And together with then is atomic emission together with the unloosen energy conservation law
Bohmian mechanics is a framework (partly well-defined inward about real especial situations) proposed to supercede the postulates of quantum mechanics yesteryear a novel classical theory that largely borrows the mathematics controlling the solid soil vector as if it were a classical wave; together with that is supplemented alongside extra beables (in the exclusively semi-successful example, positions of non-relativistic particles) that deport classically together with whose trajectories are affected yesteryear the airplane pilot wave.
The theory allows you lot to assume that if you lot mensurate the non-relativistic particles' positions, the random outcome isn't decided at the minute of the measurement. Instead, these positions were already ready earlier the measurement. And the defining supposition of the Bohmian epitome is that any measure may endure reduced to such a measure of the positions (or other beables if you lot knew what they are) together with then that the random collapse inward the criterion quantum mechanical handling of the measurements isn't ever needed. For example, it's sometimes semi-successfully claimed that the measure of particles' spins may endure reduced to the measure of the positions of the same particles. But nosotros volition consider that this is non the instance for observables that commute neither alongside the seat nor alongside the momenta such as energy.
loop corrections inward QFT. User7348 was dissatisfied alongside the claim that Bohmian mechanics fails inward this seek out together with then he asked for a "rebuttal" of my claims. There must endure one, right? Everyone who believes that Bohmian mechanics doesn't endure from these lethal defects is invited to write the pre-planned "rebuttal" of my proof.
Proofs tin rarely endure disproven together with and then far, no 1 could conduct hold offered whatever "rebuttal". Physicists largely handgrip that I am right. On this blog, aside from other interactions, I've had quite a typical telephone substitution alongside 1 Bohmian who claimed that the loops could work. So I asked him to demonstrate me the calculation of the electron's magnetic minute (up to the one-loop level) inward the Bohmian theory. The respond I got was "why would I exercise it if it has already been done?".
He plainly meant that it was done inward proper quantum acre theory governed yesteryear the standard, "Copenhagen" postulates of quantum mechanics (at most reformulated alongside a dissimilar "accent" but non a dissimilar "content"). And because he must believe that Bohmian mechanics has "conquered" the criterion quantum mechanics together with may claim credit for all of the successes of quantum mechanics (while taking no responsibleness for the alleged drawbacks), he just doesn't demand to write anything, he believes.
This is plainly silly. If you lot claim to conduct hold a theory that differs from about other 1 (e.g. the "dominant" 1 amidst the researchers) together with your theory is said to conduct hold about advantages, it follows that it's inequivalent. When it's inequivalent, it may also endure inequivalent inward the "undesirable" situations – it may neglect to reproduce the successes of the "dominant" theory you lot desire to replace. Clearly, this full general dominion – modifications that conduct hold the potential to "improve" something also conduct hold the potential to "ruin" something – holds for Bohmian mechanics, too. And endure for certain that the basic Bohmian assumptions ruin pretty much everything.
These Bohmian people frequently brand claims such as "all the physics of QFT industrial plant just fine inward Bohmian theory". References to incoherent preprints that brand similar claims are the "evidence" you lot may get. All these preprints contain about "extra" (and real ugly) mathematical constructions that are absolutely dissimilar from the criterion QM/QFT together with it's obvious that they can't endure producing the same predictions inward general. But if somebody claims that the Bohmian theory makes sense, shouldn't he endure able to write the "proper modern [Bohmian]" textbook replacing the existing textbooks of quantum acre theory? At to the lowest degree a few chapters, upward to a calculation of about annihilation processes of QED.
Needless to say, null similar that is possible. None of these calculations may genuinely endure done inward the Bohmian theory. At most, these people may say that "they're all of a abrupt small-scale together with they're satisfied alongside the 'Copenhagen' treatment". But they won't enjoin you lot what the listing of "beables" (like Bohmian particle positions) is during the annihilation or lite emission or whatever other basic procedure – together with how they deport during the process. What happens to brand for certain that the beables discovery a right statistical distribution of these quantities? These Bohmian positions are basically "one-half of the Bohmian theory" – a constituent that is completely absent inward proper QM/QFT – together with then shouldn't the Bohmians add something, basically 100%, to the Copenhagen story close all these phenomena?
These people would similar to dictate the overall philosophy. They frequently delight you lot alongside extraordinarily wonderful claims such as "observers are non needed" or "the basic framework of classical physics was to a greater extent than or less right together with no conceptual alter is needed". But when you lot desire them to utilization their theory to genuinely calculate something, they prefer to endure silent. This approach is similar to the Marxists who are real loud together with aggressive when they pocket the assets of an "evil capitalist" but when they're expected to make the same values that the "evil capitalist" was able to produce, their unloosen energy all of a abrupt fades away together with you lot listen excuses. These Marxists complain close lots of bad circumstances such as the 4 principal enemies of communism – spring, summer, autumn, together with wintertime – that sometimes atomic number 82 to failures, together with and then on. Both Bohmists together with Marxists are real loud together with aggressive when they scream what they loathe but when they're supposed to demonstrate an alternative, all the meaningful activity goes away.
Sadly, this is non just an analogy. Most Bohmists genuinely were together with are Marxists at the same minute (starting alongside David Bohm himself) together with then these 2 examples of a deportment may endure just 2 sides of the same coin.
What's fifty-fifty to a greater extent than disturbing is that these Bohmists must genuinely know that the theory fails inward the description of real basic things – such as the propagation (and emission) of photons. There are Bohmian papers explicitly stating that according to the mutual Bohmian lore, something is impossible.
Photons' moving ridge functions, beables, together with atomic emission: impossible inward the Bohmian picture
I wanted to start alongside the emission of atoms resulting from an atomic transition. It can't piece of work together with all Bohmian attempts are guaranteed to destroy the discreteness of the spectrum together with atomic number 82 to violations of the unloosen energy conservation law. But in that location is a simpler affair that doesn't work: the mundane propagation of costless photons!
Just similar electrons, photons may endure used to perform the double slit experiment. Photons create private dots on the photographic plate. By its definition, the Bohmian mechanics must conduct hold a outcome for the measure of the "photon position" that is ready earlier the measurement. Except that in that location can't endure whatever equations – at to the lowest degree non local or otherwise natural equations – that could principle the motion of such "real Bohmian photons". Why?
It's simple. Take a 2001 newspaper yesteryear Ghose+3, Bohmian trajectories for photons, that starts:
It is by together with large believed that exclusively massive fermions conduct hold Bohmian trajectories but bosons exercise not. This is unremarkably attributed to the impossibility of constructing a relativistic quantum mechanics of bosons alongside a conserved four-vector probability electrical flow density alongside a positive definite fourth dimension component. However, it has at nowadays been shown [1] that a consistent relativistic quantum mechanics of spin 0 together with spin 1 bosons tin endure developed using the Kemmer equation [2]...In the normal Bohmian theory (for a fermion), 1 uses the probability 4-current \((\rho, \vec j)\) where \(\rho=|\psi|^2\) integrates to one. The electrical flow must obey the continuity equation – together with as you lot know from about mathematics of the non-relativistic Schrödinger's equation, it does obey this equation.
To comprise photons that "know where they should create dots", you lot only demand such a 4-current \((\rho, \vec j)\) as well. However, it only cannot be inward Maxwell's theory, at to the lowest degree non inward whatever local or otherwise natural form.
The work is that the natural bilinear object inward Maxwell's theory isn't a electrical flow (a 4-component vector) but the stress-energy tensor \(T_{\mu\nu}\). The integral of \(T_{00}\) over the 3-dimensional infinite isn't one. Instead, it's the total unloosen energy – something that is proportional to the frequency via \(E=\hbar\omega\).
In proper quantum mechanics, the moving ridge business office of 1 photon basically behaves as the Maxwell's electromagnetic acre – which is yet reinterpreted probabilistically. Now, the detection of a photon is ever sensitive to about frequencies together with the Maxwell acre (or photon's moving ridge function) secretly knows close the representation of dissimilar frequencies, too.
However, if you lot assume that the Bohmian photon has a well-defined position, it only cannot conduct hold a well-defined unloosen energy at the same moment. Also, the required 4-current can't endure written as whatever business office of the fields \(A_\mu\) together with their derivatives. You only can't build whatever conserved electrical flow (with 1 index) out of electromagnetic fields.
It's slow to demonstrate the complications explicitly. The quantized electromagnetic acre may endure built as a Fock space. In a box, for every allowed \(\vec k\), in that location be 2 annihilation operators \(a_\lambda(\vec k)\) together with 2 Hermitian conjugate creation operators \(a^\dagger_\lambda(\vec k)\) – 2 because in that location are 2 polarizations for each direction.
There is a prissy formula for the total energy\[
H = \sum_{\vec k, \lambda} \hbar c |\vec k|\cdot a^\dagger_\lambda(\vec k) a_\lambda(\vec k)
\] inward the seat space, namely the integral of \(\rho_E = (E^2+B^2)/2\). However, in that location is no natural formula for the expose of photons. The expose of photons would differ from \(H\) yesteryear the omission of the factor \(|\vec k|\). While the required factor \(1/|\vec k|\) may human face elementary together with natural inward the momentum space, it is absolutely unnatural together with nonlocal inward the seat infinite – it is about sort of \(1/\sqrt{\nabla^2}\) together with believe me that it's non prissy to compute the foursquare root of about inverse Laplace operators. (Dirac constitute an ingenious method how to define a prissy "square root" of the box operator – the Dirac operator – but that's just what you lot can't exercise for bosons.)
So no local or natural formula for the expose of photons \(N\) may be inward Maxwell's theory. Consequently, you lot can't discovery whatever local or natural 4-current which is needed inward Bohm's theory. And that way that in that location can't endure whatever natural equations telling you lot how the photon should respond to the Maxwell airplane pilot wave. It just doesn't brand whatever sense.
Above, I assumed that you lot would seek to define the expose of photons yesteryear applying the "inverse foursquare root of the Laplacian" – a highly non-local operator – on the formula for the total energy. Ghose et al. chose a dissimilar approach, 1 alongside about extra bizarre matrices \(\beta_\mu\), but it's ultimately as ugly. They may force some trajectories that observe about probability densities but in that location is absolutely null natural close the mathematical manipulations needed to exercise together with then – null natural close the novel proposed laws of physics governing photons.
And you lot may cheque that none of the 68 followups of the newspaper yesteryear Ghose et al. genuinely uses this super-ugly, super-unnatural laid of equations alongside extra novel vectors. It's ultimately as ugly as the nonlocal foursquare roots of the Laplacians – together with belike equivalent at about level. All the papers exclusively utilization the bizarre formulae yesteryear Ghose et al. as a political declaration of a sort. They don't genuinely desire to exercise whatever scientific discipline alongside such things. I yell upward that they don't genuinely believe that these super-ugly, arbitrary equations are right or useful inward whatever scientific sense. They must know that they conduct hold at most fitted a outcome calculated yesteryear a dissimilar theory, rather than derived a outcome yesteryear using their ain theory. What they're doing is just an ideologically-driven propaganda. All these "solutions" are "superfluous ideological superstructures", as Werner Heisenberg accurately called the master copy Bohmian theory.
(If the weird Ghose et al. formalism to make the Bohmian photon trajectories were right, people could forthwith discovery additional evidence, consistency checks, understanding alongside hints constitute inward dissimilar ways, and/or generalizations of this formalism to other fields together with particles of the Standard Model such as the Yang-Mills fields or other phenomena – just similar inward the cute together with dynamic development of the successful scientific theories nosotros genuinely know from the physics textbooks. But the expose of these "signs" that the Bohmian ideas are on the right rail is strictly null together with the expose of hints that they're incorrect is huge. Similar advocates of these bad ideas by together with large don't attention close an arbitrary finite expose of "bad signs" because they are infinitely prejudiced.)
An obvious additional work is that the photons' trajectories conduct hold to endure superluminal at many points. The waves by together with large displace yesteryear the speed of lite but to save the interference patterns, the airplane pilot moving ridge has to force the Bohmian photons dorsum together with forth (towards the interference maxima), together with then this gives them about extra motion relatively to the averaged motion of the wave, together with the average speed of these particles on these "not quite straight" lines plainly has to endure higher than the speed of light. If you lot desire to maintain inward touching alongside lite but you lot demand detours on your trip, you lot sometimes demand to displace faster than the light, right? There's no way to "solve" this problem. The superluminal motion of these particles looks similar the motion "backwards inward time" inward other relativistic inertial systems. Too bad.
So there's genuinely no usable way to comprise photons to the Bohmian theory.
Bohmian theory is incompatible alongside lite emission yesteryear atoms
The absence of a 4-current inward Maxwell's theory – that prevents you lot from defining whatever natural "pilot moving ridge force" on the Bohmian photon – is far from beingness the exclusively work you lot would run into if you lot tried to comprise photons. Try to discovery the Bohmian description of a real elementary procedure – the emission of lite yesteryear atoms. Take a hydrogen atom. It should conduct hold about discrete spectrum, OK? The unloosen energy of the photons may endure converted to their seat using a prism (colors are separated on the rainbow).
Let's assume that the Bohmian theory correctly describes the fermions (electron, proton) that the atom is composed of. Such a positive appraisal isn't right fifty-fifty inward this express setup of a non-relativistic description of fermions but let's endure overly generous. However, this theory doesn't automatically emit light. You demand to couplet the atom to the electromagnetic field. The frequency \(\omega\) modes of the electromagnetic acre volition endure sensitive to the modes of the atom inward which the unloosen energy jumps yesteryear \(\hbar\omega\). For those, the constructive interference may add together upward together with convince the atom to create a photon.
The Bohmians desire to scrap that earlier the photons are detected, they already objectively conduct hold the soon-to-be-observed positions. If that's the case, the photon must endure actually born at about moment, inward the vicinity of the atom. (We neglect the previously discussed problems alongside the costless photon which is already also full general together with can't endure incorporated to the Bohmian theory.) OK, when is the Bohmian photon born together with what are the rules that attain this job?
Proper quantum mechanics tells you lot that you lot mustn't seek to respond this interrogation because it's meaningless. Only the observed outcomes may endure treated as "facts" together with the photons volition exclusively endure detected a long fourth dimension later they're created yesteryear the atoms. Before they're detected, the probability amplitudes are interfering alongside each other.
Much similar inward the intelligence of the loop corrections, the whole potential for the photons to appear inward 1 management of the prism or about other is due to the interference effects. To conduct hold a peril to reproduce those, the Bohmian-like theory would conduct hold to contain the whole "wave functional" (state vector of the quantum acre theory) as a classical field. Great, Bohmists know how to pocket but unfortunately for them, the solid soil vector isn't the exclusively classical marking of liberty inward their proposed theory. They also demand the photons' positions. How are those created, what are their initial values, what are the rules that principle them?
Any remotely feasible solution volition conduct hold to endure sensitive to the interference together with then it volition conduct hold to endure non-local inward time. You know, if parts of the solid soil vector conduct hold the same stage at fourth dimension \(t\) together with the fourth dimension \(t+2\pi /\omega\), in that location volition endure constructive interference that makes it likelier for a photon of unloosen energy \(\hbar\omega\) to endure born. But inward the Bohmian theory, you lot also demand to create the actual photon – 1 that volition wing inward a detail management of the prism. But to create upward one's heed whether this "actual classical particle" should endure starting fourth dimension created at the fourth dimension \(t\), you lot only demand to compare the moving ridge business office at the minute \(t\) alongside the moving ridge business office at other moments of time. Otherwise your theory can't know anything close the interference together with the right unloosen energy (and thus management inward the prism) of the photon that should endure created.
Even if you lot designed about laws – nonlocal inward infinite together with fourth dimension – that create the actual photon, you lot won't know how this photon could endure "piloted" yesteryear the Maxwellian airplane pilot wave. At whatever rate, the Bohmian photon's average speed volition laissez passer on the speed of light. And to brand things fifty-fifty worse, you're guaranteed to violate the unloosen energy conservation law.
You know, the funny affair is that inward quantum mechanics, if you lot discovery the photon whose unloosen energy is equal to the unloosen energy of an atomic transition betwixt 2 levels \(E_i,E_f\),\[
\hbar\omega = E_i - E_f,
\] you lot are performing a measure of the atom's unloosen energy together with the detection of the photon of frequency \(\omega\) automatically implies that the atom's in conclusion solid soil has to endure \(E_f\). The in conclusion moving ridge business office for the arrangement atom+photon (before the measure of the photon, however) is entangled together with guarantees the perfect correlation betwixt the photon's unloosen energy together with the atom's in conclusion energy. This perfect correlation has to handgrip because it encodes the unloosen energy conservation law. And endure for certain that you lot may experimentally verify that the unloosen energy is conserved inward this sense, inward these elementary emission processes.
No Bohmian theory is capable of guaranteeing this perfect correlation. In other words, all theories based on the Bohmian epitome are guaranteed to violate the unloosen energy conservation police force during the atomic emission of light. Why?
Well, it's simple. In quantum mechanics, the unloosen energy conservation follows from the collapse of the moving ridge business office together with yesteryear the real Definition of the Bohmian mechanics, Bohmian mechanics avoids the collapse at the minute of the measurement. In whatever Bohmian picture, the measured values must endure already prepared a femtosecond earlier the measurement.
But inward quantum mechanics, yesteryear measuring the seat of the photon inward the prism, you lot mensurate the energy, together with because the photon's unloosen energy is entangled alongside the atom's energy, a detail outcome for the photon's management (i.e. energy) collapses the atom's moving ridge business office to an unloosen energy eigenstate! Now:
The Bohmian theory never collapses the atom's moving ridge business office to an unloosen energy eigenstate. In fact, inward the Bohmian theories, the "real particle" doesn't influence the airplane pilot moving ridge at all!This is a rather vicious characteristic of the Bohmian theory: the theory is real loud close the influence of the airplane pilot moving ridge on the particle but it basically assumes that the particle doesn't touching on the airplane pilot moving ridge at all. You should ever endure suspicious close theories alongside similar "asymmetric" influences. They audio similar a theory close God who tin influence everyone else but can't endure influenced. In proper physics at the cardinal level, all interactions move inward both ways. You may say that about sort of Newton's 3rd police force (actions cause reactions) ever applies.
The absence of the collapse inward Bohmian mechanics way that the atom tin only never collapse to an unloosen energy eigenstate, fifty-fifty though the photon that has known close the atom's unloosen energy has gone through the prism together with was detected. The moving ridge functions of the Bohmian mechanics never genuinely collapse. They're exclusively meant to direct particles inward about way but if you lot mensurate something else than particles' positions – i.e. atom's unloosen energy (which you lot tin yesteryear looking at the emitted photon), this Bohmian motion-picture demonstrate only breaks downward completely.
The atom continues to endure described yesteryear a airplane pilot moving ridge that is a full general superposition that still contains nonzero probabilities for all previously allowed unloosen energy eigenstates of the atom. And the positions of the electron together with proton aren't affected yesteryear the detection of the photon – fifty-fifty though they should genuinely endure correlated alongside the photon's energy. So if you lot mensurate the unloosen energy of the atom 1 time more, Bohmian mechanics predicts that you lot may instruct incorrect values of the unloosen energy together with the unloosen energy conservation police force is violated.
The experiments demonstrate that this never happens.
It's possible to say that Bohmian mechanics removes the "collapse" from quantum mechanics together with replaces it alongside the "extra Bohmian positions". In this way, the collapse to the eigenstate of all particles' positions "works" (and is done inward advance because the soon-to-be-measured positions are already decided earlier the measurement). But inward quantum mechanics, 1 also needs infinitely many dissimilar types of collapses to dissimilar states than seat eigenstates – together with Bohmian mechanics is guaranteed to neglect inward all these situations. Its inability to collapse the "pilot wave" for an atom into an unloosen energy eigenstate was just a major example; it's obvious that Bohmian mechanics fails inward the prediction of every single measure of whatever belongings of the atom except for the locations of the fermions themselves.
One could reinterpret this "Copenhagen-Bohm match" higher upward as a direct experimental proof of the (Copenhagen) postulates of quantum mechanics. We tin genuinely experimentally prove that when a photon emitted yesteryear an atom is detected, the atom's moving ridge business office has to collapse to an unloosen energy eigenstate – together with the distributions for the positions of the nucleus together with the electron conduct hold to endure modified accordingly. This fact may endure experimentally checked. It works. Bohmian mechanics says that the collapse doesn't conduct hold house together with then it's only ruled out yesteryear this elementary experiment. Almost whatever experiment rules it out.
You mightiness endure inventing ways to "fix the Bohmian theory" together with then that the atom does collapse to the unloosen energy eigenstate 1 time the emitted photon is measured; together with the Bohmian electrons' together with nuclei's positions are abruptly modified 1 time the photon is detected, too. But such a motion-picture demonstrate volition plainly depend on the reference frame together with pause the Lorentz symmetry heavily, much similar many other phenomena you lot need. All these fixes volition endure immensely ugly.
More importantly, they volition endure advertizing hoc. You volition demand a novel create for pretty much every qualitatively novel phenomenon or experiment somebody volition invent. At the end, if you lot piece of work on these "fixes" for weeks or months together with you lot conduct hold about basic integrity, you lot should endure able to realize that "your celebrated theory" isn't genuinely producing whatever results. It is non a fixed theory at all. You are just constantly fixing together with adapting "the theory" to fit the results calculable using a different, superior theory – (Copenhagen) quantum mechanics. Other people know that in that location exists just 1 create of Bohmian mechanics that isn't embarrassing or dishonest. It's called (Copenhagen) quantum mechanics.
One may say that the procedure of "applying advertizing hoc fixes" to Bohmian mechanics is just equivalent to the publication of a novel volume of the Bible that "explains" every novel characteristic of fossils or deoxyribonucleic acid discovered yesteryear the evolutionary biologists. H5N1 novel fossil is constitute together with exhibits for certain patterns. H5N1 creationist may write a volume inward which God has a intelligence alongside Moses together with from the discussion, it follows that the dinosaur bones conduct hold to conduct hold 1 belongings or another. So the Biblical theory of Creation explains all the information – but exclusively later the Biblical theory of Creation is adapted every fourth dimension a novel fact emerges.
The instance of Bohmian mechanics is isomorphic.
You know, the work is that such theories are never used to exercise whatever actual science. These theories (and their shameless apologists) are 100% pure parasites that desire to portion the credit alongside the actual theories that may endure used to explicate or predict the phenomena inward Nature – inward these 2 cases, alongside quantum mechanics together with Darwin's evolutionary biology. And it's only bad for somebody to back upward or praise similar parasitic, unscientific theories. They don't deserve whatever credit because they're non used to explicate or empathise or predict anything. And these parasitic unscientific theories together with their advocates don't conduct hold whatever scientific majuscule to create upward one's heed close the right answers to the large questions – they can't fifty-fifty bargain alongside the smallest ones. They're exclusively proposed to dingy the waters together with fool the people into thinking that for certain "ideologically inconvenient" epitome shifts (the shift from creationism to evolution, or the shift from classical to observer-dependent quantum physics) aren't genuinely needed. Except that they definitely are needed. They are totally essential.
This was a sketch explaining why I yell upward that Bohmian mechanics belongs to the pseudointellectual cesspool, non to serious scientific research, together with that it must endure treated on par alongside creationism.