Monday, January 23, 2006

Spin Foam Vacuum dynamics

Lee Smolin's lectures are actually very good. A lot of the mathematical background can be found in the papers he cites, and some of the basics are dealt with in Penrose's Road to Reality. Penrose of course came up with the spin network.

Loop Quantum Gravity suggests that gravity is mediated by a spin foam vacuum, and this is the main rival to string 'theory'. String 'theory' is an empty frame work to describe an unobserved graviton theory using unobserved 10/11 dimensional spacetime and predicting unobserved SUSY (super symmetry) partners. There is no effort in string theory to describe or model anything observable, and the claim that it predicts gravity is empty, as it just predicts and unobserved gravity mediation scheme, without any dynamics. Loop Quantum Gravity is completely different. His recent two lectures at the Perimeter Institute on 18 Jan, Introduction to Quantum Gravity, are available on line if you have a fast internet connection.

There is very little easily digestable material about Loop Quantum Gravity. Christine Dantas has a blog with useful references: Lee Smolin's lectures can be found here (you have to ignore the main screen and scroll down to the Introduction to Quantum Gravity at the bottom of the left hand side menu).

He starts off with spatial topology, sets of all graphs possible with or without edges, embeddings in all possible graphs, valent nodes on graphs (by analogy to chemistry, I presume). He defines Hilbert spaces on an orthagonal basis, then Penrose's 'spin networks'. Finally he shows how Feynman's 'sum over histories' approach to quantum mechanics arises in the vacuum: each interaction is a graph and you sum over all the graphs describing interactions in spacetime to arrive at the 'sum over histories'.

Smolin's second lecture dealt with 'background independence' which is the problem with special relativity. I think the recent comments of Smolin make 'background independence' clear: you don't worry about how to write the metric. Motl sees this as key to SR, unaware that the testable results of SR were available from electromagnetism of FitzGerald, Lorentz and Larmor, and even E=mc2 can be obtained from electromagnetic theory.

String theory only connects different bits of unobservable, untestable, speculation:

(1) 10/11 dimensions (Calabi-Yau 6-d manifold, Kaluza-Klein 5-d spacetime),

(2) graviton (spin 2 gauge boson) speculation (falsely called "predicting gravity" by Motl and Witten, when in fact it is unobserved speculation, and string theory can't make any testable prediction of the strength of gravity or anything else)

(3) SUSY super symmetric partners. Again, an unobserved speculation, with no definite quantitative predictions to test.

(4) The "Landscape" of 10^500 vacua, one of which may be real.

String 'theory' doesn't exist or have any program to deal usefully with anything that does exist.
The vacuum does mediate force, it does have gauge bosons in it (we know this for electromagnetism...), so some kind of spin foam vacuum is real.


Blogger nige said...

A comment of mine to Motl's blog:

"GR has a symmetry principle that extends that of SR, not reduce it, so all constraints of SR remain true in GR" -Motl

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 , and .)

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.

24 Jan 2006

3:20 AM  

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