Quantum field theory phenomenology

I’ve put a sketch of the fundamental forces as a function of distance here, and an article [not] illustrated with that sketch is at http://gaugeboson.blogspot.com/UPDATE (23 Feb 2007): this illustration is inaccurate in assuming unification.

The GUT (grand unified theory) scale unification may be wrong itself. The Standard Model might not turn out to be incomplete with regards to requiring supersymmetry: the QED electric charge rises as you get closer to an electron because there’s less polarized vacuum to shield the corer charge. Thus, a lot of electromagnetic energy is absorbed in the vacuum above the IR cutoff, producing loops. It’s possible that the short ranged nuclear forces are powered by this energy absorbed by the vacuum loops.

In this case, energy from one force (electromagnetism) gets used indirectly to produce pions and other particles that mediate nuclear forces. This mechanism for sharing gauge boson energy between different forces in the Standard Model would get rid of supersymmetry which is an attempt to get three lines to numerically coincide near the Planck scale. With the strong and weak forces caused by energy absorbed when the polarized vacuum shields electromagnetic force, when you get to very high energy (bare electric charge), there won’t be any loops because of the UV cutoff so both weak and strong forces will fall off to zero. That’s why it’s dangerous to just endlessly speculate about only one theory, based on guesswork extrapolations of the Standard Model, which doesn’t have evidence to confirm it.

The whole idea of unification is wrong, if the nuclear force gauge bosons are vacuum loop effects powered by attenuation of the electromagnetic charge due to vacuum polarization; see:

Copy of a comment:


Most of the maths of physics consists of applications of equations of motion which ultimately go back to empirical observations formulated into laws by Newton, supplemented by Maxwell, Fitzgerald-Lorentz, et al.

The mathematical model follows experience. It is only speculative in that it makes predictions as well as summarizing empirical observations. Where the predictions fall well outside the sphere of validity of the empirical observations which suggested the law or equation, then you have a prediction which is worth testing. (However, it may not be falsifiable even then, the error may be due to some missing factor or mechanism in the theory, not to the theory being totally wrong.)

Regarding supersymmetry, which is the example of a theory which makes no contact with the real world, Professor Jacques Distler gives an example of the problem in his review of Dine’s book Supersymmetry and String Theory: Beyond the Standard Model:


“Another more minor example is his discussion of Grand Unification. He correctly notes that unification works better with supersymmetry than without it. To drive home the point, he presents non-supersymmetric Grand Unification in the maximally unflattering light (run α 1 ,α 2 up to the point where they unify, then run α 3 down to the Z mass, where it is 7 orders of magnitude off). The naïve reader might be forgiven for wondering why anyone ever thought of non-supersymmetric Grand Unification in the first place.”

The idea of supersymmetry is the issue of getting electromagnetic, weak, and strong forces to unify at 10^16 GeV or whatever, near the Planck scale. Dine assumes that unification is a fact (it isn’t) and then shows that in the absense of supersymmetry, unification is incompatible with the Standard Model.

The problem is that the physical mechanism behind unification is closely related to the vacuum polarization phenomena which shield charges.

Polarization of pairs of virtual charges around a real charge partly shields the real charge, because the radial electric field of the polarized pair is pointed the opposite way. (I.e., the electric field lines point inwards towards an electron. The electric field likes between virtual electron-positron pairs, which are polarized with virtual positrons closer to the real electron core than virtual electrons, produces an outwards radial electric field which cancels out part of the real electron’s field.)

So the variation in coupling constant (effective charge) for electric forces is due to this polarization phenomena.

Now, what is happening to the energy of the field when it is shielded like this by polarization?

Energy is conserved! Why is the bare core charge of an electron or quark higher than the shielded value seen outside the polarized region (i.e., beyond 1 fm, the range corresponding to the IR cutoff energy)?

Clearly, the polarized vacuum shielding of the electric field is removing energy from charge field.

That energy is being used to make the loops of virtual particles, some of which are responsible for other forces like the weak force.

This provides a physical mechanism for unification which deviates from the Standard Model (which does not include energy sharing between the different fields), but which does not require supersymmetry.

Unification appears to occur because, as you go to higher energy (distances nearer a particle), the electromagnetic force increases in strength (because there is less polarized vacuum intervening in the smaller distance to the particle core).

This increase in strength, in turn, means that there is less energy in the smaller distance of vacuum which has been absorbed from the electromagnetic field to produce loops.

As a result, there are fewer pions in the vacuum, and the strong force coupling constant/charge (at extremely high energies) starts to fall. When the fall in charge with decreasing distance is balanced by the increase in force due to the geometric inverse square law, you have asymptotic freedom effects (obviously this involves gluon and other particles and is complex) for quarks.

Just to summarise: the electromagnetic energy absorbed by the polarized vacuum at short distances around a charge (out to IR cutoff at about 1 fm distance) is used to form virtual particle loops.

These short ranged loops consist of many different types of particles and produce strong and weak nuclear forces.

As you get close to the bare core charge, there is less polarized vacuum intervening between it and your approaching particle, so the electric charge increases. For example, the observable electric charge of an electron is 7% higher at 90 GeV as found experimentally.

The reduction in shielding means that less energy is being absorbed by the vacuum loops. Therefore, the strength of the nuclear forces starts to decline. At extremely high energy, there is – as in Wilson’s argument – no room physically for any loops (there are no loops beyond the upper energy cutoff, i.e. UV cutoff!), so there is no nuclear force beyond the UV cutoff.

What is missing from the Standard Model is therefore an energy accountancy for the shielded charge of the electron.

It is easy to calculate this, the electromagnetic field energy for example being used in creating loops up to the 90 GeV scale is the energy of a charge which is 7% of the energy of the electric field of an electron (because 7% of the electron’s charge is lost by vacuumn loop creation and polarization below 90 GeV, as observed experimentally; I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424).

So this physical understanding should be investigated. Instead, the mainstream censors physics out and concentrates on a mathematical (non-mechanism) idea, supersymmetry.

Supersymmetry shows how all forces would have the same strength at 10^16 GeV.

This can’t be tested, but maybe it can be disproved theoretically as follows.

The energy of the loops of particles which are causing nuclear forces comes from the energy absorbed by the vacuum polalarization phenomena.

As you get to higher energies, you get to smaller distances. Hence you end up at some UV cutoff, where there are no vacuum loops. Within this range, there is no attenuation of the electromagnetic field by vacuum loop polarization. Hence within the UV cutoff range, there is no vacuum energy available to create short ranged particle loops which mediate nuclear forces.

Thus, energy conservation predicts a lack of nuclear forces at what is traditionally considered to be “unification” energy.

So there would seem to discredit supersymmetry, whereby at “unification” energy, you get all forces having the same strength. The problem is that the mechanism-based physics is ignored in favour of massive quantities of speculation about supersymmetry to “explain” unification, which are not observed.


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 …’

Notice in the above that the magnetic moment of the electron as calculated by QED with the first vacuum loop coupling correction is 1 + alpha/(twice Pi) = 1.00116 Bohr magnetons. The 1 is the Dirac prediction, and the added alpha/(twice Pi) links into the mechanism for mass here.

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.

‘All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs. The virtual fermions with charges opposite to the bare charge will be, on average, closer to the bare charge than those virtual particles of like sign. Thus, at large distances, we observe a reduced bare charge due to this screening effect.’ – I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.

Comment by nc — February 23, 2007 @ 11:19 am  

Return to old (partly obsolete) discussion:

The text of the post at http://gaugeboson.blogspot.com/ is:

For electromagnetic charge, the relative strength is 1/137 for low energy collisions, below E = 0.511 MeV, the lower limit so-called “infrared” cutoff. Putting this value of E into the formula gives the 10^-15 metre range of vacuum polarization around an electron. For distances within this radius but not too close (in fact for the range: 0.511 MeV < E < 92,000 MeV/92GeV, see https://nige.wordpress.com/ for further details and links. In calculating the charges (coupling strengths) for fundamental forces as a function of distance as indicated above, for all distances closer than 10^-15 metre you need to take account of the charge increase in the the formula for closest approach in Coulomb scattering where the kinetic energy of the particle is converted entirely into electrostatic potential energy E = (electric charge^2)/(4.Pi.Permittivity.Distance). The electric charge in this formula is higher than the normal charge of the particle when you get within the polarization region, because the polarization shields the charge and the less polarization between you and the particle core, the less shielding of the charge.

The two graphs above on the left hand side are the standard presentation, the sketch graph on the right hand side is a preliminary illustration of the same data plotted as a function of distance from particle core instead of collision energy. Obviously I can easily compute the full details quantitatively, but am worried about what criticism may result from the simple treatment detailed above whereby I am assuming head-on Coulomb scattering. I know from nuclear physics that the scattering may be far more complex and messy so the quantitative details may differ. For example, the treatment above assumes a perfectly elastic scatter, not inelastic scatter, and it deals with only one mechanism for scatter and one force being involved. If we are dealing with penetration of the vacuum polarization zone, the forces involved will not only be Coulomb electric scatter, but also weak and possibly strong nuclear forces, depending upon whether the particles we are scattering off one another are leptons like electrons (which don’t seem to participate in the strong nuclear force at all, at least at the maximum experimentally checkable energy of scatter to date!), or hadron constituents, quarks.

I think the stagnation in HEP (high energy physics) comes from ignoring the problem of plotting force strengths as a function of distance, as I’ve stetched above. Looking at the right hand side force unification graph, you can see that the strong nuclear force charge or coupling strength over a wide range of small distances (note distance axis is logarithmic) actually falls as the particle core is approached. This offsets the inverse-square law, whereby for constant charge or constant coupling strength the force would increase as distance from core is reduced. This offset means that over that range where the strong nuclear charge is falling as you get closer to the core, the actual force on quarks is not varying. This clearly is the physical cause of asymptotic freedom of quarks, when you consider that they are also subjected to electromagnetic forces. The very size of the proton is given by the range to which asymptotic freedom of quarks extends.

I’ve also pointed out that the variations of all these fundamental forces as a function of distance clearly brings out the fact from conservation of energy that the gauge boson radiation which causes forces is getting shielded by vacuum polarization, so that the ‘shielded’ electromagnetic force gauge boson energy (being soaked up by the vacuum in the polarization zone) is being converted into the energy of nuclear force gauge bosons.

These are physical facts. I can’t understand why other people don’t think physically about physics, preferring to steer clear of phenomenology and to remain in abstract mathematical territory, which they believe to be safer ground despite the failure of string theory to actually explain or predict anything real or useful for experiments or for actually understanding the Standard Model.

I’m writing a proper review paper (to replace http://feynman137.tripod.com/ and related pages) on quantum field theory for phenomenologists which will replace supersymmetry (string theory) with a proper dynamic vacuum model based entirely on well established empirical laws. I’m going to place all my draft calculations and analyses here as blog posts as I go, and then edit the review paper from the results. In the meantime, I’ve re-read Luis Alvarez Gaume and Miguel A. Vazquez-Mozo’s Introductory Lectures on Quantum Field Theory and find them a lot more lucid in the June 27 2006 revision than the the earlier 2005 version. They have a section now explaining pair production in the vacuum and give a threshold electric field strength (page 85) of 1.3 x 10^16 v/cm which is on the order (approximately) of the electric field strength at 10^-15 m from an electron core, the limiting distance for vacuum polarization (see https://nige.wordpress.com/ , top post, for details).

The review paper focusses on the links between two approaches to quantum field theory. On one side of the coin, you have the particles in the three generations of the Standard Model, and on the other you have the forces. However, if you can model the forces you will understand the particles, which after all are totally characterised by which forces they interact via. If you can understand physically why pairs or triads of fundamental particles have fractional electric charges (as seen outside the polarized vacuum) and why they interact by strong nuclear interactions in addition to electroweak interactions, while single particles (which don’t share their polarized vacuum region with one or two other particles) have integer electric charges (seen at large distances) and don’t participate in the strong nuclear force, then that is the same thing as understanding the Standard Model because it will tell you physically the reason for the differing electric charges and for the different types of particle charges (strong nuclear force charge is called ‘color charge’, while the gravitational field charge is simply called ‘the inertial mass’).

I think part of the answer is already known at https://nige.wordpress.com/ and http://feynman137.tripod.com/, namely when you have three charge cores in close proximity (sharing the same overall vacuum polarization shell around all of them), the electric field energy creating the vacuum polarization field is three times stronger, so the polarization is three times greater, which means that the electric charge of each downquark is 1/3 that of the electron. Of course this is a very incomplete piece of physical logic, and leads to further questions where you have upquarks with 2/3 charge, and where you have pairs of quarks in mesons. But some of these have been answered: consider the neutron which has an overall electric charge of zero, where is the electric field energy being used? By conservation of electromagnetic field energy, the reduction in electric charge indicated by fractional charge values due to vacuum polarization shielding implies that the energy shielded is being used to bind the quarks (within the asymptotic freedom range) via the strong nuclear force. Neutrons and protons have zero or relatively low electric charge for their fundamental particle number because so much energy is being tied up in the strong nuclear binding force, ‘color force’.