Quantum field theory

'Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the "mass gap:" the quantum particles have positive masses, even though the classical waves travel at the speed of light.' - http://www.claymath.org/millennium/Yang-Mills_Theory/

Is there charge in empty space? QFT is not very lucid on this. Whereas Dirac said the vacuum is full of virtual charge, and used this to predict antimatter, which was then detected by Anderson in 1932 (resulting in a Nobel Prize for Dirac), there is the issue that a vacuum completely full of charge would polarize around real charge, cancelling it completely.

Feynman, Schwinger, and Tomonaga showed that the vacuum is not full of free charge or it would cancel out real charges by becoming totally polarized. Instead, there is a limit or cutoff to the amount of polarization, at a collision energy which corresponds to a very small distance from the middle of the electron. This comes from the need to renormalize the charge of the electron, in order to force the QFT to predict the electron's magnetic moment and Lamb shift accurately.

So free (polarizable) charge pairs can only exist close to the middle of the electron, where the electromagnetic field is strong enough, presumably, to break the bonds of the vacuum sea of charges, and free the charges so that they can then become polarized and cause the right amount of shielding for QFT to work. So from causality + QFT, the vacuum doesn't contain any free charge but must be full of bound charge which is broken up into free charge in the strong fields near a fundamental particle (real charge core).

There are virtual particles polarized in the strong field near real charge cores, and these must come from some mechanism. The strong field breaks up the orderly vacuum structure for a small distance, allowing it to become polarized which shields some of the real particle charge.

The classical 'solar system' model falls because it is fake. The planets don't do around the sun in true ellipses because they perturb each other. Because all the planets are of small mass compared to the sun, the solar system looks approximately deterministic, but it isn't. You can't solve it analytically (this is the '3 body problem'), so you have to use approximations which get less and less accurate. If you want to know where the earth will be in its orbit in 100 million years, the inaccuracies are so great that all you can do is to specify the probability of finding the earth at any given distance from the sun. It is not deterministic, it is statistical on long time scales. This 3+ body problem is called Poincare chaos and has been known over 100 years. 'Classical theory', not quantum theory, is horse*hit.

Newton's is just an approximate theory. It can't calculate the real world deterministically to absolute accuracy, even given absolutely known initial conditions.The electron is a far worse case because you have (1) got the fact that the electron has equal charge to the proton it is orbiting, not a charge far smaller (mass represents gravitational 'charge' in any quantum gravity), and (2) the size scale of the range of virtual particles in the vacuum is big enough to knock and deflect the electron randomly as the electron moves in the vacuum (Heisenberg's law says product of energy of virtual particles and the time they exist is h over 2 Pi or whatever, hence by rearranging and putting in the energy for an electron-positron pair, you get the time they exist, 10^-21 second; assuming as an exaggeration they go at speed c, this gives you a maximum range of virtual particles in the vacuum of ct = 10^-12 metre).

In addition, you have the 3+ body problem of the multiple charges. Even in the simplest case, a H atom, you have proton, electron, and a third particle you use to probe to find out where the electron appears to be. This gives you 3 bodies hence Poincare chaos. In practical situations, you have many more electrons. I give sources and references for this stuff on my site at locations like http://feynman137.tripod.com/#b.

An electron has some chance of being found at a great range of locations, and the classical picture at best just indicates where it is most probably to find it. 'Most probable' is misleading if a large number of locations have equal or nearly equal probability, producing the electron 'cloud'. Quantum mechanics doesn't even estimate the statistical probability of finding an electron at a given location directly when you have anything more complex than a H atom in an empty universe. At least in that case, QM allows you to predict probabilities of finding the electron at different locations. All multi electron atoms are beyond quantum mechanics and can only be solved by introducing approximations and simplifying assumptions which make the situation into a 'corrected' version of the H atom. You can't trust any claims made by quantum mechanics gurus who wave their arms around, Feynman was right to say denounce it. Feynman says, in his book Character of Physical Law, page 57-8 (1964 Cornell lectures, broadcast on BBC2 in 1965):

'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 space/time 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.'

Feynman said, in Character of Physical Law, pp. 171-3:

'The inexperienced, and crackpots, and people like that, make guesses that are simple, but [with extensive knowledge of the actual facts rather than speculative theories of physics] you can immediately see that they are wrong, so that does not count. ... There will be a degeneration of ideas, just like the degeneration that great explorers feel is occurring when tourists begin moving in on a territory.'

It isn't electrostatic forces which control chemistry, it is the 'Pauli exclusion principle'. The key assertion of the exclusion principle for physics is that in any adjacent pair of electrons, the spins are opposite. Since spins are linked to magnetic moments in QED, this suggests that the periodic table and all bonding arrangements are based on magnetic repulsion/attraction in addition to the electric Coulomb forces. The 'Pauli exclusion principle' just says that the four quantum numbers of any electron (describing shell, its shape, etc, as well as spin) are a unique set for each electron in an atom. So far as shell number goes, this is just stating that the electron is not in two shells at once, which is just a statement that the electron behaves classical law not indeterminacy horse*hit (I'm not in two rooms at once). The Pauli exclusion principle is insightful in saying that adjacent electrons always have opposite spins: this is why most materials are non-magnetic seen from a large distance, the magnetic moments of the electrons cancel one another out. But at short range, there are magnetic forces which are important for determining atomic stucture and chemical bonding.These are always referred to as 'Pauli exclusion principle' instead of the more candid term 'magnetic force due to spin'.

See:http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html#c2 (which is a horse*hit description), andhttp://hyperphysics.phy-astr.gsu.edu/hbase/molecule/nacl.html (which at least has a graph).

Consider H-H bonding. Why should two hydrogen atoms bond together to form H_2? The H_2 molecule is in a lower energy state than 2H. The two shared electrons pair with opposite spins (one up, one down). If you drop magnets in a box and shake it up, they end up side by side, north pole of one beside south pole of the other, and vice versa. This is the lowest energy state, which occurs naturally. So all of this quantum stuff is found to have not classical, but mechanistic basis.

The accepted facts of the Standard Model are based on Yang Mills (gauge boson exchange).

Forces are caused because the radiation has momentum, like all bosons such as photons of light.

It allows quantitative predictions to be made such as forces of gravity, electromagnetism, and particle masses.

If it does raise more questions, that is science. After all, any step forward does that. The only way to stop more questions is to accept rubbish like extra dimensional string theory or Ptolemy's epicycles, or the lambda-CDM model of cosmology. Real science does raise questions, one of which is whether it is right. Message to the stringers: 'If you can predict the quantitative strength of gravity or electromagnetism better, go ahead, but until then, stop making background noise to suppress the proved verifiable facts.'

Positive and negative charges may emit gauge bosons which spin in opposite directions relative to the direction of propagation. The gauge bosons will have a regular normal (integer) spin (unlike the half integer spin of electrons which is more complex, like a Mobius strip being spun) and maybe all that distinguishes those of different charges is the direction of spin relative to the direction they go, whether it is clockwise. If you picture the gauge boson as a corkscrew, two similar corkscrews going in opposite directions (from similar charges) will oppose each other's spin and interfere. But two corkscrews with opposite spin going in opposite directions will add up without interference.

Move a fixed-area shield twice as far from you, and the fraction of the total spherical area around you which is shielded falls by the inverse square of the distance! The absolute force is equal to {the total inward force which is ~ 10^43 N for gravity, multiplied by the fraction of the total spherical volume around you which is shielded. Hence for an inward force of 10^43 N, if 1 % of the spherical area around you is shielded by a charge, the net force is simply 10^41 N.

If you want to know where these gauge bosons come from, they are emitted by accelerating charge (spinning charges have centripetal acceleration and radiate energy, they don't lose energy by doing this because all charges do it, so there is equilibrium as the universe is old).

It is simply an experimental fact that radiation is emitted due to acceleration. Centripetal acceleration due to the spin of a charge loop emits this radiation. My page http://feynman137.tripod.com/ and my blog http://electrogravity.blogspot.com/ present the evidence. For example, the gauge bosons travel in closed loops between masses, the gauge boson energy is conserved, because this is a characteristic of the loop quantum gravity derivation of general relativity (without a metric) from quantum field theory. The contraction caused by suc gauge boson radiation pressure is like running into a storm of bullets. They hit you harder (with greater momentum) if you run into them head on, since the momentum you receive depends on yor motion. This causes the contraction, just like that from the force from the air pressure on the front of a car moving at high speed. The main difference between air and the gauge bosons is that they penetrate to fundamental masses, and are not stopped by the outer layer of atoms, and they don't carry away energy by being speeded up as such, or by transferring energy into heat, because there is no mechanism by which this could occur.

If you see my old (superseded) paper on CERN Doc Server, I started off with the hydrodynamic analogy to calculate gravity first: http://cdsweb.cern.ch/search.py?recid=706468&ln=en (this paper is now obsolete and cannot be updated as CERN has closed all updates except via carbon copies from arXiv.org, which censored me in 2002). The gauge boson mechanism is mathematically equivalent, as proved by the side by side calculations on my home page at the section: http://feynman137.tripod.com/#h

Two similar charges are exchanging radiation beween one another, causing the recoil apart! The exchange is only prevented between charges or masses for neutral charged masses (gravity) and dissimilar charges (electric attraction), where the exchange continues with the surrounding universe, which causes the dissimilar charges or masses to be pushed together from the outside of the line of shielding between them.

Two masses or two opposite charges are shielding one another along the lines joining them (the lines are actually double cones, because each charge has a fixed size).

Two similar masses are exchanging beween one another, causing predominant repulsion.

Redshift occurs in the expansion of the universe, and the mechanism by which it occurs for gauge bosons need not be considered different than that by which it occurs for visible light. See http://www.astro.ucla.edu/~wright/tiredlit.htm for a disproof of all "alternatives" to cosmological redshift (redshift is easily demonstrated to be a factual mechanism, by contrast with pseudo-scientific belief system speculation on "tired light" which has no evidence behind it whatsoever).

I've said that redshift may be just a slowing down of light speed, in which case the amount of redshift is determined by the difference in speed between us and the object emitting the light. All redshift means is that we see fewer cycles per second than was emitted. The fact light is transverse rather than longitudinal like sound, does not alter the fact that if it does slow down, we will see fewer cycles per second (i.e., we will see it redshifted).

If the explanation for Michelson-Morley is as Sir Eddington says (he stated that the contraction of the instrument exactly offsets the variation in lght speed by giving it a shorter path to travel where it is slowed down), then the CBR emitted at 300,000 years after BB comes to us at 6 km/s. Light/radiation emitted at time zero will come to us at speed 0 km/s. Light emitted at half the age of the universe will come to us at 50% of c. The percentage is not a fixed fraction, but is proportional to the age of the material. All were considering is the possibility that redshift is caused by light coming to us more slowly. Hence light from the sun comes to us at c, light from galaxies at 1,500,000,000 light years comes to us at 90% of c (because they are receding from us at 10% of c), etc.

This argument is irrelevant for the gravity-electromagnetism mechanism. The figure of 10^80 hydrogen atoms in the universe is measured by multiplying the average material (directly observed) density of the universe by its spherical volume out to how far light travels in the age of the universe (time since BB).

This figure has always been the same. Back in the 1930s it was calculated by Eddington who used Hubble's grossly exaggerated value of the Hubble constant (Hubble thought it was 540 km/s/megaparsec - which is 6-8 times too high - because he under-estimated the distances to stars by confusing two populations of Cepheid variables, which he used as measuring sticks for relative distances in multiplying up absolute distances derived from accurate parallax measurements locally).

Eddington got the right answer because the two massive errors in his calculation largely cancelled each other out. He underestimated the size of the universe because the excessive Hubble constant underestimated the age of the universe (if Hubble constant H is expressed in SI units it has units of 1/seconds, and 1/H is the age of the universe ignoring gravitational deceleration, whereas 2/(3H) is the age of the universe assuming a critical density between collapse and infinite expansion, assuming falsely that gravity is independent of the BB not the result of a mechanism based on the BB), but he overestimated the density of the universe for the same reason. Hence the mass he calculated by multiplying two numbers (one a gross overestimate, and one a gross underestimate) happened to turn out fairly accurate.

Because the false (high) figure of the Hubble constant used in the 1930s implies an age of the universe 6-8 times less than today's figure (2,000 million years in the 1930s, compared to a modern figure around 15,000 million years), the apparent measured density of the universe was over-estimated by a massive factor in the 1930s.

Because masses of galaxies were not known accurately then the density estimates were known to have large error margins, but the over-estimate made the apparent density of the universe in agreement with the critical density of general relativity. Later data takes away the exaggerated (high) density value, and so there is a disagreement which is filled by the ad hoc dark matter hypothesis.

The gravity mechanism dispenses with this by showing the true density when general relativity is made a quantum theory of gravity is not the critical density but is smaller by a factor of (e^3)/2 which is a factor of just over 10. This brings the observed density of the universe today into alignment with theory. It also gets rid of dark energy because the gravity mechanism doesn't cause gravitational retardation on expansion. The postulate of dark energy comes from a small positive cosmological constant added to a general relativity cosmology with critical density (ie the Lambda-CDM model) to cancel out gravitational retardation by causing an acceleration wich cancels out the long range postulated gravitational deceleration which is not observed in supernovae redshifts. Gravity mechanism gets rid of gravitational retardation at long ranges by physical mechanism (there are several equivalent ways to formulate this argument, the most brief and least rigorous being the simple statement to people that gauge bosons are redshifted like light over vast distances, so gravity doesn't cause distant supernovae to slow down). Hence it predicted the correct supernovae recession rates via the Oct 96 issue of Electronics World, two whole years before Perlmutter's experimental results confirmed it. There is no ad hoc dark energy because that isn't needed to counteract gravitational deceleration over vast distances, because the latter is a falsehood due to ignoring the details of quantum gravity mechanism in general relativity.

SCIENTIFIC METHOD:

OBSERVATION -> DATA ->GRAPH, TABLE, MATRIX OF RESULTS -> EMPIRICAL EQUATIONS -> UNIFYING LAW -> MECHANISM.

In long discussions with Catt, he insisted that he did not comprehend the above sequence, despite my explanations of chemistry and thermodynamics as examples of the sequence. Quantum field theory and general relativity are at the stage of unifying laws, not mechanisms. Catt claims that Dirac's equation is like phlogiston or caloric, which I explained is a falsehood because phlogiston and caloric were false attempts to jump straight to a mechanism without a mathematical model which was successful. Catt tries to claim Ockham's Razor gets rid of all empirical equations or data, which is false, because those equations are simply awaiting unification and finally mechanism to explain them and at the same time predict other stuff.

The spectacular test was when Nature published Permutter's paper "A Supernovae at Half the Age of the Universe" (or whatever it was called) in1998. It fell on the curve predicted by my paper. I asked Brian Josephson to co-author the 2003 Electronics World paper to get people to listen. The mainstream always ignore and suppress or obfuscate to reverse findings. The 1971 experiment with atomic clocks flown around the world in airliners proved absolute motion, although see below how it was cleverly obfuscated to imply the exact opposite, like the M-M experiment and Aspect's entanglement experiment (the EPR paradox in the Copenhagen Interpretation was simply ignored as a disproof of the latter and taken to be proof of many universes within Bohr's mindset...):

From my page on the 1971 experiment http://feynman137.tripod.com/:

Professor Paul Davies very indirectly and obscurely (accidentally?) defends Einstein's 1920 'ether and relativity' lecture .In 1995, physicist Professor Paul Davies - who won the Templeton Prize for religion (I think it was $1,000,000), wrote on pp54-57 of his book About Time:'Whenever I read dissenting views of time, I cannot help thinking of Herbert Dingle... who wrote ... Relativity for All, published in 1922. He became Professor ... at University College London... In his later years, Dingle began seriously to doubt Einstein's concept ... Dingle ... wrote papers for journals pointing out Einstein's errors and had them rejected ... In October 1971, J.C. Hafele [used atomic clocks to defend Einstein] ... You can't get much closer to Dingle's 'everyday' language than that.'

Now, let's check out J.C. Hafele.J. C. Hafele is against crackpot science: Hafele writes in Science vol. 177 (1972) pp 166-8 that he uses 'G. Builder (1958)' for analysis of the atomic clocks.G. Builder (1958) is an article called 'ETHER AND RELATIVITY' in Australian Journal of Physics, v11, 1958, p279, which states:'... we conclude that the relative retardation of clocks... does indeed compel us to recognise the CAUSAL SIGNIFICANCE OF ABSOLUTE velocities.'

Einstein himself slipped up in one paper when he wrote that a clock at the earth's equator, because of the earth's spin, runs more slowly than one at the pole. One argument, see http://www.physicstoday.org/vol-58/iss-9/p12.html, is that the reason why special relativity fails is that gravitational 'blueshift' given by general relativity cancels out the time dilation: 'The gravitational blueshift of a clock on the equator precisely cancels the time dilation associated with its motion.'It is true that general relativity is involved here, see the proof below of the general relativity gravity effect from the Lorentz transformation using Einstein's equivalence principle. The problem is that there are absolute velocities, and special relativity by itself gives the wrong answers! You need general relativity, which introduces absolute motion, because it deals with acceleration like rotation, and observers can detect rotation as a net force, if in a sealed box that is rotating. It is not subject to the principle of relativity, which does not apply to accelerations. Other Einstein innovations were also confused:

http://www.guardian.co.uk/print/0,3858,3928978-103681,00.html, http://www.italian-american.com/depretreview.htm, http://home.comcast.net/~xtxinc/prioritymyth.htm.

'Einstein simply postulates what we have deduced . I have not availed myself of his substitutions, only because the formulae are rather complicated and look somewhat artificial.' - Hendrik A. Lorentz (discoverer of time-dilation in 1893, and re-discoverer of George FitzGerald's 1889 formula for contraction in the direction of motion due to aether).

As Eddington said, light speed is absolute but undetectable in the Michelson-Morley experiment owing to the fact the instrument contracts in the direction of motion, allowing the slower light beam to cross a smaller distance and thus catch up:

'The Michelson-Morley experiment has thus failed to detect our motion through the aether, because the effect looked for - the delay of one of the light waves - is exactly compensated by an automatic contraction of the matter forming the apparatus... The great stumbing-block for a philosophy which denies absolute space is the experimental detection of absolute rotation.'

- Professor A.S. Eddington (who confirmed Einstein's general theory of relativity in 1919), Space Time and Gravitation: An Outline of the General Relativity Theory, Cambridge University Press, Cambridge, 1921, pp. 20, 152.

Experimental confirmations which prove the mechanism:In 1996 I proved - contrary to the mainstream general relativity model of cosmology - that by the mechanism of gravity the universe is not decelerating. The mainstream model has the universe expanding ever more slowly because of the effect of gravity.This was confirmed experimentally in 1998 by Perlmutter, published in Nature (without mentioning my work, which Nature's ed, Philip Campbell, had said in an autographed letter to me on 25/26 Nov 96 that he was "not able" to publish, and a day before/later his physical sciences ed said the same thing about a review paper proposal I sent on a related mechanism topic).In addition to this, the mechanism predicts the strength of gravity and electromagnetism, the strong nuclear force, and particle masses correctly and is further checkable as the astronomical data used (like density of universe and Hubble parameter) become more accurately known.

However, two mainstream theories (sting theory for forces and the Lambda-CDM cosmology) which are entirely ad hoc and non-checkable are used to suppress my work. Verification just brings you a stream of abuse from the mainstream, nobody sits up and listens. Nature wouldn't publish my prediction in 1996, nor would they publish a paper showing how the experimental results confirmed the prediction in 1998.If you look at what "string theorists" and mainstream Lambda-CDM cosmologists are saying, they are all bitter people. Ask them about physics, and they reply by saying how impossible it is for anyone to understand them if they aren't genius.

Professor Hawking writes in an essay that two crackpots sent him mutually incompatible ideas, proving that the are both totally wrong. You can immediately see that just because two theories are incompatible, does not prove that both are wrong. One can be right and the other wrong, or both can be partly right and partly wrong, so that they are incompatible. Hawking is then a charlatan because he and others claim say general relativity is incompatible with quantum mechanics, but don't claim that this incompatibility proves both are 100% wrong. The submessage of the mainstream is clear: 'Everyone with alternatives is wrong, and I'm so clever I know everyone else is wrong without having to check or verify it.' This is not really a scientific attitude, unless science is now purely a matter of snobbery. For those of us who entered science to escape snobbery and that kind of content-less political time-wasting, that is kind of ironic.

It reminds you of the story of Faraday being forced to act as servant to Davy's wife during their European scientific tour. There was nothing scientific about that. At the end of the day it is fairly obvious that scientists and editors are unprofessional if they are being bribed to hype extra dimensional string theory, whether the bribes are paid by free market book publishers, mad eccentrics, or by tax payers via the government quangos.

On relativity and absolute motion: the cosmic background radiation is incredibly uniform in all directions except for effects due to the earth's absolute motion. This "new aether drift" was published in Scientific American in 1977 or thereabouts. There are also semi-mainstream objections to special relativity like http://arxiv.org/abs/gr-qc/0406023 but I think two things are needed to get rid of special relativity: (1) a full causal mechanism for how contraction, time-dilation etc occur due to effects of the spacetime fabric on matter and (2) a final theory which predicts everything. You aren't going to get rid of "Einstein" (although he was anti-special relativity after 1915, and gave the pro-aether speech in 1920 at Leyden) until you have a final theory which answers all physics questions.

The main issue is getting a causal electroweak symmetry breaking mechanism, but I don't think that is going to be too difficult. The really fun part will be the run-in with orthodoxy. By including general relativity and the Standard Model as limiting approximations of the final theory, plus including a summary of all the maths of quantum field theory and tensor analysis, the mainstream orthodoxy will find it ever harder to make meaningful sneers. They have a limited list of tactics, and if they call you crackpot you can point out that the only facts you are using are mainstream ones, which if you do it lucidly (i.e. briefly) enough with a single short sentence, really is a proper defence.

Responding to an email from R. P. Feynman's erstwhile co-author, Prof. Jonathan Post (might as well

From: Nigel Cook
To: jonathan post ; David Tombe ; epola@tiscali.co.uk ; imontgomery@atlasmeasurement.com.au ; Monitek@aol.com
Cc: marinsek@aon.at ; pwhan@atlasmeasurement.com.au ; graham@megaquebec.net ; andrewpost@gmail.com ; george.hockney@jpl.nasa.gov ; tom@tomspace.com
Sent: Sunday, July 23, 2006 8:53 PM
Subject: Re: Heat wave, wonderings, Re: Sodium Chloride and Magnetic Spin Moment

Dear Jonathan,

Vacuum polarization is the mechanism for renormalization which is vital in calculating the correct magnetic moment of electron predicted from Dirac equation is defined as exactly 1 Bohr magneton. By 1947 it was known this value is too low by around 0.12%

QED by Schwinger in 1948 increased it to 1 + (alpha)/(twice Pi) = 1.00116 Bohr magnetons, the added (alpha)/(twice Pi) factor being the first additional Feynman coupling diagram for the photon (or whatever the magnetic mediator is) from the electron to interact with the virtual particles and inbetween mediating magnetism from the electron core to the observer's instrument. You have to remember that the polarized vacuum of virtual charges affect the electron's (Dirac theory) characteristics. This comes from the shell game: the virtual particles in successive shells add very slightly to the magnetic field from the real electron core.

Renormalization comes about physically in this calculation because alpha is the dimensionless 1/137... factor. Vacuum polarization around the real electron core means that virtual positrons are closer to the core than virtual electrons, so there is a net electric field arrow from the polarized charge which points the opposite way to that from the core, cancelling most of the electron's charge.

The electron charge we observe from large distances is -e. But when we get closer to the electron core, by hitting electrons together at 92 GeV so that they approach closely, the charge rises by 7%. I've got an calculation which shows that if you could eliminate the polarized shielding shell around the core, you would see the charge rise by a factor of 1/alpha, or a factor of 137...

Heisenberg's uncertainty says [we are measuring the uncertainty in distance in one direction only, radial distance from a centre; for two directions like up or down a line the uncertainty is only half this, i.e., it equal h/(4.Pi) instead of H/(2.Pi)]:
pd = h/(2.Pi)
where p is uncertainty in momentum, d is uncertainty in distance.This comes from his imaginary gamma ray microscope, and is usually written as a minimum (instead of with "=" as above), since there will be other sources of uncertainty in the measurement process.
For light wave momentum p = mc,pd = (mc)(ct) = Et where E is uncertainty in energy (E=mc^2), and t is uncertainty in time.

Hence, Et = h/(2.Pi)
t = h/(2.Pi.E)
d/c = h/(2.Pi.E)
d = hc/(2.Pi.E)
This result is used to show that a 80 GeV energy W or Z gauge boson will have a range of 10^-17 m. So it's OK.
Now, E = Fd implies
d = hc/(2.Pi.E) = hc/(2.Pi.Fd)
Hence
F = hc/(2.Pi.d^2)

This force between electrons is 1/alpha, or 137.036, times higher than Coulomb's law for unit fundamental charges.Notice that in the last sentence I've suddenly gone from thinking of d as an uncertainty in distance, to thinking of it as actual distance between two charges; but the gauge boson has to go that distance to cause the force anyway.Clearly what's physically happening is that the true force is 137.036 times Coulomb's law, so the real charge is 137.036. This is reduced by the correction factor 1/137.036 because most of the charge is screened out by polarised charges in the vacuum around the electron core:

"... we find that the electromagnetic coupling grows with energy. This can be explained heuristically by remembering that the effect of the polarization of the vacuum ... amounts to the creation of a plethora of electron-positron pairs around the location of the charge. These virtual pairs behave as dipoles that, as in a dielectric medium, tend to screen this charge, decreasing its value at long distances (i.e. lower energies)." - arxiv hep-th/0510040, p 71.

Dr M. E. Rose (Chief Physicist, Oak Ridge National Lab.), Relativistic Electron Theory, John Wiley & Sons, New York and London, 1961, pp 75-6:

'The solution to the difficulty of negative energy states [in relativistic quantum mechanics] is due to Dirac [P. A. M. Dirac, Proc. Roy. Soc. (London), A126, p360, 1930]. One defines the vacuum to consist of no occupied positive energy states and all negative energy states completely filled. This means that each negative energy state contains two electrons. An electron therefore is a particle in a positive energy state with all negative energy states occupied. No transitions to these states can occur because of the Pauli principle. The interpretation of a single unoccupied negative energy state is then a particle with positive energy ... The theory therefore predicts the existence of a particle, the positron, with the same mass and opposite charge as compared to an electron. It is well known that this particle was discovered in 1932 by Anderson [C. D. Anderson, Phys. Rev., 43, p491, 1933].

'Although the prediction of the positron is certainly a brilliant success of the Dirac theory, some rather formidable questions still arise. With a completely filled 'negative energy sea' the complete theory (hole theory) can no longer be a single-particle theory.

'The treatment of the problems of electrodynamics is seriously complicated by the requisite elaborate structure of the vacuum. The filled negative energy states need produce no observable electric field. However, if an external field is present the shift in the negative energy states produces a polarisation of the vacuum and, according to the theory, this polarisation is infinite.

'In a similar way, it can be shown that an electron acquires infinite inertia (self-energy) by the coupling with the electromagnetic field which permits emission and absorption of virtual quanta. More recent developments show that these infinities, while undesirable, are removable in the sense that they do not contribute to observed results [J. Schwinger, Phys. Rev., 74, p1439, 1948, and 75, p651, 1949; S. Tomonaga, Prog. Theoret. Phys. (Kyoto), 1, p27, 1949].

'For example, it can be shown that starting with the parameters e and m for a bare Dirac particle, the effect of the 'crowded' vacuum is to change these to new constants e' and m', which must be identified with the observed charge and mass. ... If these contributions were cut off in any reasonable manner, m' - m and e' - e would be of order alpha ~ 1/137. No rigorous justification for such a cut-off has yet been proposed.'All this means that the present theory of electrons and fields is not complete. ... The particles ... are treated as 'bare' particles. For problems involving electromagnetic field coupling this approximation will result in an error of order alpha. As an example ... the Dirac theory predicts a magnetic moment of mu = mu[zero] for the electron, whereas a more complete treatment [including Schwinger's coupling correction, i.e., the first Feynman diagram] of radiative effects gives mu = mu[zero].(1 + alpha/{twice Pi}), which agrees very well with the very accurate measured value of mu/mu[zero] = 1.001...'

Is there charge in empty space? QFT is not very lucid on this. Whereas Dirac said the vacuum is full of virtual charge, and used this to predict antimatter, which was then detected by Anderson in 1932 (resulting in a Nobel Prize for Dirac), there is the issue that a vacuum completely full of charge would polarize around real charge, cancelling it completely.

Feynman, Schwinger, and Tomonaga showed that the vacuum is not full of free charge or it would cancel out real charges by becoming totally polarized. Instead, there is a limit or cutoff to the amount of polarization, at a collision energy which corresponds to a very small distance from the middle of the electron. This comes from the need to renormalize the charge of the electron, in order to force the QFT to predict the electron's magnetic moment and Lamb shift accurately.

So free (polarizable) charge pairs can only exist close to the middle of the electron, where the electromagnetic field is strong enough, presumably, to break the bonds of the vacuum sea of charges, and free the charges so that they can then become polarized and cause the right amount of shielding for QFT to work. So from causality + QFT, the vacuum doesn't contain any free charge but must be full of bound charge which is broken up into free charge in the strong fields near a fundamental particle (real charge core).

There are virtual particles polarized in the strong field near real charge cores, and these must come from some mechanism. The strong field breaks up the orderly vacuum structure for a small distance, allowing it to become polarized which shields some of the real particle charge.

Quantum field theory implies the core of each real long-lived charge is surrounded by two concentric shells of charged vacuum particles: an inner shell with opposite charge to the core, and an outer one of similar charge to the core. The electric field arrow between the two shells points the other way to that for the charge from the core bare charge, so the latter is shielded. The shielding factor calculated in a previous post in this blog is approximately 137 or 1/alpha.

The physical reason why quarks have fractional charge can be explained very simply indeed. Electric charges are shielded by the polarized vacuum field they create at short distances. If you hypothetically put three electron charges close together so that they all share the same vacuum polarization cloud, the polarization in that cloud will be three times stronger. Hence, the shielding factor for electric charge will be three times greater. So the electric charge you would theoretically expect to get from each of the three electron-sized charges confined in close proximity is equal to: -1/3e. This is the electric charge of the downquark.

Renormalization is the failure to give a rigorous reason for the empirical need of the mathematical solution to have the right asymptotic limits. The abstract QFT (including not just electron-positron polarization, but all the loops of other charges up to 92 GeV) suggests the electron charge is approximately e + e[0.005 ln(A/E)], where A and E are respectively upper and lower cutoffs, which for a 92 GeV electron-electron collision are A = 92,000 MeV, and E = 0.511 MeV.

There are some severe problems in quantum field theory pertaining to the discontinuity introduced by the cutoff needed to prevent the electric charge of a single electron from setting off an infinitely extensive polarization of the vacuum of the universe which entirely cancels the electron's electric charge. This renormalization problem is mentioned in the Dirac and Feynman quotes on http://www.cgoakley.demon.co.uk/qft/. Ultimately these problems stem to the use of statistical equations (the wavefunction in the Schroedinger equation and Dirac equation doesn't tell you detailed facts, just averaged statistics) to obtain detailed facts which they are incapable of doing. Quantum mechanics for example is compatible with the exponential decay law of radioactivity. In reality, radioactivity decays in steps due to individual decay events, and it is only the averaged overall decay rate which approximates the exponential decay curve.

Considering the log(E/A) type term, on the one hand it could be that the log(E/A) type term may be right after all, if some mechanism can be found for the lower cutoff discontinuity. This low energy cutoff implies - if correct - that vacuum polarization only begins at a certain distance from the middle of the electron, where the electromagnetic field has just enough energy, to create electron-positron pairs in the vacuum which get polarized by the field and shield the electron charge. If this is the case, then the vacuum presumably does not contain any free electron-positron pairs beyond that distance from an electron. The electric field of the electron (as mediated by gauge bosons obeying the inverse-square law) is intense enough vey near the electron core to both create free electrons from the vacuum and to polarize them.

If the issue were merely polarizing already-free virtual charges of the vacuum, no real (long lived) electrons would have any measurable electric charge at all, because the vacuum polarization would extend for infinity and would cancel out precisely 100% of the electric field from the electron, instead of the 100(1 - alpha) = 99.27%. There is a hell of a lot of difference between 100% and 99.27% shielding; the first would prevent any long range electric field at all, while the second is the observed shielding which allows a small fraction of the electron's charge to go uncancelled. The task of explaining renormalization is that of explaining why this difference exists.

However, the log(E/A) type term is definitely wrong for another reason: the upper energy limit E allows the term to increase toward infinity as distance from the middle of the electron decreases towards zero. Because the vacuum polarization over a finite distance cannot have infinite shielding, this is clearly false. The bare core charge of an electron is not infinite, but ~137e- as demonstrated above.

If we take the standard QFT electron charge formula to be e(x)/e(x = infinity) ~ 1 + [0.005 ln(A/E)], with E = 0.511 MeV and A the upper cutoff energy which is roughly inversely proportional to distance, we can roughly approximate the way the electron charge is supposed to vary as a function of distance from the middle of the electron.

For a 0.511 MeV electron-electron head on collision, the distance of closest approach is given by equating the entire kinetic energy of the moving electron to the potential energy of the electric field, (e-)^2 /(4.Pi.permittivity.distance of closest approach).

Obviously as energy increases beyond 0.511 MeV, the effective value of the electric charge (e-) decreases because there's less polarized vacuum causing electric field shielding between the two charges, and of course there can be energy losses due to elastic scatter effects (such as gamma ray emissions).However, I'll do some calculations. In the meanwhile, just take the standard formula of the type e(x)/e(x = infinity) ~ 1 + [0.005 ln(A/E)]. If as a rough approximation you put 1/(scaled distance) for A, you might expect to get a feel for how the charge is supposed to vary with distance. It is very unnatural. Normally you get a natural logarithm in rearranging an exponential equation (finding the inverse function), so you would not mathematically expect that an exponential equation would usefully approximate a logarithmic one. However, you would expect that physically a vacuum polarization shielding should have some type of exponential term.It is possible that the detailed dynamics of scattering effects like , in determining the relationship between collision energy and distance from middle of particle, make the correct relationship substantially different (from the simplistic low energy result that energy is proportional to 1/distance of closest approach).

One last piece of evidence: increasing energy means getting closer to a particle core (harder collisions, closer approaches). Under supersymmetry (SUSY) ideas, unification of strong and electroweak is supposed to occur at extremely high energy of 10^16 GeV. If this happens, it means that all forces are equal and different aspects of the same thing at a very close distance. Physically, that distance implies being so close to the particle core that there is NO intervening vacuum charge polarization (shielding) a all. Therefore, an electron at very close distances would show nuclear force effects. Hence, if supersymmetric unification ideas have any validity at all, they suggest that the role of the vacuum that I've been describing for electromagnetism, is the mechanism for the difference between electron and quark.

Now, remember, the range of the virtual charges in the vacuum is big enough to knock and deflect the electron randomly as the electron moves in the vacuum: Heisenberg's law says product of energy of virtual particles and the time they exist is h over 2 Pi or whatever, hence by rearranging and putting in the energy for an electron-positron pair, you get the time they exist, 10^-21 second; assuming as an exaggeration they go at speed c, this gives you a maximum range of virtual particles in the vacuum of ct = 10^-12 metre. I don't know that electron-positron pairs predominate in the vacuum, because that depends on the energy density of the vacuum which is not clearly known (John Baez shows that equally defensible estimates ranging from zero to[ward] infinity exist).

The higher the energy density of the vacuum, the heavier the virtual particles. However, from the unification arguments above, electrons and quarks are related: quarks are pairs or triads of electrons bound and trapped by the short range vacuum attraction effect, and because quarks are close enough to share the same polarization shells, the latter are 2 or 3 times stronger in pairs or triads of quarks, creating apparent fractional electric charges (stronger polarization type shielding causes weaker observed charge at a long distance).

The increase in the magnetic moment which results for leptons is reduced by the 1/alpha or 137 factor due to shielding from the virtual positron's own polarization zone, and is also reduced by a factor of 2Pi because the two particles are aligned with opposite spins: the force gauge bosons being exchanged between them hit the spinning particles on the edges, which have a side-on length which is 2Pi times smaller than the full circumference of the particle. To give a real world example, it is well known that by merely spinning a missile about its axis you reduce the exposure of the skin of the missile to weapons by a factor of Pi. This is because the exposure is measured in energy deposit per unit area, and this exposed area is obviously decreased by a factor of Pi if the missile is spinning quickly. For an electron, the spin is half integer, so like a Mobius strip (paper loop with half a turn), you have to rotate 720 degrees (not 360) to complete a 'rotation' back to the starting point. Therefore the effective exposure reduction for a spinning electron is 2Pi, rather than Pi.

Hence by combining the polarization shielding factor with the spin coupling factor, we can account for the fact that the lepton magnetic moment increase due to this effect is approximately 1/(2.Pi x 137) = alpha/(2.Pi) added on to the 1 Bohr magneton of the bare real electron. This gives the 1.0116 Bohr magnetons result for leptons.

We can make additional predictions using the Z boson of electroweak theory, which is unique because it has rest mass despite being an uncharged fundamental particle! You can easily see how charged particles acquire mass (by attracting a cloud of vacuum charges, which mire them, creating inertia and a response to the spacetime fabric background field which is gravity). But how does a non-composite neutral particle, the Z, acquire mass? This is essentially the question of electroweak symmetry breaking at low energy. The Z is related to the photon, but is different in that it has rest mass and therefore has a limited range, at least below electroweak symmetry breaking energy.

Z mass model: a vacuum particle with the mass of the electroweak neutral gauge boson (Z) semi-empirically predicts all the masses in the Standard Model. You use data for a few particles to formulate the model, but then it predicts everything else, including making many extra checkable predictions! Here's how. If the particle is at position A in the model illustration, it is inside the polarization range of the electron, but there is still its own polarization shell separating it from the real electron core. Because of the shielding of its own shell of vacuum polarization and from the spin of the electron core, the mass it gives the core is equal to

M(z)/(2.Pi x 137) = M(z)alpha/(2.Pi) ~ 105.7 MeV. Hence the muon!

Next, consider the lower energy state where the mass is at position B in the diagram above. In that case, the coupling between the central core charge and the mass at B is reduced by the additional distance (which empirically is a factor of ~1.5 reduction) and also the 137 or 1/alpha polarization attenuation factor. Hence

M(z).(alpha)^2 /(1.5 x 2.Pi) ~ 0.51 MeV. Hence the electron!

Generalizing, for n real charge cores (such as a bare lepton or 2-3 bare quarks), and N masses of Z boson mass at position A (a high energy, high mass state), the formula for predicting the observable mass of the leptons or hadrons is:

M(e).n(N+1)/(2.alpha) = M(z).n(N+1)(alpha)/(6.Pi).

This does make predictions! It is based on known facts of polarization in the vacuum, the details of which have evidence from many experiments. It has more physics and checkable tests going for it than the periodic table of chemistry had first proposed from sheer empirical association by Newlands and Mendeleev, which today would doubtless be suppressed sneeringly as 'numerology' (the reason for the periodic table had to await the discovery of quantum mechanics). It produces a kind of periodic table of elementary particle masses which are directly comparable to measured data. This fact-guided methodology of doing physics is in stark contrast to stringy, abject, useless extra dimensional speculation.

The stringy model doesn't predict the force mechanisms, strengths, particle masses, and cosmological results which it suppressed with censorship.

But for a comparison of the above heuristic ideas with those quantum field theory between the Tomonaga-Feynman-Schwinger quantum field theory renormalized calculation of the magnetic field increase for an electron due to the vacuum (which Dirac and Feynman, as well as others like Dr Chris Oakley, raise objects to on mathematical grounds, as being incomplete/fiddled) see:

Julian Schwinger, On Gauge Invariance and Vacuum Polarization, Phys. Rev. vo. 82 (1951), p. 664:

'This paper is based on the elementary remark that the extraction of gauge invariant results from a formally gauge invariant theory is ensured if one employs methods of solution that involve only gauge covariant quantities. We illustrate this statement in connection with the problem of vacuum polarization by a prescribed electromagnetic field. The vacuum current of a charged Dirac field, which can be expressed in terms of the Green's function of that field, implies an addition to the action integral of the electromagnetic field. Now these quantities can be related to the dynamical properties of a "particle" with space-time coordinates that depend upon a proper-time parameter. The proper-time equations of motion involve only electromagnetic field strengths, and provide a suitable gauge invariant basis for treating problems. Rigorous solutions of the equations of motion can be obtained for a constant field, and for a plane wave field. A renormalization of field strength and charge, applied to the modified lagrange function for constant fields, yields a finite, gauge invariant result which implies nonlinear properties for the electromagnetic field in the vacuum. The contribution of a zero spin charged field is also stated. After the same field strength renormalization, the modified physical quantities describing a plane wave in the vacuum reduce to just those of the maxwell field; there are no nonlinear phenomena for a single plane wave, of arbitrary strength and spectral composition. The results obtained for constant (that is, slowly varying fields), are then applied to treat the two-photon disintegration of a spin zero neutral meson arising from the polarization of the proton vacuum. We obtain approximate, gauge invariant expressions for the effective interaction between the meson and the electromagnetic field, in which the nuclear coupling may be scalar, pseudoscalar, or pseudovector in nature. The direct verification of equivalence between the pseudoscalar and pseudovector interactions only requires a proper statement of the limiting processes involved. For arbitrarily varying fields, perturbation methods can be applied to the equations of motion, as discussed in Appendix A, or one can employ an expansion in powers of the potential vector. The latter automatically yields gauge invariant results, provided only that the proper-time integration is reserved to the last. This indicates that the significant aspect of the proper-time method is its isolation of divergences in integrals with respect to the proper-time parameter, which is independent of the coordinate system and of the gauge. The connection between the proper-time method and the technique of "invariant regularization" is discussed. Incidentally, the probability of actual pair creation is obtained from the imaginary part of the electromagnetic field action integral. Finally, as an application of the Green's function for a constant field, we construct the mass operator of an electron in a weak, homogeneous external field, and derive the additional spin magnetic moment of α/2π magnetons by means of a perturbation calculation in which proper-mass plays the customary role of energy.'

More information on QFT: see Prof. Mark Srednicki's textbook at http://gabriel.physics.ucsb.edu/~mark/MS-QFT-11Feb06.pdf and the corrected Prof. Alvarez-Gaume introduction at http://arxiv.org/PS_cache/hep-th/pdf/0510/0510040.pdf (It turns out that that textbook (1st ed) was wrong as it ignored all the particle creation-annihilation loops which can be created at energies between 0.511 MeV and 92 GeV. Motl emailed the Professor then replied: "Prof. Alvarez-Gaume has written me that it was a pedagogical simplification, which I fully understand and endorse, and in a future version of the text, they will have not only the right numbers but even the threshold corrections!" The second edition corrects the error, with a footnote thanking Motl, who I had informed of the error since I don't get replies from most professors when using hotmail.)

Kind regards,
nigel

Copy of a comment submitted to Cosmic Variance blog in case deleted:

http://cosmicvariance.com/2006/07/23/n-bodies/
nigel cook on Jul 24th, 2006 at 4:07 am

‘… the ‘inexorable laws of physics’ … were never really there … Newton could not predict the behaviour of three balls … In retrospect we can see that the determinism of pre-quantum physics kept itself from ideological bankruptcy only by keeping the three balls of the pawnbroker apart.’ – Tim Poston and Ian Stewart, Analog, November 1981.

It isn’t quantum physics that is the oddity, but actually classical physics! The normal teaching of Newtonian physics (at least at low levels) falsely claims/indoctrinates the persistent lie that it allows the positions of the planets to be exactly calculated (determinism) when it does not if you have 3+ bodies, which you do. Richard P. Feynman conceded this in his book QED:

‘when the space through which a photon moves becomes too small (such as the tiny holes in the screen) … we discover that … 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 … interference becomes very important.’

The interference is due to many vacuum virtual charges:

‘All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs.’ – I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.

The duration and maximum range of these charges is easily estimated: take the energy-time form of Heisenberg’s uncertainty principle and put in the energy of an electron-positron pair and you find it can exist for ~10^-21 second; the maximum possible range is therefore this time multiplied by c, or 10^-12 metre. This is far enough to deflect electrons but not enough to be observed as vacuum radioactivity. Like Brownian motion, it introduces chaos on small scales, not large ones:

‘… the Heisenberg formulae can be most naturally interpreted as statistical scatter relations, as I proposed [in the 1934 book ‘The Logic of Scientific Discovery’]. … There is, therefore, no reason whatever to accept either Heisenberg’s or Bohr’s subjectivist interpretation …’ – Sir Karl R. Popper, Objective Knowledge, Oxford University Press, 1979, p. 303.

The Schroedinger wave equation arises naturally from a sea of particles because we know that you get waves in particle-based fluids: http://feynman137.tripod.com/#b