FRACTAL QUANTUM GRAVITY, ANTIGRAVITY

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From: ROGER BAGULA 
Subject: fractal quantum gravity, antigravity

SPIN CONSERVATION, THE GRAVITRON, QUANTUM GRAVITY AND ELECTRON 
ANNIHILATION BY R. L. BAGULA  23 NOV. 1997?


	It seems that if you work long enough and hard enough something truly 
fundamental will hit you in the face. Then, it is a matter of if you 
have the guts and self confidence to do anything about it. The concept 
of :

	1) gravitron + neutrino = photon

is a little big for me. It comes down to the graviton being a 
symmetrical Klein group type of tensor field and the neutrino being an 
So(n) and Su(n) antisymmetrical group in the lepton camp. The concept of 
the lowest levels of a particulate nature have the characteristics 
necessary for a Maxwell electromagnetic field. The neutrino has the 
electric field part of the total and the graviton has the magnetic 
part.

	The trouble begins when we try to get a conservation of spin in
1) above. I had mentioned in previous TFTN articles that electron 
annihilation lacks spin conservation:

	2) e(+, 1/2) + e(-, -1/2) = 2*hv(0,1)

where I am using ( charge, spin) to show these characteristics. In 
contrast the neutron decay is balanced in charge and spin:

	3) n(0,1/2) = p(+,1/2) + e(-,1/2) + aN(0,-1/2)

	What we need is a version of equation 1) in which the spin of these 
neutral particles is conserved:

	1) a Gv(0,2) + aN(0,-1/2) = hv(0,1) + N(0,1/2)

where Gv is the graviton and aN and N are the antineutrino and 
neutrino. Now, we can rewrite 2) as well in a balanced form: 

	2) a Gv(0,2) + e(+,1/2) + e(-,-1/2) = 2*hv(0,1)

as the singlet reaction. The triplet follows as:

	4)  Gv(0,2) + e(+,1/2) + e(-,1/2) = 3*hv(0,1)

All these reactions now have spin and charge balanced for the first 
time.

	The Bell error inequality that I made a Mandelbrot iteration was 
responsible for me seeing this in interpreting the output:

	5) E(2*t? = 2*E(t) + c

and 

	6) E(t) = exp(-t^2/2)

which is the normal Gaussian error without the integration constant.  The 
question is: Why does the time measurement error so well define the 
positronium system? I even notice in the output that the photonıs wave 
length lengthens as it yields up energy to the central" quark 
intermediate/broken symmetry state". It is a two dimensional model at 
best even with the saturation heights in a five dimensional situation. 
Both charge and spin behave more like time than space. The error in time 
seems to be produced by the trade off between conservations of spin, 
charge and energy in a quantum world ruled by Heisenberg uncertainty. 
The spin flipping we see in ESR becomes the quantum gravity 
process:(electron spin resonance)

	7) hv(0,1) + e(-,1/2) = Gv(0,2) + e(-,-1/2)

	So that ESR becomes a source of gravitational radiation quanta! 
We have a controllable and modulatable source of gravitons. We need a 
"receiver" to make a radio like system of communication. A graviton 
equivalent of a laser or maser  seems like a good idea as well. In 
superconductors the paired bundle of electrons as a delocalized 
probability function has potential as an absorber in which the 
gravitons absorbed would probably reduce the conductivity. 

	The ability to send and to receive gravitational radiation would 
make many tests of our theories of field able to be experimentally tested. 
I would like to see if the graviton and neutrino actually travel at the 
speed of light or not. This fundamental symmetric/antisymmetric model 
makes it more probable that they do. Which still leaves us with the 
question of why and where the gravitation constant comes from. The electron 
charge seems to be a fault of the group-tensor geometry of the field in 
relativistic terms, but that uses the gravitation constant to define the 
geometry!  As usual this spin conservation quantum gravity approach to 
the fundamental electron and photon interactions raises more questions 
than it answers, but it does make possible some new experiments that 
might answer some very old questions! These reactions can be
made into quantum mechanical equations of a model form. It also makes 
the famous Feynman diagrams for photon-electron interactions wrong as 
incomplete.  

	In the book "THE COSMIC CODE",  Heinz Pagels says that graviton 
interactions are simply too weak to be seen. If we think in terms of the
energy of the graviton, he is right, but not in terms of the quantum 
reactions in which it seems to interact.  I have to credit Ron Weeden for 
pointing out the Klein group version of the Poincare disk in the Mumford 
code.  In his essay in  THE BEAUTY OF FRACTALS Dr. Mandelbrot takes credit 
for some work in this area as well. 

	It was the realization that the Klein groups and the quantum 
groups of particle physics were two sides of the same coin that allowed me 
to finally make this connection on a reason level. It was John de Rivazıs 
ideas on parallel universe experiments that led me back to the Bell 
experiment  and Bohmıs hidden variables. The graviton interaction has 
been the action of hidden variables until now.

	It actually frightened me when I realized how fundamental these 
concepts were and I wondered how they had been overlooked by Fermi and 
Einstein. If these two had seen these reactions we would be at least a 
century ahead with the unified theory they would have produced. The 
relationship of spin to charge that is found in group theory versions of 
quantum gravities is formalized by these simple reactions. They give us 
a quantum gravity hypothesis that seems to be able to be experimentally 
checked. 

	Now,  we know where to look. Do the STANDARD MODEL  physics people 
have the guts to do the looking? BY R. L. BAGULA  23 NOV. 1997?**********************
Return-Path: 

Hi zeropoint,

I'm afraid a little more explanation is needed by me
along the way to fully appreciate Roger Bagula's work.

Parts of it make sense to me now.  Maybe the rest will
when I get further along.

Interestingly, relationship 9) g/e^2=1 with slight modifications
was used in ddtc.doc as part of the gg/ee ratio calculation.

If Roger has any more detail discussing his formula content.
For example, the meaning of e*(e(i,j).... with respect to the
different usages of e.  This would be helpful.  

Don't do too much work on this, my quantum stuff seems to be
coming together pretty well at the moment.

Thanks for your help!

Warmest regards,    Rich :)
*********************

CAUSALITY, CAUCHY AND THE STATE OF MEASURING THE UNIVERSE
	BY R. L. BAGULA 25 SEPT 1997?

	In doing the work relating information to special relativity I ran into the problem of "causality" and that of when and how a measurement is 
taken. The state of Schroedinger's cat is one of the , now, classical 
results of this type of problem. In Russell's "Principles of 
Mathematics" he makes a big deal of relationships of velocity, 
acceleration and force in dynamics and Newton's theory. I want to try to 
clarify the concept of causality in a five dimensional world and the 
results of the realization that for a "state" to exist it must be 
observed/ measured.

	First, we have to look at causality as if we were limited to four
dimensions. Suppose we have a train of events:

	1) e(1),e(2),e(3),...e(n)

and a series of times associated with the events:

	2) t(1),t(2),t(3)...t(n)

We can pair these up as:

	3){ e(n),t(n) }

Now, how does the process of a spatial event take place in time?

	4) { e(n),t(n) }->{ e(n+1),t(n+1) }

There are two step wise paths that add up to 4):

	5) { e(n),t(n) }->{ e(n+1),t(n) }->{ e(n+1),t(n+1) }
	6) { e(n),t(n) }->{ e(n).t(n+1) }->{ e(n+1),t(n+1) } 

The two intermediate states are like the dead/alive cat in 
Schroedinger's experiment. We all think as if only 4) were necessary 
in the event causality! I haven't specified what the events are in space
 that the time sequence goes with. In iterative work we think of the k 
variable as time like and use:

	7) t(k+1) = t(k)+1

In the reality of nature the time series is probably:

	8) t(n+1) = t(n)+f(n)*dt~t(n)+dt

for infinitesimal dt! So that an event in space that involves matter may 
also be an iterative sequence like:

	9) e(n+1) = f(n)*e(n)+g(n)*de(n)+h(n)*dt~e(n)+de(n)+dt

with an event infinitesimal as well. This is only one of very many 
functional possibilities for the event sequence. That the time sequence 
is independent of the  event sequence is no longer considered as true or 
that something as simple as 8) as in the Newtonian physics is true! The 
gauge theories and Lorentz geometry have changed that. We can yet use 
the mechanics that Cauchy put in place for sequences in dealing with a 
more real picture in four dimensions.

	In the five space picture we are faced with adding a second parallel 
time sequence that is thought of as happening in reverse order to the 
four dimensional time:

	10) { e(n),t(n),t1(n) }->{ e(n+1),t(n+1),t1(n+1) }

and instead of two intermediates, there are a whole family of 
intermediate states in two basic classes in which t changes before t1 and t1 
change before t to total six "reactions" in sets of three each. We may think 
of the t1 first changes as antimatter-like and the t change first as 
matter-like as a convention. The result of the six paths makes causality 
a much harder question, both philosophically and practically! And 
instead of the alive /dead cat having just two states possible, it, now, 
has up to 12 different possible states that it can take on! In a 
universe that develops from one infinitesimal instant to the next, but 
not necessarily in the expected direction, causality becomes connected 
to  conservation of information. We are faced with the question in 
neutron decay of which came first the anti-electron neutrino or the 
decay of the neutron:

	11) va(e)+n(0)->P(+)+e(-)  (neutrino usually on other side)

Since the anti-neutrino is progressing in it's time ,backward to that of 
the four dimensional matter neutron! The weak field theory puts a W in 
between the two events we observe, but we can see from the six state 
analysis that such a model is at best incomplete! Worse, there are real 
conservation problems with the Weinberg-Salaam model! The mathematics 
just works better than previous models!

	I have got ahead of myself by introducing a "real" event into my 
argument. What do we observe about particles? In Russell he talks in the 
Hertzian model of (space, time, mass) as the observable/ measure set. In 
books on physics today we find that a particle specification has:

	12) (space, time, antitime, mass, charge, spin) 

which comes to five dimensions and three conditions/ fields. In quantum 
group theory we find an intimate connection of spin to charge. In many 
books a lot is  made of conservation laws and their breaking. Symmetry 
of the paths between events is connected to group theory and the wave 
functions for event series calculations reflect this! The connection of 
mass and charge in quantum gravity  calculations has allowed us to think 
in a form like:

	13) g*U(1)*su(2)*su(3) : the standard GUTS model

with a gravitational scalar group added to the Weinberg group. I have in 
my work found that a product symmetry of an infinite type based on 
primal forces:

	14) g*U(1)*su(2)*su(3)*su(5)*su(7)...su(Prime(n))

is indicated, but the truncation to the su(5) level is about all that we 
can handle at present. Decays of Pions take place in 10^-6 sec ranges, but 
W(+) decays are much quicker! To say that there may be "other" states between 
the n(0) and the p(+) than just the weak theory states of W(+) and Z(0) that 
depend on this higher symmetry is hard and even harder to prove! In trying to 
understand how weak theory works I have always run into a mass 
energy level that is much higher than the decay involved, that appears 
out of the vacuum and disappears back into it! If we pick a point in 
space that involves a particle, we can measure the properties of 12), 
but not at the same time (uncertainty). In the case of the intermediate 
particles in a fundamental particle decay which seem to involve both 
weak particles and quark changes, we seem to be specifying the state of 
the Schroedinger's cat without being able to actually look at the cat! 
	We know that particles like the W(+) and Z(0) do exist at the edge of 
our level of present observation energy. We talk about Higgs particles 
as being the "next" states to be verified in our theories of field 
dynamics. This point of view is far from Russell's denial of "forces" 
and arguments about causality! We don't see quarks, but observe the 
results of them in particle "jets" at energies that make me afraid to be 
a mile from ground central!
	What about us who do the observation/ measuring? How is what passes for 
self aware intelligence possible in an inanimate universe as we believe 
exists in a GUTS model?  We have Per Bak's theory of a universe that 
pragmatically experiments in a self-organizing criticality method until 
"complexity" like human life comes into existence in a chaotic manner as 
a result of a causal string of "selective" events. In the cat experiment 
we see the necessity of the observer/measurer to the state: the 
assumption is that an intelligent observer is involved! The progression 
of events in 10) took place for billions of years after the big bang 
without an intelligent observer existing until after the fact in 
mankind! We are doing our best to make up for our lost time, but the 
major observation of this type takes place in the virtual reality of the 
minds of the few most intelligent of humans who are interested in such 
things. Why, for instance, do I spend time writing this analysis of universal 
principles over recording my fractal results? Because it is by understanding 
at a fundamental level that we are able to invent machines that run off the 
fields that we investigate. 
	Hertz was a scientist, but his name is used in frequencies of all 
harmonics today. Radio came from Maxwell's theoretical work and atomic power 
plants from an understanding of Einstein's relativity! Thus, we are more than 
observers...we are creative inventors as well and engineers. From a true 
understanding of 10) and 14) above, we may invent machines that defy four 
dimensional causality laws! The laser resulted from understanding of the 
interaction on a quantum level of light with certain kinds of matter. 
	We have never actually seen the excited states that are being pumped! 
Suppose we have a beam of Pions captured in magnetic ring and we know that 
events like the six states between 10) are happening and we choose to pump up 
one of the intermediate states with external radiation so that the decay is 
delayed and controlled?

	15) Pion(+)->muon(+)+v(muon)

	We can, then, pulse the decay in a coherent manner like a laser. This 
example is offered as a "hypothetical" way in which such research could 
be useful in doing things we can not now do. In the unification of 
forces we see that not only electromagnetic/ group-like forces are 
involved in particle formation, but also gravitational radiation. In any 
change of state gravitational field changes take place at the same time 
as the electromagnetic ones! We have become masters of measuring the 
electromagnetic involved changes and mostly ignored the gravitational 
ones except for raw mass change! We do the easy things first and leave 
the harder ones for the later people. We are becoming that later people!
We have people who still think that neutrinos don't exist, because they 
have never seen one! In the reaction:

	16) e(+)+e(-)-> 2*hv( two photons form singlet spins: 1/2,-1/2)

we see the loss of static charge and mass at one time. When we add spin:

	17) e(+,1/2)+e(-,1/2)-> 3*hv(three photons from triplet)

we see loss of spin as equivalent to loss of mass and charge and at a 
much slower rate of decay. 
	What are the intermediate steps in this event sequence and can they be 
"reached" using external means? What seems so simple is not when you try to 
put mathematics to it (QED) and has led to the child-like Feynman diagrams of 
virtual states. I state again that we are a long way down the road from 
denying forces and infinitesimals as Russell does to diagramming photons 
interacting with electrons. We must try to make our thought processes are 
clear and logical as Russell in a much more complex scheme of events. This 
seems to be one reason that Feynman never endorsed weak field theory: he 
thought it was "incomplete" and pasted on! He was a brilliant man who liked 
his thoughts simple and easy to understand as nature seems always to act. 
	That the photons coming from 16) are "chaotic" in their energy seems to 
show that a complex intermediate reaction is involved, a distribution of 
photons from zero energy to two electron masses results with a center 
near 2*me/3, I think. This makes one think that not two but three 
particles are involved in the decay as if the flipped spin were acting 
like another lepton ( naybe? a neutrino?). Thus, the triplet decay has a very 
quark-like quality to it! If we increased our quantum level to a muon 
and pumped it, could we get a change from lepton to meson and from there 
to hadron? If the proton does decay, them a synthesis of the reverse 
process might produce protons or their like? It is this kind of reversed 
causality in our thinking that fundamental issues gives us!
	Anyone in Newton's time thought that the answer to mechanics had been 
found and the planets were in their correct orbits! Today, in the world 
that Weinberg and Hawking have given us, the photon, electron and quark 
are in their orbits and all is right with the quantum world? They were 
wrong in Newton's time and the last conclusion is as miss guided. The 
world that 13) shows us has flaws, some we already know and others that will become obvious as time goes on. It is in our understanding of causality and measure in a five dimensional world view that will advance our knowledge. Information theory and quantum fuzzy logic along with fractal dynamics will provide  a bridge to that advance by giving us the tools for understanding.

				RESPECTFULLY,
				ROGER L. BAGULA
***********************************

Singularities In Relativity: Coordinate Transforms 
by R. L. BAGULA 17 AUG 1997?

From: ROGER BAGULA 
Subject: bell and nonlocality

Dear zeropoint,
I found this in the NASA stuff on tunneling by Dr Chiao,
Roger
---------------------------------------------------------

Chiao and his group at Berkeley have done work in recent years on 
the tunneling of photons through a barrier. The photons apparently 
reach the detector at a speed faster than that of light.    (see 
references below) The question remains, however, as to exactly what 
is traveling faster than light. The actual wave front goes at light 
speed, so Chiao and co-workers argue that the signal itself isnıt 
superluminal. Other groups disagree, including Nimtz and co-workers, 
who have transmitted Mozart 40th at five times light speed (see 
references below).

       Our recommendation was that tunneling experiments be tried on 
particles with non-zero rest mass, considering questions such as:

1) are superluminal effects observed with matter as well as massless 
photons? 
2) can more insight be offered in the debate over signal definition? 

TUNNELING involves a quantum mechanical process that requires a 
particle be in a region of space where its kinetic energy is 
negative. Although this has long been predicted by quantum theory 
and observed in experiments, the precise nature of the process isnıt 
understood. A negative kinetic energy implies an imaginary speed, 
which is considered non-physical. Various interpretations have been 
developed over the years to explain the process.

My own interest in this comes from a mathematical game I designed as 
a Teaching Fellow at Harvard and later used as a professor when I 
taught modern physics; see Asaro, Catherine, "Complex speeds and 
special relativity," American Journal of Physics, 63(4), April 1996. 
The idea is to extend speed to a complex number in special 
relativity. Mathematically the singularity at light speed then 
disappears.In other words, a particle with an imaginary component to 
its speed can reach a superluminal regime by going around light 
speed like a car going around an infinitely high tree blocking the 
road. I should stress that this is only a mathematical exercise 
(albeit an entertaining one); to my knowledge no physical 
interpretation exists for imaginary speed, either in quantum theory 
or relativity. However, the observations need interpretation and may 
offer ideas for breakthrough physics. The equations in the complex 
speed formulation bear a strong resemblance to those for absorptive 
dispersion and resonance scattering theory, both which involve 
extending a real physical quantity into the complex plane. It would 
also be intriguing to see if the complex speed formulation has any 
predictions to make for tunneling through barriers. A number of 
researchers at the workshop also offered thoughtful research 
suggestions on extending the work, which I hope to post more about 
after I study them.

Our group had time to discuss several other proposals, including an 
intriguing suggestion by John G. Hartley to exploit the uncertainty 
principle in the position and speed of a luminal particle, such as a 
photon, to see if a "quantum fuzz" exists in the definition of light 
speed. If so, it might account for a
superluminal speed in a manner similar to the way the uncertainty in 
the energy of a tunneling particle can be used to inteterpret its 
negative kinetic energy.

All of this work is still speculative, of course. However, the 
breakout groups did identify a number of areas that show research 
promise. In any case, it was exciting and a lot of fun. Imagine it: 
NASA invites you to an invitation-only conference, sits you down at 
a table with some of the best minds in physics, and says "Okay, 
figure out how to go faster than the speed of light!"


For those interested in further reading on the superluminal 
tunneling, here are a few references. Many other references can be 
found either in these articles or through literature searches.

       Chiao, R. Y., Kozhekin, A.E., and Kurizki, G. (1996) 
"Tachyonlike Excitations in Inverted Two-Level Media," Phys. Rev. 
Let., 77(7), 1254?257; 

	Steinberg, A. M., Kwiat, P. G., and Chiao, R. Y. (1993) 
"Measurement of the Single-Photon Tunneling Time," Phys. Rev. Let., 
71(5), pp. 708?11; Chiao, R. Y., Kwiat, P. G. and Steinberg. A. M. 
(1993) "Faster than Light?" Scientific American, August, pp. 52?0. 

       Spielman, Ch., Szip?cs, Stingl, A., and Krausz, F. (1994) 
"Tunneling of Optical Pulses through Photonic Band Gaps," Phys. Rev. 
Lett., 73(17) 2308?311.
 
       Rafagnia, A., Fabeni, P., Pazzi, G.P., and Mugnai, D. (1993) 
"Anomalous pulse decay in microwave propagation: A plausible 
connection to the tunneling time," Phys. Rev. E, 48(2)
1453. 

       Enders, A. and Nimtz G. (1992) "On superluminal barrier 
traversal," J. Phys. I France, 2 1693?698; Enders, A. and Nimtz G. 
(1993) "Evanescent-mode propagation and quantum tunneling," Phys. 
Rev. E, 48(1), pp. 632?34; Nimtz, G., Enders, A., and Spieker, H. 
(1993) "Photonic Tunneling Times," Phys. I. France, 4 pp. 565?70; 

	Heitmann, W. and Nimtz G. (1994) "On causality proofs of 
superluminal barrier traversal of frequency band limited wave
packets," Physics Letters A, 196, pp. 154?58; 

	Brodowsky, H. M., Heitmann, W., and Nimtz,  G. (1996) 
"Comparison of experimental microwave tunneling data with 
calculations based on Maxwell"s Equations," Physics Letters, A 222, 
p. 125. 

       Olkhovsky, V. S. and Recami, E. (1992) "Recent Developments 
in the Time Analysis of Tunneling Processes," Physics Reports, 
214(6), pp. 339?56; 

	Olkhovsky, V. S., Recami, E., Raciti, F., and Zaichenko, 
A.K. (1995) "More about Tunneling Times, the Dwell Time and the 
ŒHartman Effect,? J. Phys. I France, 5 pp. 1351?365; 

	Mugnai, D., Ranfagni, A., Ruggeri, R., Agresti, A., and 
Recami, E. (1995) "Superluminal processes and signal velocity in 
tunneling simulation," Physics Letters A, 209, pp. 227?34.

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