### Introduction to Quantum Gravity, Parts 3 and 4

Parts 3 and 4 of Dr Lee Smolin's

*Introduction to Quantum Gravity*are now available. The previous lectures in the series showed how the path integral is the sum of the spatial topography graphs for all the reactions, and how background independence from special relativity arises when you take the metric out.

Last night's lectures deals with the problem of time, and gauge symmetries. To me, papers by quantum field theorists and general relativists look as if the author has a barely hidden message to the reader: all worthwhile physics is abstract mathematics. I love applied mathematics, I love trying to understand quantitative relationships and empirical equations. This is of course discouraged strongly in theoretical physics, which is about abstract maths, not physical theory.

String 'theory' is of course the extreme example. You need to get as far away from string 'theory' failures as possible. String 'theory' failed because it used unobserved extra dimensions to 'predict' unobservable gravitons and it used undetectable supersymmetric partners to 'predict' a unification at an energy far beyond the capability of a particle accelerator the size of the solar system. That is unhelpful. The maths of string 'theory' is also an inelegant mess. It fails to predict testable particle masses or force strengths, because it is not tied to reality: trash in, trash out. Loop quantum gravity should steer clear of outright speculative time-wasting.

Feynman’s statements in Davies & Brown, ‘Superstrings’ 1988, at pages 194-195:

“… I do feel strongly that this is nonsense! … I think all this superstring stuff is crazy and is in the wrong direction. … I don’t like it that they’re not calculating anything. … why are the masses of the various particles such as quarks what they are? All these numbers … have no explanations in these string theories - absolutely none! … “. (From Tony Smith.)

Thomas Larrson on Woit's blog lists further expert conclusions:

Sheldon “string theory has failed in its primary goal” Glashow

Martinus “string theory is a figment of the theoretical mind” Veltman

Phil “string theory a futile exercise as physics”Anderson

Bob “string theory a 50-year-old woman wearing way too much lipstick” Laughlin

Dan “string theory is a complete scientific failure” Friedan

String theorists made a big mistake: for them SR is more important than the physical fabric theory, GR, because SR comes naturally from strings. So because SR is incompatible with accelerations (twins paradox), unlike GR, string theorists are stuck with no curvature!

"GR has a symmetry principle that extends that of SR, not reduce it, so all constraints of SR remain true in GR" - Motl's false claim (at his blog)

We know how E got GR. He expressed Newton's gravity as a field equation and found that you have to include a contraction. The Newtonian field equation is R = 4.Pi.GT, but in 1915 E found that to correct it you need to put a contraction in to the left hand side (curvature), and correct the right hand side (mass-energy) by doubling it: R - x = 8.Pi.GT.

The physical contraction of earth's radius is by 1/3 MG/c^2 = 1.5 mm.

The physical content of GR is the OPPOSITE of SR:

‘… the source of the gravitational field can be taken to be a perfect fluid…. A fluid is a continuum that ‘flows’... A perfect fluid is defined as one in which all antislipping forces are zero, and the only force between neighboring fluid elements is pressure.’ – Professor Bernard Schutz, General Relativity, Cambridge University Press, 1986, pp. 89-90.

Notice that in SR, there is no mechanism for mass, but the Standard Model says the mass has a physical mechanism: the surrounding Higgs field. When you move a fundamental particle in the Higgs field, and approach light speed, the Higgs field has less and less time to flow out of the way, so it mires the particle more, increasing its mass. You can't move a particle at light speed, because the Higgs field would have ZERO time to flow out of the way (since Higgs bosons are limited to light speed themselves), so inertial mass would be infinite. The increase in mass due to a surrounding fluid is known in hydrodynamics:

‘In this chapter it is proposed to study the very interesting dynamical problem furnished by the motion of one or more solids in a frictionless liquid. The development of this subject is due mainly to Thomson and Tait [Natural Philosophy, Art. 320] and to Kirchhoff [‘Ueber die Bewegung eines Rotationskörpers in einer Flüssigkeit’, Crelle, lxxi. 237 (1869); Mechanik, c. xix]. … it appeared that the whole effect of the fluid might be represented by an addition to the inertia of the solid. The same result will be found to hold in general, provided we use the term ‘inertia’ in a somewhat extended sense.’ – Sir Horace Lamb, Hydrodynamics, Cambridge University Press, 6th ed., 1932, p. 160. (Hence, the gauge boson radiation of the gravitational field causes inertia. This is also explored in the works of Drs Rueda and Haisch: see http://arxiv.org/abs/physics/9802031 http://arxiv.org/abs/gr-qc/0209016 , http://www.calphysics.org/articles/newscientist.html and http://www.eurekalert.org/pub_releases/2005-08/ns-ijv081005.php.)

So the Feynman problem with virtual particles in the spacetime fabric retarding motion does indeed cause the FitzGerald-Lorentz contraction, just as they cause the radial gravitationally produced contraction of distances around any mass (equivalent to the effect of the pressure of space squeezing things and impeding accelerations). What Feynman thought may cause difficulties is really the mechanism of inertia!

In his essay on general relativity in the book ‘It Must Be Beautiful’, Penrose writes: ‘… when there is matter present in the vicinity of the deviating geodesics, the volume reduction is proportional to the total mass that is surrounded by the geodesics. This volume reduction is an average of the geodesic deviation in all directions … Thus, we need an appropriate entity that measures such curvature averages. Indeed, there is such an entity, referred to as the Ricci tensor …’ Feynman discussed this simply as a reduction in radial distance around a mass of (1/3)MG/c2 = 1.5 mm for Earth. It’s such a shame that the physical basics of general relativity are not taught, and the whole thing gets abstruse. The curved space or 4-d spacetime description is needed to avoid Pi varying due to gravitational contraction of radial distances but not circumferences.

The velocity needed to escape from the gravitational field of a mass (ignoring atmospheric drag), beginning at distance x from the centre of mass, by Newton’s law will be v = (2GM/x)1/2, so v2 = 2GM/x. The situation is symmetrical; ignoring atmospheric drag, the speed that a ball falls back and hits you is equal to the speed with which you threw it upwards (the conservation of energy). Therefore, the energy of mass in a gravitational field at radius x from the centre of mass is equivalent to the energy of an object falling there from an infinite distance, which by symmetry is equal to the energy of a mass travelling with escape velocity v.

By Einstein’s principle of equivalence between inertial and gravitational mass, this gravitational acceleration field produces an identical effect to ordinary motion. Therefore, we can place the square of escape velocity (v2 = 2GM/x) into the Fitzgerald-Lorentz contraction, giving g = (1 – v2/c2)1/2 = [1 – 2GM/(xc2)]1/2.

However, there is an important difference between this gravitational transformation and the usual Fitzgerald-Lorentz transformation, since length is only contracted in one dimension with velocity, whereas length is contracted equally in 3 dimensions (in other words, radially outward in 3 dimensions, not sideways between radial lines!), with spherically symmetric gravity. Using the binomial expansion to the first two terms of each:

Fitzgerald-Lorentz contraction effect: g = x/x0 = t/t0 = m0/m = (1 – v2/c2)1/2 = 1 – ½v2/c2 + ...

Gravitational contraction effect: g = x/x0 = t/t0 = m0/m = [1 – 2GM/(xc2)]1/2 = 1 – GM/(xc2) + ...,

where for spherical symmetry ( x = y = z = r), we have the contraction spread over three perpendicular dimensions not just one as is the case for the FitzGerald-Lorentz contraction: x/x0 + y/y0 + z/z0 = 3r/r0. Hence the radial contraction of space around a mass is r/r0 = 1 – GM/(xc2) = 1 – GM/[(3rc2]

Therefore, clocks slow down not only when moving at high velocity, but also in gravitational fields, and distance contracts in all directions toward the centre of a static mass. The variation in mass with location within a gravitational field shown in the equation above is due to variations in gravitational potential energy. The contraction of space is by (1/3) GM/c2.

This is the 1.5-mm contraction of earth’s radius Feynman obtains, as if there is pressure in space. An equivalent pressure effect causes the Lorentz-FitzGerald contraction of objects in the direction of their motion in space, similar to the wind pressure when moving in air, but without viscosity. Feynman was unable to proceed with the LeSage gravity and gave up on it in 1965. However, we have a solution…

‘Recapitulating, we may say that according to the general theory of relativity, space is endowed with physical qualities... According to the general theory of relativity space without ether is unthinkable.’ – Albert Einstein, Leyden University lecture on ‘Ether and Relativity’, 1920. (Einstein, A., Sidelights on Relativity, Dover, New York, 1952, pp. 15, 16, and 23.)

‘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), MA, MSc, FRS, Space Time and Gravitation: An Outline of the General Relativity Theory, Cambridge University Press, Cambridge, 1921, pp. 20, 152.

‘It has been supposed that empty space has no physical properties but only geometrical properties. No such empty space without physical properties has ever been observed, and the assumption that it can exist is without justification. It is convenient to ignore the physical properties of space when discussing its geometrical properties, but this ought not to have resulted in the belief in the possibility of the existence of empty space having only geometrical properties... It has specific inductive capacity and magnetic permeability.’ - Professor H.A. Wilson, FRS, Modern Physics, Blackie & Son Ltd, London, 4th ed., 1959, p. 361.

‘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.

If the electron moves at speed v as a whole in a direction orthogonal (perpendicular) to the plane of the spin, then the c speed of spin will be reduced according to Pythagoras: v2 + x2 = c2 where x is the new spin speed. For v = 0 this gives x = c. What is interesting is that this model gives rise to the Lorentz-FitzGerald transformation naturally, because: x = c(1 - v2 / c2 )1/2 . Since all time is defined by motion, this (1 - v2 / c2 )1/2 factor of reduction of fundamental particle spin speed is therefore the time-dilation factor for the electron when moving at speed v.

Motl's quibbles about the metric of SR is just ignorance. The contraction is a physical effect as shown above, with length contraction in direction of motion, mass increase and time dilation having physical causes. The equivalence principle and the contraction physics of spacetime "curvature" are the advances of GR. GR is a replacement of the false SR which gives wrong answers for all real (curved) motions since it can't deal with acceleration: the TWINS PARADOX.

Strangely, the ‘critics’ are ignoring the consensus on where LQG is a useful approach, and just trying to ridicule it. In a recent post on his blog, for example, Motl states that special relativity should come from LQG. Surely Motl knows that GR deals better with the situation than SR, which is a restricted theory that is not even able to deal with the spacetime fabric (SR implicitly assumes NO spacetime fabric curvature, to avoid acceleration!).

When asked, Motl responds by saying Dirac’s equation in QFT is a unification of SR and QM. What Motl doesn’t grasp is that the ‘SR’ EQUATIONS are the same in GR as in SR, but the background is totally different:

‘The special theory of relativity … does not extend to non-uniform motion … The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion. Along this road we arrive at an extension of the postulate of relativity… The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant). …’ – Albert Einstein, ‘The Foundation of the General Theory of Relativity’, Annalen der Physik, v49, 1916.

More Dr Motl rubbish exposed: http://www.math.columbia.edu/~woit/wordpress/?p=338 (I think Motl/'Bottle' [

*as in 'hit the bottle' or Dutch courage*] is saying below

**'The landscape of 10^500 vacua predicted by string theory are better than the 1 vacua dealt with by LQG. All you kids out there, remember: theories so vague that they are compatible with every scheme are best, because they can’t be falsified. Don’t risk your career on a potential dead end… join Bottle’s fan club today!'**

*):*

Luboš Motl Says: January 30th, 2006 at 8:46 am

Dear Peter,

your comments about the “landscape problem” have really no relevance for the calculation of the Yukawa couplings in the heterotic model of Ovrut et al.

The topic of your blog is to transform everything to the “landscape problem” - much like a student who has learned the birth of date of William Shakespeare and wants to transform every exam question about history and literature to the number 1564.

But one can’t discuss any concrete physics questions in this way. Sorry.

BestBottle

woit Says: January 30th, 2006 at 9:23 am

This is off-topic for the posting about a parody blog, but then again, maybe not, because Lubos and his blog increasingly seem to be a parody.

The scientific point at issue is about a very recent paper claiming to calculate Yukawa couplings in a specific heterotic string background. When Lubos wrote a post hyping this result, I wrote in a comment pointing that that the authors were ignoring the main problems with doing this: how do deal with the moduli and supersymmetry breaking. These problems are what lead to the landscape, since the only known way of fixing the moduli leads to exponentially large numbers of possibilities.

There was an exchange of comments, with Lubos displaying the usual string theory partisan mixture of insult, ad hominem attack and straw man argument. Faced with having this pointed out to him, he moved on to the next tactic: censorship. Here’s the comment that he evidently had no answer for, so dealt with by deleting it:

“Lubos,

Your tactic is always the same: ignore the point I’m making (one that you know well is quite serious), then make up things I never said in order to use those to criticize me as ignorant. This behavior is stupid, dishonest, and highly scientifically unethical. You should be ashamed of yourself.

Let’s look at how your dishonesty works explicitly:

1.In this case, you are ignoring the problem posed by the moduli, and you are well aware that it is a deadly one. The paper in question notesexplicitly that fermion masses will depend on the moduli.

2.You claim to show that I’m wrong and don’t know what I’m talking about by writing:

“Nope. We are not choosing fluxes “in order to stabilize the moduli”.”

I never wrote that “We are choosing fluxes in order to stabilize the moduli”, I just said that the numbers like 10^500 that one hears for the size of the Landscape come from the number of choices of the fluxes, and these correspond to ways to stabilize the moduli. Do you know of a way of stabilizing all the moduli that doesn’t involve this? If so, lets hear it. If not, acknowledge that you were dishonest to bring this up.

As for supersymmetry breaking, your claim that:

“marginal operators can’t be classically affected by supersymmetry breaking”

is irrelevant. We’re not doing classical physics here.

If you have any honest points to make, I’ll respond to them, but I’m not going to waste any more time dealing with your dishonesty, interspersed with stupid, nasty, personal attacks. When you were a young graduate student, this kind of behavior was a bit amusing. At your age and stage of your career, it’s just pathetic.”

## 2 Comments:

Comment to http://mustelid.blogspot.com/2006/01/dynamical-amplification-of-polar.html

Lubos is prejudiced toward string theory crap, "predicting" the existence of unobservable gravitons without testable numbers, using extra dimensions!

Lee Smolin's Loop Quantum Gravity, specifically the Spin Foam Vacuum, is modelling the physics of known processes causing force. Smolin shows that the Feynman "sum over histories" is equivalent to summing graphs for the spatial topography of each interaction in the vacuum for Penrose's spin networks.

General relativity is the Newtonian law expressed as a field potential, with a special "contraction" term put in to make the whole thing self-consistent for energy conservation.

Newton's law: R = G

General relativity: R - r = G

where r is contraction. (Lubos thinks, wrongly, that GR = SR + gravity, whereas the framework os GR is entirely different to SR, implying a spacetime fabric to produce accelerations, which SR specifically excludes hence the twins paradox.)

Feynman showed the general relativity contraction of Earth's radius is (1/3)GM/c^2 = 1.5 mm

This contraction is radial (along gravitational field lines) only, not transverse, so circumference is unaffected. Hence the value of Pi (circumference of planet/diameter) would be increased due to gravity, if there are only 3 dimensions. By treating c.dt as fourth dimension, you keep Pi intact.

Why the contraction? Answer: by Einstein's equivalence principle between inertial and gravitational mass, the increase in inertial mass given by the Lorentz transformation can be related to that due to gravity. A simple physical argument using escape velocity and the equivalence principle shows that the Lorentz transformation can be applied to gravity, the result is the (1 - v2/c2)^1/2 transformation is converted to gravity by putting escape velocity into v, giving the gravitational contraction of general relativity, (1 - 2GM/(rc2))^1/2 (see http://feynman137.tripod.com).

So the spacetime fabric is the result of general relativity, and this is the unification with the Standard Model of quantum field theory (which postulates all mass of fundamental particles is due to a surrounding vacuum perfect fluid, the Higgs field).

Swiss theorist G.L. LeSage first put forward a physical pressure model of gravity in 1747, and was independently followed by a Russian, M.V. Lomonosov in 1848.

What really happens is that Feynman's interpretation of quantum field theory - gauge boson exchange causing force in Feynman diagrams - is literally correct, physically.

Masses exchange gauge bosons, which travel at light speed, hit masses, and exert pressure from all directions. The energy bounces back in the same direction it came from, like a reflection. Shielding by two masses nearby causes gravity.

LeSage and others are wrong to treat the gauge bosons as a gas, because there is no mutual interaction between them, but only interactions between them and mass.

By promoting extra dimensional speculation as truth, Lubos is destroying the chances of real research getting a look in:

1. Feynman diagrams, the physics behind the maths of quantum field theory, show that forces arise from the exchange of gauge bosons (coming from distances at light speed, hence coming from times in the past).

2. The big bang mass has an increasing speed, in our observable spacetime, from 0 toward speed of light c with times past of 0 toward 15 billion years (or distances of 0 to 15 billion light-years), giving outward force by Newton’s 2nd empirically based law: F = ma = m.dv/dt = m(c - 0) / (age of universe) = mcH, where H is Hubble’s constant (based on v = HR, where R is distance).

3. Newton’s 3rd empirically based law suggests equal inward implosion force, carried by gauge bosons, which shielded by mass, proves gravity and electromagnetism to within 1.65%

http://motls.blogspot.com/2006/02/buy-danish-products.html :

Copy of a "fast comment":

Dear Lubos,

You claim that Dirac's theory unifies SR and QM, when in fact Dirac's equation (which is his theory) is an expansion of the time-dependent Schroedinger equation to include the mass-energy result which comes from electromagnetism (there are dozen's of derivations of E=mcs, not merely SR). The time-dependent Schroedinger equation is similar to Maxwell's "displacement current", which actually doesn't describe real electric current but the energy flow in the vacuum when a capacitor or such like charges by induction.

Maxwell's theory of "displacement current" was a spin foam vacuum:

Maxwell’s 1873 Treatise on Electricity and Magnetism, Articles 822-3: ‘The ... action of magnetism on polarised light [discovered by Faraday not Maxwell] leads ... to the conclusion that in a medium ... is something belonging to the mathematical class as an angular velocity ... This ... cannot be that of any portion of the medium of sensible dimensions rotating as a whole. We must therefore conceive the rotation to be that of very small portions of the medium, each rotating on its own axis [spin] ... The displacements of the medium, during the propagation of light, will produce a disturbance of the vortices ... We shall therefore assume that the variation of vortices caused by the displacement of the medium is subject to the same conditions which Helmholtz, in his great memoir on Vortex-motion [of 1858; sadly Lord Kelvin in 1867 without a fig leaf of empirical evidence falsely applied this vortex theory to atoms in his paper ‘On Vortex Atoms’, Phil. Mag., v4, creating a mathematical cult of vortex atoms just like the mathematical cult of string theory now; it created a vast amount of prejudice against ‘mere’ experimental evidence of radioactivity and chemistry that Rutherford and Bohr fought], has shewn to regulate the variation of the vortices [spin] of a perfect fluid.’

Lorentz invariance is as the name suggests Lorentz not SR invariance.

Lorentz invariance is aetherial. Even if you grasp this and start calling the contraction a metaphysical effect unrelated to physical dynamics of the quantum vacuum, you don't get anywhere.

Feynman's innovation was introducing spacetime pictures, because you need to see what you are doing clearly when using mathematics. The increase in the magnetic moment of an electron that Feynman, Schwinger and Tito came up with is 1 + 1/(2.Pi.137), where the first term is from Dirac's theory and the second is the increase due to the first Feynman coupling correction to the vacuum.

The 1/(2.Pi.137) is from a renormalised or cut-off QFT integral, but the heuristic meaning is clear. The core of the electron has a charge 137 times the observed charge, and this is shielded by the polarised vacuum as Koltick's 1997 PRL published experiments confirm (the 1/137 factor changes to 1/128.5 as collision energy goes to 100 GeV or so; at unification energy it would be 1/1 corresponding to completely breaking thro

Nigel Cook | Homepage | 02.06.06 - 3:24 am | #

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-ough the veil of polarised vacuum).

Renormalisation is limiting the interaction physically to 1 vacuum particle rather than an infinite number, and that particle is outside the veil so the association is 137 times weaker at low energies, and the geometry causes a further reduction by 2Pi (because the exposed length of a spinning loop particle seen as a circle is 2Pi times the side-on or diameter size). So that is physically what is behind adding 1/(2Pi.137) 0r 0.00116 to the core's magnetic moment (which is unshielded by the polarised veil, because that only attenuates electric field).

In addition, the same mechanism explains the differing masses for different fundamental particles. If the Standard Model mass causing particle (Higgs field particle) is inside the polarised veil, it experiences the core strength, 137 times Coulomb, and is strongly associated with the particle core, increasing the mass.

But if the Higgs field particle is outside the polarised veil, it is subject to the shielded strength, 137 times less than the core charge, so the coupling is weaker and the effective miring mass by the Higgs field is 137 times weaker.

This idea predicts that a particle core with n fundamental particles (n=1 for leptons, n = 2 for mesons, and obviously n=3 for baryons) coupling to N virtual vacuum particles (N is an integer) will have an associative inertial mass of Higgs bosons of:

(0.511 Mev).(137/2)n(N + 1) = 35n(N + 1) Mev,

where 0.511 Mev is the electron mass. Thus we get everything from this one mass plus integers 1,2,3 etc, with a mechanism.

Many of these ideas are equally applicable to string theory or LQG, since they're dealing with practical problems.

Tell me if you would have dismissed Feynman's diagrams in 1948 as crackpot, like Oppenheimer did at first.

Best wishes,

Nigel

Nigel Cook | Homepage | 02.06.06 - 3:25 am | #

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