John Baez's derivation of Newton's law from Einstein's, without tensors!
I like the approach at http://math.ucr.edu/home/baez/einstein/node6a.html where Baez and Bunn obtain the Newtonian result using simple maths. It is educationally profound, since Einstein started off by putting the Newtonian result into tensor calculus and the applying the contraction to make the maths consistent (conservation of mass-energy in a gravitational field). It is the contraction term which leads to the different predictions of general relativity from Newtonian gravitation, but the contraction is only significant at high speeds and/or in strong gravitational fields. Baez considers the volume contraction simply here: http://math.ucr.edu/home/baez/einstein/node3.html.
Understanding electroweak symmetry breaking
There are four vector bosons of electroweak force and how various models of the Higgs vacuum simply shield three of them at low energies but can't attenuate them if they have high energy. I like the Higgs boson idea as the cause of mass, because lepton and hadron masses are close to integers (see http://feynman137.tripod.com/).
QFT at present has the electric charge of the particle core shielded partly by the polarised fermions and other charges of the vacuum. For example, high energy electron collisions have experimentally shown increased Coulomb force, due to partially breaking through the vacuum polarisation veil.
One way to see unification is therefore as a complete breaking down of the polarised vacuum around the particle core. The 1/137 coupling constant is therefore the shielding factor. The reason the strong nuclear force is much stronger than electromagnetism, is that the radius of the vacuum veil is about the size of a nucleon. Within that distance, there is little shielding so the force is 137 times stronger, while outside the veil it is just Coulomb's law.
It should be possible to calculate the vacuum particle density as a function of distance from the core, using semi-classical models of polarised fluids. Of course nobody will want to do it as it is unfashionable. However with more abstract ideas (string theory) getting nowhere, perhaps simplicity is best.
I've today started another blog about loop quantum gravity at http://lqg.blogspot.com/, the alternative to strong theory. Loop quantum gravity is advocated by Lee Smolin and others, and is a non-perturbative quantum field theory explanation in terms of a spin foam vacuum (a modern 'a----r', for those who can fill in the gaps with the letters e, t, h, and e). According to quantum field theory, the virtual particles in the vacuum spend part of their time as spinning fermions and such like, and part of their time as bosons. (Bosons convert into pairs of oppositely charged fermions, which annihilate a brief time later, back into bosons.) The fabric of spacetime is very rich. Unfortunately nobody wants to know. Which is why 10/11 dimensional string theory has the upper hand.
By the way, I've sent Lee Smolin several messages over the years, and received only one reply. He ignored all the scientific messages, and replied to one on a completely different topic to say he wasn't interested in that (it concerned some abuses of science from a physics journalist). Oh well, at least he wasn't downright rude. Danny Ross Lunsford, who has discredited the Kaluza-Klein reducible 5-dimensional unification of general relativity and electromagnetism by establishing a new non-reducible 6-dimensional unification which is compatible with reality (at least, Lunsford's scheme gets rid of the cosmological constant and suggests gravity is a residual of the QED force rather than a separate QFT), is rude sometimes, but thankfully usually about string theorists.
John Baez on the Vacuum
http://math.ucr.edu/home/baez/vacuum.html talks about the speeding up of the universe.
The error here is that quantum field theory shows forces result from the exchange of gauge bosons. Gravity is a push effect as demonstrated A here.
Cosmologists have very few concrete data but those data are good (Hubble red-shifts of galaxy clusters and supernovas, cosmic background radiation, and abundances of the elements observed from line spectra in the universe).
Cosmologists tend to always assert speculative interpretations, for example see http://cosmicvariance.com/2005/12/19/the-universe-is-the-poor-mans-particle-accelerator/
The deduction by Sean Carroll there that general relativity and the gravitational constant G had the same value within 3 minutes of the big bang is easily overturned.
Fusion of light elements is the addition of protons and neutrons by the attractive strong nuclear force, which is short ranged. For this to occur, protons must overcome the Coulomb repulsion force, which is an inverse square law like gravity, which is responsible for the compression causing fusion. Therefore, if gravity constant G varies and electromagnetism (e.g. Coulomb's law) varies the same way, you don't get a change in fusion. So you can't say anything about the early universe proving that gravity was the same then.
There are numerous examples of sloppy arguments of this sort which are stubbornly asserted. The greatest are the dark matter and dark energy speculations. Some interpretations of galactic rotation (using simplistic models), can be used to imply that there may be some dark matter present to make the curves flatten out.
Friedmann's use of GR is completely fraudulent. He assumes that the expansion of the universe us slowed down by gravitational attraction. Nobody has ever proved that gravity is attractive, rather than a shielding of a pressure effect (fluid model for spacetime fabric in GR), because there is no official quantum gravity yet. If gravity is a push due to gauge bosons exchanged between masses, there is not going to be a slowing down of the expansion of the universe by gravity, so Friedmann's solutions are inapplicable.
The treatment of the push gravity dynamics shows that the multiplying constant in the density is not the 3/8 factor derived by Friedmann but 3/(4e^3), which is 10.04 times lower, so both dark matter and dark energy (postulated to overcome gravitational deceleration at extreme distances) are falsified by the real physics.
Luis Alvarez-Gaume and Miguel A. Vazquez-Mozo, Introductory Lectures on Quantum Field Theory, arXiv.org hep-th/0510040 v1, 5 October 2005.These guys have now made a major step in developing a classical model of QFT, see pp 70-71, 83-85:
p71: "... the electromagnetic coupling grows with energy... the polarisation of the vacuum [ether] ... electron-positron pairs around the location of the[core 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)."
p85: "Here we have illustrated the creation of particles [pair-production asquantum tunnelling] by semiclassical sources in Quantum Field Theory... what one observer calls the vacuum will be full of particles for a different observer [hence special/restricted relativity is incomplete, giving way to the absolute motion implicit in accelerations and general motion, hence general relativity is an ether theory not a non-ether theory]."
It is curious to see restricted/special relativity being abandoned on page 85 with the technically obscure words: "The breaking of such invariance, as happened in the case of coupling to a time-varying source analyzed above, implies that it is not possible anymore to define a state which would be recognised as the vacuum by all observers."
So special relativity is ditched because of quantum field theory! Didn't Dirac do this in his paper sating quantum field theory implies an ether, published in Nature in 1951? Or did he make the error of talking clearly?‘… with the new theory of electrodynamics we are rather forced to have an aether.’ – P.A.M. Dirac, ‘Is There an Aether?,’ Nature, v.168, 1951, p.906. See also Dirac’s paper in Proc. Roy. Soc. v.A209, 1951, p.291.
‘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 [physical continuum] 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.)
‘In many interesting situations… 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.’ – Bernard Schutz, General Relativity, Cambridge University Press, 1986, pp. 89-90.
‘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 stumbling-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: General Relativity Theory, Cambridge University Press, Cambridge, 1921, pp. 20, 152.
Sean Carroll now presents a graph of evidence that dark energy varies with time: http://cosmicvariance.com/2006/01/11/evolving-dark-energy/
I love this expert cosmology. The fact that they keep modifying the theory to fit the new observations really shows how expert these guys are. Thanks Peter, for your patience with them!