ~ 1/(n)^0.5 . This is the Riemann Hypothesis .
Now , see a Universum of 2-dimensional descriptors z=a+ib
Sum all of them . Add together all the possible things that can be thus described .
This can be done as follows :
From z=a+ib Raise both sides to the e
e^(z) = e^(a) . e^i(b)
Raise both sides to the ln(j) power where j is real integers.
j^(z) = j^(a) . e^(b/ln(j))
Now , sum them :
Zeta=Sum of j^(z) for j=1 to infinity
Now we extract all possible statements that embody some Conservation Law . Beth(1)
This means that Zeta is zero for the set of extracted statements if and only if (b/ln(j)) is of the order of Beth(0) and a=(-1/2)
Tensors .
The above is a definition of a tensor for a discontinous function .
Riemann’s Zeta function.
This can describe any delineated system .
If Zeta = 0 , conservation laws apply .
Zeta = Sigma(1/j )^z for j=1,2,3,…,infinity and z=a+ib , where z is complex and i =(-1)^0.5
The z bit is in two dimensions as discussed above .
This function has a deep underlying meaning for infinite systems .
If you unpack the Right-Hand side on a x-yi plane you get a graph that looks like a random walk .
If every point is visited that a random walk would visit over infinity (ie all) , without clumping , then Zeta can only be non-trivially zero if a=(-1/2) .
Why (x – yi) plane ? See “Why 2 “ above . The system is fractal . Two dimensions are necessary in any delineated system .
Remember , randomwalk distance from origin = step*sqrt(number of steps) .
So if the steps = 1/ ( sqrt(number of steps) ) , then the Origin might be reached if and only if a= -1/2
This is easily proven .
If a= - 1/2 , then b can be any real function . This would include Beth(0) and Beth(1) , but not higher orders of beth .
If a= -1/2 and b is an unreal number , then a cannot be equal to -1/2 anymore . Conservation cannot hold at any level .
Consequences:
Conservation Laws can only hold for Beth(0) and Beth(1) systems .
This is forced by the two dimensions of delineation .
Mathematically , this means that Beth(2+) systems of feedbacks can only be described in terms of attractors or/and fractal systems (ie not in isolation)
Physically , conservation of energy and momentum need not hold for Beth(2+) systems .
This has an interesting corollary in decryption (unpacking) . A Beth(2) mind unpacking Beth(0) or Beth(1) encryption is functionally equivalent to Non-Conservation of Energy .
Some other consequences :
If a< -½ , then Riemannian Orbitals are described . Beth(any)
Also described as nuclei , atoms .
If a> -½ , then a diffuse cloud is described . Beth(any)
Also described as magnetic effects .
What does this mean?
Present technology uses Beth(x) technology in a rather haphazard way .(Quantum physics) .
A better understanding will bring about a sudden change in capability .
Andre
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units of wine. Although Portugal can produce a unit of cloth with fewer hours of work (90 hours) than England, it must forego producing a greater amount of wine (
units) to do so. Accordingly, England is said to possess a comparative advantage in cloth even though Portugal possesses an absolute advantage in cloth. A similar argument would show that Portugal has both an absolute and comparative advantage in wine.
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