Quantum mechanics revisited by Lee Smolin in 2006 and Lubos Motl’s arXiv trackback to it

In an earlier post, it was explained that mainstream first quantization (e.g., the Schroedinger wave equation or the Heisenberg matrices) was known non-relativistic since the 1920s and to falsely quantize the wrong variables: first quantization falsely keeps the Coulomb field potential classical and makes position/momentum intrinsically uncertain, instead of allowing the random, chaotic exchange of field quanta between charges to produce the indeterminism and uncertainty of atomic electron orbits.

“Bohr … said: “… one could not talk about the trajectory of an electron in the atom, because it was something not observable.” … Bohr thought that I didn’t know the uncertainty principle … it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up …”

- 1965 physics Nobel Laureate Richard P. Feynman, quoted in Jagdish Mehra, The Beat of a Different Drum (Oxford, 1994, pp. 245-248).

“Niels Bohr brainwashed a whole generation of theorists into thinking that the job of interpreting quantum theory was done 50 years ago.” – 1969 physics Nobel Laureate Murray Gell-Mann.

For more evidence about Bohr’s deep ignorance of physics and his crank propaganda, see the 325 page 1999 book Quantum Dialogue by the expert on the history of quantum mechanics, Professor Mara Beller (1945-2004), or read her article The Sokal Hoax: At Whom Are We Laughing?

The widely-ignored (due to Bohr’s brainwashing first quantization/uncertainty principle lie) Fig. 65 from Richard P. Feynman’s 1985 book QED illustrates how individual electromagnetic field quanta exchanges cause indeterministic electron orbits: ‘I would like to put the uncertainty principle in its historical place … If you get rid of all the old-fashioned ideas and instead use the ideas that I’m explaining in these lectures – adding arrows [path amplitudes] for all the ways an event can happen – there is no need for an uncertainty principle!’ – Richard P. Feynman, QED, Penguin Books, London, 1990, pp. 55-56. ‘… with electrons: when seen on a large scale, they travel like particles, on definite paths. But 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. … we have to sum the arrows to predict where an electron is likely to be.’ – Richard P. Feynman, QED, Penguin Books, London, 1990, Chapter 3, pp. 84-5. Hence, the indeterminate electron motion in the atom is simply caused by second-quantization: the field quanta randomly interacting and deflecting the electron.

So the mainstream argument for the uncertainty principle is based on the assumption that first quantization (the false, non-relativistic, Heisenberg matrix mechanics and Schroedinger wave equation) quantum mechanics is true, when in fact such first quantization has been known to be a convenient lie since 1927 when discovered incompatible with relativity. It’s convenient for teaching quantum mechanics because the people who teach it are just concerned with use of the mathematical machinery, and don’t care about the underlying physical processes, since the atom calculations in quantum mechanics are simplest when using the false physical model of first quantization. Because atomic electrons only orbit at speeds of about 1% of the velocity of light, the fact that first quantization (such as Heisenberg’s matrix mechanics and Schroedinger’s wave equation) is non-relativistic and false in the relativistic limit will not pose a significant error, and such non-physical quantum mechanical descriptions of atoms do produce useful predictions, just as Ptolemy’s physically inaccurate, highly convoluted medieval geocentric epicycle predictions were approximately correct and in some ways (circular orbits) easy to calculate with, prior to the Copernican solar system and Keplerian elliptical orbit. What the mainstream has done is to take a physically false theory of primitive 1927 quantum mechanics (first quantization, unlike the later physically correct second quantization – i.e. non-classical, with a field quanta-mediated Coulomb potential – of QFT by Dirac, Feynman et al.), and use the inaccurate physically reasoning of that false model as if it were true in order to try to discredit the concept of quantum gravity, by showing that Schroedinger’s equation violates the equivalence principle between inertial and gravitational mass.

The mainstream quantum mechanics hyping of the uncertainty principle fails to see that Schroedinger’s equation also violates relativity, which is precisely why Dirac came up with his relativistic quantum field equation. Yes, Schroedinger’s equation is in disagreement with gravitational observations. No, that doesn’t mean quantum gravity is impossible: it just means that Schroedinger’s equation is wrong as was known by Dirac and others back in the 1920s.

There is an Orwellian “double-think” (“the act of simultaneously accepting as correct two mutually contradictory beliefs“) manifesting itself in physics about first and second quantization: instead of proclaiming first quantization to be wrong, everyone in the mainstream and even outside it seems to endlessly refuse to see that first and second quantization are incompatible physically (although the predictions for bound states are similar, in the non-relativistic limit for approximate calculations). As we shall see below in this post, this problem is particularly severe for string theorist Lubos Motl, and it is also behind the failure of less mainstream-dominated researchers like Professor Lee Smolin to come to understand quantum mechanics. When I write up the quantum gravity paper, I will have to go into the details of this contradiction to show how first quantization has led to quantum mechanics confusion, blocking progress in quantum gravity.

In the previous post, we finally formulated and presented the draft diagram that has been desperately lacking since the mechanism idea originated in 1996. There was a limit to how much progress could be made without getting the geometry crystal clear. I don’t like the presentation, but it (1) is fact based and (2) makes checkable predictions which have been confirmed.

The post before that was called Second quantization (Quantum Field Theory of Dirac, Feynman et al.) is physically correct and debunks the non-relativistic, physically wrong first quantization approximation to Quantum Mechanics (Schroedinger and Heisenberg).

To summarize, the Heisenberg and Schroedinger approaches to quantum mechanics are non-relativistic; they’re useful approximations for bound states (electrons bound to atoms) but they’re fundamentally wrong in principle because they use the wrong hamiltonian energy formula. They fail to put space and time on an equal footing, i.e. they don’t incorporate relativity, and they wrongly model the Coulomb electric field potential energy classically as a continuous and non-fluctuating parameter, ignoring the fact that in QED – as experimentally proved by the Casimir effect and by such facts as the quantum tunnelling of 8.78 MeV alpha particles out from polonium-212 nuclei through a classically impenetrable 26 MeV “Coulomb barrier” – the electromagnetic field is experimentally known to be mediated by the exchange of virtual (off-shell) photons in a stochastic manner between electromagnetic charges. It is precisely the quantum field nature of the real Coulomb potential (as opposed to its classical formulation) that makes the orbital electron’s motion indeterministic and non-classical, and which causes the “Coulomb barrier” faced by an alpha particle in the nucleus to vary chaotically with time about its average value, occasionally weakening enough for an alpha particle with classically insufficient energy to escape or “tunnel out”.

Similarly, in nuclear fusion of protons, the stochastic nature of the real quantized Coulomb field allows “tunnelling in” and significant fusion cross-sections to exist at energies which are totally forbidden by the classical Coulomb barrier.

Hence, the whole reason for the indeterminancy in quantum mechanics is falsely assumed to be an intrinsic uncertainty in the position and momentum product of a real (on-shell) particle. Wrong. That assumption is so-called ‘first quantization’, where the uncertainty principle is used in the form of operators for uncertainties in momentum or position, and the classical Coulomb field energy potential is assumed true.

In fact, the chaotic motion of the electron is not due to intrinsic uncertainty by itself, but is due to the uncertainty in the exchange of virtual (off-shell) photons between the nucleus, the orbital electron, and other charges around it. The electric field is chaotic on small spacetime scales because the numbers of field quanta being exchanged to produce the Coulomb force is smaller than it is on large scales. This effect is like the transition from classical, steady air pressure on large areas to Brownian motion on micron sized dust particles where individual air molecule impacts don’t average out perfectly and random, chaotic motion results!

If you try to measure the position of an electron by firing a photon at it, sure, then the uncertainty principle can be used correctly to describe the minimum uncertainty in position and momentum. But generally, as Feynman stated in his book QED, you don’t need an uncertainty principle.

Instead, you just need to sum over the histories of many chaotic virtual photon exchanges and the randomness in that quantum field replaces the classical Coulomb field and explains the reason why a wave equation is statistically a good model for finding the probability that the electron will be found in a given location.

This is called “second quantization”, and Dirac’s quantum field theory equation of 1929 is an example, although it is falsely presented in many treatments as an addition to the basic ideas of quantum theory, when in fact it is totally incompatible because it’s relativistic, not non-relativistic, and thus has a totally different hamiltonian, describing energy of the system. Feynman’s sum-over-histories or “path integrals” approach to quantum mechanics is vital for understanding physically the difference between second quantization (QED) and non-relativistic first quantization (Heisenberg/Schroedinger quantum mechanics).

‘You might wonder how such simple actions could produce such a complex world. It’s because phenomena we see in the world are the result of an enormous intertwining of tremendous numbers of photon exchanges and interferences.’

- Richard P. Feynman, QED, Penguin Books, London, 1990, p. 114.

‘Underneath so many of the phenomena we see every day are only three basic actions: one is described by the simple coupling number, j; the other two by functions P(A to B) and E(A to B) – both of which are closely related. That’s all there is to it, and from it all the rest of the laws of physics come.’

- Richard P. Feynman, QED, Penguin Books, London, 1990, p. 120.

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

- R. P. Feynman, The Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

We should add a bit more about the history of attacks against (and defence of) the causal basis of quantum fields in producing indeterminancy and debunking non-relativistic Heisenberg/Schroedinger first quantization (so-called “QM”). Dirac in 1929 came up with the Dirac equation which replaces first quantization and is relativistic, unlike QM. Bohr apparently never understood the difference between first and second quantization, as shown by his 1948 Pocono conference attack on Feynman’s second quantization path integrals which was quoted above (which were initially presented in non-relativistic format as a conceptually simple alternative to first-quantization, but are easily made relativistic and now are used in relativistic high energy particle physics, e.g. the Standard Model).

Bohr never retracted his irrational beliefs in the first-quantization uncertainty principle religion. But Dirac, having come up with the relativistic quantum field theory equation, knew that Bohr’s religion was wrong, although he was unable to counter its propaganda. Dirac loved relativity but could see that atomic “indeterminancy” arises not from Bohr’s command, but instead from particle interactions with the vacuum (relevant quotations from Dirac are in comments here, here and here):

‘Physical knowledge has advanced much since 1905, notably by the arrival of quantum mechanics, and the situation has again changed. If one examines the question in the light of present-day knowledge, one finds that the aether is no longer ruled out by relativity, and good reasons can now be advanced for postulating an æther. . . .

‘We must make some profound alterations to the theoretical idea of the vacuum. . . . Thus, with the new theory of electrodynamics we are rather forced to have an æther.’ – P. A. M. Dirac, ‘Is There an æther?’, Nature, v168 (1951), pp. 906-7.

‘Infeld has shown how the field equations of my new electrodynamics can be written so as not to require an æther. This is not sufficient to make a complete dynamical theory. It is necessary to set up an action principle and to get a Hamiltonian formulation of the equations suitable for quantization purposes, and for this the æther velocity is required.’ – P. A. M. Dirac, ‘Is there an æther?’, Nature, v169 (1952), p. 702.

This causal explanation of quantum indeterminancy didn’t go down very well against the anti-aether propaganda (and some of Dirac’s arguments were simplistic and wrong, anyway, including his “Dirac sea” aether and some details of his theory of the “large numbers coincidence”). Dirac’s defence of aether in the 1950s coincided with a dramatic reversal from his early pragmatic view of physics. On page 7 of his 1930 book The Principles of Quantum Mechanics Dirac stated:

‘The only object of theoretical physics is to calculate results that can be compared with experiment.’

But on 7 May 1963 Dirac told Thomas Kuhn during an interview:

‘It is more important to have beauty in one’s equations, than to have them fit experiment.’

- Dirac, ‘The Evolution of the Physicist’s Picture of Nature’, Scientific American, May 1963, 208, 47.

What Dirac clearly has in mind in 1963 is the excellent prediction of the Feynman-Schwinger-Tomonaga QED virtual particle mechanism Lamb shift and magnetic moment of the electron and muon. Dirac strongly objected to Feynman’s extension of his quantum field theory and he rejected the renormalization of charge and mass with arbitrary cutoffs on running couplings at high energy to prevent infinities in the equations, a procedure which he considered an ugly ad hoc fix. This is despite the fact that it was a paper about the role of “action” in quantum field theory by Dirac which prompted Feynman’s path integrals formulation. Schroedinger’s time-dependent wave equation has an exponential solution whereby the wavefunction as a function of time is proportional to e^-iHT/ħ where H is the energy operator (Hamiltonian), T is time and ħ is Planck’s constant over twice Pi. Squaring this wavefunction gives the probability of finding the particle, i.e., the exponential represents a kind of “amplitude”. Dirac took e^-iHT/ħ and derived the more fundamental lagrangian amplitude for action S, i.e. e^iS/ħ. Feynman showed that summing this amplitude factor e^iS/ħ over all possible paths or interaction histories gave a result proportional to the total probability for a given interaction. This is the path integral. Notice that the amplitude depends on the size of the action relative to Planck’s constant: where S/ħ is a big number, you get classical physics, and if S/ħ is small then you get quantum mechanics. But although it is derived from the time-dependent Schroedinger equation, it is not any longer theoretically equivalent to that equation, because it is now being summed or integrated over, to make it represent endless different interactions from virtual particles which contribute to the outcome.

In other words, the path integral, by summing over all possible interactions, in effect includes the quantum field particle creation and annihilation operators, allowing random field fluctuations to introduce statistical variations on small scales where the action S for a path is small. This is totally ignored in first quantization procedures and is omitted from the time-dependent Schroedinger formulation which doesn’t include the many virtual particle interaction contributions to the end result, and therefore lacks the proper mechanical basis for the indeterminancy and statistical basis of quantum mechanical predictions. Dirac, like Bohr and others, objected to Feynman’s path integrals at Pocono in 1948: “Dirac had proved … that in quantum mechanics, since you progress only forward in time, you have to have a unitary operator. But there is no unitary way of dealing with a single electron.”

Dr Chris Oakley also quotes Dirac stating: “[Renormalization is] just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr’s orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number.”

Dr Oakley quotes Feynman (in his 1985 book QED) stating: “The shell game that we play … is technically called ‘renormalization’. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It’s surprising that the theory still hasn’t been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate.”

The fact is that calculus itself suffers from the reductionist fallacy: discontinuties are ignored, so in the real world you can’t treat real length’s the same way as you do in mathematics (e.g., a hundred feet of rope in the form of 100 separate 1-foot long lengths is less use to a sailor than a single length of 100 feet of rope; the law of addition may tell you that both are mathematically similar but in the real world it’s obvious that there is an important difference). The mathematical model of any physical process is never completely accurate: it’s just a convenient calculating procedure. Regarding renormalization, it cuts off a running coupling from making a charge tend towards infinity at an arbitary high energy. Mathematically, this introduces a discontinuity. But physically, the real world has such cutoffs on natural laws we use every day. E.g., the inverse-square law of solar radiation would predict infinite energy density at zero distance from the sun’s core. But we have to cutoff the application of the inverse-square law at the sun’s radius: inside the sun’s radius, the inverse-square law breaks down because it is a plasma of ions and not a vacuum.

This is a good example of how a mathematical law holds up to a point and then breaks down when pushed further, due to a simple change in the physical mechanism of what it is modelling! These introduce a mathematical discontinuity naturally due to physical effects you can understand. Renormalization cutoffs in QFT are similar: as renormalization investigators like Wilson argued, it is physically logical to take a high-energy cutoff because as you go to higher energy, particles approach more closely and eventually they would be so close that there would not be enough spacetime between them for virtual particles to pop into existence, become polarized by the field, and thus shield the field. Hence, at extremely high energy, the distance scales become so small that the physical basis for the running coupling (the shielding of charge due to the polariation of virtual particles) cannot fit into the small space. The “grain size” of the vacuum is the smallest space that the virtual particle creation and polarization processes can fit into. At higher energy, the coupling (relative charge) is no longer running (varying) as a function of energy, because there is no more shielding: it remains constant at higher energy simply because there is no physical mechanism at play at higher energy (smaller distances) for vacuum shielding of charge.

Dr Oakley’s work focusses on the Haag theorem of 1955, which is a mathematical attack on renormalization that shows that a free field vacuum of virtual particles doesn’t exist. However, in a gauge theory, the virtual particles are not a free field vacuum as such: they are always being exchanged between real charged particles, e.g. between real electrons. If you take away the charges in the universe, the vacuum field of exchanged quanta would no longer exist, because those virtual quanta which mediate force fields only exist when being exchanged between particles. So the field quanta don’t exist independently of the real particles: they are not a free field vacuum. E.g., you can, as we have seen in the previous post and others, accurately model the gauge interaction process physically by treating real charges as radiating black holes: the radiation behaves as field quanta (gauge bosons). Every electron in the universe is radiating field quanta “gauge bosons”. Thus, every electron in the universe is also receiving field quanta: in steady state situations (with no net forces acting to produce accelerations) there is an equilibrium of exchange of field quanta between charges. This interaction picture simply does not imply the existence of “free field particles” in the vacuum, which Haag objects to. The field quanta aren’t free but are instead generated by the real particles in the universe, which act as both sources and sinks for the virtual particles. In addition, as we have pointed out before, there are no annihilation-creation operators for a free vacuum: Schwinger showed that there is a cutoff on pair-production in the vacuum and it simply can’t occur where the steady electric field strength is less than 1.3 x 10¹⁸ volts per metre which only exists out to 33 fm from the centre of a unit charge like an electron! In the vacuum beyond that small 33 fm distance, there are no creation-annihilation spacetime Feynman diagram loops, because the field strength is simply too weak to make virtual fermions pop into existence from the ground state of the vacuum. (For proof, just see equation 359 in Dyson’s http://arxiv.org/abs/quant-ph/0608140 and equation 8.20 in Luis Alvarez-Gaume, and Miguel A. Vazquez-Mozo’s http://arxiv.org/abs/hep-th/0510040.)

This is the low-energy or IR cutoff to the logarithmic running coupling formula in QFT corresponding to electron collision energies on the order of 1 MeV: at lower energies and thus at distances beyond 33 fm, the charge of the electron no longer falls due to the running coupling, but is constant because there is no further pair production and polarization of the vacuum. Forces then vary merely due to the geometric (inverse square law) effect of distance on the spreading out of force-mediating gauge boson exchange radiation. However, if you read popular accounts of quantum field theory, they all ignore equation 359 in Dyson’s http://arxiv.org/abs/quant-ph/0608140 and equation 8.20 in Luis Alvarez-Gaume, and Miguel A. Vazquez-Mozo’s http://arxiv.org/abs/hep-th/0510040, and instead claim that the entire vacuum is full of virtual particles spontaneously popping into existence and being annihilated. Nope. It isn’t. This is why long-range forces vary according to the geometric inverse-square law over large distances, without an additional logarithmic or exponential attenuation factor (which you do need when modelling shorer range forces where pair production does exist, e.g. the weak and strong nuclear forces). Over larger distances than 33 fm from a fundamental particle, due to the IR cutoff the vacuum doesn’t contain any Feynman diagram loops: it merely contains bosonic exchange radiations. There can be no spontaneous pair production of virtual fermions where the electric field is below Schwinger’s 1.3 x 10¹⁸ volts/metre threshold, because the field is then too weak to allow them to be created. (Think of the photoelectric effect for an analogy to this threshold: you can only release electrons from a metal by photon impacts if the photon energy exceeds a threshold energy called the work function of the electron. In other words, charges have a binding energy, and you must deliver more than that binding energy before you can free them.)

Like Dirac, Einstein also objected to Bohr, but obviously he did not side with Dirac and objected to first quantization on different grounds to Dirac (because Einstein simply didn’t want any particles, but just classical “continuum” fields such as extensions to general relativity), and Einstein was also widely ignored in favour of Bohr’s philosophy (Smolin’s 2006 book for instance quotes Dyson as skipping a meeting with Einstein, after Dyson read Einstein’s latest papers and decided they were poor).

Bohr simply wasn’t aware that Poincare chaos arises even in classical systems with 2+ bodies, so he foolishly sought to invent metaphysical thought structures (complementarity and correspondence principles) to isolate classical from quantum physics. Poincare chaos means that chaotic motions on atomic scales can result from 2+ electrons influencing one another, e.g. from the randomly produced pairs of charges (creation-annihilation “loops” on spacetime Feynman diagrams) which exist randomly within 10^-15 metre from an electron (where the electric field is over Schwinger’s threshold for spontaneous pair-production in the vacuum, about 1.3 x 10¹⁸ v/m) causing deflections in motion (these effects might average out over long times and large distances, but would cause more chaotic motion on smaller time and distance scales). The failure of determinism (predictable closed orbits, etc.) is therefore present in classical, Newtonian physics, which can’t even deal with a collision of 3 billiard balls. Newtonian physics works in the solar system only because the planets all have masses – i.e. gravitational charges – far smaller than the mass of the sun, reducing it to effectively a two-body problem where only the masses of the planet under consideration and the sun are important for calculating the gravitational force. By contrast, in the atom, the electrons carry charges which are a much larger fraction of the nuclear charge with opposite sign (for a hydrogen atom the electron has an identical amount of electric charge as the nucleus), so mutual interference between electrons in nearby atoms (or electron shells in the same atom), will cause a massive amount of chaos in the subatomic world which isn’t seen in the solar system where the sun’s mass dominates (over 99.8% of the mass of the solar system is the sun) and planet-planet interactions are therefore relatively trivial:

‘… the ‘inexorable laws of physics’ … were never really there … Newton could not predict the behaviour of three balls … In retrospect we can see that the determinism of pre-quantum physics kept itself from ideological bankruptcy only by keeping the three balls of the pawnbroker apart.’

– Dr Tim Poston and Dr Ian Stewart, Analog, November 1981.

So why is this fact – that the chaos of quantum mechanics is simply due to the random exchange of virtual particles in the quantum electromagnetic field between charges in atoms – being covered-up?

Professor Lee Smolin at the Perimeter Institute has enlightened me as to why the mainstream ignores this: I’ve just read his 2006 arXiv paper http://arxiv.org/abs/quant-ph/0609109, ‘Could quantum mechanics be an approximation to another theory?’ Smolin simply fails to discriminate first from second quantization, then goes into details of deriving the Schroedinger equation (first quantization, i.e. wrong quantum mechanics) from stochastic processes. In other words, he completely ignores Feynman’s explanation that the field quanta cause indeterminism in the atom and other small-scale phenomena (such as light passing through nearby double slits and being influenced by the electromagnetic fields of the electrons in the slits) and talks instead about modifying Bohm’s 1952 discredited “hidden variables” ideas:

“We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by averaging over variables which are not internal to the subsystem, which may be considered non-local hidden variables. We find conditions for arriving at quantum mechanics through such a procedure. The key lesson is that the effect of the coupling to the external degrees of freedom introduces noise into the evolution of the system degrees of freedom, while preserving a notion of averaged conserved energy and time reversal invariance.

“These conditions imply that the effective description of the subsystem is Nelson’s stochastic formulation of quantum theory. We show that Nelson’s formulation is not, by itself, a classical stochastic theory as the conserved averaged energy is not a linear function of the probability density. We also investigate an argument of Wallstrom posed against the equivalence of Nelson’s stochastic mechanics and quantum mechanics and show that, at least for a simple case, it is in error.”

ArXiv, being controlled by string theory partisans who don’t like Smolin’s loop quantum gravity, have permitted a trackback to the paper from Dr Lubos Motl’s blog post called “Wavefunctions and hydrodynamics: crackpots vs. rational thinking”, where Lubos writes:

“It is no secret that I consider all people whose main scientific focus is a revision of the basic postulates of quantum mechanics – and a return to the classical reasoning – to be crackpots. They just seem too stubborn and dogmatic or too intellectually limited to understand one of the most important results of the 20th century science.

“Every new prediction based on the assumption that there is a classical theory that underlies the laws of quantum mechanics has been proven wrong. The local hidden variables have first predicted wrong outcomes in the EPR experiments and later they predicted the validity of Bell’s inequalities and we know for sure that these inequalities are violated in Nature, just like quantum mechanics implies and quantifies. The non-local hidden variables predict a genuine violation of the Lorentz symmetry. I think that all these theories predict such a brutal violation of the Lorentz symmetry that they are safely ruled out, too. But even if someone managed to reduce the violation of the laws of special relativity in that strange framework, these theories will be ruled out in the future. Their whole philosophy and basic motivation is wrong.

“The whole political movement to return physics to the pre-quantum era is a manifestation of a highly regressive attitude to science – an even more obvious crackpotism than the attempts to return physics to the era prior to string theory. But among the proposals to undo the 20th century in physics, some of the papers are even more stupid than the average.”

As with his string theory propaganda, Lubos is wrong about the Bell inequality tests as shown by the following evidence:

“In some key Bell experiments, including two of the well-known ones by Alain Aspect, 1981-2, it is only after the subtraction of ‘accidentals’ from the coincidence counts that we get violations of Bell tests. The data adjustment, producing increases of up to 60% in the test statistics, has never been adequately justified. Few published experiments give sufficient information for the reader to make a fair assessment.” – http://arxiv.org/PS_cache/quant-ph/pdf/9903/9903066v2.pdf

“The quantum collapse [in the mainstream interpretation of first quantization quantum mechanics, where a wavefunction collapse occurs whenever a measurement of a particle is made] occurs when we model the wave moving according to Schroedinger (time-dependent) and then, suddenly at the time of interaction we require it to be in an eigenstate and hence to also be a solution of Schroedinger (time-independent). 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.” – Thomas Love, California State University.

Lubos then goes on and on about Smolin’s paper because Smolin claimed to debunk Wallstrom’s objection to Nelson’s hidden variables (actually Smolin was not defending Nelson, he argues that Wallstrom simply gives a false reason to debunk Nelson and states that the real problem in Nelson are Hilbert space states with discontinuous wavefunctions). I do have to agree with Lubos on the issue that the few people with influence who are probing the foundations of quantum mechanics, like Professor Smolin, are not approaching the subject correctly. The correct approach is to describe quantum fields throughout the universe by summing over histories; i.e., the physical use of path integrals (by analogy to their use in Brownian motion) for modelling the results of field quanta exchange as force fields. Instead, Smolin and others avoid simple modelling at all costs, and choose to work on the problem using variations of old approaches which are failures.

David Bohm’s hidden variables theory was first published in his 1952 paper “A suggested interpretation of quantum theory in terms of hidden variables, I and II”, Physical Review v. 85, pp. 166-93. Bohm ignored the evidence for quantum fields causing indeterminancy as accepted in second quantization (quantum field theory) and instead abstrusely and controversially introduced “hidden variables” to explain the chaotic, Brownian motion-type indeterminancy of electron orbits, deriving the first-quantization Schroedinger equation! Bohm’s error is plain to see: he should have been rebuilding quantum mechanics using quantum field theory, with Feynman’s path integrals to sum the exchange of field quanta between charges in the universe, instead of trying to derive the epicycle-like non-relativistic first quantization model of quantum mechanics.

Later, in 1969, Edward Nelson published his “Derivation of the Schroedinger equation from Newtonian mechanics” in Physical Review, v. 150, p. 1079. The title alone tells you why Lubos and other string theorists get so angry with this stuff: they want their complex, stringy mathematical ugliness to replace the deep simplicity in the world just as Ptolemy’s geocentric epicycles of 150 A.D. won out over Aristarchus’ more physically correct solar system of 250 B.C.; their stringy mathematics is analogous to Ptolemy’s geocentric, non-physical epicycles (where the correct theory is not such a mathematical landscape of endless ad hoc epicycles with many fine-tuned anthropic-derived parameters, but is simply a solar system with elliptical rather than circular orbits).

Nelson also wrote a book, “Quantum fluctuations” (Princeton University Press, 1985), available as a PDF download. It doesn’t address anything interesting and although the aim is very interesting, it focusses on the wrong theory (first quantization quantum mechanics, not QFT/second quantization). Another book with similar errors is Peter R. Holland’s “The Quantum Theory of Motion: An Account of the De Broglie-Bohm Causal Interpretation of Quantum Mechanics”, Cambridge University Press, 1995. Although the aim is good, the method and results are wrong because it again focusses on deriving the wrong theory!

To understand why they are all wrong, imagine this is the year 1500 A.D. and some errors in Ptolemy’s geocentric universe epicycle theory have been found using more accurate measurements of planetary positions. Instead of everyone trying different things to solve the problem, the mainstream all goes and adds more epicycles to cover up the problems (exactly like today’s string theorists addressing the problems of the Standard Model); while the heretics such as Copernicus try to resurrect Aristarchus’s solar system complete with its own system of circular orbits and epicycles to explain retrograde motion. Nobody works on elliptical orbits. Both the mainstream and the heretics work on false models. Everyone wrongly agrees that circles are the most beautiful mathematical tool and that nature must have planets moving in circles: they only disagree on whether the earth or the sun is the centre.

Arthur Koestler’s 1959 “The Sleepwalkers: A History of Man’s Changing Vision of the Universe” actually counted the epicycles up and found 40 in Ptolemy’s Earth-centred-system in his “Almagest” of 150 A.D., versus 80 in Copernicus’s solar system of 1500 A.D. (which used circular orbits with epicycles instead of ellipses like Kepler). This was contrary to the prevailing history of science, which insisted that Copernicus was accepted on the basis of Occam’s Razon due to having the fewer epicycles than Ptolemy. Actually sometimes more complex theories are closer to nature and there were different reasons why Copernicus was preferred. (Viz: Mercury and Venus are always observed from Earth to be on a bearing within 90 degrees of the position of the sun, a fact which is explained very simply in the solar system model by Mercury and Venus having orbits closer in to the sun than the Earth’s orbit. Additionally, the apparent size of the Moon seen from Earth in Ptolemy’s model should vary by a factor of two monthly due to its epicycles, when in fact it doesn’t appear to vary in size.)

The road ahead, by analogy to the road to the atom: How our knowledge of matter was developed through guesswork, experiment-forced correction of simplistic theory, and a reluctant acceptance for unpredicted complexity

‘In considering the history of thought, it is necessary to distinguish the real stream, determining a period, from the ineffectual thoughts casually entertained. In the eighteenth century every well-educated man read Lucretius and entertained ideas about atoms. But John Dalton made them efficient in the stream of science …’ – Alfred North Whitehead, Science in the Modern World, Harvard, 1925.

‘… John Dalton made the theory quantitative. By showing how the weights of different atoms relative to one another could be determined, he introduced a feeling of reality into a purely abstract idea. … Most of his weights were subsequently proved to be erroneous, but Dalton sowed the seed which grew, where others had previously merely turned over the soil. … It provided an explanation or, at least, an interpretation of many chemical facts and, of greater consequence, it acted as a guide to further experimentation and investigation. … A fact may be defined as something for the actual existence of which there is definite evidence. A theory or hypothesis, on the other hand, is a purely conceptual attempt to explain or interpret known facts. While facts are presumably established and unalterable, a theory may be altered or discarded if it proves to be inadequate.’ – Samuel Glasstone, Sourcebook on Atomic Energy, D. van Nostrand, 2nd ed., New York, 1958, pp. 2-3. (Copyright of the U.S. Government.)

There were two rival theories of matter in Ancient Greece, circa 500 B.C. Leucippus and his student Democritus thought matter ultimately composed of void and tiny fundamental ‘atoms’ (this name meaning ‘non-divisible’, from the Greek, a-temnein). Empedocles and Aristotle rejected the atomic hypothesis, preferring a theory in which all matter is formed from a combination of one or more of four fundamental ‘elements’: air, earth, fire and water.

In 1774, Antoine Laurent Lavoisier proved that air is not an element but a mixture of (mainly) nitrogen and oxygen, only the latter of which supports combustion. In 1781, Joseph Priestley and Henry Cavendish similarly debunked the theory that water is a fundamental element, by proving it to be a compound of hydrogen and oxygen. In 1808, John Dalton’s New System of Chemical Philosophy was published, containing relative masses measured for various types of atom, i.e., various elements.

Dalton made serious errors in assuming that water was a simple compound of equal numbers of hydrogen and oxygen atoms (HO), and that ammonia was similarly simple (NH). These and other errors caused Dalton to deduce incorrect masses for oxygen and nitrogen atoms of 7 and 5 relative to hydrogen, instead of 14 and 15 using the true formulae H₂O and NH₃, respectively. The correct masses of oxygen and nitrogen atoms relative to hydrogen are 16 and 14. Despite errors, Dalton’s idea caused progress.

In 1811, Amadeo Avogadro argued that, under constant temperature and pressure, the density of any gas is directly proportional to the relative mass of its constituent molecules:

‘Setting out from this hypothesis, it is apparent that we have the means of determining very easily the relative masses of the molecules of substances obtainable in the gaseous state.’

For practical purposes, Avogadro’s law led to the concept of the gram-molecule or ‘mole’ whereby the atomic mass of a molecule to roughly that of hydrogen – or, as defined precisely, to one-twelfth of the mass of carbon-12 – expressed in units of grams, is the mass of one mole. E.g., for water (H₂O), one mole is roughly 2 + 16 = 18 grams. According to Avogadro’s law, one mole of any gas occupies a volume of 1 litre at 1 atmosphere pressure and 0 ^oC temperature. In 1905, Albert Einstein worked out a diffusion equation for the Brownian motion of small dust grains hit by air molecules which was used by experimentalist Jean Perrin in 1908 and subsequent researchers to calculate that there are about 6.022 x 10²³ molecules in one mole of any substance. This permitted the masses of different atoms to be estimated.

In 1816, William Prout stated his hypothesis that all atomic masses were integral multiples of the mass of hydrogen. This was statistically defended by Lord Rayleigh in 1901:

‘The atomic weights tend to approximate to whole numbers far more closely than can reasonably be accounted for by any accidental coincidence … the chance of any such coincidence being the explanation is not more than 1 in 1000.’

Detractors of Prout’s hypothesis pointed out that the accurately measured masses of chlorine and copper (about 35.5 and 63.5) were definitely not integers. Instead of the hypothesis being abandoned as empirically false, the non-integer masses were later explained by the discovery of isotopes due to a variable numbers of neutrons present in the nucleus of atoms of a given element, as well as the mass of the nuclear fields which bind nuclear particles together. The presence of neutrons was not merely a problem in producing non-integer average masses for some elements. Neutrons also introduced complexity into the relationship between the chemical properties of elements and their relative masses.

John Newlands in 1865 tried to arrange the known elements into a table on the basis of their weights and chemical properties. He discovered a ‘law of octaves’ in which the eighth most massive atom has similarities to the first, and so on. However, due to Newland’s omission of undiscovered elements, Newland’s law was simplistic, and wrongly related iron with sulphur and gold with iodine.

In 1869, Mendelyeev published his periodic table that correctly associated the properties of elemental atoms of different masses by allowing some empty spaces in the table to ensure that the properties in each column correlated correctly. Three of the gaps were soon filled by the discovery of gallium in 1875, scandium in 1879 and germanium in 1886, which had the properties predicted by Mendelyeev. As a result of these correct predictions, Mendelyeev’s periodic table was taken seriously and was first reported in English in the London Chemical News journal of December 1875.

Mendelyeev’s periodic table contains vertical columns correlating the chemical properties of elements and horizontal ‘periods’ containing an increasing number of elements: 2 in the first period (hydrogen and helium), the 8 elements in each of the next two periods (lithium to neon, and sodium to argon), followed by 18 in the following period (potassium to krypton).

The Pauli exclusion principle of quantum theory, by imposing constraints on the combinations of electron pairing in atomic shells, explains this periodic table of the elements.

One deep lesson from this history of matter is that we have to follow and model experimental data when theoretical guesswork fails or is uncheckable: science isn’t concerned with uncheckable speculations. Another deep lesson is that the theory of the atom which resulted wasn’t anything like the “beautiful” regular geometric solids idea of the ancient Greeks, and the atoms were not even unsplittable. If you try to ignore and censor out advances without checking them on the basis that your “gut reaction” is that they don’t look pretty, you are in effect just a gutless supporter of mainstream groupthink. If the scientific evidence supports a model (be it intuitive, counterintuitive, simple, complex, “elegant”, or “ugly”, a model with many fans and promoters, or none at all), you need to take it seriously. Otherwise, you’re just acting emotionally, not scientifically.

New presentation of quantum gravity

Fig. 1 – new presentation of quantum gravity, based on both the recent discussion with Doug Sweetser in the About page comments, and an attempt to explain the mechanism to a science teacher, during an hour long run in the park this evening. Note that this predicts the actual strength of gravity, e.g. it predicts the value of the gravitational parameter G. This is not a non-predictive theory like string theory, based on 6/7 extra dimensions that nobody can observe and adding 100 or more extra unknown parameters plus a multiverse of 10⁵⁰⁰ extra universes to the Standard Model of particle physics. It’s a predictive theory based on factual inputs, not a non-predictive theory which is based speculations about yet other speculations (Planck scale unification, wrong spin-2 gravitons, etc.).

The mainstream spin-2 graviton theory can’t calculate anything checkable, since it has to falsely ignore graviton contributions in the surrounding universe, which are immense due to the fact that (1) the masses of galaxies in the surrounding universe are immense and (2) the gravitons from such distant masses are converging from a great distance as they are exchanged with masses here, which is the opposite of divergence. This spin-1 graviton theory is the only possible falsifiable theory of quantum gravity for this reason: it is based on observable facts seen in nature. By Newton’s 2nd law, the cosmological acceleration (a = Hc ~ 7 x 10^-10 ms^-2) of the mass of the universe (~3 x 10⁵² kg of observable luminous matter, according to NASA’s Hubble Space Telescope) implies a force outward from any observer of F = Ma = 2 x 10⁴³ Newtons. Newton’s 3rd law implies an equal and opposite force (i.e. inward directed, towards the observer). From the possibilities of known particle physics (gravity and the Standard Model), this force must be carried by gravitons, implying the mechanism in Fig. 1 which gives gravity as the asymmetry when this force is shadowed by masses with a cross-section for graviton interactions equal to the black hole event area of the mass of that fundamental particle, which is a fact that is empirically justified in the earlier post linked here. The blach hole event horion radius for an electron is 1.35 x 10^-57 metre, so it has a cross-section of just 5.73 x 10^-114 m². This small cross-section is why gravity is so weak compared to other forces (e.g., the gravitational attraction between two apples is negligible, and you need immense masses like the mass of the earth to make the gravitational interaction significant, whereas other fundamental forces show up when dealing with just a few particles).

There is an radial inward force of 2 x 10⁴³ Newtons which is the 3rd law reaction to the observed cosmological acceleration of the universe around the observer. This is an immense force, but because the cross-section for quantum gravity is so small, gravity gets cut down to the observed strength by the shadowing effect in Fig. 1.

The gravitational attraction force given by Newton’s law with parameter G obtained in the usual way empirically (from the twisting of a fibre by the attraction of large lead spheres in the laboratory) can now be calculated theoretically as proved in Fig. 1 above. It is accurate, with errors well within the error in the estimate of the mass of the observable universe (3 x 10⁵² kg which is taken from page 5 of the NASA report linked here). Fig. 1 also summarizes the flaws in trying to extend LeSage’s inaccurate and useless theory of gravity to this theory in order to ignore it (which is like falsely claiming Darwin’s evolution is wrong because Lamarke came up with an inaccurate and misleading theory of evolution before Darwin sorted out the facts of evolution; it superficially impresses the gullible, but it is a false argument itself): LeSage’s theory is based on real radiation, not virtual (off-shell) radiation like gauge bosons (which don’t heat up objects or slow them down by causing drag). In any case, quantum gravity will imply that there are gravitons throughout the vacuum, so if this naive objection were true, it would be a problem for spin-2 gravitons just as spin-1 gravitons. Actually, there are interactions between gravitons and moving masses: these cause the FitzGerald contraction in length in the direction of motion (head-on pressure effect), the increase in mass (snowplow effect), and for static masses the radial contraction (compression) which leads to various curvature effects in the approximation to quantum gravity which is known as general relativity.

Above: LeSage’s shadow theory was developed originally by Newton’s friend Fatio, but was a failure because it couldn’t predict anything:

(1) Fatio and LeSage didn’t know Weyl’s gauge theory whereby two gravitational charges will exchange off-shell virtual particles, gravitons, to cause gravity (which is the case in the other fundamental particle interactions in the Standard Model). So they falsely speculated that gravity was caused by dust like particles which would cause drag, slowing down the planets and heating them up by impacts. Maxwell and Kelvin later pointed out these flaws, debunking the Fatio-LeSage theory.

(2) They didn’t know that we’re surrounded by immense masses in all directions and that according to any Weyl gauged quantum gravity theory, we will be exchanging gravitons with those surrounding masses. There is no way to prevent or justifiably ignore the consequences of this graviton exchange with immense distant masses.

(3) They didn’t know about the recession of matter, so they couldn’t predict the cosmological acceleration of the universe correctly ahead of measurement (which we did publish in 1996, two years before discovery), and then use that value to calculate the outward force of receding mass M by Newton’s 2nd law, F = Ma. They couldn’t in consequence apply Newton’s 3rd law to get the equal and opposite inward-diected, graviton mediated force. They also didn’t have any evidence about the graviton interaction cross-sectional area for matter; they didn’t know the evidence that it is black hole sized.

There are other ignorant claims to be found on the internet. For example, http://www.mathpages.com/HOME/kmath209/kmath209.htm states falsely that the isotropy of the universe is 1 part in 100,000 without specifying the area of sky that this this amount of cosmic background radiation temperature fluctuation applies to: the page claims that this amount of anistropy would cause “fluctuations in the “weight” of a 1 pound object (in the shape of a slender rod, to make it sensitive to the directional flux) on the order of 100 pounds”. It gives no time-frame for the period of oscillation of this density, or the ratio of length to diameter of the rod, just the pseudoscientifically value word “slender” (which is non-quantitative). Actually, this is totally false because if a long slender rod is made, it will not fluctuate in mass due to the anisotropy because the anisotropy is not fluctuating! The same pattern of anisotropy in the cosmic background radiation exists across the sky. Rotating the rod makes no difference whatsoever, because the rod is composed of individual fundamental particles! The sum of forces acting on those particles is no different regardless of the orientation of the rod. With a cross-section for graviton interactions of 5.73 x 10^-114 m² for an electron, there is no significant chance (even with the mass of the earth) that two fundamental particles will lie on a single given line of sight. Hence, the shape of a given mass is irrelevant for the mass sizes we are concerned with in the case of rods in a laboratory. There are also false “arguments” that gravitons have to travel faster than light, cause heating to melt objects, cause drag forces, and so on, which are based upon studiously ignoring the off-shell nature of force-mediating virtual particles, Weyl gauge bosons. Does your fridge magnet glow red-hot from exchanging gauge bosons with the fridge door? No? Electromagnetism between fundamental charged particles is 10⁴⁰ times stronger than gravity, so if gravitons are supposed to cause heating then electromagnetism would cause a heating effect 10⁴⁰ times worse than gravitons! That debunks the idea that gauge bosons cause any type of heating, including drag effects which cause objects moving in a real (on-shell, not off-shell) fluid to heat up.

All of the objections to this mechanism of gravity are similar in their off-the-top-of-my-head stupidity and ignorance to the objections Feynman’s path integrals received from Oppenheimer, Bohr, Teller and others at Pocono in 1948; they are based on ignoring the facts and simplistically dismissing progress.

Consider Oppenheimer’s attempt to censor Feynman’s path integrals without listening at all, as described by Freeman Dyson (Stuckelberg was working on the same idea independently, but was ignored and – as with Zweig’s quarks – he received no Nobel Prize). It’s remarkable that genius in the past has consisted to such a large degree in overcoming apathy (Oppenheimer was not just a stubborn exception who objected to path integrals. E.g., Feynman is quoted by Jagdish Mehra in The Beat of a Different Drum, pp. 245-248, saying that Teller, Dirac and Bohr all also claimed to have “disproved” path integrals: Teller’s disproof consisted of saying that Feynman didn’t have to take account of the exclusion principle, Dirac disproved it for not having a unitary operator, and Bohr disproved it because he believed that Feynman didn’t know the uncertainty principle: “it was hopeless to try to explain it further.” So without Dyson’s brilliance at explaining ideas, Feynman’s path integrals would probably have been ignored.)

“… take the exclusion principle … it turns out that you don’t have to pay much attention to that in the intermediate states in the perturbation theory. I had discovered from empirical rules that if you don’t pay attention to it, you get the right answers anyway …. Teller said: “… It is fundamentally wrong that you don’t have to take the exclusion principle into account.” … Dirac asked “Is it unitary?” … Dirac had proved … that in quantum mechanics, since you progress only forward in time, you have to have a unitary operator. But there is no unitary way of dealing with a single electron. … Bohr … said: “… one could not talk about the trajectory of an electron in the atom, because it was something not observable.” … Bohr thought that I didn’t know the uncertainty principle … it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up …”

- Richard P. Feynman, in Jagdish Mehra, The Beat of a Different Drum (Oxford, 1994, pp. 245-248).

http://www.mathpages.com/HOME/kmath209/kmath209.htm compiles equally false dismissals of physical mechanisms from “geniuses” of physics, with added nonsense thrown in (like the mass variation claim we have just debunked):

Historical Assessments of the Fatio-Lesage Theory

It’s an interesting historical fact that the attitudes of scientists toward the Fatio-Lesage “explanation” of gravity have varied widely, not just from one scientist to another, but for individual scientists at different moments. This is exemplified by Newton’s ambivalence. On one hand, he told Fatio that if gravity had a mechanical cause, then the mechanism must be the one Fatio had described. … he explicitly denied (in a famous letter to Bentley) the intelligibility of bare action at a distance, but he just as explicitly rejected (in a letter to Leibniz) the notion that space is filled with some material substance (a la Descartes) that communicates the force of gravity. His alternative was to say that gravity is caused by the will and spirit of God, not by any material cause. Of course, he gave consideration to various possible material mechanisms, and even included some Queries in the latter editions of Opticks, speculating on the possibility of an ether …

Even setting outside the outlandishness of the explanation, Newton was never able to extract from Fatio’s idea any testable consequence that could support it, so the idea remained an occult mechanism which, according to Newton, is not the proper purview of science.

Subsequent scientists have had similarly ambivalent reactions to the theory of Fatio and Lesage. For example, Euler originally expressed interest in Le Sage’s theory, stating (in the same conditional manner employed by Newton) that if gravity is due solely to impulse forces, then something like Lesage’s theory must be true. However, Euler ultimately rejected Lesage’s theory …

This striking ambivalence regarding the Fatio-Lesage theory has many other examples. Herschel spoke for many scientists when he said it was “too grotesque to need serious consideration”, whereas Thomson and Tait gave it serious consideration, the latter even asserting that it was “the only plausible answer which has yet been propounded”. Darwin too gave the idea “serious consideration”, but he also said “no man of science is disposed to accept it as affording the true road”.

Several of the founders of modern kinetic theory, including both John Herapath in 1820 and John James Waterston in 1845, began their investigations by trying to devise mechanical explanations of gravity. Herapath seems to have been influenced explicitly by Lesage’s writings, whereas Waterston was apparently one of the many independent discoverers of the concept. …

I remember a discussion on Physics Forums in which all the errors in LeSage’s theory and dismissals of it by famous physicists were straightened out over many hundreds of comments. Finally the discussion thread was closed by an administrator who falsely stated that at some point in the above discussion, a decisive dismissal of physical mechanisms had been given, but he couldn’t remember what it was, although it proved that it was pointless to go on discussing the topic. This is of course wrong, but it is what happens in such pointless discussions. Feynman had tried to defend himself against Bohr, who closed the discussion in the same way by falsely claiming that Feynman didn’t know the uncertainty principle. If he had shouted back, Bohr would doubtless have just become either angry or smug and would have still ignored the physics Feynman was putting forward.

It is important to “stand upon the shoulders of giants” in physics in order for them to pay attention to your idea. (The Feynman suppression episode in 1948 reminds you of a famous joke by the late Sidney Coleman: “If I have seen further than others, it is by standing between the shoulders of midgets”.) By building on new foundations which Bohr was ignorant of (and biased against), Feynman guaranteed that he would be ignored and falsely dismissed by an arrogant and ignorant Bohr. Feynman’s continuing censorship today for second-quantization are in favour of a mechanism (virtual, field quanta multipath interference) causing the indeterminancy of fundamental particles on small scales:

“… Bohr … said: ‘… one could not talk about the trajectory of an electron in the atom, because it was something not observable.’ … Bohr thought that I didn’t know the uncertainty principle … it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up …”

- Richard P. Feynman, quoted in Jagdish Mehra’s biography of Feynman, The Beat of a Different Drum, Oxford University Press, 1994, pp. 245-248. (Fortunately, Dyson didn’t give up!)

‘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 [path amplitudes] for all the ways an event can happen – there is no need for an uncertainty principle!’

- Richard P. Feynman, QED, Penguin Books, London, 1990, pp. 55-56.

‘… when the space through which a photon moves becomes too small … we discover that light doesn’t have to go in straight [narrow] lines, there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But 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 becomes very important, and we have to sum the arrows to predict where an electron is likely to be.’

- Richard P. Feynman, QED, Penguin Books, London, 1990, Chapter 3, pp. 84-5.

The indeterminate electron motion in the atom is simply caused by second-quantization: the field quanta randomly interacting and deflecting the electron.

However, the physically false, non-relativistic Heisenberg/Schroedinger approach is easier to apply to bound states like atoms, so it is falsely taught as QM, just as the Bohr atom is falsely taught in high schools.

Here is a solid example of the failure of first quantization mathematics:

“The quantum collapse [in the mainstream interpretation of first quantization quantum mechanics, where a wavefunction collapse occurs whenever a measurement of a particle is made] occurs when we model the wave moving according to Schroedinger (time-dependent) and then, suddenly at the time of interaction we require it to be in an eigenstate and hence to also be a solution of Schroedinger (time-independent). 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.”

– Dr Thomas S. Love, Departments of Mathematics and Physics, California State University.

“In some key Bell experiments, including two of the well-known ones by Alain Aspect, 1981-2, it is only after the subtraction of ‘accidentals’ from the coincidence counts that we get violations of Bell tests. The data adjustment, producing increases of up to 60% in the test statistics, has never been adequately justified. Few published experiments give sufficient information for the reader to make a fair assessment.”

– http://arxiv.org/PS_cache/quant-ph/pdf/9903/9903066v2.pdf

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

- R. P. Feynman, The Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

Obviously, one diagram cannot summarize all of the justifications and implications. However, there is a need in physics to make clear how simple nature really is, as proved by the failure of non-relativistic first quantization and the success of simple path integrals in second quantization (representing fields as exchanged off-shell quanta).

‘Underneath so many of the phenomena we see every day are only three basic actions: one is described by the simple coupling number, j; the other two by functions P(A to B) and E(A to B) – both of which are closely related. That’s all there is to it, and from it all the rest of the laws of physics come.’

- Richard P. Feynman, QED, Penguin Books, London, 1990, p. 120.

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

- R. P. Feynman, The Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

‘You might wonder how such simple actions could produce such a complex world. It’s because phenomena we see in the world are the result of an enormous intertwining of tremendous numbers …’

- Richard P. Feynman, QED, Penguin Books, London, 1990, p. 114.

What is the way forward? Well, this spin-1 graviton exchange mechanism deals neatly with gravitation and dark energy as both being quantum gravity effects, and this modifies the Standard Model. So my preferred option is to write a paper, titled maybe ‘A Simple Change to the Standard Model for Inclusion or Quantum Gravity, with Predictions and Validation’, and/or a full textbook explaining first the maths of the Standard Model, and then explaining the evidence for makin the slight corrections needed to incorporate quantum gravity.

A second option (maybe when the first gets ignored) is to follow in the footsteps of a great physicist and write a satrical ‘Dialogue Concerning Two New Sciences’, comparing the failures of over-hyped mainstream false spin-2 speculative, non-falsifiable string theory to the successful predictions of this censored, entirely fact-based theory (note that the black hole cross-section has empirical evidence discussed in the post linked here).

The relationship between the black hole cross-section for gravity and the mechanism for electromagnetism is discussed in earlier posts here and here. The gauge boson of electromagnetism is a virtual photon with 4-polarizations, not the 2-polarizations that normal photons have. The two extra polarizations are required to make attraction work in the framework of Weyl’s gauge theory. The repulsion law works fine even using 2-polarization photon exchange: you get hit by a photon from a similar charge, and it knocks you away from the similar charge. If you fire a photon to that similar charge, you recoil away from that other charge. So similar charges repel. Fine. But attraction requires adding two extra polarizations to the field quantum of electromagnetism. The field around an electron is negative: we know the electron has negative charge because of the field, which is mediated by virtual photons. We don’t know anything about the electron’s core, only about its field. We’ve only probed matter to energies on the order of 100 GeV or so, and we’ll never collide charges hard enough to see beyond the field effects to the core. So the whole notion of “charge” really needs to be applied to what we see with charge, which is the field, not the unobservable inner core of an electron. Hence, in electromagnetism the virtual photons can be treated as charged. The normal objection to this turns out false. It used to be objected that massless charges can’t move or they would generate infinite magnetic self-inductance. But actually, in Weyl’s theory virtual particles are exchanged in two directions at once, e.g. from charge A to charge B and back the other way. This two-way exchange is possible – even though one-way motion is impossible – because the superimposed magnetic curls of the field vectors will cancel out if two-way exchange is occurring. Many photons are exchanged in each direction simultaneously, so this works.

With two oppositely spin-1 charged field quanta mediating electromagnetism and one uncharged spin-1 field quanta mediating gravity, we have 3 massless gauge bosons which seem to be described by an SU(2) symmetry without mass. This suggests a modification to the Standard Model, where at present SU(2) gauge bosons are given mass by a speculative untested, non-falsifiable “Higgs mechanism”. Modifying it so that left-handed SU(2) gauge bosons acquire mass still gives the weak force but allows gravity to be included in a reformed Standard Model.

The coupling strengths of gravity and electromagnetism are different at observed low energy by a factor of about 10⁴⁰, gravity being the weaker. This is explained in a simple path-integral random walk between charges: the existence of two different electric charges but only one gravitational charge means that you can get a random-walk of gauge boson exchange between electric charges which adds up differently to that between gravitational charges. The random walk result is numerically equal to the size of one step multiplied by the square-root of the number of steps. It turns out that on average the outward divergence of receding field quanta is compensated for by the inward convergence of approaching field quanta, so all we need to do is to multiply gravitational charge strength by the square root of the number of particles in the universe (about 10⁸⁰) to get the electromagnetic charge strength in QFT: this turns out to be accurate within experimental error (10⁴⁰).

What is physically happening is that fundamental particles are black holes, radiating high energy particles which behave as field quanta (virtual particles) since they are of extremely small wavelength. The black hole radiating power for electrons calculated from Hawking’s formula predicts a fundamental force 10⁴⁰ times stronger than gravity; hence this is electromagnetism. Gravity is about 10⁴⁰ times weaker due to the random-walk mechanism illustrated in previous posts.

Second quantization (Quantum Field Theory of Dirac, Feynman et al.) is physically correct and debunks the non-relativistic, physically wrong first quantization approximation to Quantum Mechanics (Schroedinger and Heisenberg)

Above: just as Bohr’s atom is taught in school physics, most mainstream general physicists with training in quantum mechanics are still trapped in the use of the “anything goes” false (non-relativistic) 1927-originating “first quantization” for quantum mechanics (where anything is possible because motion is described by an uncertainty principle instead of a quantized field mechanism for chaos on small scales). The physically correct replacement is called “second quantization” or “quantum field theory”, which was developed from 1929-48 by Dirac, Feynman and others.

The discoverer of the path integrals approach to quantum field theory, Nobel laureate Richard P. Feynman, has debunked the mainstream first-quantization uncertainty principle of quantum mechanics. Instead of anything being possible, the indeterminate electron motion in the atom is caused by second-quantization: the field quanta randomly interacting and deflecting the electron.

“… Bohr … said: ‘… one could not talk about the trajectory of an electron in the atom, because it was something not observable.’ … Bohr thought that I didn’t know the uncertainty principle … it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up …”

- Richard P. Feynman, quoted in Jagdish Mehra’s biography of Feynman, The Beat of a Different Drum, Oxford University Press, 1994, pp. 245-248. (Fortunately, Dyson didn’t give up!)

‘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 [path amplitudes] for all the ways an event can happen – there is no need for an uncertainty principle!’

- Richard P. Feynman, QED, Penguin Books, London, 1990, pp. 55-56.

‘When we look at photons on a large scale – much larger than the distance required for one stopwatch turn [i.e., wavelength] – the phenomena that we see are very well approximated by rules such as “light travels in straight lines [without overlapping two nearby slits in a screen]“, because there are enough paths around the path of minimum time to reinforce each other, and enough other paths to cancel each other out. But when the space through which a photon moves becomes too small (such as the tiny holes in the [double slit] screen), these rules fail – we discover that light doesn’t have to go in straight [narrow] lines, there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that [individual random field quanta exchanges become important because there isn't enough space involved for them to average out completely, so] 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 becomes very important, and we have to sum the arrows [in the path integral for individual field quanta interactions, instead of using the average which is the classical Coulomb field] to predict where an electron is likely to be.’

- Richard P. Feynman, QED, Penguin Books, London, 1990, Chapter 3, pp. 84-5.

His path integrals rebuild and reformulate quantum mechanics itself, getting rid of the Bohring ‘uncertainty principle’ and all the pseudoscientific baggage like ‘entanglement hype’ it brings with it:

‘This paper will describe what is essentially a third formulation of nonrelativistic quantum theory [Schroedinger's wave equation and Heisenberg's matrix mechanics being the first two attempts, which both generate nonsense 'interpretations']. This formulation was suggested by some of Dirac’s remarks concerning the relation of classical action to quantum mechanics. A probability amplitude is associated with an entire motion of a particle as a function of time, rather than simply with a position of the particle at a particular time.

‘The formulation is mathematically equivalent to the more usual formulations. … there are problems for which the new point of view offers a distinct advantage. …’

- Richard P. Feynman, ‘Space-Time Approach to Non-Relativistic Quantum Mechanics’, Reviews of Modern Physics, vol. 20 (1948), p. 367.

‘… I believe that path integrals would be a very worthwhile contribution to our understanding of quantum mechanics. Firstly, they provide a physically extremely appealing and intuitive way of viewing quantum mechanics: anyone who can understand Young’s double slit experiment in optics should be able to understand the underlying ideas behind path integrals. Secondly, the classical limit of quantum mechanics can be understood in a particularly clean way via path integrals. … for fixed h-bar, paths near the classical path will on average interfere constructively (small phase difference) whereas for random paths the interference will be on average destructive. … we conclude that if the problem is classical (action >> h-bar), the most important contribution to the path integral comes from the region around the path which extremizes the path integral. In other words, the article’s motion is governed by the principle that the action is stationary. This, of course, is none other than the Principle of Least Action from which the Euler-Lagrange equations of classical mechanics are derived.’

- Richard MacKenzie, Path Integral Methods and Applications, pp. 2-13.

‘… light doesn’t really travel only in a straight line; it “smells” the neighboring paths around it, and uses a small core of nearby space. (In the same way, a mirror has to have enough size to reflect normally: if the mirror is too small for the core of neighboring paths, the light scatters in many directions, no matter where you put the mirror.)’

- Richard P. Feynman, QED, Penguin Books, London, 1990, Chapter 2, p. 54.

There are other serious and well-known failures of first quantization aside from the nonrelativistic Hamiltonian time dependence:

“The quantum collapse [in the mainstream interpretation of first quantization quantum mechanics, where a wavefunction collapse occurs whenever a measurement of a particle is made] occurs when we model the wave moving according to Schroedinger (time-dependent) and then, suddenly at the time of interaction we require it to be in an eigenstate and hence to also be a solution of Schroedinger (time-independent). 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.” – Thomas Love, California State University.

“In some key Bell experiments, including two of the well-known ones by Alain Aspect, 1981-2, it is only after the subtraction of ‘accidentals’ from the coincidence counts that we get violations of Bell tests. The data adjustment, producing increases of up to 60% in the test statistics, has never been adequately justified. Few published experiments give sufficient information for the reader to make a fair assessment.” – http://arxiv.org/PS_cache/quant-ph/pdf/9903/9903066v2.pdf

First quantization for QM (e.g. Schroedinger) quantizes the product of position and momentum of an electron, rather than the Coulomb field which is treated classically. This leads to a mathematically useful approximation for bound states like atoms, which is physically false and inaccurate in detail (a bit like Ptolemy’s epicycles, where all planets were assumed to orbit Earth in circles within circles). Feynman explains this in his 1985 book QED (he dismisses the uncertainty principle as complete model, in favour of path integrals) because indeterminancy is physically caused by virtual particle interactions from the quantized Coulomb field becoming important on small, subatomic scales! Second quantization (QFT) introduced by Dirac in 1929 and developed with Feynman’s path integrals in 1948, instead quantizes the field. Second quantization is physically the correct theory because all indeterminancy results from the random fluctuations in the interactions of discrete field quanta, and first quantization by Heisenberg and Schroedinger’s approaches is just a semi-classical, non-relativistic mathematical approximation useful for obtaining simple mathematical solutions for bound states like atoms:

‘You might wonder how such simple actions could produce such a complex world. It’s because phenomena we see in the world are the result of an enormous intertwining of tremendous numbers of photon exchanges and interferences.’

- Richard P. Feynman, QED, Penguin Books, London, 1990, p. 114.

‘Underneath so many of the phenomena we see every day are only three basic actions: one is described by the simple coupling number, j; the other two by functions P(A to B) and E(A to B) – both of which are closely related. That’s all there is to it, and from it all the rest of the laws of physics come.’

- Richard P. Feynman, QED, Penguin Books, London, 1990, p. 120.

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

- R. P. Feynman, The Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

Sound waves are composed of the group oscillations of large numbers of randomly colliding air molecules; despite the randomness of individual air molecule collisions, the average pressure variations from many molecules obey a simple wave equation and carry the wave energy. Likewise, although the actual motion of an atomic electron is random due to individual interactions with field quanta, the average location of the electron resulting from many random field quanta interactions is non-random and can be described by a simple wave equation such as Schroedinger’s.

This is fact, it isn’t my opinion or speculation: professor David Bohm in 1952 proved that “brownian motion” of an atomic electron will result in average positions described by a Schroedinger wave equation. Unfortunately, Bohm also introduced unnecessary “hidden variables” with an infinite field potential into his messy treatment, making it a needlessly complex, uncheckable representation, instead of simply accepting that the quantum field interations produce the “Brownian motion” of the electron as described by Feynman’s path integrals for simple random field quanta interactions with the electron.

Quantum tunnelling is possible because electromagnetic fields are not classical, but are mediated by field quanta randomly exchanged between charges. For large charges and/or long times, the number of field quanta exchanged is so large that the result is similar to a steady classical field. But for small charges and small times, such as the scattering of charges in high energy physics, there is some small probability that no or few field quanta will happen to be exchanged in the time available, so the charge will be able to penetrate through the classical “Coulomb barrier”. If you quantize the Coulomb field, the electron’s motion is indeterministic in the atom because it’s randomly exchanging Coulomb field quanta which cause chaotic motion. This is second quantization as explained by Feynman in QED. This is not what is done in quantum mechanics, which is based on first quantization, i.e. treating the Coulomb field V classically, and falsely representing the chaotic motion of the electron by a wave-type equation. This is a physically false mathematical model since it omits the physical cause of the indeterminancy (although it gives convenient predictions, somewhat like Ptolemy’s accurate epicycle based predictions of planetary positions):

Fig. 1:The Schrodinger equation, based on quantizing the momentum p in the classical Hamiltonian (the sum of kinetic and potential energy for the particle), H. This is an example of ‘first quantization’, which is inaccurate and is also used in Heisenberg’s matrix mechanics. Correct quantization will instead quantize the Coulomb field potential energy, V, because the whole indeterminancy of the electron in the atom is physically caused by the chaos of the randomly timed individual interactions of the electron with the discrete Coulomb field quanta which bind the electron to orbit the nucleus, as Feynman proved (see quotations below). The triangular symbol is the divergence operator (simply the sum of the gradients in all applicable spatial dimensions, for whatever it operates on) which when squared becomes the laplacian operator (simply the sum of second-order derivatives in all applicable spatial dimensions, for whatever it operates on). We illustrate the Schrodinger equation in just one spatial dimension, x, above, since the terms for other spatial dimensions are identical.

Dirac’s quantum field theory is needed because textbook quantum mechanics is simply wrong: the Schroedinger equation has a second-order dependence on spatial distance but only a first-order dependence on time. In the real world, time and space are found to be on an equal footing, hence spacetime. There are deeper errors in textbook quantum mechanics: it ignores the quantization of the electromagnetic field and instead treats it classically, when the field quanta are the whole distinction between classical and quantum mechanics (the random motion of the electron orbiting the nucleus in the atom is caused by discrete field quanta interactions, as proved by Feynman).

Dirac was the first to achieve a relativistic field equation to replace the non-relativistic quantum mechanics approximations (the Schroedinger wave equation and the Heisenberg momentum-distance matrix mechanics). Dirac also laid the groundwork for Feynman’s path integrals in his 1933 paper “The Lagrangian in Quantum Mechanics” published in Physikalische Zeitschrift der Sowjetunion where he states:

“Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue …

“Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. … The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. … the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially nonrelativistic in form …”

Schroedinger’s time-dependent equation is: Hy= iħ.dy /dt, which has the exponential solution:

y_t = y_o exp[-iH(t – t_o)/ħ].

This equation is accurate, because the error in Schroedinger’s equation comes only from the expression used for the Hamiltonian, H. This exponential law represents the time-dependent value of the wavefunction for any Hamiltonian and time. Squaring this wavefunction gives the amplitude or relative probability for a given Hamiltonian and time. Dirac took this amplitude e^-iHT/ħ and derived the more fundamental lagrangian amplitude for action S, i.e. e^iS/ħ. Feynman showed that summing this amplitude factor over all possible paths or interaction histories gave a result proportional to the total probability for a given interaction. This is the path integral.

Schroedinger’s incorrect, non-relativistic hamiltonian before quantization (ignoring the inclusion of the Coulomb field potential energy, V, which is an added term) is: H = ½ p²/m. Quantization is done using the substitution for momentum, p -> -iħ{divergence operator} as in Fig. 1 above. The Coulomb field potential energy, V, remains classical in Schroedinger’s equation, instead of being quantized as it should.

The bogus ‘special relativity’ prediction to correct the expectation H = ½ p²/m is simply: H = [(mc²)² + p²c²]², but that 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 electron is spin-1/2 so it has a spin of only half the amount of a spin-1 particle, which means that the electron must rotate 720 degrees (not 360 degrees!) to undergo one revolution, like a Mobius strip (a strip of paper with a twist before the ends are glued together, so that there is only one surface and you can draw a continuous line around that surface which is twice the length of the strip, i.e. you need 720 degrees turning to return it to the beginning!). Since the spin rate of the electron generates its intrinsic magnetic moment, it affects the magnetic moment of the electron. Zee gives a concise derivation of the fact that the Dirac equation implies that ‘a unit of spin angular momentum interacts with a magnetic field twice as much as a unit of orbital angular momentum’, a fact discovered by Dirac the day after he found his equation (see: A. Zee, Quantum Field Theory in a Nutshell, Princeton University press, 2003, pp. 177-8.) The other two solutions are evident obvious 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). 

Much of the material above is from the previous post (I’m putting it here on a separate post because that previous post began with sorting out errors in mainstream cosmology, which may have put off some bigoted and dogmatic people who are only interested in non-cosmology aspects of quantum field theory; it also helps me towards assembling background/draft material for a forthcoming book/paper).

To understand how the path integrals approach explains the double slit experiment, see this post. To see how scientific criticisms of mainstream first quantization lies have been censored out of mainstream journals by dogmatic mathematical simpletons who lack a grasp of the nature of science itself (‘Science is the organized skepticism in the reliability of expert opinion.’ – Richard Feynman in Lee Smolin, The Trouble with Physics, Houghton-Mifflin, 2006, p. 307), see this post. There’s a completely causal explanation: the photon is not a point but has transverse spatial extent; when it encounters two nearby slits (closer than a wavelength) part diffracts through each slit and the recombination on the other side gives rise to the photon whose probability of landing at any point depends on both slits, not just one of them.

String theorists who believe dogmatically that mathematical elegance, mystery and beauty in physics rather than hard evidence of agreement with experiment, are the central requirements, should listen to Einstein and Boltzmann:

“I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler.”

- A. Einstein, December 1916 Preface to his book Relativity: The Special and General Theory, Methuen & Co., London, 1920.

Ugly but useful mathematics

Heisenberg’s uncertainty principle p.x = h-bar is quantized by turning uncertainties in momentum p and position x into non-commuting operators (which I’ll signify by simply placing square brackets around them), and replacing h-bar with -i{h-bar}. This gives [p,x] = h-bar. The two solutions to that are firstly [x] = i{h-bar}d/dp with [p]=p, and secondly [p] = -i{h-bar}d/dx with [x] = x. Either of these solutions is a first quantization of classical physics.

Then you do the same thing replacing momentum p = E/c and x = ct for light, giving p.x = (E/c)(ct) = E.t, which allows you to replace the product of uncertainties p.x in Heisenberg’s uncertainty principle with the product of uncertainties in energy and time, E.t. Repeating the previous recipe for quantization on this energy-time Heisenberg uncertainty principle then gives us [E,t] = h-bar. This has the two solutions: [E] = -i{h-bar}d/dt with [t] = t, and [t] = i{h-bar}d/dE with [E] = E.

Taking [E] = -i{h-bar}d/dt, this gives Schroedinger’s time-dependent equation when it acts on wavefunction Psi, with energy operator [E] = H, the Hamiltonian:

H{Psi} = -{h-bar}d{Psi}/dt

Rearranging

(1/{Psi})d{Psi} = -H.dt/(i{h-bar})

integrating this gives:

ln {Psi} = -Ht/(i{h-bar})

(ln {Psi}_t) – (ln {Psi}_0) = -Ht/(i{h-bar})

Taking both sides to natural exponents to get rid of the natural logarithms on the left hand side:

({Psi}_t)/({Psi}_0) = exp(-Ht/(i{h-bar}))

hence

{Psi}_t = {Psi}_0 * exp(-Ht/(i{h-bar}))

Thus the time-dependent wavefunction equals simply the time-independent wavefunction multiplied by the exponential amplitude factor, exp(-Ht/(i{h-bar})).

The product of the Hamiltonian operator for energy with time is analogous to the integral of the Lagrangian for energy over time, so let Ht = {integral symbol}L dt = S, action. Thus the relative amplitude of a wavefunction (representing the contribution from one Feynman diagram or one “path” in the path integral) is given by:

exp(-Ht/(i{h-bar})) = exp(-S/(i{h-bar})).

So the path integral amplitude factor is very simply related to both the Heisenberg matrix mechanics and the Schroedinger wave equation. However, just as Ptolemy’s model and the solar system both modelled the same planets in different ways, there are physical differences. First quantization is physically wrong. Second quantization is physically correct in the way Feynman presents it.

For a detailed derivation of the time-dependent Schroedinger equation using the path integrals formulation, see David Derbes, “Feynman’s derivation of the Schroedinger equation”, Am. J. Phys. v64, issue 7, July 1996, pp. 881-4.

Update:

Relevant copy of a comment to Professor Johnson’s Asymptotia:

“Gell-Mann is best known as the person who came up with the idea of quarks, the particles that make up (for example) protons and neutrons, the building blocks of atomic nuclei.”

It took genius to publish such a speculative idea. According to William H. Cropper’s book Great physicists (Oxford U.P., p. 418), George Zweig’s paper on that theory was “emphatically rejected” by Physical Review but Murray Gell-Mann was “older and wiser” so he “anticipated a negative reception at the Physical Review to such bizarre entities as unobservable, fractionally charged elementary particles, and he published his first quark paper in Physics Letters. Zweig’s theory went unpublished except in a CERN report, but it and its author acquired a certain reputation. When Zweig sought an appointment at a major university, the head of the department pronounced him a ‘charlatan’.”

It’s good that Gell-Mann managed to anticipate and avoid that censorship so cleverly, or we wouldn’t have quark theory, with the SU(3) strong interaction part of the Standard Model. Another example: Pauli’s attempt to censor Yang-Mills theory in February 1954 because the particles are massless (Pauli had already discarded the idea for this “failure”) is another example (Yang simply sat down when Pauli persisted in objecting).

Consider Oppenheimer’s attempt to censor Feynman’s path integrals without listening at all, as described by Freeman Dyson (Stuckelberg was working on the same idea independently, but was ignored and – as with Zweig’s quarks – he received no Nobel Prize). It’s remarkable that genius in the past has consisted to such a large degree in overcoming apathy (Oppenheimer was not just a stubborn exception who objected to path integrals. E.g., Feynman is quoted by Jagdish Mehra in The Beat of a Different Drum, pp. 245-248, saying that Teller, Dirac and Bohr all also claimed to have “disproved” path integrals: Teller’s disproof consisted of saying that Feynman didn’t have to take account of the exclusion principle, Dirac disproved it for not having a unitary operator, and Bohr disproved it because he believed that Feynman didn’t know the uncertainty principle: “it was hopeless to try to explain it further.” So without Dyson’s brilliance at explaining ideas, Feynman’s path integrals would probably have been ignored.)

“… take the exclusion principle … it turns out that you don’t have to pay much attention to that in the intermediate states in the perturbation theory. I had discovered from empirical rules that if you don’t pay attention to it, you get the right answers anyway …. Teller said: “… It is fundamentally wrong that you don’t have to take the exclusion principle into account.” … Dirac asked “Is it unitary?” … Dirac had proved … that in quantum mechanics, since you progress only forward in time, you have to have a unitary operator. But there is no unitary way of dealing with a single electron. … Bohr … said: “… one could not talk about the trajectory of an electron in the atom, because it was something not observable.” … Bohr thought that I didn’t know the uncertainty principle … it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up …”

- Richard P. Feynman, in Jagdish Mehra, The Beat of a Different Drum (Oxford, 1994, pp. 245-248).