Rank-1 tensors (vectors) are used in electromagnetism because the field is defined in terms of the simple rank-1 gradients and curls of Faraday’s imaginary “field lines”; in general relativity, however, field lines are not used and curvatures describing accelerations (second-order differential equations) are used to describe the field. Thus the use of rank-1 tensors in electromagnetism and rank-2 tensors in gravitation stems from the differing physical definitions of the “field” in each case (diverging or curling lines in electromagnetism, but accelerations in gravitation), not to the difference in the spin of the field quanta (spin-1 for electromagnetism, spin-2 for gravitation).
MAXWELL’S RANK-1 EQUATIONS AND GENERAL RELATIVITY RANK-2 EQUATIONS
Newton’s law of gravitation was proposed in 1665 and Coulomb’s electrostatics force law was proposed in 1785.
In Newton’s theory, force F is related to gravitational charge (mass), m, by the relationship
F = ma,
Where acceleration, a, leads to “rank-2” i.e. second-order spacetime equations because, a = d2x/dt2.
In Maxwell’s equations, the corresponding force laws are
F = qE and F = qvB sin N
Where q is electric charge, qv sin N is effectively the magnetic charge, E is electric field, and B is magnetic field.
This definition leads to “rank-1” i.e. first-order differential equations, because the fields E and B are not represented in electromagnetism by rank-2 or second-order spacetime equations like acceleration, a = d2x/dt2. The field E and B by contrast are defined as first-order or rank-1 gradients, i.e. E is the gradient of volts/metre, E = dV/dx.
This is the fundamental reason why Maxwell’s equations are rank-1, whereas the accelerations and spacetime curvatures in general relativity utilize rank-2 tensors.
The most curious thing is the false correlation by physically ignorant string theorists and others of spin-1 fields to rank-1 tensors in electromagnetism and of spin-2 fields to rank-2 tensors in general relativity. The correlation is fictitious, because the choice of rank-1 tensors in electromagnetism is purely due to a difference between the way the field is defined in electromagnetism and the way it is defined in general relativity. In electromagnetism, the field is defined by means of Faraday’s diverging or curling field lines, which are modelled in Maxwell’s equations by summing over simple first-order gradients (rank-1 tensors). If Faraday had not gone in for the field line concept, then you can bet we would today have a model of electromagnetism in terms of accelerations, i.e. rank-2 tensors.
There is no physical basis for popular claims that electromagnetism is intrinsically a rank-1 calculus system and that gravitation is intrinsically a rank-2 calculus system. It’s down to historical chance that Maxwell followed Faraday and used gradients of field lines, first order or rank-1 tensors to represent electromagnetic fields instead of directly representing electromagnetic forces in terms of accelerations (second-order equations, rank-2 tensors). If Maxwell had chosen to write his equations in terms of accelerations rather than via the the curls and divergencies of Faraday’s imaginary (fictitious) “field lines” (rank-1 tensors), then we would have spin-1 electromagnetic fields represented by rank-2 tensor equations insteadf of rank-1. It’s purely down to historical fluke. Once Maxwell had formulated his equations using Faraday’s unobservable field lines as rank-1 tensor equations, they became the usual groupthink physics dogma and nobody was willing to try to rebuild the theory in terms of rank-2 tensors.
Similarly, if Einstein and Hilbert in 1915 had formulated the field equation of general relativity using rank-1 tensors by analogy to the field lines of electromagnetism (instead of in terms of spacetime curvature which describes acceleration more directly), gravitation would be described by rank-1 field equations. In summary, the distinction between rank-1 and rank-2 tensor field equations in electromagnetism and gravitation is solely down to the choice of using the divergences and curls of field lines in 3 dimensional space to model electromagnetic fields and the choice of using spacetime curvatures (accelerations) to model gravitational fields. It is quite possible to model fields described in different ways by the use of different ranks of tensors. It’s got nothing to do with the spin of the graviton, because you could model electric forces with a rank-2 spacetime curvature equation and you could reformulate general relativity in terms of a rank-1 Faraday-type field line model where imaginary gravitational field lines diverge outward from mass/energy particles just as imaginary electric field lines diverge outward from electric charges in Faraday’s picture. Do you grasp this point? If you do grasp it and have some time to waste, maybe you will try arguing with the ignorant, lying bigots who are behind Wikipedia’s spin-2 graviton propaganda lies:
“If it exists, the graviton must be massless (because the gravitational force has unlimited range) and must have a spin of 2. This is because the source of gravity is the stress-energy tensor, which is a second-rank tensor, compared to electromagnetism, the source of which is the four-current, which is a first-rank tensor. Additionally, it can be shown that any massless spin-2 field would be indistinguishable from gravity, because a massless spin-2 field must couple to the stress-energy tensor in the same way that the gravitational field does.”
A massless spin-2 field would (if it existed) be indistinguishable from gravity because it couples to the stress-energy tensor like gravity. So what? That doesn’t prove that gravity is due to a massless spin-2 field. It certainly doesn’t disprove spin-1 gravitons, which correctly predicted in 1996 the acceleration of the universe as measured two years later by Perlmutter’s group, something that the non-falsifiable spin-2 gravity “predictions” has never done. The sole success of spin-2 gravitons hype efforts has been to stop the publication of the facts, the falsifiable predictions which were later confirmed by the discovery of the acceleration of the universe as predicted. These people are so ignorant and plain stupid that you are wasting your time if you even say hi to them. Like the Nazis, they are big shots and they know it all too well. Like the Nazis, they have their fellow travellers: the people who have the brains to see, like Prime Minister Chamberlain, that appeasement and shaking hands with these scum brings the applause of the crowd. It’s extremely hard to know how to proceed against a widely lauded groupthink consensus of ignorant liars who censor the arXiv.org, the “peer” (peer?, bigoted mainstream critic, more line)-reviewed journals and the sci-fi obsessed mainstream Hollywood-led media.
(The text above is extracted from the final section of the earlier post linked here, for the reason that the earlier post was primarily concerned with arXiv trackbacks, and it is always a good idea to separate out topics in different posts, or else some people who are not interested in one topic will stop reading a post before reaching material embedded in it which is of more interest to them.)
First versus second quantization quantum mechanics
On Facebook, Dr Jack Sarfatti is reviewing Professor Yakir Aharonov’s ideas. Aharnonov is the physicist famous for the Aharonov-Bohm effect, which disproves the idea that electric and magnetic field strengths fully describe the electromagnetic field. This fact becomes intuitively obvious when you notice that you can “cancel out” magnetic or electric fields with nearby opposite poles or opposite charges, without destroying the energy density of the field. Similarly, you can pass two waves with opposite amplitudes through one another and despite the wave feature being temporarily “cancelled” during the period they are passing through one another and overlapping, when they emerge after passing through one another, they are fully restored with no energy loss! (The contrapuntal model of the charged capacitor is another example, suggesting that charged massless SU(2) gauge bosons deliver electromagnetic forces, leaving U(1) hypercharge to generate spin-1 quantum gravity.)
The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle shows a measurable interaction with an electromagnetic field despite being confined to a region in which both the magnetic field B and electric field E are zero.
The Aharonov–Bohm effect shows that the local E and B fields do not contain full information about the electromagnetic field, and the electromagnetic four-potential, A, must be used instead. – Wikipedia.
Measurements do not necessarily disturb the quantum system, e.g. eigenoperator measurements do not. Aharonov introduced new kinds of “weak” and also “protective” measurements. … Remember Newton’s passion for Alchemy did not detract from his mechanical equations for gravity.
Measurements often disturb systems, by probing them with particles. Maybe the question is whether first-quantization indeterminate wavefunctions are physically “collapsed” (rather than just mathematically in a model of the process) by the act of taking a measurement of a system. Dr Thomas Love of California State University argues in a preprint he sent me that it’s just a mathematical error of first-quantization, with the time-dependent Schroedinger equation describing the particle prior to interaction, then a switch to the time-independent equation to model the particle’s eigenstate at interaction time:
“The collapse of the wave function is due to a discontinuity in the equations used to model the physics, it is not inherent in the physics.”
Feynman in his 1985 book QED says the same about the first-quantization hype of the uncertainty principle. It’s a problem with Schrodinger/Heisenberg first-quantization, and Feynman offers second-quantization QFT as a replacement. In first-quantization, which is normal textbook “quantum mechanics”, the particle is treated as intrinsically indeterminate while the Coulomb field around it is treated classically. QFT (second-quantization) introduced by Dirac and Feynman, is the exact opposite: the chaotic entity is the field the particle is immersed in, with its creation and annihilation operators. The motion of an atomic electron, according to Feynman’s 1985 book, is not inherently chaotic, but the chaos is produced by the random interferences it experiences with the quantum Coulomb field (which Schroedinger/Heisenberg ignore by treating the field classically in their first-quantization quantum mechanics):
“I would like to put the uncertainty principle in its historical place: when the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of old-fashioned ideas … But at a certain point the old fashioned ideas would begin to fail, so a warning was developed that said, in effect, ‘Your old-fashioned ideas are no damn good when …’. If you get rid of ALL the old-fashioned ideas and instead use the ideas that I’m explaining in these lectures – adding arrows [arrows = phase amplitudes in the path integral] for all the ways an event can happen – there is no NEED for an uncertainty principle! … on a small scale, such as inside an atom, the space is so small that there is no main path, no ‘orbit’; there are all sorts of ways the electron could go, each with an amplitude. The phenomenon of interference [of on-shell particles by off-shell field quanta] becomes very important …”
- Richard P. Feynman, QED, Penguin, 1990, pp. 55-6, & 84.
For a debunking of the fudged experiments of Prof. Alain Aspect on “quantum entanglement”: http://arxiv.org/abs/quant-ph/9903066
After making this comment, Dr John Gribbin, the famous 1st quantization quantum mechanics proponent and “In Search of Schroedinger’s Cat“-author, responded:
Measurements ALWAYS disturb systems!
John, if I today measure a supernova explosion flash that was set off a billion years ago, do I ‘disturb’ that system? I think you are excluding a category of measurements of this kind (where the system is self-luminous), when you say ‘Measurements ALWAYS disturb systems’. I can measure distant systems without really disturbing them, just by … See Moremeasuring light they emit in my direction. This doesn’t affect the supernova that occurred a billion years ago!
Similarly, Einstein asked if the observer influences the wavefunction of the Moon: ‘Is the Moon there when you aren’t looking at it?’ Clearly, the action of the moon is way bigger than h-bar, so the Moon is to be treated as a classical system, but even if it were just a particle, an observer of a photon emitted by it a quarter of a million miles away will not have any influence on it. Hope this is a friendly sounding response!
He then replied:
John Wheeler for one would disagree. Check out “delayed choice” experiments. John
Hi John, thanks. ‘The fundamental lesson of Wheeler’s delayed choice experiment is that the result depends on whether the experiment is set up to detect waves or particles.’ – http://en.wikipedia.org/wiki/Wheeler’s_delayed_choice_experimentI agree that the observer’s equipment determines whether he sees the wave or particle properties of the photon, but I don’t see how this affects the system which emits the photon in the first place!
In his Nobel prize speech, Feynman mentions the influence of Wheeler’s ideas of electrons travelling backwards in time on his early (failed) attempts to formulate QED. Feynman didn’t get anywhere with that. I haven’t even seen any Nobel Prizes awarded for Aspect’s quantum entanglement experiments (which depend on an ad hoc elimination of 60% of inconvenient results, dismissed as “accidentals”), or for Cramer’s transactional “handshake” interpretation of QM (with its backward time travel). But 2nd quantization QFT has won many prizes for accurate prediction of experimental data, and yet is still being ignored in popular books on 1st quantization quantum mechanics debunked by Feynman 25 years ago in his book QED.