Update (12 January 2010): around us, the accelerating mass of the universe causes an outward force that can be calculated by Newton’s 2nd law, which in turn gives an equal inward reaction force by Newton’s 3rd law. The fraction of that inward force which causes gravity is simply equal to the fraction of the effective surface area of the particle which is shadowed by relatively nearby, non-accelerating masses. If the distance R between the two particles is much larger than their effective radii r for graviton scatter (exchange), then by geometry the area of the shadow cast on surface area 4*Pi*r^{2} by the other fundamental particle is Pi*r^{4}/R^{2}, so the fraction of the total surface area of the particle which is shadowed is (Pi*r^{4}/R^{2})/(4*Pi*r^{2}) = (1/4)(r/R)^{2}. This fraction merely has to be multiplied by the inward force generated by distant mass m undergoing radial outward observed cosmological acceleration a, i.e. force F = ma, in order to predict the gravitational force, which is not the same thing as LeSage’s non-factual, non-predictive gas shadowing (which is to quantum gravity what Lemarke’s theory was to Darwin’s evolution, or what Aristotle’s laws of motion were to Newton’s, i.e. mainly wrong). In other words, the source of gravity and dark energy is the same thing: spin-1 vacuum radiation. Spin-2 gravitons are a red-herring, originating from a calculation which assumed falsely that gravitons either would not be exchanged with distant masses, or that any effect would somehow cancel out or be negligible. Woit states:

“Many of the most well-known theorists are pursuing research programs with the remarkable features that:

Although making the most basic quantum gravity predictions can be done with “high school mathematics”, the deeper gauge symmetry connection of quantum gravity to the Standard Model of particle physics does require more advanced mathematics, as does the job of deriving a classical approximation (i.e. a corrected general relativity for cosmology) to this quantum gravity theory, for more detailed checks and predictions. When Herman Kahn was asked, at the 1959 congressional hearings on nuclear war, whether he agreed with the Atomic Energy Commission name of “Sunshine Unit” for strontium-90 levels in human bones, he replied that although he engaged in a number of controversies, he tried to keep the number down. He wouldn’t get involved. Doubtless, Woit has the same policy towards graviton spin. What I’m basically saying is that the fundamental particle is that causing cosmological repulsion, which has spin-1. This causes gravity as a “spin-off” (no pun intended). So if spin-1 gravitons are hard to swallow, simply name them instead spin-1 dark energy particles! Whatever makes the facts easier to digest…

Fig. 1 – new presentation of quantum gravity, based on both the recent discussion with Doug Sweetser in the About page comments, and an attempt to explain the mechanism to a science teacher, during an hour long run in the park this evening. Note that this predicts the actual strength of gravity, e.g. it predicts the value of the gravitational parameter G. This is *not* a non-predictive theory like string theory, based on 6/7 extra dimensions that nobody can observe and adding 100 or more extra unknown parameters plus a multiverse of 10^{500} extra universes to the Standard Model of particle physics. It’s a predictive theory based on factual inputs, not a non-predictive theory which is based speculations about yet other speculations (Planck scale unification, wrong spin-2 gravitons, etc.).

The mainstream spin-2 graviton theory can’t calculate anything checkable, since it has to falsely ignore graviton contributions in the surrounding universe, which are immense due to the fact that (1) the masses of galaxies in the surrounding universe are immense and (2) the gravitons from such distant masses are *converging* from a great distance as they are exchanged with masses here, which is the opposite of divergence. This spin-1 graviton theory is the only possible falsifiable theory of quantum gravity for this reason: *it is based on observable facts seen in nature.* By Newton’s 2nd law, the cosmological acceleration (a = Hc ~ 7 x 10^{-10} ms^{-2}) of the mass of the universe (~3 x 10^{52} kg of observable luminous matter, according to NASA’s Hubble Space Telescope) implies a force outward from any observer of F = Ma = 2 x 10^{43} Newtons. Newton’s 3rd law implies an equal and opposite force (i.e. inward directed, *towards* the observer). From the possibilities of known particle physics (gravity and the Standard Model), this force must be carried by gravitons, implying the mechanism in Fig. 1 which gives gravity as the asymmetry when this force is shadowed by masses with a cross-section for graviton interactions equal to the black hole event area of the mass of that fundamental particle, which is a fact that is empirically justified in the earlier post linked here. The blach hole event horion radius for an electron is 1.35 x 10^{-57} metre, so it has a cross-section of just 5.73 x 10^{-114} m^{2}. This small cross-section is why gravity is so weak compared to other forces (e.g., the gravitational attraction between two apples is negligible, and you need immense masses like the mass of the earth to make the gravitational interaction significant, whereas other fundamental forces show up when dealing with just a few particles).

There is an radial inward force of 2 x 10^{43} Newtons which is the 3rd law reaction to the observed cosmological acceleration of the universe around the observer. This is an immense force, but because the cross-section for quantum gravity is so small, gravity gets cut down to the observed strength by the shadowing effect in Fig. 1.

The gravitational attraction force given by Newton’s law with parameter G obtained in the usual way empirically (from the twisting of a fibre by the attraction of large lead spheres in the laboratory) can now be calculated theoretically as proved in Fig. 1 above. It is accurate, with errors well within the error in the estimate of the mass of the observable universe (3 x 10^{52} kg which is taken from page 5 of the NASA report linked here). Fig. 1 also summarizes the flaws in trying to extend LeSage’s inaccurate and useless theory of gravity to this theory in order to ignore it (which is like falsely claiming Darwin’s evolution is wrong because Lamarke came up with an inaccurate and misleading theory of evolution before Darwin sorted out the facts of evolution; it superficially impresses the gullible, but it is a false argument itself): LeSage’s theory is based on real radiation, not virtual (off-shell) radiation like gauge bosons (which don’t heat up objects or slow them down by causing drag). In any case, quantum gravity will imply that there are gravitons throughout the vacuum, so if this naive objection were true, it would be a problem for spin-2 gravitons just as spin-1 gravitons. Actually, there are interactions between gravitons and moving masses: these cause the FitzGerald contraction in length in the direction of motion (head-on pressure effect), the increase in mass (snowplow effect), and for static masses the radial contraction (compression) which leads to various curvature effects in the approximation to quantum gravity which is known as general relativity.

Above: LeSage’s shadow theory was developed originally by Newton’s friend Fatio, but was a failure because it couldn’t predict anything:

(1) Fatio and LeSage didn’t know Weyl’s gauge theory whereby two gravitational charges will exchange off-shell virtual particles, gravitons, to cause gravity (which is the case in the other fundamental particle interactions in the Standard Model). So they falsely speculated that gravity was caused by dust like particles which would cause drag, slowing down the planets and heating them up by impacts. Maxwell and Kelvin later pointed out these flaws, debunking the Fatio-LeSage theory.

(2) They didn’t know that we’re surrounded by immense masses in all directions and that according to any Weyl gauged quantum gravity theory, we will be exchanging gravitons with those surrounding masses. There is no way to prevent or justifiably ignore the consequences of this graviton exchange with immense distant masses.

(3) They didn’t know about the recession of matter, so they couldn’t predict the cosmological acceleration of the universe correctly ahead of measurement (which we did publish in 1996, two years before discovery), and then use that value to calculate the outward force of receding mass M by Newton’s 2nd law, F = Ma. They couldn’t in consequence apply Newton’s 3rd law to get the equal and opposite inward-diected, graviton mediated force. They also didn’t have any evidence about the graviton interaction cross-sectional area for matter; they didn’t know the evidence that it is black hole sized.

There are other ignorant claims to be found on the internet. For example, http://www.mathpages.com/HOME/kmath209/kmath209.htm states falsely that the isotropy of the universe is 1 part in 100,000 without specifying the area of sky that this this amount of cosmic background radiation temperature fluctuation applies to: the page claims that this amount of anistropy would cause “fluctuations in the “weight” of a 1 pound object (in the shape of a slender rod, to make it sensitive to the directional flux) on the order of 100 pounds”. It gives no time-frame for the period of oscillation of this density, or the ratio of length to diameter of the rod, just the pseudoscientifically value word “slender” (which is non-quantitative). Actually, this is totally false because if a long slender rod is made, it will not fluctuate in mass due to the anisotropy because the anisotropy is not fluctuating! The same pattern of anisotropy in the cosmic background radiation exists across the sky. Rotating the rod makes no difference whatsoever, because the rod is composed of individual fundamental particles! The sum of forces acting on those particles is no different regardless of the orientation of the rod. With a cross-section for graviton interactions of 5.73 x 10^{-114} m^{2} for an electron, there is no significant chance (even with the mass of the earth) that two fundamental particles will lie on a single given line of sight. Hence, the shape of a given mass is irrelevant for the mass sizes we are concerned with in the case of rods in a laboratory. There are also false “arguments” that gravitons have to travel faster than light, cause heating to melt objects, cause drag forces, and so on, which are based upon studiously ignoring the off-shell nature of force-mediating virtual particles, Weyl gauge bosons. Does your fridge magnet glow red-hot from exchanging gauge bosons with the fridge door? No? Electromagnetism between fundamental charged particles is 10^{40} times stronger than gravity, so if gravitons are supposed to cause heating then electromagnetism would cause a heating effect 10^{40} times worse than gravitons! That debunks the idea that gauge bosons cause any type of heating, including drag effects which cause objects moving in a real (on-shell, not off-shell) fluid to heat up.

All of the objections to this mechanism of gravity are similar in their off-the-top-of-my-head stupidity and ignorance to the objections Feynman’s path integrals received from Oppenheimer, Bohr, Teller and others at Pocono in 1948; they are based on ignoring the facts and simplistically dismissing progress.

Consider Oppenheimer’s attempt to censor Feynman’s path integrals without listening at all, as described by Freeman Dyson (Stuckelberg was working on the same idea independently, but was ignored and – as with Zweig’s quarks – he received no Nobel Prize). It’s remarkable that genius in the past has consisted to such a large degree in *overcoming apathy* (Oppenheimer was not just a stubborn exception who objected to path integrals. E.g., Feynman is quoted by Jagdish Mehra in *The Beat of a Different Drum*, pp. 245-248, saying that Teller, Dirac and Bohr all also claimed to have “disproved” path integrals: Teller’s disproof consisted of saying that Feynman didn’t have to take account of the exclusion principle, Dirac disproved it for not having a unitary operator, and Bohr disproved it because he believed that Feynman didn’t know the uncertainty principle: “it was hopeless to try to explain it further.” So without Dyson’s brilliance at explaining ideas, Feynman’s path integrals would probably have been ignored.)

“… take the exclusion principle … it turns out that you don’t have to pay much attention to that in the intermediate states in the perturbation theory. I had discovered from empirical rules that if you don’t pay attention to it, you get the right answers anyway …. Teller said: “… It is fundamentally wrong that you don’t have to take the exclusion principle into account.” … Dirac asked “Is it unitary?” … Dirac had proved … that in quantum mechanics, since you progress only forward in time, you have to have a unitary operator. But there is no unitary way of dealing with a single electron. … Bohr … said: “… one could not talk about the trajectory of an electron in the atom, because it was something not observable.” … Bohr thought that I didn’t know the uncertainty principle … it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up …”

– Richard P. Feynman, in Jagdish Mehra, The Beat of a Different Drum (Oxford, 1994, pp. 245-248).

http://www.mathpages.com/HOME/kmath209/kmath209.htm compiles equally false dismissals of physical mechanisms from “geniuses” of physics, with added nonsense thrown in (like the mass variation claim we have just debunked):

Historical Assessments of the Fatio-Lesage Theory

It’s an interesting historical fact that the attitudes of scientists toward the Fatio-Lesage “explanation” of gravity have varied widely, not just from one scientist to another, but for individual scientists at different moments. This is exemplified by Newton’s ambivalence. On one hand, he told Fatio that if gravity had a mechanical cause, then the mechanism must be the one Fatio had described. … he explicitly denied (in a famous letter to Bentley) the intelligibility of bare action at a distance, but he just as explicitly rejected (in a letter to Leibniz) the notion that space is filled with some material substance (a la Descartes) that communicates the force of gravity. His alternative was to say that gravity is caused by the will and spirit of God, not by any material cause. Of course, he gave consideration to various possible material mechanisms, and even included some Queries in the latter editions of Opticks, speculating on the possibility of an ether …

Even setting outside the outlandishness of the explanation, Newton was never able to extract from Fatio’s idea any testable consequence that could support it, so the idea remained an occult mechanism which, according to Newton, is not the proper purview of science.

Subsequent scientists have had similarly ambivalent reactions to the theory of Fatio and Lesage. For example, Euler originally expressed interest in Le Sage’s theory, stating (in the same conditional manner employed by Newton) that if gravity is due solely to impulse forces, then something like Lesage’s theory must be true. However, Euler ultimately rejected Lesage’s theory …

This striking ambivalence regarding the Fatio-Lesage theory has many other examples. Herschel spoke for many scientists when he said it was “too grotesque to need serious consideration”, whereas Thomson and Tait gave it serious consideration, the latter even asserting that it was “the only plausible answer which has yet been propounded”. Darwin too gave the idea “serious consideration”, but he also said “no man of science is disposed to accept it as affording the true road”.

Several of the founders of modern kinetic theory, including both John Herapath in 1820 and John James Waterston in 1845, began their investigations by trying to devise mechanical explanations of gravity. Herapath seems to have been influenced explicitly by Lesage’s writings, whereas Waterston was apparently one of the many independent discoverers of the concept. …

I remember a discussion on Physics Forums in which all the errors in LeSage’s theory and dismissals of it by famous physicists were straightened out over many hundreds of comments. Finally the discussion thread was closed by an administrator who falsely stated that at some point in the above discussion, a decisive dismissal of physical mechanisms had been given, but he couldn’t remember what it was, although it proved that it was pointless to go on discussing the topic. This is of course wrong, but it is what happens in such pointless discussions. Feynman had tried to defend himself against Bohr, who closed the discussion in the same way by falsely claiming that Feynman didn’t know the uncertainty principle. If he had shouted back, Bohr would doubtless have just become either angry or smug and would have still ignored the physics Feynman was putting forward.

It is important to “stand upon the shoulders of giants” in physics in order for them to pay attention to your idea. (The Feynman suppression episode in 1948 reminds you of a famous joke by the late Sidney Coleman: “If I have seen further than others, it is by standing between the shoulders of midgets”.) By building on new foundations which Bohr was ignorant of (and biased against), Feynman guaranteed that he would be ignored and falsely dismissed by an arrogant and ignorant Bohr. Feynman’s continuing censorship today for second-quantization are in favour of a mechanism (virtual, field quanta multipath interference) causing the indeterminancy of fundamental particles on small scales:

“… Bohr … said: ‘… one could not talk about the trajectory of an electron in the atom, because it was something not observable.’ … Bohr thought that I didn’t know the uncertainty principle … it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up …”

– Richard P. Feynman, quoted in Jagdish Mehra’s biography of Feynman, The Beat of a Different Drum, Oxford University Press, 1994, pp. 245-248. (Fortunately, Dyson didn’t give up!)

‘I would like to put the uncertainty principle in its historical place: When the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of old-fashioned ideas … But at a certain point the old-fashioned ideas would begin to fail, so a warning was developed that said, in effect, “Your old-fashioned ideas are no damn good when …” If you get rid of all the old-fashioned ideas and instead use the ideas that I’m explaining in these lectures – adding arrows [path amplitudes] for all the ways an event can happen – there is no need for an uncertainty principle!’

– Richard P. Feynman, QED, Penguin Books, London, 1990, pp. 55-56.

‘… when the space through which a photon moves becomes too small … we discover that light doesn’t have to go in straight [narrow] lines, there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that there is no main path, no “orbit”; there are all sorts of ways the electron could go, each with an amplitude. The phenomenon of interference becomes very important, and we have to sum the arrows to predict where an electron is likely to be.’

– Richard P. Feynman, QED, Penguin Books, London, 1990, Chapter 3, pp. 84-5.

The indeterminate electron motion in the atom is simply caused by second-quantization: the field quanta randomly interacting and deflecting the electron.

However, the physically false, non-relativistic Heisenberg/Schroedinger approach is easier to apply to bound states like atoms, so it is falsely taught as QM, just as the Bohr atom is falsely taught in high schools.

Here is a solid example of the failure of first quantization mathematics:

“The quantum collapse [in the mainstream interpretation of first quantization quantum mechanics, where a wavefunction collapse occurs whenever a measurement of a particle is made] occurs when we model the wave moving according to Schroedinger (time-dependent) and then, suddenly at the time of interaction we require it to be in an eigenstate and hence to also be a solution of Schroedinger (time-independent). The collapse of the wave function is due to a discontinuity in the equations used to model the physics, it is not inherent in the physics.”

– Dr Thomas S. Love, Departments of Mathematics and Physics, California State University.

“In some key Bell experiments, including two of the well-known ones by Alain Aspect, 1981-2, it is only after the subtraction of ‘accidentals’ from the coincidence counts that we get violations of Bell tests. The data adjustment, producing increases of up to 60% in the test statistics, has never been adequately justified. Few published experiments give sufficient information for the reader to make a fair assessment.”

– http://arxiv.org/PS_cache/quant-ph/pdf/9903/9903066v2.pdf

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

– R. P. Feynman, The Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

Obviously, one diagram cannot summarize all of the justifications and implications. However, there is a need in physics to make clear how simple nature really is, as proved by the failure of non-relativistic first quantization and the success of simple path integrals in second quantization (representing fields as exchanged off-shell quanta).

‘Underneath so many of the phenomena we see every day are only three basic actions: one is described by the simple coupling number, j; the other two by functions P(A to B) and E(A to B) – both of which are closely related. That’s all there is to it, and from it all the rest of the laws of physics come.’

– Richard P. Feynman, QED, Penguin Books, London, 1990, p. 120.

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

– R. P. Feynman, The Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

‘You might wonder how such simple actions could produce such a complex world. It’s because phenomena we see in the world are the result of an enormous intertwining of tremendous numbers …’

– Richard P. Feynman, QED, Penguin Books, London, 1990, p. 114.

What is the way forward? Well, this spin-1 graviton exchange mechanism deals neatly with gravitation and dark energy as both being quantum gravity effects, and this modifies the Standard Model. So my preferred option is to write a paper, titled maybe ‘A Simple Change to the Standard Model for Inclusion or Quantum Gravity, with Predictions and Validation’, and/or a full textbook explaining *first* the maths of the Standard Model, and *then* explaining the evidence for makin the slight corrections needed to incorporate quantum gravity.

A second option (maybe when the first gets ignored) is to follow in the footsteps of a great physicist and write a satrical ‘Dialogue Concerning Two New Sciences’, comparing the failures of over-hyped mainstream false spin-2 speculative, non-falsifiable string theory to the successful predictions of this censored, entirely fact-based theory (note that the black hole cross-section has empirical evidence discussed in the post linked here).

The relationship between the black hole cross-section for gravity and the mechanism for electromagnetism is discussed in earlier posts here and here. The gauge boson of electromagnetism is a virtual photon with 4-polarizations, not the 2-polarizations that normal photons have. The two extra polarizations are required to make attraction work in the framework of Weyl’s gauge theory. The repulsion law works fine even using 2-polarization photon exchange: you get hit by a photon from a similar charge, and it knocks you away from the similar charge. If you fire a photon to that similar charge, you recoil away from that other charge. So similar charges repel. Fine. But attraction requires adding two extra polarizations to the field quantum of electromagnetism. The field around an electron is negative: we know the electron has negative charge because of the field, which is mediated by virtual photons. We don’t know anything about the electron’s core, only about its field. We’ve only probed matter to energies on the order of 100 GeV or so, and we’ll never collide charges hard enough to see beyond the field effects to the core. So the whole notion of “charge” really needs to be applied to what we see with charge, which is the field, not the unobservable inner core of an electron. Hence, in electromagnetism the virtual photons can be treated as charged. The normal objection to this turns out false. It used to be objected that massless charges can’t move or they would generate infinite magnetic self-inductance. But actually, in Weyl’s theory virtual particles are exchanged in two directions at once, e.g. from charge A to charge B and back the other way. This two-way exchange is possible – even though one-way motion is impossible – because the superimposed magnetic curls of the field vectors will cancel out if two-way exchange is occurring. Many photons are exchanged in each direction simultaneously, so this works.

With two oppositely spin-1 charged field quanta mediating electromagnetism and one uncharged spin-1 field quanta mediating gravity, we have 3 massless gauge bosons which seem to be described by an SU(2) symmetry without mass. This suggests a modification to the Standard Model, where at present SU(2) gauge bosons are given mass by a speculative untested, non-falsifiable “Higgs mechanism”. Modifying it so that left-handed SU(2) gauge bosons acquire mass still gives the weak force but allows gravity to be included in a reformed Standard Model.

The coupling strengths of gravity and electromagnetism are different at observed low energy by a factor of about 10^{40}, gravity being the weaker. This is explained in a simple path-integral random walk between charges: the existence of two different electric charges but only one gravitational charge means that you can get a random-walk of gauge boson exchange between electric charges which adds up differently to that between gravitational charges. The random walk result is numerically equal to the size of one step multiplied by the square-root of the number of steps. It turns out that on average the outward divergence of receding field quanta is compensated for by the inward convergence of approaching field quanta, so all we need to do is to multiply gravitational charge strength by the square root of the number of particles in the universe (about 10^{80}) to get the electromagnetic charge strength in QFT: this turns out to be accurate within experimental error (10^{40}).

What is physically happening is that fundamental particles are black holes, radiating high energy particles which behave as field quanta (virtual particles) since they are of extremely small wavelength. The black hole radiating power for electrons calculated from Hawking’s formula predicts a fundamental force 10^{40} times stronger than gravity; hence this is electromagnetism. Gravity is about 10^{40} times weaker due to the random-walk mechanism illustrated in previous posts.