Saturday, June 24, 2006

What is QFT?

In 1997 Steven Weinberg published a fascinating little article What is Quantum Field Theory, and What Did We Think It Is? On 17 pages he managed to give three totally different definitions of Quantum Field Theory ...and I quote:
  1. "The bottomline is that quantum mechanics plus Lorentz invariance plus cluster decomposition implies quantum field theory." This suggests to me that QFT is just a mathematical formalism that allows one to satisfy these three respectable principle. It is not prohibited to look for other formalisms that satisfy the same principles. Weinberg himself says that there is no proof that QFT is the only option.
  2. "In its mature form the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields." Probably I was wrong, and there is no way around fields. Fields rule!
  3. "The present educated view of the standard model, and of general relativity, is again that these are leading terms in effective field theories." Translation: quantum field theory is not fundamental. QFT is simply a low-energy approximation to some truly fundamental theory. Needless to say that nobody has a clue what this truly fundamental theory is.

Which of these three statements is (more) correct? "Bottomline", "mature form", or"educated view"? I'll tell you my opinion in another post.


Blogger nige said...

I don't agree with Weinberg's point 1.

Lorentz invariance for the Hamiltonian doesn't give the a sef consistent equation. You have to modify Lorentz invariance to get the Dirac equation.

The Lorentz Hamiltonian is

H = [(mc2)^2 + p^2c^2]^2,

Dirac's is:

H = apc + bmc^2,

which is totally different to the Lorentz/special relativity trash.

Sunday, July 9, 2006 at 6:19:00 AM PDT  
Blogger nige said...

Although the Klein-Gordon equation is reconciled with the Lorentz/special relativity formula above, it only deals with second order variation of the wavefunction.

This is why I get infuriated by Lubos Motl claiming that QFT is the unification of SR and QM. It isn't.

In addition to the fact SR doesn't work in QFT (proved by the fact Dirac's Hamiltonian is so different from that predicted by SR), QFT also has a vacuum with properties which SR dismisses.

Of the next five quotations disproving SR, the first two were found by Dr Thomas Love and are taken from his paper Towards and Einsteinian Theory of Quantum Gravity:

‘... the law of the constancy of the velocity of light. But ... the general theory of relativity cannot retain this law. On the contrary, we arrived at the result according to this latter theory, the velocity of light must always depend on the coordinates when a gravitational field is present.’ - Albert Einstein, Relativity, The Special and General Theory, Henry Holt and Co., 1920, p111.

‘... the principle of the constancy of the velocity of light in vacuo must be modified, since we easily recognise that the path of a ray of light ... must in general be curvilinear...’ - Albert Einstein, The Principle of Relativity, Dover, 1923, p114.

‘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.

‘According to the general theory of relativity space without ether is unthinkable.’ – Albert Einstein, Sidelights on Relativity, Dover, New York, 1952, p23.

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

Sunday, July 9, 2006 at 6:27:00 AM PDT  

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