The correct unification scheme

The top post here gives a discussion on the problem of unifying gravity and standard model forces: gauge boson radiation is exchanged between all charges in the universes, while electromagnetic forces only result in particular situations (dissimilar or similar charges) .  As discussed below, gravitational exchange radiation interacts indirectly with electric charges, via some vacuum field particles which become associated with electric charges.  [This has nothing to do with the renormalization problem in speculative (string theory) quantum gravity that predicts nothing.  Firstly, this does make predictions of particle masses and of gravity and cosmology.  Secondly, renormalization is accounted for by vacuum polarization shielding electric charge.  The mass changes in the same way, since the field which causes mass is coupled to the charge by the already renormalized (shielded) electric charge.]

The whole idea that gravity is a regular quantum field theory, which causes pair production if the field is strong enough, is totally speculative and there is not the slightest evidence for it.  The pairs you get produced by an electric field above the IR cutoff corresponding to 10^18 v/m in strength, i.e., very close (<1 fm) to an electron, have direct evidence from Koltick’s experimental work on polarized vacuum shielding of core electric charge published in the PRL in 1997.  Koltick et al. found that electric charge increases by 7% in 91 GeV scattering experiments, which is caused by seeing through the part of polarized vacuum shield (observable electric charge is independent of distance only at beyond 1 fm from an electron, and it increases as you get closer to the core of the electron, because you have less polarized dielectric between you and the electron core as you get closer, so less of the electron’s core field gets cancelled by the intervening dielectric).

There is no evidence whatsoever that gravitation produces pairs which shield gravitational charges (masses, presumably some aspect of a vacuum field such as Higgs field bosons).  How can gravitational charge be renormalized?  There is no mechanism for pair production whereby the pairs will become polarized in a gravitational field.  For that to happen, you would first need a particle which falls the wrong way in a gravitational field, so that the pair of charges become polarized.  If they are both displaced in the same direction by the field, they aren’t polarized.  So for mainstream quantum gravity ideas work, you have to have some new particles which are capable of being polarized by gravity, like Well’s Cavorite.

There is no evidence for this.  Actually, in quantum electrodynamics, both electric charge and mass are renormalized charges, with only the renormalization of electric charge being explained by the picture of pair production forming a vacuum dielectric which is polarized, thus shielding much of the charge and allowing the bare core charge to be much greater than the observed value.  However, this is not a problem.  The renormalization of mass is similar to that of electric charge, which strongly suggests that mass is coupled to an electron by the electric field, and not by the gravitational field of the electron (which is way smaller by many orders of magnitude).  Therefore mass renormalization is purely due to electric charge renormalization, not a physically separate phenomena that involves quantum gravity on the basis that mass is the unit of gravitational charge in quantum gravity.

Finally, supersymmetry is totally flawed.  What is occurring in quantum field theory seems to be physically straightforward at least regarding force unification.  You just have to put conservation of energy into quantum field theory to account for where the energy of the electric field goes when it is shielded by the vacuum at small distances from the electron core (i.e., high energy physics).

The energy sapped from the gauge boson mediated field of electromagnetism is being used.  It’s being used to create pairs of charges, which get polarized and shield the field.  This simple feedback effect is obviously what makes it hard to fully comprehend the mathematical model which is quantum field theory.  Although the physical processes are simple, the mathematics is complex and isn’t derived in an axiomatic way.

Now take the situation where you put N electrons close together, so that their cores are very nearby.  What will happen is that the surrounding vacuum polarization shells of both electrons will overlap.  The electric field is two or three times stronger, so pair production and vacuum polarization are N times stronger.  So the shielding of the polarized vacuum is N times stronger!  This means that an observer more than 1 fm away will see only the same electronic charge as that given by a single electron.  Put another way, the additional charges will cause additional polarization which cancels out the additional electric field!

This has three remarkable consequences.  First, the observer at a long distance (>1 fm) who knows from high energy scattering that there are N charges present in the core, will see only a 1 charge at low energy.  Therefore, that observer will deduce an effective electric charge which is fractional, namely 1/N, for each of the particles in the core.

Second, the Pauli exclusion principle prevents two fermions from sharing the same quantum numbers (i.e., sharing the same space with the same properties), so when you force two or more electrons together, they are forced to change their properties (most usually at low pressure it is the quantum number for spin which changes so adjacent electrons in an atom have opposite spins relative to one another; Dirac’s theory implies a strong association of intrinsic spin and magnetic dipole moment, so the Pauli exclusion principle tends to cancel out the magnetism of electrons in most materials).  If you could extend the Pauli exclusion principle, you could allow particles to acquire short-range nuclear charges under compression, and the mechanism for the acquisition of nuclear charges is the stronger electric field which produces a lot of pair production allowing vacuum particles like W and Z bosons and pions to mediate nuclear forces.

Third, the fractional charges seen at low energy would indicate directly how much of the electromagnetic field energy is being used up in pair production effects, and referring to Peter Woit’s discussion of weak hypercharge on page 93 of the U.K. edition of Not Even Wrong, you can see clearly why the quarks have the particular fractional charges they do.  Chiral symmetry, whereby electrons and quarks exist in two forms with different handedness and different values of weak hypercharge, explains it.

The right handed electron has a weak hypercharge of -2.  The left handed electron has a weak hypercharge of -1.  The left handed downquark (with observable low energy, electric charge of -1/3) has a weak hyper charge of 1/3, while the right handed downquark has a weak hypercharge of -2/3.

It’s totally obvious what’s happening here.  What you need to focus on is the hadron (meson or baryon), not the individual quarks.  The quarks are real, but their electric charges as implied from low energy physics considerations, are totally fictitious for trying to understand an individual quark (which can’t be isolate anyway, because that takes more energy than making a pair of quarks).  The shielded electromagnetic charge energy is used in weak and strong nuclear fields, and is being shared between them.  It all comes from the electromagnetic field.  Supersymmetry is false because at high energy where you see through the vacuum, you are going to arrive at unshielded electric charge from the core, and there will be no mechanism (pair production phenomena) at that energy, beyond the UV cutoff, to power nuclear forces.  Hence, at the usually assumed so-called Standard Model unification energy, nuclear forces will drop towards zero, and electric charge will increase towards a maximum (because the electron charge is then completely unshielded, with no intervening polarized dielectric).  This ties in with representation theory for particle physics, whereby symmetry transformation principles relate all particles and fields (the conservation of gauge boson energy and the exclusion principle being dynamic processes behind the relationship of a lepton and a quark; it’s a symmetry transformation, physically caused by quark confinement as explained above), and it makes predictions.

It’s easy to calculate the energy density of an electric field (Joules per cubic metre) as a function of the electric field strength.  This is done when electric field energy is stored in a capacitor.  In the electron, the shielding of the field by the polarized vacuum will tell you how much energy is being used by pair production processes in any shell around the electron you choose.  See page 70 of for the formula from quantum field theory which relates the electric field strength above the IR cutoff to the collision energy.  (The collision energy is easily translated into distances from the Coulomb scattering law for the closest approach of two electrons in a head on collision, although at higher energy collisions things will be more complex and you need to allow for the electric charge to increase, as discussed already, instead of using the low energy electronic charge.  The assumption of perfectly elastic Coulomb scattering will also need modification leading to somewhat bigger distances than otherwise obtained, due to inelastic scatter contributions.)  The point is, you can make calculations from this mechanism for the amount of energy being used to mediate the various short range forces.  This allows predictions and more checks.  It’s totally tied down to hard facts, anyway.  If for some reason it’s wrong, it won’t be someone’s crackpot pet theory, but it will indicate a deep problem between the conservation of energy in gauge boson fields, and the vacuum pair production and polarization phenomena, so something will be learned either way.

To give an example from, there is evidence that the bare core charge of the electron is about 137.036 times the shielded charge observed at all distances beyond 1 fm from an electron.  Hence the amount of electric charge energy being used for pair production (loops of virtual particles) and their polarization within 1 fm from an electron core is 137.036 – 1 = 136.036 times the electric charge energy of the electron experienced at large distances.  This figure is the reason why the short ranged strong nuclear force is so much stronger than electromagnetism.

Smolin, Woit, the failure of string theory, and how string theory responds

Professor Lee Smolin has been attacked by various string theorists (particularly Aaron Bergmann and Lubos Motl), but now Professor Clifford Johnson has seemingly joined in with Aaron and Lubos in a post where he claims that pointing out the failure of string theory in books is unsatisfactory because it puts “their rather distorted views on the issues into the public domain in a manner that serves only to muddle”.

This seems to be a slightly unfair attack to me.  Clifford is certainly trying hardest of all the string theorists to be reasonable, but he has stated that he has not read the books critical of string theory, which means that his claim that the books contain ‘distorted views’ which ‘muddle’ the issues, is really unfounded upon fact (like the claims of string theory).

Dr Peter Woit has a nice set of notes summarising some problems with string theory here.  These are far more sketchy than his book and don’t explain the Standard Model and its history like his book, but the notes do summarise a few of the many problems in string theory.  String theorists, if they even acknowledge the existence of critics at all (Witten has written a letter to Nature saying that he doesn’t, instead he suggests that string theorists should ignore objections while continuing to make or to stand by misleading claims that string theory ‘predicts’ gravity, such as Witten’s own claim of that in the April 1996 issue of Physics Today), dismiss any problem with string theory as a ‘storm in a teacup’, refuse to read the books of critics, misrepresent what the critics are saying, so the arguments don’t address the deep problems.

For instance, Clifford wrote in a particularly upsetting comment:

“For example, a great deal of time was spent by me arguing with Peter Woit that his oft-made public claim that string theory has been shown to be wrong is not a correct claim. I asked him again and again to tell us what the research result is that shows this. He has not, and seems unable to do so. I don’t consider that to be informed criticism, but a very very strong and unfair overstatement of what the current state of on-going research is.”

Peter Woit explains on page 177 of Not Even Wrong (which, admittedly, Clifford is unaware of since he has not read the book!) that using the measured weak SU(2) and electromagnetic U(1) forces, supersymmetry predicts the SU(3) force incorrectly high by 10-15%, when the experimental data is accurate to a standard deviation of about 3%. So that’s failure #1.

Moreover, Peter Woit also explains on page 179 that supersymmetry makes another false prediction: it predicts a massive amount of dark energy in the vacuum and an immense cosmological constant, totally contradicted by astronomy and too high by a factor of 10^55 or 10^113 depending on whether the string theory is minimally supersymmetric or a supersymmetric grand unified theory, respectively.

Either way, Dr Woit explains: ‘This is almost surely the worst prediction ever made by a physical theory that anyone has taken seriously.’ So that’s failure #2.

This is not a problem with the standard model of particle physics: comparing string theory to the standard model is false.  A student who answers one of the questions on a paper and gets it wrong, derives no excuse from pointing to another who achieved 99%, despite happening to get the same single question wrong. Any assessment by comparison needs to take account of successes, not just errors. In one case the single error marks complete failure, while in the other it’s trivial.

It’s still a a string error, whether the standard model makes it as well, or not as the case may be. String theorists have a different definition of the standard model for this argument, more like a speculative theory than an empirical model of particle physics.  The standard model isn’t claimed to be the final theory. String is. The standard model is extremely well based on empirical observations and makes checked predictions. String doesn’t.

That’s why Smolin and Woit are more favourable to the standard model. String theory if of any use should sort out any problems with the standard model. This is why the errors of string theory are so alarming. It is supposed to theoretically sort things out, unlike the standard model, which is an empirically based model, not a claimed final theory of unification.



More Scenes From the Storm in a Teacup, VII

by Clifford, at 2:18 am, March 13th, 2007 in science, science in the media, string theory

“You can catch up on some of the earlier Scenes by looking at the posts listed at the end of this one. Through the course of doing those posts I’ve tried hard to summarize my views on the debate about the views of Smolin and Woit – especially hard to emphasize how the central point of their debate that is worth some actual discussion actually has nothing to do string theory at all. Basically, the whole business of singling out string theory as some sort of great evil is rather silly. If the debate is about anything (and it largely isn’t) it is about the process of doing scientific research (in any field), and the structure of academic careers in general. For the former matter, Smolin and Woit seem to have become frustrated with the standard channels through which detailed scientific debates are carried out and resolved, resorting to writing popular level books that put their rather distorted views on the issues into the public domain in a manner that serves only to muddle.  …” 

Everything that happens involves particle physics, so it determines the nature of everything, and is just a few types of fundamental particles and four basic fundamental forces, or three at high energy, where electro-weak unification occurs.

It’s better to have debates and disputes over scientific matters that can potentially be resolved, than have arguments over interminable political opinions which can’t be resolved factually, even in principle. I don’t agree that a lack of debate (until new experimental data arrives) is the best option. The issue is that experiments may resolve the electroweak symmetry breaking mechanism, but they won’t necessarily change the facts in the string theory debate one bit. Penrose explains the problem here on pp. 1020-1 of Road to Reality (UK ed.):

34.4 Can a wrong theory be experimentally refuted? … One might have thought that there is no real danger here, because if the direction is wrong then the experiment would disprove it, so that some new direction would be forced upon us. This is the traditional picture of how science progresses. … We see that it is not so easy to dislodge a popular theoretical idea through the traditional scientific method of crucial experimentation, even if that idea happened actually to be wrong. The huge expense of high-energy experiments, also, makes it considerably harder to test a theory than it might have been otherwise. There are many other theoretical proposals, in particle physics, where predicted particles have mass-energies that are far too high for any serious possibility of refutation.’

I’ve written a very brief review of Lee Smolin’s book on, which for brevity concentrates on reviewing the science of the book that I can review objectively (I ignore discussions of academic problems).  Here is a copy of it:

Professor Lee Smolin is one of the founders of the Perimeter Institute in Canada. He worked on string theory in the 1980s and switched to loop quantum gravity when string theory failed.

Before reading this book, I read Dr Peter Woit’s book about the failure of string theory, Not Even Wrong, read his blog, and watched Smolin’s lectures (available streamed online from the Perimeter Institute website), Introduction to Quantum Qravity, which explain the loop quantum gravity theory very clearly.

Smolin concentrates on the subject from the perspective of understanding gravity, although he helped develop a twisted braid representation of the standard model particles. Loop quantum gravity is built on firmer ground that string theory, and tackles the dynamics behind general relativity.

This is quite different from the approach of string theory, which completely ignores the dynamics of quantum gravity. I should qualify this by saying that although the stringy 11-dimensional supergravity, which is the bulk of the mainstream string theory, M-theory (in M-theory 10 dimensional superstring is the brane or membrane on the bulk, like an N-1 dimensional surface on an N-dimensional material), does contain a spin-2 mode which (if real) corresponds to a graviton, that’s not a complete theory of gravitation.

In particular, in reproducing general relativity, string theory suggests a large negative cosmological constant, while the current observation-based cosmological model has a small positive cosmological constant.

In addition to failing there, string theory also fails to produce any of the observable particles of the standard model of physics. This is because of the nature of string theory, which is constructed from a world sheet (a 1-dimensional string when moved gains a time dimension, becoming a 1,1 “worldsheet”) to which 8 additional dimensions are added to satisfy the conformal symmetry of particle physics, assuming that there is supersymmetric unification of standard model forces (which requires the assumption that every fermion in the universe has a bosonic super partner, which nobody has ever observed in an experiment). If supersymmetry is ignored, then you have to add to the worldsheet three times as many dimensions for conformal symmetry, giving 26 dimensional bosonic string theory. That theory traditionally had problems in explaining fermions, although Tony Smith (now censored off arXiv by the mainstream) has recently come up with some ideas to get around that.

The failure of string theory is due to the 10 dimensions of supersymmetric superstring theory from the worldsheet and conformal symmetry requirements. Clearly, we don’t see that many dimensions, so string theorists rise to the challenge by a trick first performed with Kaluza’s 5-dimensional theory back in the 1920s. Klein argued that extra spatial dimension can be compactified by being curled up into a small size. Historically, the smallest size assumed in physics has been the Planck length (which comes purely from dimensional analysis by combining physical constants, not from an experimentally validated theory or from observation).

With 10 dimensional superstring, the dimensions must be reduced on a macroscopic scale to 3 spatial dimensions plus 1 time dimension, so 6 spatial dimensions need compactification. The method to do this is the Calabi-Yau manifold. But this cause a massive problem in string theory, called the landscape. String theory claims that particles are vibrating strings, which becomes very problematic when 6 dimensions are compactified, because the vibration modes possible for a string then depend critically on the size and shape parameters of those 6 compactified dimensions. The possibilities are vast, maybe infinite.

It turns out that there are at least 10^500 ways of producing standard model or vacuum ground state from such strings containing Calabi-Yau manifolds. Nobody can tell if any of those solutions is the real standard model of particle physics. For comparison, the age of the universe is something like 10^17 seconds. Hence, if you had a massive computer trying to compute all the solutions to string theory from the moment of the big bang to now, it would have to work at a speed of 10^483 solutions per second to solve the problem (a practically impossible speed, even if such timescales are available). A few string theorists hope to find a way to statistically tackle this problem in a non-rigorous way (without checking every single solution) before the end of the universe, but most have given up and try to explain particle physics by the anthropic principle, whereby it is assumed that there is one universe for each of the 10^500 solutions to string theory, and we see the one standard model which has parameters which are able to result in humans.

More radical string theorists proclaim that if you fiddle around with the field theories underlying general relativity and the standard model, you can create a landscape of unobserved imaginary universes from those theories, similar to string theory. Therefore, they claim, the problems in string theory are similar to those in general relativity and the standard model. However, this analogy is flawed because those checked theories are built up on the basis of observations of particle symmetries, electrodynamics, energy conservation and gravitation, and they also produce checkable predictions. In short, there is no problem due to the imaginary landscape in those theories, whereas there is a real problem caused by the landscape in string theory, because it prevents a reproduction (post-diction) of existing physics, let alone predictions.

Smolin suggests that the failure of string theory to explain general relativity and the standard model of particle physics means that it may be helpful if physicist get off the string theory bandwaggon and start investigating other ideas. Woit makes the same point and gives the technical reasons.

The problem is that string theory has over the past two decades become a cult topic supported by endless marketing hype, magazine articles, books, even sci fi films. Extra dimensions are popular, and the heroes of string theory have gotten used to being praised despite having not the slightest shred of evidence for their subject. Recently, they have been claiming that string theory mathematics is valuable for tackling some technical problems in nuclear physics, or may be validated by the discovery of vast cosmic strings in space. But even the mathematics of Ptolemy’s earth centred universe epicycles had uses elsewhere, so this defense of string theory is disingenious. It’s not clear that string theory maths solves any nuclear physics problems that can’t be solved by other methods. Even if it does, that’s irrelevant for the issue of whether people should be hyping string as being the best theory around.

Smolin’s alternative is loop quantum gravity. The advantage of this is that it builds up Einstein’s field equation less a metric (so it is background independent) from a simple summing of interaction graphs for the nodes of a Penrose spin network in the 3 spatial dimensions plus time dimension we observe. This sum is equivalent to taking a Feynman path integral, which is a basic method of doing quantum field theory. The result of this is general relativity without a metric. It is not a complete theory yet, and is the very opposite of string theory in many ways.

While string theory requires unobservables like extra dimensions and superpartners, loop quantum gravity works in observable spacetime using quantum field theory to produce a quantum gravity consistent with general relativity. Ockham’s razor, the principle of economy in science, should tell you that loop quantum gravity is tackling real physics in a simple way, whereas string theory is superfluous (at least until there is some evidence for it).

Obviously there is more progress to be made in loop quantum gravity, which needs to become a full Yang-Mills quantum theory if gravity is indeed a force like the other standard model forces. However, maybe the relationship between gravity and the other long-range force, electromagnetism, will turn out to be different to what is expected.

For instance, loop quantum gravity needs to address the problem that of whether gravity is a renormalizable quantum field theory like the standard model Yang-Mills theories. This will depend on the way in which gravitational charge, ie mass, is attached to or associated with standard model charges by way of some sort of “Higgs field”. The large hadron collider is due to investigate this soon. Renormalization involves using a corrected “bare charge” value for electric charge and nuclear charges which is higher than that observed. The justification is that very close to a particle, vacuum pair production occurs in the strong field strength, the pairs polarize and shield the bare core charge to the observed value seen at long distances and low energies. For gravity, renormalization poses the problem of how gravitational charge can be shielded? Clearly, masses don’t polarize in a gravitational field (they all move the same way, unlike electrons and positrons in an electric field) so the mass-giving “Higgs field” effect is not directly capable of renormalization, but is capable of indirect renormalization if the Higgs field is being associated with particles by another field like the electric field, which is renormalized.

These are just aspects which appeal to me. One of the most fun parts of the book is where Smolin explains the reason behind “Doubly Special Relativity”.

Peter Woit’s recent book Not Even Wrong has a far deeper explanation of the standard model and the development of quantum field theory, the proponents and critics of string theory, and gives the case for a deeper understanding of the standard model in observed spacetime dimensions using tools like the well established mathematical modelling methods of representation theory.

Both books should really be read to understand the overall problem and possibilities for progress by alternative ideas despite the failure of string theory.

Update: in the comments on Asymptotia, Peter Woit has made some quick remarks from a web cafe in Pisa, Italy.  Instead of arguing about the substance of his remarks, Aaron Bergmann and Jacques Distler are repeatedly attacking one nonsense sentence he typed where he wrote a contradiction that a cosmological constant can correspond to flat spacetime, whereas the cosmological constant implies a small curvature.  Unable to defend string theory against the substance of the charge that it is false, they are now attacking this one sentence as a straw man.  It’s completely unethical.  The fact that a string theorist will refusing to read the carefully written and proof-read books and then choose instead to endlessly attack a spurious comment on a weblog, just show the level to which their professionalism has sunk.  Jacques Distler does point out correctly that in flat spacetime the vacuum energy does not produce a cosmological constant.  Instead of splitting attacking critics of completely failed theories, he should perhaps admit the theory has no claim to be science.