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Comparison of an Heuristic (Trial and Error Model) Spin Foam Vacuum to String Theory
Nigel Cook
Lee Smolin in recent Perimeter Institute lectures, Introduction to Quantum Gravity, showed how to proceed from Penrose’s spin network vacuum to general relativity, by a sum over histories, with each history represented geometrically by a labelled diagram for an interaction. This gets from a quantum theory of gravity (a spin foam vacuum) to a background-independent version of general relativity, which dispenses with restricted/special relativity used as a basis for general relativity by string theorists (the alternative to the spin foam vacuum explored by Smolin and others). See
http://christinedantas.blogspot.com/2006/02/hand-of-master-parts-1-and-2.htmlIt seems that there are two distinct mechanisms for forces to be propagated via quantum field theory. The vacuum propagates long ranges forces (electromagnetism, gravity) by radiation exchange as discussed in earlier papers kindly hosted by Walter Babin, while short-range forces (strong and weak nuclear interactions) are due to the pressure of the spin foam vacuum. The vacuum is below viewed by analogy to an ideal gas in which there is a flux of shadowed radiation and also dispersed particle-caused pressure.
The radiation has an infinite range and its intensity decreases from geometric divergence. The material pressure of the spin foam vacuum is like an ideal gas, with a small mean-free-path, and produces an attractive force with a very short range (like air pressure pushing a suction plunger against a surface, if the gap is too small to allow air to fill the gap). The probabilistic nature of quantum mechanics is then due to the random impacts from virtual particles in the vacuum on a small scale, which statistically average out on a large scale. This model predicts the strength of gravity from established facts and the correct mechanism for force unification at high energy, which does not require supersymmetry:
http://nigelcook0.tripod.com/, http://electrogravity.blogspot.com/2006/02/heuristic-explanation-of-short-ranged_27.htmlConservation of energy for all the force field mediators would imply that the fall in the strength of the strong force would be accompanied by the rise in the strength of the electroweak force (which increases as the bare charge is exposed when the polarised vacuum shield breaks down in high energy collisions), which implies that forces unify exactly without needing supersymmetry (SUSY). For the strength of the strong nuclear force at low energies (i.e., at room temperature):
Heisenberg's uncertainty says
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=mc2), 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 is 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.
The unified Standard Model force is F = hc/(2.Pi.d^2)
That's the superforce at very high energies, in nuclear physics. At lower energies it is shielded by the factor 137.036 for photon gauge bosons in electromagnetism, or by exp(-d/x) for vacuum attenuation by short-ranged nuclear particles, where x = hc/(2.Pi.E)
All the detailed calculations of the Standard Model are really modelling are the vacuum processes for different types of virtual particles and gauge bosons. The whole mainstream way of thinking about the Standard Model is related to energy. What is really happening is that at higher energies you knock particles together harder, so their protective shield of polarised vacuum particles gets partially breached, and you can experience a stronger force mediated by different particles.
Quarks have asymptotic freedom because the strong force and electromagnetic force cancel where the strong force is weak, at around the distance of separation of quarks in hadrons. That’s because of interactions with the virtual particles (fermions, quarks) and the field of gluons around quarks. If the strong nuclear force fell by the inverse square law and by an exponential quenching, then the hadrons would have no volume because the quarks would be on top of one another (the attractive nuclear force is much greater than the electromagnetic force).
It is well known you can’t isolate a quark from a hadron because the energy needed is more than that which would produce a new pair of quarks. So as you pull a pair of quarks apart, the force needed increases because the energy you are using is going into creating more matter. This is why the quark-quark force doesn’t obey the inverse square law. There is a pictorial discussion of this in a few books (I believe it is in "The Left Hand of Creation", which says the heuristic explanation of why the strong nuclear force gets weaker when quark-quark distance decreases is to do with the interference between the cloud of virtual quarks and gluons surrounding each quark). Between nucleons, neutrons and protons, the strong force is mediated by pions and simply decreases with increasing distance by the inverse-square law and an exponential term something like exp(-x/d) where x is distance and d = hc/(2.Pi.E) from the uncertainty principle.
Mainstream, M-theory of strings extrapolates the well-tested Standard Model into the force unification domain of 10^16 GeV and above using unobserved extra dimensions and unobserved super-symmetric (SUSY) partners to the normal particles we detect. The Standard Model achieved a critical confirmation with the detection of the short-ranged neutral Z and charged W particles at CERN in 1983. This confirmed the basic structure of electroweak theory, in which electroweak forces have a symmetry and long range above 250 GeV which is broken by the Higgs field mechanism at lower energies, where only the photon (out of electroweak force mediators, photon, Z, W+ and W-) continues to have infinite range.
In 1995, string theorist Edward Witten used M-theory to unify 10 dimensional superstring theory (including SUSY) with 11 dimensional supergravity as a limit. In the April 1996 issue of Physics Today Witten wrote that ‘String theory has the remarkable property of predicting gravity’. Sir Roger Penrose questioned Witten’s claim on page 896 of Road to Reality, 2004: ‘in addition to the dimensionality issue, the string theory approach is (so far, in almost all respects) restricted to being merely a perturbation theory’.
The other uses of string theory are for providing a quantum gravity framework (it allows an spin-2, unobserved graviton-type field, albeit without any predictive dynamics) and SUSY allows unification of nuclear and electromagnetic forces at an energy of 10^16 GeV (way beyond any possible high energy experiment on Earth).
In summary, string theory is not a scientific predictive theory, let alone a tested theory. The spin foam vacuum extension of quantum field theory as currently discussed by Smolin and others is limited to the mathematical connection between the framework of a quantum field theory and general relativity. I think it could be developed into a predictive unified theory very easily, as the components in this and earlier papers are predictive of new phenomena and are also consistent with those theories of modern physics which have been tested successfully. There is no evidence that string theory predictive of anything that could be objectively checked. Peter Woit of Columbia University has come up against difficulty in making the string theory mainstream listen to an objective criticism of the scientific failures of string theory, see:
http://www.math.columbia.edu/~woit/arxiv-trackbacks.html.