dirac’s equation and the sea of negative energy, part 2, by d.l. hotson

8/6/2019 Diracs Equation and the Sea of Negative Energy, Part 2, by D.L. Hotson

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IS S U E 4 4 , 2 0 0 2 I n f i n i t e E n e r g y

Sum m ary o f Part 1 (Infin ite Energy , Issue # 43)We show th at th e Stan dard Mo del (SM) of particle ph ysics is

totally inadequate by any reasonable criteria, violating the

basic scientific rules of simplicity, m ath emat ical consistency,

causality, and conservation. All these violations stem from

the 1930s, when by a mathematical trick the Dirac wave

equation was truncated to eliminate its negative energy solu-

tions. Recent developm ents, ho wever, have shown th at time

is quantized (Treiman, 2000), thereby eliminating the very

basis of that mathematical trick, as it would involve massive

violations of conservation of mass/energy.

The energy equation and Diracs equation call for both

positive and negative energy. Thus they are symmetricalwith respect to energy, as are the forces of physics. We

show th at p ositive (repulsive) forces increase positive ener-

gy, while negative (attractive) forces, such as gravitation,

the strong nuclear force, and the Coulomb force between

unlike charges, all increase negative energy. According to

the modern kinetic theory of mass-energy, negative energy

would merely be a vibration of charges at right angles to

our ordinary dim ensions, in an imaginary direction. The

equations of QM, wh ich all include i, therefore indicate

that these functions are complex , including vibrations in

imagin ary direction s. This understan din g explain s sever-

al anomalies with the electron, such as its velocity eigen-

value of c, which can only be in an imaginary direc-

tion. It also explains the electrons anomalous spin of/2.The solution s to Diracs equation describe a spin or field

in wh ich electron ch anges to positron every , the quantum

of time, (2e2/3mc3, equal to 6.26 x 10 -24 seconds). An elec-

tron-positron pair (epo) therefore must form a neutral

spin-zero boson with electron and positron alternating every

. A quantum field such as the Dirac spinor field mustgive

rise to particles, unlimited numbers of them (Gribbin,

1998b). Therefore, th e Dirac field m ust give rise to a sea of

negative-energy bosons which, since they are below zero,

m ust form a un iversal Bose-Einstein Con den sate (BEC).

This universal BEC can n ot exist in t he p resence of un bal-

anced charges, so every unbalanced charge must instantly be

surrounded by epos raised from negative to positive energy.

They connect and neutralize every unbalanced charge, form-ing th e electrom agnetic field, which is com posed of chains

of one-dimensional epos connecting and balancing every

unbalanced charge. They carry charge by proxy.

The universal BEC cant abide positive energy either.

When an electron jumps from a higher energy level to a

lower one, thereby losing (positive energy) angular

momentum, this momentum is absorbed and carried by

th e epos that surroun d it, forming a wave of epos carrying

angular momentum, which carry the photon according

to the Feynman path integral version of QM. The pat-

tern of th ese epos form t he p hot ons wave.

A The ory of Everythin g?We have seen th e power of Diracs equation , when all of it is

taken seriously. In a sense, thou gh, Dirac took it even m ore

seriously. It is not an equation of the electron , as it is popu-

larly called. It is a relativistic generalization of the

Schrdin ger wave equation, wh ich is said to contain m ost

of physics and all of chemistry. Dirac thought of it as a

Theory of Everythinghe tho ught th at its solution s sho uld

include everythin g th at waves, i.e. every possible particle. As

he was deriving it , he hoped it would have only one solu-

tionthe one, unitary particle out of which everything

could be made (Dirac, 1933). Then, when he found that it

had multiple solutions, he thought that one of its solutions

m ust be the proton as at that time, the proton and t he elec-

tron were the only known particles, and it was fervently

believed that t hey were the only particles. This is why Dirac,

in several of his early attempts to use the equation, entered

in as the mass th e average m ass of electron and proton (Pais,

1994). This didnt work, convincing him that the other

real particle (th e oth er positive energy one) had to have the

same m ass as the electron, bu t th e oppo site charge. Thus h e

predicted th e positron , but gave up h is dream th at his equa-

tion was a Theory of Everything. (Of course the discover-

ies of the neutron and the posi tron, an d th e convict ion that

th e ph oton also was a particle, didn t h elp an y.)

So, powerful thou gh th is equation is, it did no t live up t oits discoverers expectations. It was not unitary, and failing

th at, it was n ot even a Theory of Everything.

The annoying thing is, it should be. It generalizes a very

generally applicable equationthe Schrdinger wave equa-

tionand makes it covariant. We have seen that every one

of its requirements an d p redictions, including th e n egative-

energy epo, has withstood every test. It is as valid and widely

applicable an equation as has ever been discovered. It is as gen-

eral as the whole universe. It shoulddescribe everything that

waves. Yet as solut ion s, in stead of general ones, it ha s particu-

lar ones: just the positive energy electron and positron, and

their negative energy counterparts. In a sense, though, that is

unitary: two of the four are just different energy states of the

same particles, and electron and positron turn into each other

Diracs Equation and the Sea of Negative Energy _____________________________ P A RT 2 _____________________________

D.L. Hotson*

What if Dirac was right to begin with

about his equation? What if those

four kinds of electron, two negative

and two positive, are all one needs to

build a u n iverse?


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IS S U E 4 4 , 2 0 0 2 I n f i n i t e E n e r g y 2

ture, instead of increasing all the way down to zero? This is

because, if the boundary between positive and negative is

2.7K, photons with less energy than this would randomly

drop back into the condensate and out of our realitythe

less positive energy, the faster they would drop, forming the

lower curve of the black body.

If our positive energy reality is indeed made of exhaust

from the BEC, then everything must be made of electrons

and positrons, as that is all the BEC has to offer. However,

pair production, on e epo at a t ime splitting in to electron

and positron, leaves no n et positive energy balance, as equal

nu m bers of them m ust sink b ack int o th e sea. Th e BEC m ust

have some other means of permanently expelling the large

amou n ts of positive en ergy th at m ake up ou r reality.

-decayTh ere is a major, un n oted an om aly in th e relative abun dan ces

of the th ree en tities out o f which all stable matt er is made. Thenu mb ers of electron s and p roton s appear to be exactly equal.

(By charge conjugation [C] and charge conservation as out-

lined above, they must be exactly equal.) An d wh ile th e m ost

comm on element , hydrogen, con tains no neut rons, there is an

excess of neutron s in th e mo re com plex elemen ts. If you coun t

the unknown but probably large number of neutron stars,

there seem to be nearly as many neutrons as protons. Thus

th ere appear to be nearly twice as many nucleons as electrons.

However, un like the simp le electron , which seems to h ave

no parts, there is abundant evidence that nucleons are not

fund amen tal. They do h ave parts, almo st certainly not just a

few parts, but swarms of t h em (Krisch, 1 987; Pais, 1994; Rith

and Schfer, 1999). Somehow those parts must have beenassembled to make the nucleon. Modern theory dismisses

this as just another miracle. However, if nucleons came

together in the same kind of way as the chemical elements,

with compound units being compounded of simple ones, we

would expect electrons to be much more numerous than

nu cleons. How can a compoundentity be more abundant than

a simple on e? Simple hyd rogen is about 1012 times more abun-

dant th an comp oun d uranium, which m asses about 238 times

as much. The comp oun d n ucleon masses nearly 2000 times as

mu ch as the simple electron , so by th is comp arison we wou ld

expect electron s to be at least 1013 times more abund ant.

every half cyclethey are really the same particle, merely out-

of-phase with each other (Huang, 1952). So one could say that

th e four solutions to Diracs equation are un itaryth ey describe

four kind s of electron, d ifferentiated by state an d phase.

What if Dirac was right to begin with about his equation?

Wh at if th ose four kind s of electron, two n egative and two po s-

itive, are all one n eeds to bu ild a un iverse? Th ere are, after all,

n o wave equations for quarks, or for gluons, or for any of th e

other supposedly fundamental particlesyet they all wave.

Could th is m ean th at they are not fun dam ental at all? We will

leave this question h anging wh ile we consider a related o n e.

Wh ere Do You Take Out the Garbage?This famous question, invariably asked of architecture stu-

den ts with regard to th eir beloved projects, has much wider

applicability. No organism (or energetic machine, for that

matter) can function indefinitely in an environment of its

own waste products. (A dilem m a th at increasingly confronts

the increasing numbers of mankind.)

The BEC, as these equations outline it, is not perhaps an

organism, but it is an energetic machine. Overall, it is com-

pletely ordered, covered by a single wave function. But in

detail, it is a hive of activity, full of charges going at the

speed of light. Its frantically gyrating epos fill every crannyin every dimen sion of th e n egative en ergy realm . However,

the close quarters and random configurations must fre-

quently put electron adjacent to electron in positions that

generate considerable amounts of positive energy. (Like

charges repel, wh ich is p ositive energy.) Th e BEC can t stan d

po sitive en ergy. It mustget rid of it.

The BECs we can gen erate, at tem peratu res near 0K, n eed

fierce refrigeration to m aint ain th eir integrity. Th e Big BEC is

somewhere below zero. How is it refrigerated? Where do its

waste products go? Where does the BEC take out the

garbage, and wh ere is its garbage pile?

I suggest that we are sitting in it. We seem to be, to put it

blun tly, BEC excremen t.

The BEC m ust generate p ositive en ergy in great q uan tities.

All of its dimensions are full, even if it could accommodate

the stuff. It has to get rid of it. So it is no coincidence that

our reality h as a large positive energy balan ce. We are th e

BECs dump. (Literally, its heat dump.)

We have seen th at th e effective boun dary between th e pos-

itive and negative energy realms is several degrees above

absolute, as BECs, superconductivity, and superfluidity all

begin to h appen th ere. Mercury becomes a supercondu ctor at

4.1K. An ideal gas will form a condensate at 3.1K. However,

for real substances, because of interactions between the mole-

cules, the figure is somewhat lower. (The critical temperature

for helium liquid is 2.2K.) This would seem to put th e boun d-

ary right around 2.7K, or at least too close to this figure to becoincidence. We would expect the number of photons

dum ped from th e BEC to peak th ere, falling off random ly on

either side of this peak to form a black body spectrum peak-

ing at th is temp erature. This would seem to be th e mo st prob-

able explanation for some or all of the microwave back-

ground . In any case, this vast n um ber of ph oton s seems much

more likely to come from the negative territory adjacent to it,

than from a Bang at the complete other end of the spectrum.

(Th e infin ite tem peratures of a Bang can n ot be th e proximate

cause of an en ergy field n ear absolute zero.)

Why would the numbers of photons peak at this tempera-

In a total and massive reversal of our

expectations, the compound nucleon

appears to be nearly twice as abundant

as the simple electron. This immense

an om aly cries out for an explanation . It

is the clearest kind of indication thatth e production of n ucleons th emselves

an d th e process of nu cleosyn th esis fol-

low entirely different kinds of laws for

some unknown reason.


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no oth er process is/was of any imp ortance.

So just from th is, we can be almo st totally certain th at wh at-

ever else happened, the universe we know began as a whole

bunch ofneutrons, and n oth ing but n eutrons. (Ano ther indica-

tion th at n o Bang h appen ed.) But th ere is one oth er sign ificant

fact. Beta decay is a weak interaction. As such, it does not

obey the symmetry rules obeyed in virtually all other interac-

tions. It is left-handed. Specifically, it violates both parity (P)

and charge conjugation (C) (Pais, 1994), which is the produc-

tion of m atter and an timatter in equal amou nts. Since a mas-

sive violation of C is n ecessary to p rodu ce a un iverse of matt er

rath er th an an tim atter, beta d ecays violation of C is h ighly sig-

nificant. (We will examine the specifics later.)

Sherlock Holmes was of the opinion that singularity is

almost always a clue. An d con cern ing th e neutron we have

three singularities, each reinforcing our thesis that the uni-

verse began with large num bers of lone n eutron s. Each n eu-

tron was born ano malously left-han ded, with th e extraordi-

narily long mean lifetime of 15 minutes, and with the fur-

ther very peculiar property of being completely stable once

inside a nucleus. Without any one of these unique proper-

ties, th e neu tron s decay wou ld not produce the peculiar

abundances of the universe we observe. Each of these pecu-

liarities would seem to be evidence for this scenario; togeth-er they virtually exclude any other.

So the big question now is: How does one make a neu-

tron? Well, this argument certainly suggests an answer. We

have seen that according to every experiment ever per-

formed, matter an d an timatter are always produced in exact-

ly equal amounts. The experimental evidence therefore

demands a universe equally of matter and antimatter. Since

the universe must be composed of equal amounts of matter and

antimatter, and since the early universe was composed uniquely

of neutrons, the neutron must be composed of equal amounts of

matter and antimatter. Its very sim ple: th e n eutron mu st be

mad e of electron -positron pairs.

On e further indication : we sh owed earlier th at th e epo on e-

dimensional string must be c in length, or 1.87 x 10-15

meters long. If the neutron is made of epos, presumably this

string length would h ave to be th e diam eter of the neu tron.

Within th e lim its of the scattering m easuremen ts, this is exact-

ly the measured diameter of the nucleon .

So it wou ld seem th at th ere are several differen t app roaches,

all of which suggest th at Dirac was right th e first time abou t h is

equation. Perhaps it is a Theory of Everything, and a unitary

on e at th at. Everyth ing seem s to be m ade of epos: th e electro-

magnetic field, the wave, the photon. If the neutron could

be made of them also, that would be a clean sweep, at least of

th e un iverses stable en tities.

Neutrosynthesis

We might say that the Dirac equation, by having only four

roots,predicts th at everythin g else, in cludin g the n eutron , must

be made of electrons and positrons. How many epos make a

neutron? The question is far from trivial. The answer can not

be 919, the mass ratio between epo an d n eutron. There would

be 919 x 2 like charges packed into a tiny space. The binding

energy would have to be 80 or 90%, to h old such an aggrega-

tion together, even if it were mostly charge condensed. So

919 epos would mass, at most, about 370 electron masses. We

might keep in min d th e Pauli exclusion principle, which regu-

Instead, in a total and massive reversal of our expectations,

th e com poun d n ucleon appears to be nearly twice as abun dan t

as the simple electron. This immense anomaly cries out for an

explanation. It is the clearest kind of indication th at th e pro-

duction of nu cleons th emselves and th e process of nucleosyn-

th esis follow ent irely different kin ds of laws for som e un kn own

reason. Nucleosynthesis takes place in stars, and involves an

additive process: individual nucleons, or at most alpha parti-

cles, are added one by one to produce the heavier elements.

This explains the relative rarity of these heavier elements, as

m uch mo re energy, special cond ition s, and quite a bit of luck

(or fine tun ing) are n ecessary to p roduce th em.

However, because of their anomalous abundances, com-

pou nd n ucleon s must be produced in some entirely different

manner than the additive process that produces the heavy

elements. This is a major indicator of what that process

might beand what it is not. (It virtually rules out, for

instance, the production of these abundances in a Bang,

big or little, as production in a Bang would mimic the

additive processes of solar nucleosynthesis, and produce

orders of magnitude more leptons than nucleons.)

If th ere were som e on e known subatomic process whose end

products were neutrons, protons, and electrons in their very

anomalous observed abundances, with almost equal numbersof each, we could be virtually certainto a vanishingly small

uncertaintythat this is the process by which the universe

came about. Is there such a known process? As it turns out,

th ere is exactly one such kn own process: it is called -decay.

Outside a nucleus, the neutron is unstable, but with an

extraordinarily long mean lifetime. Whereas all of the other

known unstable particles decay in nanoseconds or less, often

m uch less, th e neutron han gs aroun d for 14.8 min utes on aver-

age. After this un iquely long lifetime, a lon e neu tron will break

down, emitting an electron an d an antineutrino, an d turn ing

into a proton . Th e antin eutrino is alm ost never seen again it

could go through light-years of lead without interacting. But

this process produces electrons and protons in exactly equal

numbers. (They of course form hydrogen, the most abundant

atom.) Moreover, the neutron itself, if it happens to be

absorbed in to a n ucleus du ring its 15-min ute m ean lifetim e, is

again com pletely stable. (Except in certain radioactive n uclei.)

And in stars, where nu cleons are combined into n uclei, there

is abun dan t energy available to fuse electron s an d prot on s back

into neutrons, where needed (Conte, 1999). This, of course,

happens wholesale, in degenerate stars.

So given enough neutrons, th e process of beta decay, alone an d

unaided, would produce exactly the very strange abundances

of the universe we observe. Moreover, we know of no other

process who se end produ cts would be electrons and proton s in

exactly equal n um bers, and n eutrons in ap proximate equality.

And since all stable matter in the universe is composed of justth ese three produ cts in just th ese proportions, it follows th at

We can be almost totally certain that

whatever else happened, the universe

we know began as a whole bunch of

neutrons, and n othing but neutrons.


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4

proton-electron mass ratio from the two numbers 10

and 136, together with the nu mb er of un ity, 1. . .

Eddingtons 1, 10, and 136 are members of a well-

known mathematical series that goes 1, 10, 45, 136,

325. . .etc. . .Th e n ext n um ber in that series is 666.

(Sirag, 1977b)

Edd in gton s series is (n 2)(n 2 + 1)/2, n = 1, 2, 3, etc. As

Sirag points out, this group-theoretical point of view

accords with Diracs above statement that four-dimension-

al symmetry requires ten dimensions of curvature, ordegrees of freedom, in General Relativity (Dirac, 1963).

Several of th e strin g an d sup erstrin g th eories also requ ire a

space of ten dimensions (Sirag, 2000), and as we saw, an

electron can vibrate in 136 different ways in ten dimen-

sions. If we order these 136 vibrational modes two at a

timeone for electron, one for positron (as in the epo)

this would give 136 x 135, or 18,360 different ways for a

lepton , join ed as an epo, to vibrate in 10 dimen sion s. (Th is

is Sirags computation, but he lacked the idea of electron-

positron pairs. He ordered them two at a time . . .e.g. ,

on e for prot on , on e for electron . . .)

Thus a combination of 9180 electron-positron pairs

would be a very stable arrangement, filling all of the possi-

ble vibration al modes in ten d imen sion s. We might im agine

th em arrayed in a 10-dimen sion al vortex or h ypersph ere.

(Note that this arrangement would come about in the nega-

tive-energy BEC. As is well known, the only way th at a BEC

can ro tate is in a vortex.) Moreover, Krisch (1987) h as sh own

that colliding protons act like little vortices, shoving each

oth er around preferentially in th eir spin direction s.

Wh at wou ld be th e m ass of such an aggregation? Well, in

quantum theory, one measures the energy, or mass, by tak-

ing the temporal sine attribute of the wave. Since time is

on ly one of th e 10 dimen sion s, th is would give the aggrega-

tion a mass of 18360/10, or 1836 electron-masses. Since it is

composed of 9180 electron-positron pairs, such an entity

would h ave 0 charge: it would be n eutral.All symmetries are conserved in this arrangement, with

exactly equal amoun ts of matter and antim atter. Th ere is no

reason why such an ent i ty might not be produced, and

lates how m any electron s may occupy a given shell in an atom

by the possible number of different vibrational modes (differ-

ent quantum numbers).

We have seen earlier that for reasons of symm etry the u ni-

verse must have ten dimensions, six of them (the negative

energy realm of the BEC) in imaginary directions with

respect to our four (Dirac, 1963; Sirag, 1977b, 2000). How

many different ways can an electron or positron vibrate in

ten dimensions? We might answer that by an analogy with

the periodic table.

Each electron shell con tains the n um ber of electron s that

can vibrate in differen t ways. (The electrons quan tum nu m -

bers.) At present, the periodic table consists of 100 elements

in eight complete shells (if you count the rare earth ele-

m ents) with 16 or so elements in an in comp lete nin th shell.

(Element 118 was claimed to have been synthesized at the

Lawrence Livermore National Laboratory in 1999, but they

have recently retracted that claim [Gorman, 2001].)

Com pletin g that shell would give 118 elemen ts, and a tenth

comp lete shell would add ano th er 18, for a tot al of 136. So

if elem ents were stable to atom ic num ber 136, elemen t 136

would be a noble gas with 136 electrons in 10 complete

shells. This means that there are 136 different ways for elec-

trons to vibrate in 10 shells. Each of these shells amounts toan addit ional degree of freedom for the vibrating electron. If

we substitute 10 degrees of freedom, or dimensions , for these

10 shells, it seems inescapable that t h ere again wou ld be 136

different ways for electrons to vibrate in 10 dimensions.

These nu m bers figure prom inen tly in on e of the po ssible

designs for a n eutron mad e of electron-positron pairs. This

model was largely suggested by Saul-Paul Sirag (1977a) as a

combin atorial mod el of th e proton . He, however, consid-

ered it mere n um ber-jugglin g. Th e last tim e I talked to h im,

he was no longer interested in it , so I pirate it without

scruple. With a few minor additions and changes, it turns

out to be a plausible model of the neutron.

. . . From Eddin gton s group -theoretical poin t of view,creatures to whom space-time has four dimensions will

find algebraic structures having 10 elements and 136

elemen ts playin g a very fundam ental role.

Eddington attempted, unsuccessfully, to derive the

With t h is sin gle, simp le m odel for th e production of n eutron s from th e un ique solu-

tions to Diracs equation, we arrive at the extremely anomalous numbers of elec-

tron s, protons, and n eutron s in our reali ty. Moreover, th is also explain s the prepon -

derance of hydrogen over every other atom. Also explained is the oddity that elec-

tron and proton, which are seemingly very different particles, nonetheless haveexactly th e sam e electric ch arge. A prot on is seen t o be sim ply a neut ron th at h as lost

a single electron , leavin g it with an extra positron . An d th e electron is no t created

as it leaves the neutron; it was there all along. . .Moreover, it would seem to admit

of th e possibility th at en ergy, special con dition s, an d catalysis m igh t synt h esize n eu-

trons at low temperatures, possibly explaining some or all of the neutrons, trans-

m utation s, and excess heat produ ced in cold fusion.


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Moreover, some 90% of th e epos that m ake up th e Sirag

mo del have 0 spin, being pure on e-dimen sion al vibrations

in imaginary directions. The remaining 10% share real

angular mom entu m , mostly canceling, which m ust, overall,

amou n t to spin 1/2. But as th is is a real spin, there is noth -

ing to say that a real extended neutron with the large

real mass of some 1838e is not really spinning with a

real angular momentum of 1/2. In order to obey Fermi-

Dirac statistics, it must have this half-integer angular

mo men tum , but it is not n ecessary to assign th at spin t o an

individual electron or epo con stituen t wh en it can simply be

a property of the extend ed n eutron itself.

The Strong Nuclear ForceHowever, the p rime m erit of th is model h as to be its repre-

sent ation of th e stron g nu clear force. Here we need to n ote

a strange coincidence: the mass of the proton, in electron-

masses, is roughly th e same as the strength of the p roton s

strong force, in electron-forces. (Mass of proton: 1836 elec-

tron-masses. Strength of the electromagnetic force: the fine

structure constant = e2/hc = 1/137; strength of strong

force: g2/hc = ~15. Ratio: ~15 x 137, som ewh ere aroun d 2000

[Sh an kar, 1994].)

Thus th e ratios of the m asses and of th e forces are rough-ly the same, around 2000. This is a major clue to the

natu re of th e stron g force.

Gravitation and the Coulomb force both have simple

inverse square shapes that operate over long distances.

Theoretically, at least, th ey never dro p to zero. However, the

shape of the strong force between nucleons is radically dif-

ferent an d very peculiar. Up to a distan ce of aroun d a fermi

(10-15 m .), it is very stron gly repu lsive, keeping th e nu cleons

apart. Th en, for no apparent good reason , it ch anges abrupt-

ly to very stron gly attractive, th en drop s off very rapidly, so

th at at a distance of aroun d th ree fermis it becomes imm eas-

urable. Th is peculiar shap e has n ever been successfully mod-

eled by an y th eory.

Note h ow current th eory, in wh ich th e fudge is an accept-

ed scien tific procedu re, solves this prob lem. Sin ce current

theory cant model this observed force, it simply ignores it,

and instead invent s (fudges) an unobserved (fifth!) force car-

ried by eight gluons (designed to be unobservable) between

eighteen or thirty-six quarks (also designed to be unobserv-

able) inside th e n ucleon . It then suggests that t his fudged

gluon force in some unspecified way leaks out of the

nucleon to make up the peculiar shape of the measured

strong force. However, our epo m odel of th e nu cleon m od-

els this very peculiar shape simply and intuitively.

Because of th e un certainty p rinciple, the n ucleon , with its

measured diameter of aroun d 1.9 fermis, can n ot be a perfect

sphere, but must be a pulsating spheroid. However, the eposthat make it up have asymptotic freedomthey vibrate

ind ividu ally, and each lepto n is free to form a relation ship with

any available antiparticle. This means that, as two nucleons

approach each other, at a distance of about three fermis, elec-

tron-positron pairs will begin to form, not just within the

nucleons, but between them. (Pairs of internucleon epos

would have to form at the same time, keeping the total num-

ber of paired charges in each nucleon at 9180.) This would

cause a strong, short-range attraction between the nu cleons as

more and more pairs formed. This would increase to a maxi-

mum at around 1.5 fermis, after which it would rapidly turn

expelled from the BEC (thrust into our reality) whenever

the random fluctuations of the BEC produced a positive

energy of 1836 electron-masses, and spin energy in all ten

dimen sion s. (The suggestion is that it would be produ ced in

a vorticular storm in the BEC, which would have spin

energy in all ten dimensions.) Moreover, since it has only

10% po sitive energy and 90% n egative or bindin g energy,

such an entity wou ld be stable despite packin g 9180 ch arges

of like polarity into a very small h yperspace. Th is is th e Sirag

model of the nucleon, slightly modified. Note that in our

BEC of unlimited density, there is already an electron and a

positron in exactly the p ositions required for this syn th esis

(nothing needs to move), so only the positive energy and

the spin is required to produce a neutron.

The m ass of a neu tron is, of cou rse, 1838.684 electron m ass-

es, not 1836. Ho wever, mass is a tricky bu sin ess. The effective

m ass can be q uite different from t h e bare mass, as is sh own

in the conduction atoms of a metal (Pais, 1994). Because of

their interaction with other electrons and with the positive

core, their effective mass can vary from 0.3e to over 10e. And

in a supercon ductor, con densed state electrons can h ave an

effective m ass th at can b e 1000 tim es the real electron m ass.

We will later show that epos in a nucleon are in a semi-con-

den sed state. Furth ermore, there are in dications th at m ass mayvary with time (Narlikar and Das, 1980).

Am on g th e felicities of th is m od el, Sirag point s out th at if

you divide the 18360 successively by 9, 8, 7, and 6, you get

the approximate mass-ratios of the other baryons, the

Lambd a, the Xi, the Sigm a, and th e Om ega. Since they h ave

larger ratios of positive (disrup tin g) en ergy to n egative (bin d-

ing) en ergy, th ese baryon s are pro gressively less stable.

With th is single, simple m odel for th e production of neu-

trons from th e un ique solution s to Diracs equation, we

arrive at the extremely anomalous numbers of electrons,

protons, and neutrons in our reality. Moreover, this also

explains the preponderance of hydrogen over every other

atom . Also explain ed is th e oddity th at electron and proton ,

which are seemingly very different particles, nonetheless

have exactly the same electric charge. A proton is seen to be

simply a neutron that has lost a single electron, leaving it

with an extra positron . An d th e electron is no t created as

it leaves the neutron; it was there all along.

Moreover, it would seem to adm it of the p ossibility th at

energy, special conditions, and catalysis might synthesize

neutrons at low temperatures, possibly explaining some or

all of the neutrons, transmutations, and excess heat pro-

duced in cold fusion .

This model must, however, address the spin of the neu-

tron . T.E. Phip ps Jr. (1976, 1986 ) also suggests a m odel of t h e

neut ron m ade of electron-positron s, but h is m odel runs into

difficulty with the neutron, which has a spin of 1/2 , justlike the electron an d po sitron. But if one h as equal n um bers

of electron s and p ositron s, each with opp osite and canceling

spins, the resulting neutron should have spin 0, whereas it

of course has spin 1/2, like all of the fermions.

But this reflects current physics tendency to regard the

spin of the electron as somehow not a real spin, but a

pure quantum effect, as Bohr liked to call it. But we have

shown above that it can indeed be regarded as a real spin,

with real angular mom entu m , if on e regards it as a complex

spin, having angular momentum in one or more imagi-

n ary direction s as well as its c2 spin in real directions.


6/24


together gravitation, similar to LeSages ultramundane cor-

puscles, whereas the other negative-energy forces act by

pulling together. We suggest a model on the lines of these

other pulling together (negative-energy) forces, which also

ut ilizes a residual effect of electrom agn etism.

MagnetogravitationDiracs equation predicts that the magnetic moment of the

electron sho uld h ave a value ofe2m . This is the magnetic

moment balanced by the BEC, attaching every unbalanced

charge to a charge of opposite polarity, thus bringing the

BEC back into balance. As shown above, however, the pres-

ence of unlimited nu m bers of epos and th eir associated ph o-

tons give Diracs value a tiny unbalanced correction, multi-

plying Diracs value by 1.0011596522, the g factor. This fig-

ure represents th e best agreemen t between th eory and exper-

iment in all of science.

As a consequence, every electron has a tiny unbalanced

m agnetic mom ent at th e sam e ph ase of its cycle. Since time

is quan tized, every electron will reach t h is ph ase of its cycle

at the same instant. For its stability, the BEC must balance

th is tin y imbalance as well. It can on ly do th is by initiating

one extra epo chain. This epo chain will have far less

indu ced strength th an th e oth er, balanced chain s, sin ce it isinduced by this feeble unbalanced magnetic moment rather

th an th e powerful Coulomb force. However, it cannot connect

anywhere, since every electron has the same unbalanced

m om ent at th e same p hase angle. (So do es every positron , at

the opposite phase angle.) Thus these feeble epo chains will

simply extend into space, connecting at one end to every

electron an d p ositron (hence to all real matter), but being

unconnected at the other end. However, these unconnected

chains, extending into space, will cause a tiny unbalanced

attraction between all matter. Since the number of chains

per u n it area of space will decrease as 1/r2, it is evident that

th is tiny un balanced attraction h as the form of gravitation.

Moreover, this magnetogravitation reacts to changes in

mass instantaneously (or at least in time .) This explainswhy the Earth and Sun dont form a couple, and why the

Earth feels gravitation from th e Sun at th e Sun s instan ta-

n eous position , rather th an its retarded position , as is sho wn

by astronomical observations (Van Flandern, 1998).

This model of gravi tat ion solves many problems with

other models, including numerous experiments which

seem t o sho w th at gravitat ion can be shielded, cont rary to

Newton ian gravi tat ion and General Relat ivity (Majorana,

1930; Allais, 1959; Saxl, 1971; Jeverdan, 1991, and Van

Flandern, 1998). In a careful ten-year series of experi-

me nt s , Ma j ora na de mons t ra t e d t ha t l e a d sh i e l d i ng

between th e Earth and a lead sph ere measurably lessen ed

th e weight o f the sphere, while sh ielding above th e sphereh ad n o effect . This would seem to supp ort pull ing togeth-

er gravitat ion an d to d isprove pushin g together mod els

such as LeSages, Van Flan dern s, an d Put h offs. Allais,

Saxl, and Jeverdan carefully observed the behavior of var-

ious kinds of pendulum during different solar eclipses. All

three pendulums exhibi ted major anomalous behavior at

the onset of total i ty, indicat ing that the moon strongly

interfered with the gravi tat ional connect ion between the

Earth and the Sun at that t ime. This provides major evi-

den ce for our epo ch ain mo del of gravitat ion.

Furth er analytical work will h ave to be don e to verify th at

into a strong repulsion (since the individual epos have to

maintain their average 1.87 fermi separation), keeping the

n ucleon s a stable distance from each oth er.

Moreover, a maximum of 918 such internucleon pairs

could form, the number vibrating in the direction joining

th e two n ucleon s, on e-tenth of the total. This would give the

interaction the strength of 1836e, and exactly explain the

strength of the strong force, about 2000 times as strong as

th e Coulom b force (Sh ankar, 1994).

Now, what is the chan ce that a comp letely wrong m odel ofthe nucleon would exactly match both the strength and the

very peculiar shap e of th is most in dividual of forces? After fifty

or so years of effort, the huge physics establishment admitted-

ly has failed utterly to provide a model that comes close to

m atch ing th at peculiar shape o f the n uclear force. Yet Diracs

equation provides a model that fits like lock and key.

Diracs Theory o f Everyth in gThis model simply, intuitively, and clearly explains the size

of the nucleon, the mass of the nucleon, the very peculiar

shape of th e strong n uclear force, the strength of the strong

nuclear force, and the strange fact that the very different

proton and electron have charges of exactly the same

strength. No other model explains any of these features, including

the very cum bersome Quantum Chrom odynam ics of th e SM.

The neutron thus constructed is the source of electron,

proton, and neutron in their very anomalous abundances,

hence of all stable matter in the universe. This makes the

amounts of matter and ant imatter in the universe exactly

equal, as experiment demands, and as no other model pro-

vides. We saw earlier that the electromagnetic field, the

photon, and th e wave are all epo manifestations neces-

sary for the stability of the BEC. So we have complete clo-

sure: the BEC must be produced by the Dirac zeroth

quantum field. For its stability, it in turn must produce

our universe, using only the particles called for by the Dirac

equation, which as we can now see predicts that the ent ireun iverse is made from just th ese four kinds of electron .

Einstein spent much of his life trying to unify the four

forces. We have shown that the strong nuclear force is

n oth ing but electrom agnetism . Moreover, th e weak nuclear

force has since been unified with the electromagnetic in the

electroweak theory (Weinberg, 1967; Salam, 1968). This

leaves only gravitation. Puthoff (1989, 1993) suggests that

gravitation is a residual effect of the ZPF of the vacuum elec-

tromagnetic field, i.e. a residual effect of electromagnetism.

Again, however, this paper suggests a different structure and

origin for t h e ZPF. Moreover, Puth offs gravitation is push ing

After fifty or so years of effort, the

huge physics establishment admitted-

ly has failed ut terly to provide a m odel

that comes close to matching that

peculiar shap e of th e n uclear force. Yet

Diracs equation provides a model that

fits like lock and key.


7/247


th is tiny un balance, which m ust happen, h as the force as well

as th e characteristics of gravitation . If th is hypo th esis is cor-

rect, all of th e matt er and all of the forces in th e un iverse are

seen to be the result of just these four kinds of electron, ful-

filling Diracs un itary d ream.

InertiaInertia, however, has been a riddle ever since Foucault

showed that his pendulum responded, not to any local

frame of reference, but apparently to the frame of the fixed

stars. This became the basis of Machs principle, which

states that the fixed stars, or (since they arent fixed) the

sum to tal of mass in th e un iverse, som ehow reaches out toaffect pendulums and gyroscopes. (And somehow knocks

you down when the subway starts suddenly). Though this

action at a distance appears to violate causality, and its

apparently fixed frame of reference violates relativitys ban

of any such fixed frame, Einstein set out to incorporate

Machs principle into relativity. In th e end , tho ugh, h e h ad

to ad m it he was not successful.

Haisch, Rueda, and Puthoff (1994) made a very plausible

case that inertia is a residu al effect of th e ZPE. They were n ot,

however, able to quantify the effect. As this study presents a

rather differen t picture of th e ZPE, th e question is worth anoth -

er look. To go along with the kinetic theory of mass-energy,

we present what m igh t be called th e kin etic th eory of inertia.

(Or possibly the gyroscopic th eory of inertia.)

A gyroscop e establishes a vectoral plane of an gular mo m en-

tum . An y chan ge in th e angle of th at vectoral plane is strong-

ly resisted. As shown by Diracs equation , an electron h as a cir-

cular vibration in two real direction s, giving it a real en er-

gy of mc2. However, it also retain s its (negative energy) vibra-

tion at c in an imaginary direction. Thus its oscillation is

circular but comp lex, having bo th a real and an imaginary

component, and giving it the anomalously large angular

momentum of /2 in any real direction.

This makes th e electron a little gyroscope. However, since

this vibration is complex, part real and part imaginary,

this angular mom entum plane can n ot point in any real

direction , as is also th e case with t h e orbital electron s angu-lar momentum vector, as mentioned above.

This means th at acceleration in any real direction mu st

act to chan ge the angle of th e electron s (com plex) angular

momentum vectoral plane and thus will be resisted with a

force equal to an d in a direction opp osite to th e acceleration ,

and proportional to the electrons real mass-energy.

Diracs Operator Th eory or Tran sform ation al version of

QM represented the wave function as a vector rotating in

phase space. This kinetic theory of inertia represents a vec-

toral plane rotating in a complex space. How this results in

inertia can be seen by looking at th e wave fun ction that rep-

resents a p article with d efinite mo m entu m. The length (value)

of the complex nu mber is the same at all positions, but its

ph ase angle increases steadily in th e direction o f th e particles

mo tion, th e x direction , making it a complex helix in shape.

The rate of this complex rotation in its axial (x) direction is

th e measure of the m om entu m. As x increases by a distance of

h/ p, this phase angle makes one complete rotation (Taylor,

2001). Increasing the momentum (an acceleration in the

real x direction, increasing p), acts to decrease the distance

h/ p, on the exact analogy of a coiled spring being compressed.

(QM represents momentum as a spatial sine wave or helix.)

However, since is a complex number, acceleration in the

(real) x direction increases the pitch of this complex phase

angle and so is resisted by the electron-gyroscope. This com-

pression acts to store the energy added by the acceleration

according to the Lorentz relationship. Compressing the dis-

tance h/ p to zero would require (and store) infinite energy.

(One might picture this complex helical oscillation as the par-

ticles flywheel, storing energy as it is accelerated.)

Since th e com plex gyroscope-electron mustresist an accel-

eration in any real direction , wh at can th is resistance be

but inertia? An d since th is resistance m ust be p roportion al

to its real mass-energy (that rotating in real directions)

it wou ld seem to m eet all of th e criteria. It is also sim pler an dmore intuitive than any other, depending solely on the

un deniable fact th at th e electrons rotation is complex . We

suggest that any time a QM relationship includes i (and

most of them do) the resulting function will only be

explained by reference to th ese extra dimen sion s.

We have shown that all stable matter, an d arguably all mat-

ter, is com pou n ded of electron -positron pairs with large imag-

inary components, so that all matter would exhibit this

gyroscop ic in ertia in prop ortion to its real m ass-energy.

Note that this is a local model of inertia, depending on

the fact that the spins of all real particles are complex ,

extending into extra dimensions. Thus it eliminates the

m agic action -at-a-distan ce of Mach s principle, in wh ich th e

fixed stars somehow reach out across light-years to knock

you down when the subway starts suddenly. It further

explains why only real energy particles, with complex

spins, have inertia, hence mass. Negative energy epos, and

also th e positive-energy epos that m ake up th e electromag-

netic field, have on e-dimen sion al vibrations, hen ce no vec-

toral plane, hen ce no m ass or inertia. This is why th e nega-

tive energy sea and its effects, which collectively may be

termed the aether, is virtually undetectable, and offers no

resistance to the motion of real objects.

Th e Neutrino Several matters remain to be explained, however. The first is

another question of spin. The neutron is a spin 1/2 particle,obeying Fermi statistics. So is the proton, and so is the elec-

tron . Th erefore, in Beta decay, to con serve an gular mom ent um

th e neutron m ust get rid of this h alf un it of spin, /2, as well

as of a rand om am oun t of real energy. (Th is energy is the dif-

ference between th e mass/energy of th e neutron and th e sum s

of the mass/energies of the proton, the electron, and the

momentum energy of the ejected electron. It is a random

amount because the electron emerges with a spread of veloci-

ties.) Fermi invented a particle, the neutrino, on the

model of the photon, to take away this spin and energy.

(Now called the antineutrino by modern convention.)

The negative energy sea and its

effects, which collectively may be

termed the aether, is virtually unde-

tectable, an d o ffers n o resistance to th e

m otion of real objects.


8/24


fin d th at on ly left-han ded vortices are possible. However,

there seems to be no way at present of choosing between

th ese possibi l it ies, and th ere may be m ore. Th e impo rtant

fact is that, locally at least, we get only left-handed neu-

tron s from th e BEC; otherwise we would h ave no n et pos-

itive energy balance.

Other important matters remain unexplained. The 9180

pairs of epos in th e neutron m ust perform an elaborate bal-

let in the form of a ten-dimensional vortex. Mathematical

analysis of this elaborate dance is needed, which should

show wh y th is structure is slightly un stable, while the p ro-

tons similar dance, performed with one empty chair, is

apparently completely stable. It should also show why this

stability is extended to the neutron, when it joins in the

even more elaborate dance of the compound nucleus.

(Neutron and p roton apparently change places during this

dan ce, so th at th e empty chair feature is shared between

them, possibly offering a hint to this stability.)

A study of condensation offers further clues to this sta-

bi l i ty. Ninety percent of the epos in a neutron vibrate in

imaginary direct ions at any one t ime; therefore the neu-

tron has a large negat ive energy balance, and cou ld be said

to be poised on th e verge of cond ensat ion.

(Th e followin g argum ent is adap ted from Taylor [2001].)Take a samp le of liquid h el ium contain ing a m acroscopic

nu m ber of atoms, N. Cool it un t i l it app roaches a state of

minimum energy. It then has a wave funct ion N. Sin ce

th is depends on th e individual states of all N atom s, it is a

very complicated funct ion. If we now examine a sample

contain ing N + 1 ato m s, it wil l have a wave fun ct ion N +

1, depen ding on N + 1 states. By comp arin g N + 1 with N,

one can define a funct ion f(x ). This depends on just one

state x, the posi t ion o f th e extra atom . This f(x) repre-

sents the order param eter, and al lows the sample to con-

den se, as i t defines the quan tum amp litud e for adding on e

extra ent i ty. Thus in the condensate this f fixes the order

of the every hel ium atom, breaking the symmetry to givethe ent ire condensate the same, arbi trary phase angle,

hence the same wave function. The loss of a single elec-

tron, in the case of the neutron, would give the resul t ing

proton an extra posi tron, wh ich m ight similarly define i ts

order parameter, making i t a total ly stable cond ensate.

If this model is correct, this analysis should also yield

exact agreem ent with th e experim ental values of the m ag-

ne t ic momen t of the n eut ron and proton, which a re lack-

ing in the SM. Moreover, analysis of the proton as a con-

densate should explain many of the scat tering resul ts ,

which n ow are obscure. It sho uld also even tual ly be possi-

ble to model all of the unstable particles revealed in cos-

m ic rays an d p article accelerator collision s as fragmen tary,

temp orary associat ions of epos. (We n ote th at th e binary isth e base ofall number systems, and suggest that any par-

t icle that seems to require combinat ions of three-based

quarks can also be m odeled using binary epos. Th e quark

is a noble effort at order and simplicityit simply is not

basic enou gh.)

However, the m odel also m akes predict ion s that sh ould

have readily measurable effects in the macrocosm. Those

effects should manifest themselves wherever there are

large numbers of ions, which force the BEC to extraordi-

nary len gths to balance th is in stabil ity in i ts midst . Th ese

large numbers of ions are called plasmas.

However, like the ph oton , the neutrino has n o charge, and

therefore violates our kinetic definition of energy. But as the

electron emerges from the neutron, it is immediately surround-

ed by polarized epos, and these can absorb real angular

momentum. However, absorbing this spin makes the epo a

spin 1/2 boson, which is unstable. It must immediately pass

on the spin th e way the ph oton (epho) passes on the spin 1

energy, forming a n eutrino wave on the m odel of our pho-

ton wave of polarized epo s, which wo uld travel at sign al veloc-

ity. However, no real electron can accept 1/ 2 un it of spin, so

th e (anti)neutrino wave must con tinue on indefinitely, un til it

meets with rare and exceptional conditions such as one in

which an electron and a proton can combin e with it to re-form

into a neutron. (Such conditions are not so rare in a star.) It is

the detection of such rare interactions as this which have been

proclaimed the discovery of the neutrino. Thus the neu-

trino is no more a separate particle than is the photon.

The Antineutron?We mu st deal with o n e furth er difficulty. We have suggest-

ed th at a vorticular storm in th e BEC seem s to be th e source

of the neutrons which, ejected into our four dimensions,

h ave produ ced th e stable m atter of our reality. However,

vort ices come in left-handed and right-handed ver-sions. Presumably, a left-handed vortex would produce

on ly left-han ded neutron s, and expel th em into our real-

ity. But what about a right-handed vortex? It would pre-

sumably produce right-handed neutrons (ant ineutrons)

which decay into ant iprotons and posi trons. (Part icle

accelerators produce both kinds.) These would form anti-

hydrogen and presumably ant ioxygen, ant icarbon, and

the rest. Is it possible that there are places in our reality

where right-handed vortices have produced whole galax-

ies of antim atter? At first sight th is seems q uite p ossible, as

from afar an antimatter galaxy would be indistinguishable

from one made of matter. However, it also seems unlikely

th at an y n earby galaxies are ant imatter, as one wou ld th ink

that sooner or later matter and ant imatter must meet andannihi la te , which would produce f loods of eas i ly-

detectable 0.511 MeV phot on s, which are not in evidence.

There are at least two more possibilities. First, the BEC

may be separated into a northern hemisphere and a

southern hemisphere. On our planet, the vortices we call

hurricanes or typhoons rotate exclusively counterclock-

wise in th e north ern h emisphere and clockwise in th e south -

ern. This would place a great gulf between the matter

galaxies and the antimatter galaxies, so that they would sel-

dom or n ever meet. (Astronom ers h ave mapp ed several such

great gulfs or voids aroun d 200 m illion ligh t years across

in wh ich few or no galaxies are foun d. If such a gulf separat-

ed matter galaxies from antimatter galaxies, there would be

no annihilation, hence no means of distinguishing an

antimatter galaxy.)

Altern atively, th e BEC m ay in some u nkn own fashion act

as a sorting device, sending only left-handed neutrons

to o ur reality, wh ile expelling right -hand ed n eutron s into

a reality on the other side of the BEC. Presumably this

would be into four more (im aginary) d imen sion s, wh ich

would also have a positive-energy balance, but would be

made of antimatter. Perhaps in the future we will find that

for some reason the BEC must act as a sorter to left-hand-

ed and right-handed universes. Or, alternatively, we may


9/249


gas-giant planets. All of them have anomalies, mysteries we cant explain.

Regularities in the spacing of the satellites of these planets have long been noted,and ascribed vaguely to reson ances, th ough reson ances of whathas n ever been

specified. Celestial mechanics, based solely on gravitation, has never been able to

accoun t for th em. For one t hin g, resonan ces are in voked to explain th e Kirkwood

gaps in the spacing of asteroids in the belt between Mars and Jupiter. These are

periods in which n o asteroids are found , and wh ich occur at harmo n ics (1/2, 1/3,

etc.) of the period of Jupiter. However, some of these harmonics have a clumping

of satellites, rather th an a gap. An d th e th ree in n er Galilean satellites of Jup iter are

locked into near octave harmonics, with periods within 0.0036 of a 1::2::4 ratio,

and there are other octave relationships in the satellites of Saturn. A gravitational

resonance cant explain both a gap (an instability) and a stable relationship at th e

sam e harm on ic ratio, so some oth er factor must explain on e or the oth er.

There is a very strange un explained ano m aly in th e cases of the gas giants

an d th eir satellites. Th e semi-major axis of our Mo on s orbit is som e 30 Earth

diameters, wh ereas the inn ermost satell ites of these gas giants orbi t n o m orethan one or two diameters of the primary from these giant dynamos. With

th e Earth and th e Moon , t idal forces slow th e Earths rotat ion and force the

Moon ever further from us.

However, Jupiters moon Io orbits only 3.5 Jupiter diameters away. Tidal

forces on Io are strong enough to wrack the satellite, making it the most vol-

canically active object in t h e solar system. W h y h avent these fierce tidal forces

long since moved Io far away from its primary? It can not be a new satellite, as

Io exhibits profound differences from the other Galilean satellites, indicating

th at th ese powerful tidal forces have wracked Io for m an y m illion s of years. Yet

instead of having been moved away by these tidal forces, as required by celes-

tial mechanics, it seems locked immovably in place, a mere three and a half

PlasmasDavid Boh m s early work at Berkeley

Radiation Laboratory included a land-

mark study of plasmas (Bohm, 1980,

1987). To h is surprise, Boh m fou n d th at

ions in a plasma stopped beh aving like

individuals and started acting as if they

were part of a larger, interconnected

whole. In large numbers, these collec-tions of ions produced well-organized

effects. Like some amoeboid creature,

th e plasma con stantly regen erated itself

and enclosed all impurities in a wall in

a way similar to the way a biological

organism might encase a foreign sub-

stance in a cyst. Similar behavior has

been observed by Rausher (1968),

Melrose (1976), and o th ers, and is now

a commonplace of plasma physics.

However, no one has ever explained

h ow a collection of ion s can act in con -

cert.But this is exactly the behavior of one

of our BECs, formed in the laboratory attemperatures near 0K and consisting of an

aggregation of bosons.

An y BEC m ust h ave an exact balan ce

of positive and n egative ch arges. An ion

cant be tolerated, and m ust be expelled

by the BEC. It is suggested that the

above behavior of a plasma is not

because it is self-organizing, but

because th e un iversal BEC can t t olerate

a collection of un balanced ions, and so

organizes this irritation into a plasma

pocket of least irritation, tending

toward a spherical form. This plasma

pocket acts, in some ways, as if it were

itself a BEC. The o rganization exh ibited

is because some of its attributes,

ordered an d con trolled by th e BEC, are

governed by a sin gle wave function.

Our hypothesis is that any aggrega-

tion of plasma will behave to a certain

extent as a single unit, acting as if self-

organ izin g, because, since it is into lera-

ble to the Big BEC, it is isolated as a

body, organized by the BEC, and thus

partially governed by a single wave

function. Since the wave function is

determined by th e BEC, whose comp o-n ents vibrate on ly at c, the period of th e

wave fun ction w ou ld n ecessarily be, for

a spherical plasma pocket, its light-

diameter. This is according to

Hamiltons Law of least action also, as

in quantum theory the longest-wave-

length vibration will have the least

energy. Thus the light-diameter vibra-

tion will be th e stable, least energy on e.

The largest collections of plasmas in

our vicinity have to be the Sun and the

Figure 4. Uranus and satellites.


10/24

IS S U E 4 4 , 2 0 0 2 I n f i n i t e E n e r g y 1 0

shou ld orbit at these n odes.

This is exactly what is shown in

Figures 4, 5, and 6, for Uranus, Saturn,

and Jupiter. Mean distances (semi-major

axes) of the satellites are from the

Astronomical Almanac for 1996. Since th e

rapidly spinning gas giants are notably

oblate, the top of clouds (equatorial

radius) is used as the first node.

These systems match the exponential

regression curves with R2 (coefficient of

determinat ion) values ranging from

0.9978 to 0.9993. (A statistician would

say that R2 is a measure of the propor-

t ion of variat ion in y tha t can be

explain ed by th e regression lin e using x.

The remainder is the percentage attrib-

utable to chance, chaos, or to other

variables.) This indicates that at least

99.78% of the value of the semi-major

axis, the satellites orbital position, can

be attributed to the function of the x-

value, i ts (quantum) period number.

This leaves rather little (from 0.07% to0.22%) to chan ce or to o th er variables.

In n ature, such (quan tum ) periodicity

is exhibited only in the n ormal modes of

wave behavior. Therefore we can say

with some certainty that each of these

th ree figures con stitutes a wave signatu re,

as clear and definite as the well-known

Airy pattern that they resemble. And

since the wave clearly originates with

the gas-giant planet, as explained by the

sea of charge requ ired by th e Dirac equ a-

tion, the waves existence can be consid-

ered confirmed. Moreover, it is clearly

more powerful than the powerful tidal

forces. (With Jupiter, something else is

also going on. We will discuss this later.)

This would seem to be th e clearest kind

of evidence for this requirement of the

Dirac equation. Each of the figures

dem on strates th at a wave of polarization, at

least 99.78% determined by its normal

mode period number, originates with

th ese spinn ing bod ies of plasma. That all

three show th e same wave behavior would

seem to eliminate all further doubt.

Moreover, as is to be expected, the inner

satellites of each planet, where the wavefunction would have the largest ampli-

tud e, fit best.

The only selection involved in these

figures is in the rings, in which small

chunks of matter are evidently disinte-

grating under extreme tidal forces and

evolving from one node to another.

(Neptune, the other gas giant, is not

included. It shows evidence of some

major disturbance that stripped it of

Pluto and Charon, its former satellites

Jupiter diameters away. It m ust be held in place by som e force even more powerful

than the powerful tidal force, a force totally unexplained by celestial mechanics.

It has further been no ted th at th e spacing of th e satellites of these gas giantsseems to follow a distribution similar to Bodes Law for the planets, though

this defies explanation, given these immense tidal forces (Miller, 1938;

Richardson, 1945; Ovenden, 1972; Spolter, 1993.) Our new understanding of

Diracs equ ation , however, does offer an explan ation . Th ese giant spin n ing bod -

ies of plasma are organized by the BEC and therefore have a single wave func-

tion. They are ch arged bod ies spinn ing in an ocean of charge, and mu st set up

standin g waves in t h at ocean .

For it h as never before been rem arked th at th efirst term of the Bode-like dis-

tribution, in each case, is the equatorial radius of the rapidly rotating body of

plasma that makes up the gas giant planet. (See Figures 4, 5, and 6.) The wave

function governing the spinning body of plasma necessarily has a node at the

surface of the planet. By Schrdingers equation, however, that wave function

would n ot be lim ited to th e planet itself, but would exten d, with greatly atten-uated (1/r2) amplitude out from the planet, forming a (longitudinal) standing

wave. Everywh ere but at a n ode, the waveform h as am plitude, and wou ld act to

polarize the vacuum. (It would raise in state epos from negative to positive

energies, polarizing them to point in real directions.) But because the wave-

form caused by th e spin n ing plasm a polarizes the vacuum everywhere but at

a no de, this vacuum polarization would add am oun ts of energy to any matter

(dust, gas, asteroids, etc.) not at a node, nudging the matter towards a node.

There it wou ld collect over millions of years, like sand on a tapped drum h ead,

forming rings of material, which eventually would collect into one or more

satellites. These no des wou ld n ecessarily be at h arm on ics of th e plan ets radius.

Its satellites, unless they are new captures in transition, or disturbed somehow,

Figure 5. The spacing of Saturn and its satellitesexponential regression.


11/241 1


However, by far the largest body of

plasm a in o ur system is the Sun , with

over 99.7% of the systems mass.

Wha t o f its standin g waves?

The SunBy the argument used with the gas

giant planets, the p lanets of the solar

system should fal l on nodes that are

harm on ics of the Sun s radius. (In th eSuns case, we will demonstrate that

th ese harm on ics are octaves, powers of

2.) But the gas giant planets are far

from th e Sun and rotat ing very rapid-

ly, so that their waves of polarization

are the strongest influence on their

satellites, as shown in Figures 4, 5,

and 6. The solar system, however, is

dynamic, changing with t ime. The

Sun i s an energe t ic furnace tha t

export s angular momentum to the

plane ts , as the Nobel i s t Hannes

Alfvn (1981) first demonstrated.

This is the principal, supposedlyconclusive argum ent t h at is advan ced

by conventional astronomers against

such attempted correlations as Bodes

Law. They say the positions of the

planets must change with t ime, so

any correlat ion at present would not

have been so in th e past , and wil l n ot

be so in the future, and therefore

mu st be coincidence.

The Sun export s angular momen-

tum by means of the solar wind, the

Sun s m agn etic field, tidal forces, and

radiation pressure. All of these trans-

fer angular mom entum from the Sun

to th e planets, both slowing th e Sun s

rotat ion and increasing the planets

distances from the Sun. Together, at

l eas t for the inner plane ts , these

forces are clearly stronger than the

polarization cau sed by th e Sun s wave

funct ion . Therefore, all of th e planets

out to Jupiter have over bi l l ions of

years been moved from their original

octave positions. This is one reason

for the seemingly anom alous distribu-

t ion of angular momentum in the

solar system, in which the planets,no t a b l y Jup i t e r , ha ve muc h more

angular momentum than the par-

ent body. (This may not h ave been

the case in the early solar system,

when the Sun was rota t ing much

faster, as the strength of this wave

funct ion would seem to be a product ,

among other factors, of the veloci ty

of rotat ion of the bod y of plasm a.)

However, Ovenden (1972) with his

least interaction action calculations,

[Van Flandern, 1993]. Its present clearly disturbed system exhibits only a lim-

ited regu larity).

The figures show th e best fit value in term s of a power ofe, base of natu ral log-

arith ms. The po wers reduce to 1.253 for Saturn , 1.480 for Uranus, and 1.621 for

Jupiter. That the satellites regularly fall at harmonics of the planets diameters is

clear. Why nodes fall at those particular harmonics, which are different for each

planet, seem to be related to the planets diameters, hence the periods of their

fundamental wave functions. We will discuss this further at a later time.

That we live in an ocean of charge, of which we are as little aware as a fish in an

ocean of water, will be difficult for many to accept. Even more difficult to accept is

th e above proof th at a planet such as Jupiter is th e source of a standing wave th at h as

amplitude millions of kilometers from its surface. Despite our preconceptions,though, waves in this ocean of charge, as required by Diracs equation, would seem

to b e confirm ed beyon d all reasonable doubt by th e above correlation s.

Moreover, studies have shown th at th e plan ets, particularly Venu s and Jupiter,

h ave a prono un ced affect on th e electron densities in th e Earths ion osphere, the

effect peaking when these planets are close to the Earth (Harnischmacher and

Rawer, 1981). The authors had no explanation for this effect, so it took consider-

able courage to publish their findings. But the above standing waves of polariza-

tion exactly account for this effect. Venus is the planet that comes closest to us,

an d Jupiter is a powerh ou se whose standin g wave affects all of the plan ets. This

means that wave functions, harmonics, beats, and interference will ultimately prove

to be as important in the m acrocosm as t hey are in th e quantum world.

Figure 6. The spacing of Jupiter and its satellitesexponential regression.


12/24


(semi-major axis x 2) of Saturns orbit is within .0035 of

211 t imes the d iameter of the Sun , that o f Uran us is with-

in .0025 of 212 t imes that diameter, and that of Pluto is

within 0.035 of 213 t imes th at diam eter. (Since th e diame-

ter of the Sun is som ewhat im precise and seems to vary by

about 300 kilometers over the course of the 11-year cycle

[Gillilan d, 1981 ] these octaves can be con sidered exact.)

Neptune, as Van Flandern (1993) shows, was the victim

of some energetic event, probably a collision or close

encounter with some major body, which, we propose,

caused i t to lose sufficient angular momentum so that i t

dropp ed int o i ts presen t (n on -octave) posit ion. Th is freed

i ts satel li tes Pluto an d Ch aron to contin ue aroun d th e Sun

with t h e approxim ate semi-major (octave) axis of the orig-

inal Neptun e, with th eir added orbi tal angular mom entu m

(which was original ly around Neptune) throwing them

into their present eccentric orbi t . Pluto then captured

Ch aron as its satellite.

Keplers Universal Harmony?Quan tum t heor y treats everyth ing as wave at all tim es, except

for a measuremen t situation, wh ich no on e un derstand s. Both

th e Schrdinger and th e Dirac equations are wave equations. We

predicted above that wave functions, harmonics, beats, andinterference will ultimately prove to be as important in the

macrocosm as they are in th e quan tum world. However, since

time is quantized, the important harmonics should be har-

monics of , that quantum of time. We live in an ocean of

showed that interactions between the planets serve to keep

them in approximately equal spacing. Thus the planets, as

they evolved from original octave positions, would maintain

th eir approxim ate spacing, so that th eir present position s sh ow

th e rou ghly regular spacing in dicated by Bodes Law, the lim it

of wh ich is th e original octave relationsh ip. (See Figure 7, a log-

arithmic plot of the solar system.)

The principle argument by conventional astronomers is

th at, because th e solar system is dyn am ic, Bodes Law m ust be

coincidence. However, because Ovendens least interaction

action keeps the spacin g regular, at any time during th eir evo-

lution from octave positions, the p lanets would have formed a

Bode-like configuration, merely with different coefficients.

So this argument fails. (We will later suggest a further factor

wh ich m ight act to keep th e spacing of th e planets regular. We

will furth er sh ow th at th ough th ese inn er planets h ave retreat-

ed from their original octave positions, they all now orbit on

anoth er harmon ic nod e.)

Plan ets in side of Mercury eith er have been vaporized by

th e Sun , or never man aged to gath er in to a planet . Mercury

itself keeps one foot in the original octave position, its

perihelion distance falling at the original octave node, and

its t ravels through higher ampli tude regions of the wave

fun ction m ight, as we will see, accoun t for th e excess rota-t ion of i ts perihel ion without recourse to curved empty

space. (An oxymoron, as Phipps [1986] pointed out.)

However, Saturn , Uranus, and Pluto remain at th e orig-

inal octave positions. (See Figure 7.) The mean diameter

Figure 7. Solar system spacing.


13/241 3


charges vibrating at th at quan tum beat.

Therefore the harmonics, particularly

the octaves (powers of 2) of that beat

should, by Hamiltons law, be the least-

energy configurations of energetic bod-

ies, particularly bodies of plasm a, in th e

macrocosm. Every energetic body of plas-

ma should act, in some ways, as a quan-

tum object. And the quantum object it

resembles, as we will sh ow, is the BEC,

which organizes its wave function.

However, the n ucleon , which m akes up

about 99.97% of the universes mass, is

a structure that vibrates in ten dimen-

sions. Therefore the harmonics of 10

should be n early as im portan t.

Moreover, there is a time, h/ mec2,

equal to 8.09 x 10 -21 seconds, that

Heisenberg considered to be th e fun -

damental t ime (Heisenberg, 1936,

1938a, 1944). In 1925, when Einstein

recom m end ed de Broglies theory o f

m atter waves to h is thesis comm ittee,

he suggested that the inverse of thistime, m ec

2/h , be considered a un iversal

electromagnetic limit frequency. And

this time is within 1% of 10 x 27,

another indication that octaves of 10

should be important .

It has been objected that harmonics

of quantum objects can not be project-

ed to m acrocosmic dimensions because

small errors wou ld be so m agnified as to

lose all accuracy. However, since time is

quan tized, and since we live in an ocean

oscillating at that frequency, the exact

h armon ics would be rein forced all along

the way, with the least-energy configu-rations tending to minimize any such

errors. An example is the resonance

between two of the hyperfine levels of

the cesium atom, used in the atomic

clock because of its rock-solid stability.

This frequency, which defines the inter-

national second, is within 0.005 of

being an exact octave of (6.26 x 10-24

s. times 244 = 1.101 x 10-10 s. Th e period

of the cesium resonance, 1/9 129 631

770 Hz, is 1.095 x 10-10 s.) This gets us

over half way to the macrocosm with-

ou t n otable loss of accuracy.

The second th ing we n ote is that the

m ean light -diameter of Jup iter, the sec-

ond most energetic body in the solar

system, is also almost an exact octave

of this quantum of time. (This would

be the period of its wave function.)

Since Jupiter is notably oblate, the

m ean diam eter is based on its volume:

D = 2(3V/4)1/ 3 .(Mean diameter of

Jupiter = 139,193 km. Light-diameter =

0.46432 s. x 276 = 0.47299 s. or less

th an 2% different .) Equ ally rem arkably, th e diam eter of th e Sun (1,391,980 km .) is,

to 5 significan t figures, exactly 10 times th e m ean d iameter of Jupiter. And th e diam-

eter of just on e star has been m easured with an y accuracy. That star is th e blue giant

Sirius, the brightest star in the sky, which has been repeatedly measured by stellar

interferometer.By the average of its measurements, its diameter is 2.04 times the diame-

ter of the Sun, its light-diam eter within 0 .001 3 of 10x 277, an almost exact octave both

of 10 and of the Suns light-diameter. Other stars have also been measured, but the

probable errors of these measurements are so large that one can only say at present

that it looks like th eir diameters mightall be harmonics of or of 10. Much more

refined m easuremen t techn iques are now possible; ho wever, astronom ers appear to

shy away from such measurements. Could they be afraid of what they will show?

We predict that all measurable stars will prove to have light-diameters that are har-mo n ics of with octaves of and 10 predominating.

We need to deal here with two objections sure to be raised to these figures. It

has been objected that the light-diameter of a massive body could not be

impo rtant, because the velocity of ligh t in a body such as th e Sun would be very

different from that in a vacuum: c = 1/(00)1/ 2. Light in a massive body slows,

depend ing on its perm ittivity and permeability. However, th e wave function is

determined by the BEC, in which the wave always travels exactly at cmax . The

above wave fun ction s of the gas giant p lanets supp ort th is; and we will present

further evidence to this effect in what follows.

Second, it has been objected that figures based on octaves, beats, and harmonics


14/24


sound like numerology. This is a favorite ploy to discount

n um bers we don t likeas if there were someth ing wron g with

n um bers, or as if we could present and collate data oth er than

numerically. Numbers we like are data; numbers we dont

like are numerology. However, as noted above, almost the

on ly place in ph ysics where who le (quan tum ) num bers appear

is in the normal modes of wave behavior. But we also have

indicated, and will demonstrate in what follows, that all

ph ysics is qu an tum ph ysics, since all m atter is wave, and th ere-

fore all ph ysics devolves ultimately to th e (quant um ) no rmal

modes of wave behavior. Ultimately, therefore, all physics is

numerology.

With this in mind, a quick look through the Nautical

Almanac reveals a host of periods or resonances of macro-

scopic objects that are almost exact octaves either of or of

10. Every body of the solar system has a major period that is

within a few percent of an octave either of or of 10. (This peri-

od is either the light-diameter of the object, the light-diameter

of its orbit, or its sidereal period.) Many have more than one

octave value. The sidereal period of Earth, for instance, falls

within abou t h alf a percent o f an octave of (6.26 x 10-24 x 210 2

= 3.174 x 107 seconds; sidereal period of Earth = 3.156 x 107

secon ds. Differen ce = 0.57%). Th e farthest from an octave is

Mars, whose sidereal period falls a fat 6% from an octavevalue. However, Mars, as we will see, falls much closer to

another, stronger harmonic.

This result beggars coincidence. The resulting regression

statistics (see Table 1 an d Figures 8 and 9) for bo th and 10

h ave R2 values of better than 0.999999, meaning that there

is no question that the figures are related, and related to

th eir (quan tum ) period n um bers, which are octaves, powers

of 2. Again , th is is the clearest possible wave signature.

With a range of 110 octaves, the exponential regression

charts are meaningless, so we have shown logarithmic linear

regressions bot h of th e entire range (Figures 8 an d 9), and of th e

range covering only the solar system (Figure 10, which shows

both regressions over the range of the solar system). Taken in

any detail or combination, the R2 values of better than

0.999999 show that the octave relationship is unquestionable,

with the possibility that the relationship is chance being less

th an 1 in 1,000,000. Moreover, th e Sun series and th e Jup iter

series remain almost exactly parallel, exactly an order of mag-

nitude apart, throughout their entire ranges. There is a slight

divergence from a power of 2 in both regressions (on the order

of 1.9995) which is probably n ot significant, ind icating m erely

that in the upper reaches of the regression the bodies are far

away from the source of the harm on ic wave.

It seems eviden t th at when th e inn er planets were forced

out of their initial octave positions by the angular momen-

tum transferred from th e Sun , th ey mo ved relatively rapidly

to th e next n earby h arm on ic. (By Keplers third law a planet

whose period is an octave of or 10 would have a light-diameter that is also a harmonic, though not an octave.)

They could defend this harmonic position for a longer

period, before being forced to the next harmonic. This

would seem to be wh y mo st of the planets no t still at octave

Figure 8. Sun serieslog linear regression.


15/241 5


distances have octave periods.

However, Jupiter is the powerhouse of the planets. It has

the most angular momentum, both rotat ional and orbi tal ,

and its harmonic is the primary, the harmonic. It is note-

worth y that th e plane of the ecliptic is roughly th e plane of

Jupiters orbit. The Sun rotates a full 7 away, and only near-

by Mercury orbits over the Suns equator, with Venus split-

ting th e difference with an inclin ation of 3.4 degrees.

Moreover, th e Sun s export of angular mom entu m stops

at Jupiter. The outer planets orbit, apparently undisturbed,

at th eir original octave distan ces. But Jupiter h as moved t o

an apparent ly unassai lable posi t ion, the intermodulation

harmonic between i ts harmonic and the Suns 10 beat.

(Its orbits ligh t-diameter is with in a percent of ( + 10 ) x

286 .) Moreover, there apparently is a back-eddy of this

intermodulat ion beat that affects the next two inner peri-

ods, the asteroids and Mars. Those asteroids which remain

orbit where Jupiter permits them. The average mean orbit

light-diameter of the ten largest asteroids is exactly at 12

x 285 , the in termodu lat ion beat . And Mars, next in, is with -

in 2% of 13 x 284 , which apparently also allows it to be

near an octave period harmonic. (Jupiters harmonic. See

Table 1.) (Yes, th is soun ds like nu m erology again . But

once we acknowledge that we live in an ocean of charge,then waves, beats, interference, and harmonics become

data , not n um erology.)

Mercury is a fascinating case. We mentioned that it keeps

one foot at its original octave positionits perihelion

light-distance is within less than a percent of 10 x 280 , the

Sun s octave. Yet its aph elion distan ce is with in a co up le of

percen t of x 2 84 , Jupiters harmonic. Like a good quantum

object, it oscillates between t h e Sun s harm on ic and Jup iters

harmonic. Meanwhile its sidereal period is within 1% of yet

another octave, x 210 0. No won der all th e an gular m om en-

tum exported from the nearby Sun cant budge it from its

positionit is locked into three separate harmonics.

Th is would app ear to solve a long-stand ing problem con-

cerning Mercury. The dynamics of a small body orbiting

close to a large body tend to remove the eccentricity from

th e small bodys orbit and p lace it on a n ode of its stand ing

wave. The Galilean satellites of Jupiter, for instance, have

eccentricities ranging from 0.002 to 0.009they are in per-

fectly behaved, almost perfectly circular orbits. The inner

satellites of Saturn have even lessTethys has a measured

eccen tricity of 0.00000. By con trast, Mercury, closest to th e

Sun , h as by far th e m ost eccentric orbit (0.2056) of any p lan-

et, if you exclude Pluto, which is probably an escaped satel-

lite of Neptu n e. But like the cesium at om s reson an ce

between two h yperfine levels, the Mercury quan tum object

reson ates betwee

dirac’s equation and the sea of negative energy, part 2, by d.l. hotson

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