Lubos Motl in the fast comments to his post on Lorentz initially responded to a comment about gravitons causing the Lorentz contraction of moving bodies (since the gravitons being exchanged with distant masses in the surrounding universe will be relatively blueshifted when you are moving into them, since by de Broglie’s particle-wave duality all particles including gravitons have a frequency and wavelength) by claiming:
‘… you don’t distinguish real physical gravitons from virtual gravitons. Forces are caused by virtual gravitons and they don’t really have well-defined frequencies.’
When it was pointed out to Lubos that this is a false statement about virtual particles (which only differ from real particles in having a limited lifespan according to the uncertainty principle, since they have don’t have the energy to survive for long), because the virtual photons in experimentally demonstrated Casmir force generate a force specifically because two nearby metal plates exclude virtual photons of certain frequencies, he then deleted all the related comments including his own earlier reply.
See http://en.wikipedia.org/wiki/Relativity_priority_dispute for some background information:
‘In 1900 Henri Poincaré published a paper in which he said that radiation could be considered as a fictitious fluid with an equivalent mass of mr = E / c2. He derived this interpretation from Lorentz’s ‘theory of electrons‘ which incorporated Maxwell’s radiation pressure.’
‘… Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field.’ – H. A. Lorentz, The Theory of Electrons, 1916 reprint, p. 230.
‘I considered my time transformation only as a heuristic working hypothesis.’ – H. A. Lorentz, “Conference on the Michelson-Morley Experiment”, The Astrophysical Journal, v. 68 (1928), pp. 345-351.
The mechanical vacuum “explanations” for the Lorentz contraction were dumped because they were ad hoc models made with glue and string that came in a landscape of metastable vacua otherwise called aethers. There was no way to pick out the correct one from that enormous landscape even using the anthropic principle, so they couldn’t make falsifiable predictions. If one aether model failed, there were plenty more in the landscape of aether models to try instead.
None of those metastable vacua made falsifiable predictions, so they were dumped for being not even wrong, not for being tested and found inaccurate. Because the parameters for particles of the metastable vacua could be arbitrarily adjusted to virtually any value (maybe having an infinite sized landscape of variants) to try to fit observations, it wasn’t science.
Einstein’s problem with the landscape of Lorentzian metastable vacua was Mach’s problem: it was a lot of worthless blather and hype with was nothing scientific in it.
Good luck to Lubos and others with string theory, which has even more unknown variables due to unobservably small compactified extra dimensions, giving a vast landscape.
Fact: modern gauge theories suggest that gravitons are being exchanged in the vacuum between masses, thereby accounting for gravitational field phenomena and also (by the equivalence principle) inertial force.
Fact: when a particle moves, especially when it gains relativistic velocities, it will interact more with gravitons being exchanged with masses in the direction it is headed in, than in other directions. The gravitons will be blueshifted in their wavelength (all particles including gravitons will have a wavelength by de Broglie’s wave-particle duality) when you move towards masses that are exchanging gravitons with you, and there are masses in the universe in all directions from us! This is a fact; it will happen. Gravitons are virtual particles which exist for a time governed by the uncertainty principle, but like all virtual particles they have physical properties. E.g., take the Casimir effect which works by the exclusion of certain frequencies of virtual photons from between two metal plates, causing a net force!
Fact: when you move into a blue-shifted beam of radiation, the extra momentum of that radiation will create effects.
It’s like an aircraft moving in the air. As it goes faster, air molecules hit the front of the plane harder than they do the back of the plane. So there is a longitudinal contraction force, with the force on the nose slightly squeezing the aircraft along its length in the direction of motion. This is one of the forces the aircraft must withstand. Anyone who can’t grasp this analogy to gauge bosons like gravitons flying around the vacuum and causing contraction of moving things in the direction of motion, is crackpot.
Even Einstein grasped this at the end of his life when he wrote to Besso in 1954:
“I consider it quite possible that physics cannot be based on the [classical differential equation] field principle, i.e., on continuous structures. In that case, nothing remains of my entire castle in the air, [non-quantum] gravitation theory included…”
Special and general relativity are classical theories: (1) Dirac found that he had to abandon the hamiltonian for energy suggested by special relativity, and it was this change which led to quantumfield theory, while (2) general relativity is a continuum theory or classical approximation, not a quantum theory of gravity.
The non-relativistic hamiltonian is defined as:
H = ½ p2/m.
However it is of interest that the ‘special relativity’ prediction of
H = [(mc2)2 + p2c2]2,
was falsified by the fact that, although the total mass-energy is then conserved, the resulting Schroedinger equation permits an initially localised electron to travel faster than light! This defect was averted by the Klein-Gordon equation, which states:
ħ2d2y/dt2 = [(mc2)2 + p2c2]y.
While this is physically correct, it is non-linear in only dealing with second-order variations of the wavefunction. Dirac’s equation simply makes the time-dependent Schroedinger equation (Hy = iħ.dy/dt) relativistic, by inserting for the hamiltonian (H) a totally new relativistic expression which differs from special relativity:
H = apc + b mc2,
where p is the momentum operator. The values of constants a and b can take are represented by a 4 x 4 = 16 component matrix, which is called the Dirac ‘spinor’. This is not to be confused for the Weyl spinors used in the gauge theories of the Standard Model; whereas the Dirac spinor represents massive spin-1/2 particles, the Dirac equation yields two Weyl equations for massless particles, each with a 2-component Weyl spinor (representing left- and right-handed spin or helicity eigenstates). The justification for Dirac’s equation is both theoretical and experimental. Firstly, it yields the Klein-Gordon equation for second-order variations of the wavefunction. Secondly, it predicts four solutions for the total energy of a particle having momentum p:
E = ±[(mc2)2 + p2c2]1/2.
Two solutions to this equation arise from the fact that momentum is directional and so can be can be positive or negative. The spin of an electron is ± ½ ħ = ± h/(4p). This explains two of the four solutions! The other two solutions are evident when considering the case of p = 0, for then E = ± mc2. This equation proves the fundamental distinction between Dirac’s theory and Einstein’s special relativity. Einstein’s equation from special relativity is E = mc2. The fact that in fact E = ± mc2, proves the physical shallowness of special relativity which results from the lack of physical mechanism in special relativity. E = ± mc2 allowed Dirac to predict antimatter, such as the anti-electron called the positron, which was later discovered by Anderson in 1932 (anti-matter is naturally produced all the time when suitably high-energy gamma radiation hits heavy nuclei, causing pair production, i.e., the creation of a particle and an anti-particle such as an electron and a positron).
Notice that E = ± mc2 is not just a version of E = mc2, instead it is correct and E = mc2 is in error mathematically: e.g. if you have the equation a2 = b2, it doesn’t mean that a = b. That isn’t a general truth of a2 = b2. If a = -2 and b = 2, then a2 = b2 is true but a = b is not true. The correct solution is:
a = (b2)1/2 = ± b.
Since a = ± b, it is not generally a truth that a = b. That will only be correct in some circumstances, and in a mathematics examination you have to give the correct answer, not an answer that is right in only some circumstances. So a = ± b is correct and a = b is incorrect. Similarly, E = ± mc2 is correct and E = mc2 is incorrect.
Negative results are not a mathematical fiction, they are real antimatter! Relativity is at best just a classical approximation to a small class of examples of relativity: e.g., special relativity applies to a universe devoid of antimatter, acceleration, and therefore gravity so it applies to a universe devoid of gravitating mass and energy. That’s got nothing to do with our universe.
Just like Ptolemy’s epicycles in the earth centred universe which predicted planetary positions as observable in the sky (but not the three dimensional motion of planets, e.g., the distance to the planets at any time and the distance of the moon from the earth), special and general relativity do make checkable predictions because they are built on assumptions which have been chosen in order for them to do so. The successes of general relativity come from inserting the empirical principle of the conservation of mass-energy into the gravitational field, and inserting the Newtonian law for gravity as the asymptotic approximation for non-relativistic velocities and weak gravitational fields (this is done to insert the gravity constant G into general relativity’s field equation properly, i.e. to normalize the theory, because it doesn’t predict G automatically). In particularly, general relativity applies to classical field lines, i.e. non-quantum fields. Again, like epicycles it’s a useful approximation in certain cases, but it breaks down in other cases such as high energy physics where quantum phenomena such as looped Feynman interactions like pair production and annihilation are important. General relativity also leads to difficulties on large scales in cosmology because it doesn’t predict the acceleration of the universe, it just models it in the way Ptolemy added new ad hoc epicycles to incorporate new corrections. It’s a great classical approximation to gravity, even so.
Good news for string theorists, they are guaranteed to find evidence for string no matter what the LHC experiments show!
Dr Peter Woit has reported some news that will give Lubos and other string theorists cause for celebration:
‘If no superpartners at all are found at the LHC, and thus supersymmetry can’t explain the hierarchy problem, by the Arkani-Hamed/Dimopoulos logic this is strong evidence for the anthropic string theory landscape. Putting this together with Lykken’s argument, the LHC is guaranteed to provide evidence for string theory no matter what, since it will either see or not see weak-scale supersymmetry.’ (Emphasis added.)
– Awaiting a Messenger From the Multiverse, http://www.math.columbia.edu/~woit/wordpress/?p=717