Solving the “Problem of the Cosmological Constant”
R. D. Pearson 10/1/07
The Big Bang theory for creation of the universe gained impetus in 1980 when Alan Guth introduced his idea of “inflation”. Unfortunately the creation it postulated could not be switched off. Consequently the theory implied that the universe is expanding at a rate billions of billions of times greater than is remotely possible. This presented a problem, called that of the “cosmological constant”, which to this day remains an unsolved vexed question as far as cosmologists are concerned. However, as described here, a solution was published in Russia in 1994.
The big bang is said to have started from a “quantum fluctuation” from the void of zero energy (nothingness) that should have collapsed to nothing again after a brief instant. Before this happened, however, Guth’s idea of inflation cut in causing a fantastically rapid explosion during which all the energy we know about appeared from nothing and within a ball of only one metre radius. And from Einstein’s E= mc2 energy E can transmute into the mass m of matter. The gas-like cloud continued to expand under its own inertia with much of its energy condensing to form the universe of stars and planets that we observe - as described by Guth and Steinhardt (1989.)
Unfortunately the theory was flawed from the start by the problem of the cosmological constant. It also said the expansion was forever slowing due to gravity. Then all cosmologists were astounded and dismayed by the results of observations of remote supernovae, published by Schwarzchild. B. (1998), which conclusively showed the expansion was speeding up.
But this is not all that is wrong in both cosmology and physics.
New Scientist gave an alarming report about the state of physics in their 10th Dec.05 issue. It concerned the “International Solvay Conference” that had taken place in Brussels the previous week. Nobel laureate David Gross in summing up admitted they were in a state of utter confusion and that some new approach was needed. Everything they were doing like string theories and the search for quantum gravity had failed, but nobody had any idea what to do next. Now top physicist Lee Smolin (2007) has just published a book saying his generation has failed to achieve anything worthwhile in over the last quarter of a century despite greater numbers of physicists than ever before and unprecedented high levels of funding. The award of $60,000 to Professor Cahill in 2005 to find an alternative to relativity and propose new experiments highlights that physicists are now recognising that Einstein’s theories are unsatisfactory.
But, as we shall soon see, ECM theory has already provided a satisfactory alternative. Several physicists, including the Nobel laureate Brian Josephson, have attempted but failed to fault the logic.
I think I found the reason for this sad state of affairs, way back starting in 1984, when I discovered an alarming logical error concerning gravity and later four logical errors in Guth’s inflation theory. Worse, every effort I made to point these out by writing to scientific journals only resulted in letters of rejection that showed all assessors, except one, had received inadequate grounding in both mechanics and thermodynamics. The one exception was the famous physicist, Professor J. Vigier of Paris. In his reply dated 2nd August 1987 he admitted the first critique was valid and said it needed publication. But even he was unable to get it into Physics Letters A for which he was the gravitational consultant.
When it becomes impossible for sound critiques to get past assessors or editors then science is in danger of diversion onto false tracks. The evidence suggests this has already happened. First let me say that I stand in awe of the physicists’ brilliance in sophisticated mathematics, that applying to “quantum field theory” in particular. This explains the strange way the components of atoms work. The late and famous physicist, Richard Feynman (1985), lucidly explains this QED theory.
The final conclusion I reached, however, was that the physicists have blind spots that could be readily addressed by people of my own discipline. This is the mathematically based but practical branch of physics known as “mechanical engineering”.
In 1987 I therefore set about trying to solve the problem of the cosmological constant. Its seriousness was highlighted two years later when Nobel Laureate Steven Weinberg (1989) published an article that said, “The cosmological constant represents a veritable crisis for physics”.
It was clear that to find a solution to the creation problem it was necessary to introduce the idea of a background medium consisting of primary particles made of two opposite kinds of energy – positive and negative. These must be equivalent to the Yin and Yang of Eastern philosophies. The two kinds form a background I call “i-ther” and had to consist of a balance of these two kinds of primary particle, the “primaries”. Opposite kinds could cancel each other to leave the nothingness of the void; this represents mutual annihilation. Creation would be the converse case: nothing giving rise to opposite somethings. A basic law of physics known as, “The conservation of energy” would be satisfied in this way and yet the universe could arise spontaneously from nothing.
So both pure creation and annihilation could now occur. But what would determine which case would apply in given circumstances? The answer was that another basic law of physics called, “The conservation of momentum” had also to be satisfied. What this means is explained in detail with reference to FIG.8.1.
Analysis then showed, as explained with reference to FIG.11.6, that when primaries of opposite energies collided only two at a time, then momentum conservation forced energy gains to occur. Each gained energy of its own kind in balanced amounts so that, if added together, the sum was zero: the value of the void. Repeated collisions of many such primaries caused a violently explosive creation.
Fortunately the amorphous gas-like fluid so generated was unstable. If a chosen direction is considered positive then primaries moving that way are accredited positive momentum. Identical primaries moving in the opposite direction have negative momentum. Hence if large numbers arrive at a point or line from all possible directions then their total momentum is zero even before collision. This is also the condition resulting if annihilation occurs. So primaries arriving from all directions yield a condition favouring total annihilation and, since this is also the condition for minimum energy, annihilation must occur.
So the whole rapidly growing cloud of primaries now spontaneously self–organised into a myriad of flow cells, each cell being minute even compared with an atom. In these, collision breeding continued at an unabated rate. But now primaries were driven to annihilation centres in each cell where almost, but not quite, all the energy created was destroyed. A minute net creation remained causing an ever-accelerating expansion of the universe. The greater the acceleration the greater the i-theric density needed to produce that acceleration. This resulted in a smaller net rate of creation since at some high density primaries become so crowded that annihilation dominates. So a feedback mechanism exists to control the now slowly accelerating expansion.
A creation scenario had now appeared that provided a paradox-free solution to the problem of the cosmological constant and, at the same time, yielded the prediction of a universe in a state of ever-accelerating expansion: so matching observation. This was predicted in 1992: long before its observation in 1998.
An Alternative to Relativity-Exact Classical Mechanics (ECM)
For those who need more detail, the new approach was based on revisions of Newtonian mechanics as described in the new book, Pearson (2007). Revision of Newton’s original mechanics was required since it is inadequate for representing objects moving at very high speeds or in strong gravitational fields. Einstein’s theory called “general relativity” matches most observation under these circumstances but unfortunately could not be applied to the creation problem. This was because Einstein’s postulates do not allow energy to be measured from any absolute datum and for creation an absolute zero for energy is provided by the void. The i-ther needed to arise from the void.
Consequently a replacement had to be derived before the creation problem could be fully addressed. I started from scratch to produce a totally different mechanics that did not rely on any kind of relativity theory. It had to avoid internal contradiction and incompatibility with quantum theory. A solution was found by adopting Newton's three laws of motion, Euclidean geometry with universal time and with all motion, inclusive of light in vacuum, measured from an absolute datum: meaning local space.
The resulting ECM derivation fits all the experiments, usually considered Einstein’s unique achievements even though his “time dilation” does not exist (clocks simply run slow due to mass increase). Does this also provide a solution for the problem of quantum gravity? It certainly eliminates the difficulties that have prevented general relativity from providing this “holy grail” of the physicists after more than 60 years of futile worldwide effort.
Unfortunately, publication in Western journals was found to be impossible. All assessors made it clear that relativity must not be challenged. Fortunately, the famous inventor of the caesium beam atomic clock, Dr. Louis Essen FRS came to the rescue by proposing that I deputize for him at a forthcoming scientific conference in Russia where, he said, I would find scientists with more open minds. So the ECM theory was published in the proceedings of the Russian Academy of Sciences and Arts, Pearson (1991). The solution for the cosmological constant is embedded in a further paper in the Russian proceedings of the following year, Pearson (1994).
Later the reason for failure to surmount the barriers of peer review in the West came from the disillusioned Australian physicist Brian Martin (1997). In his book he shows that the assessors of physics journals operate a “secret closed shop”, This renders publication impossible in the West unless an author has a Ph.D in physics as a minimum qualification: they refuse to recognise any contribution from the discipline of engineering.
Quantum physicists admit that “reality” is a vexed question
There is more to relate. Quantum theory tells us that each sub-atomic particle exists in a limbo state of “superposition” until observed by a conscious intelligence. In this limbo state an object, for example, can be spinning in both directions at once. So nothing can be truly real until consciously observed. This unreality remains an unresolved vexed question of physics. It means that in some way consciousness had to evolve prior to the creation of matter. The new approach could provide the answer to this conundrum.
Annihilation centres provide the key to this newly opening door. They are more than dots or lines: they are blobs or filaments occupying a surprisingly large proportion of the total volume of space. Primaries are constantly arriving at their surfaces, move in under their own inertia and mutually squeeze each other out of existence. A tangle of filaments connecting with blobs can arise forming an infinite variety of shapes. Furthermore enormous power is generated in each i-theric cell between creation and annihilation. Such conditions match those that, according to Gribbin (2004), create spontaneous organisation by chaos. The i-theric structure can be arranged to look like replicas of the neural networks of our brains and might have arisen, by a form of evolution, from such self-organisation. So background intelligence might exist able to organise energy to create what we see as matter.
This is not the first time background intelligence has been inferred. Dr N.A. Kozyrev (http://www.divinecosmos.com) in uncovering his “torsion fields” shows he considers an intelligent “Aether” must exist. However, he gives no detail of its structure and, according to the new approach, the Aether or alternatively the “quantum vacuum” would exist as the next emergent level of existence. Pearson (1997) describes how consciousness could be connected with the solution to the problem of the cosmological constant. This was achieved in a Western scientific journal, by simply avoiding mention of qualifications altogether.
Another finding is that black holes described by ECM theory are very different from those of general relativity. Black holes no longer have “event horizons” inside which time goes backwards, nor do they house matter at impossible “singularities” as in GR. In ECM theory primaries, not matter; exist as cores of finite size in process of mutual annihilation at the centres of black holes. So they are now seen as supplementary annihilation centres. They help reduce acceleration of the expanding universe. However, if the acceleration were to cease altogether the i-theric density would fall to zero and then everything would have vanished back into the void from which it emerged. It is a frightening thought that the universe must exist in a state of accelerating growth forever or disappear!
Details of momentum conservation
FIG.8.1 from the new book, Pearson (2007), gives a plan view of a momentum balance. It consists of two pendulums of identical length and having spherical bobs. The fulcrums are arranged so that the balls just touch when hanging still. The threads holding the high bounce balls (or ½” to 1” dia. ball bearings) are preferably not less than about two metres long and the horizontal distance of the swing is limited to a quarter of the length of the pendulums. Then the speed at impact is directly proportional to the horizontal distance of the swing to better than 1% accuracy. Every science classroom should have one since it confirms the law of conservation of momentum, shows what it means and gives the student a very hands on understanding of the physical meaning of the terms “positive and “negative”.
In the example shown a “driver” ball is set in motion to hit a stationary “driven” ball. The driver ball of mass ma makes contact at velocity v1 with the driven ball of mass mb. Then both scatter with velocities v2 and u2 respectively. However, it is the “components” such as vX of these scatter velocities, which are of primary interest. The product of mass m and velocity v or u defines momentum. Velocity is speed with the direction of motion also defined. An arrow to a scale representing the magnitude mv or mu, with the arrowhead pointing in the direction of motion, can be used to represent momentum. In FIG.8.1 vX is the “component” of velocity v2 measured in the X direction and a component of momentum can also be represented by an arrow pointing in the X direction..
We consider the driver ball moving in direction X at first and calculate its momentum mav1. Then we measure and add the two momentum components mavX and mbuX. In every experiment, whatever the masses ma and mb, which can be identical or different, it is found that the sum of these two scatter momenta is equal to mav1 the initial momentum of the driver ball. This demonstrates what is meant by the conservation of momentum. In this example the balls had equal mass so the arrows can, in this special case, represent velocity as well as momentum.
But the balls scattered in the Y direction as well. Although neither ball had any initial momentum in this direction both leave with momentum in this Y direction. Has this violated momentum conservation? No. This is where the idea of positive and negative come in. The upward direction of Y is arbitrarily called the positive direction so that the opposite direction is called the negative direction. So one ball has a positive momentum component mavY with the other –mbuY. The experiment shows these cancel to zero: the same as the initial total. So again momentum is conserved.
Both balls can be in motion before impact and even if the balls are made of plasticene and stick together the law is still found to hold true. Also this law can be derived by simple algebra from Newton’s laws of motion and so the experiment also confirms these laws. It therefore also provides a useful example of the scientific method in which experiment is used to check the theory.
What is also of great interest for solving the creation problem, however, is the reversal in direction of all momentum arrows in the upper figure, to represent primaries of negative mass. This means they are made of negative energy and inspection shows momentum is again conserved. It follows that our universe could be made of negative energy and we would never know this was so.
Consequently negative energy is just as probable as the positive kind and works as its mirror image. To solve the creation problem it is necessary to consider the existence of both kinds at the ultimate level of reality and then find what happens when the two kinds interact by collision.
The ECM theory shows that energy, not mass, is the true building substance of everything in existence as shown by Pearson (2007).
From Newton’s second law an unrestrained object, when pushed by a “force of action”, moves in the direction that force is pointing. A force, pushing an object free to move, causes it to accelerate. The moving force produces “mechanical work”, a form of energy that is transferred to the object causing it to gain energy of motion. This “kinetic energy” adds to the “rest energy” from which the object was made when standing still to yield a “sum energy” corresponding to “inertial mass”. This means mass increases with speed in contrast to the assumption used in the original Newtonian mechanics.
Negative energy primaries accelerate in the opposite direction to the force of action so that the energy of mechanical work is negative. This negative energy adds to the negative rest energy from which the object is made so that a mirror image of the positive kind appears. Two negative primaries in collision will bounce away just as do billiard balls, as can be illustrated by FIG. 8.1, so there is nothing strange about negative kinds. It is only when opposites interact that strange things are predicted.
Now that the law of conservation of momentum is understood it can be applied to the collision breeding of opposites as illustrated by FIG.11.6 also taken from the new book. At A primaries of positive and negative energies meet head on. Since the negative primary carries momentum P- in a direction opposite its motion the momenta of both collision partners point in the same direction and so add up to P+ + P-.. The only condition to maintain momentum conservation across the collision is for both to remain unchanged.
At B the collision is offset so that scattering occurs. No change of momenta can occur in the X direction for the same reason as applied to case A but now transverse momenta PT+ and PT- are added in both positive and negative Y directions so that they cancel. However, as shown at C these add to those in the X direction (“vectorially” as illustrated) so that each has an increased momentum P2 as compared with the incident value P.
An increase of momentum demands an increase in energy and so each primary has been forced to gain energy of its own kind by the collision. Then, as shown at D both are deflected in the same transverse direction.
In this example the masses were assumed equal and opposite. Then it is readily shown that the added momentum component has to be exactly transverse as otherwise the two energy gains will not balance.
In general collisions occur at all angles between 0 and 180 degrees but a complete analysis taking this into account shows that on average there is an energy gain from the two particle collisions of primaries of opposite energies equal to 20% of initial kinetic energies.
This represents a huge rate of creation but fortunately the resulting gas like cloud is unstable: annihilation also being possible. The cloud self-organises into a myriad of minute cells having annihilation cores at their centres. The creation still going on is almost cancelled and in this way the problem of the cosmological constant is resolved.
Further detail can be obtained from a new book entitled “Creation Solved? (228 pages: 29 figs. Hardback 6”´9” £19.50 plus p&p) published in May 2007. It is mainly descriptive but is a primer for a mathematical text to follow shortly, See website www.pearsonianspace.com
[3392 words including title]
To show how easy maths can be
Some very simple maths highlights one of the theorists blind spots
Most people think they will never understand maths since it looks too difficult - but appearances can be deceptive! I have therefore set out below a simple derivation with every step fully explained. Please try to follow this slowly and carefully. Then I am sure you will see the light.
This derivation has also been selected to illustrate one of the simple blind spots from which physicists and cosmologists seem so prone. That the universe is in a state of ever-accelerating expansion has been staring them in the face since 1929 and none of them, even today, seem to have noticed that this was so!
Most people, seeing equations where letters appear instead of numbers, immediately assume this is something beyond their scope and quickly close the pages. If you feel this way, then please study this appendix carefully. It needs to be studied step by step, making sure the simple logical rules are obeyed at each step before moving to the next one. You will then discover, to your great surprise and satisfaction, that you understood it after all!
Another reason for this appendix is to show how cosmologists and physicists, despite their incredible mathematical prowess, have missed a very simple bit of logic.
Everybody, worldwide and for 78 years, seems to have missed this very simple thing. Others of a similar nature can be identified. This in no way discredits the theorists. What it seems to imply is that the very sophistication of their discipline is creating blind spots that are obvious to people of allied disciplines, trained to look at things in a different and less sophisticated way. They ought to be accepted as participants in physics.
Two simple rules of maths
The letters that appear in equations are just like numbers. Indeed they represent numbers and so can be treated in the same way. The advantage of using letters as symbols, to represent numbers, is that equations result into which numbers can then be substituted. This makes further calculations easy. The rules are simple:
1 The equals sign means that the part on its right hand side will have exactly the same numerical value as that on the left hand side when numbers are substituted. When the numbers are associated with units, like those of mass, length or time, these units must also balance across the equals sign.
2 To maintain equality, everything done to one side has to be done to the other as well. For example, if the number 2 is used to multiply the right side, then 2 must multiply the left side as well. Similarly 2 could be added to both sides, subtracted or divided by 2. This applies for any other number or any symbol that is used in this way.
Now to derive the blind spot
(It involves the ever-accelerating expansion of the universe)
In 1929 the astronomer, Edwin Hubble, discovered that remote galaxies are receding from us at a velocity directly proportional to their distance from us. It follows that by multiplying this separating distance, we will denote as x, by what is known as the “Hubble constant” Ho, the recession velocity v can be calculated. This can be expressed in mathematical shorthand by the following equation:
v = Hox 
(Note that the multiplication sign is omitted to comply with convention)
Now the velocity of an object moving in a straight line is identical to its speed: both mean that the distance covered by the object is divided by the time taken. For a general case where conditions may vary over time, velocity needs to be defined as a short distance covered by an object divided by the short time taken. “Short” or “small” is symbolised by the Greek letter d, pronounced “delta”. So with t standing for time we can write:
v = dx/dt 
Furthermore, if an object is speeding up i.e. accelerating, then acceleration, symbol a , is defined as a small change in velocity divided by the short time taken to produce this velocity change.. This can be expressed as:
a = dv/dt 
Hence to find the acceleration implied by equation  both sides can first be expressed in terms of small changes to be written as:
dv = H0 dx
Now divide both sides by the short time dt needed to make these changes in velocity and distance and we get:
But dv/dt is given as a from  and dx/dt is given by  as v.
So these equivalences can be substituted in  to give:
a = Hov 
And v is given by  and can be substituted in  to finally yield:
a = HoHox 
The term HoHo is called Ho ”squared”, written as Ho2, and so  can be written:
a = Ho2x 
This shows galaxies must accelerate away from us in direct proportional to their distance away.
Now, if you followed that derivation carefully, I am sure you found it not so difficult.
As a matter of fact this is homing onto the “differential calculus” in which things like dx anddt tend to indefinitely small “elements”. This developed into the powerful mathematical tool first derived by our most famous scientist, Sir Isaac Newton. Also his “integral calculus” is the reverse procedure and can be applied to equation . This makes Guth’s inflation occur some 800 billion years ago – a massive increase on the 13.7 billion years ago estimated by cosmologists from the same equation and data but assuming a constant speed of recession for any galaxy. Then a puzzle appears. According to astronomers, some stars seem older than the universe!
If the equations still seem to have no meaning then they will as soon as they are used. Astronomers measure distances in “megaparsecs” (MPC) and 1 MPC = 3.26 million light years. . Hubble’s constant is reported as 71 km/s per MPC. So if a galaxy is 10 million light-years away from us, then by substitution in equation  it should be found that its speed of recession is 218 km/s.
Now a light-year is the distance light travels in one year at a speed of 300,000 kilometres/second and there are 31,600,000 seconds in a year so even one light-year is a long way and, according to ECM theory, the universe has a radius of about 20,000 million light-years!
Equation  has identified the blind spot. Although Hubble’s equation appeared in 1929, nobody noticed that it implied an accelerating expansion. This simple derivation invalidates both Hoyle’s theory of continuous creation of a universe extending to infinite distance. Also if cosmologists had derived equation  they would never have accepted the Big Bang theory that followed.
The main point of this appendix is to show that people from allied disciplines could be of help to cosmology and physics if only such assistance was appreciated and recognised. It appears that the immense mathematical sophistication of theorists, whose value is not disputed, must be leaving them with blind spots that less sophisticated disciplines are more suited to notice.
[1083 words](including titles Appendix only)
[4543 words total including titles and appendix]
Feynman, Richard P. (1985): QED The Strange Theory of Light and Matter
Princeton University Press (1985)
Gribbin, John (2004): Deep Simplicity: Chaos, Complexity and the Emergence of Life: Penguin Books
Guth, A. & Steinhardt, P (1989): The Inflationary Universe pp 34 to 60
The New Physics edited by Paul Davies: Cambridge University Press
Martin, Brian (1997): Suppression Stories: “Fund for Intellectual Dissent”, Box U129 Wollongong University NSW 2500, Australia. http://www.uow.edu.au/arts/sts/bmartin/dissent/documents/
Pearson, R.D (1991): Alternative to Relativity including Quantum Gravitation: Second International Conference on Problems in Space and Time: St. Petersburg, (Sept. 1991) pp 278-292.
Pearson, R.D.(1994): Quantum Gravitation and the Structured Ether
Sir Isaac Newton Conference. St. Petersburg (March 1993) pp 39-55
Petrovskaja Academy of Sciences & Arts
Pearson, R. D.(1997): Consciousness as a Sub-Quantum Phenomenon
Frontier Perspectives, Spring/Summer 1997, Vol.6,No.2 pp70-78
(inadvertently omitted from contents list)
Pearson, R. D. (2007): CREATION SOLVED? PART I of a trilogy
www.pearsonianspace.com Hardback £19.50 +p&p 211 pages each 6”´9” inc. 28 figs.
Schwarzchild, B (1988): Very distant Supernova Suggest that the Cosmic Expansion is
Speeding Up: Physics Today, Vol.51(6) pp.17-19 (1988)
Smolin, Lee (2007): The Trouble with Physics: Allen/Lane, Penguin
Weinberg, Stephen (1989): The Cosmological Constant Problem
Reviews of Modern Physics, Vol.61 (1) Jan 1989