Category Archives: Bohmian mechanics

The Elephant In The Room

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Coincidently with the previous post here defending Pilot Wave Theory, a pair of articles appeared defending the standard interpretation of Quantum Mechanics. Both are dismissive of PWT in a way that underscores the basic incoherence of the modern, math-first approach to doing physics. The first of these articles is a typical screed from Ethan Siegel in which he martials a lot of known scientific facts and then assembles them into a circular argument that assumes the “standard model” to be correct, thus “proving” once again that the “standard model” as described by Siegel and acclaimed by all right-thinking scientists is the One True Model that all must revere. I’m not going to waste time on picking apart this particular circular argument. It is the arguments against PWT that are the subject of this post.

The other article by Philip Ball appeared in Quanta Magazine. In 2018 Ball published an even-handed account of quantum physics, Beyond Weird. This current work is primarily a discussion of a theory of decoherence developed by the physicist Wojciech Zurek. Decoherence is an attempt to explain how a particle evolves from the indeterminate “superposition of states” condition described by the standard interpretation to the “deterministic” state of everyday reality and standard physics where particles are not smeared out but always locally distinct. As with the Siegel article I’m only going to focus on the arguments used to dismiss Pilot Wave Theory from consideration as an alternative to the preferred dogma.

Both authors take the standard interpretation of quantum physics as a given. That standard interpretation can be characterized as an offshoot of Neil Bohr’s claim that the wavefunction represented all that could be known about the quantum state – it was fundamentally indeterminate and nothing could be known about the properties (location, spin, etc.) of a quantum particle prior to its observation (detection, measurement). To this was subsequently added the “explanation” that the indeterminacy was caused by the fact that the particle was not in any particular location prior to detection but was, in fact, smeared out in a “superposition of states”.

It was further stipulated that the smeared out state could not be observed because the very act of observing, or detecting it would cause a mathematical formalism, the wavefunction, to collapse instantaneously ensuring that the particle would always be found at some particular location. That particular location however, could not be predicted except as a probability by the wavefunction. It is necessary at this point to step back and consider what a breathtakingly absurd, not to mention utterly unscientific, account of physical reality that is.

Absurd the standard interpretation may be, but it is nonetheless an unquestioned premise of both Ball and Siegel in their respective articles. The reason it is so casually accepted is not merely because of what might be called the groupthink, dogma, and inertia that pervades the scientific academy. There is at root, the underlying premise of mathematicism – the scientifically baseless belief that mathematics somehow underlies and determines the nature of physical reality. Mathematicism is what allows otherwise rational people to believe that a particle must be smeared out in a superposition of states – because some mathematical wavefunction does not describe where the particle is.

In distinct contrast to this widely accepted wavefunction-only account of quantum behavior there stands Pilot Wave Theory which is not merely an alternative interpretation of the wavefunction-only story but constitutes a mathematically and physically distinct model of the quantum realm. In addition to the wavefunction, PWT also has a guiding equation which describes the interaction between a particle and a pilot wave which produces the statistical outcomes described by the wavefunction. The statistical outcomes of PWT are the same because it has the same statical formalism, the wavefunction.

This brings us to the objections raised against PWT by those who prefer the standard interpretation. Ethan Siegel has this to say on the matter:

“Contained in these non-local hidden variable theories are the hopes of everyone who seeks to make deterministic sense of the quantum Universe, and the hope that somewhere, somehow, there’s a way to extract more information about reality and what outcomes will occur than standard, conventional quantum mechanics permits.“

This is basically a strawman argument that seeks to characterize PWT as representing a “hope” to extract information or something about reality that the standard model does not permit. This deliberately sidesteps the fact that PWT produces exactly the same statistical results as the standard interpretation while providing a physically realistic description of the behavior of quantum particles as arising from a typical interaction of a particle with a wave.

For his part Philip Ball is a little more nuanced but his objection ultimately boils down to an aesthetic choice:

“Others invoke the description postulated by Louis de Broglie and later developed by David Bohm, in which a particle does have well-defined properties, but it is steered by a mysterious “pilot” wave that produces the strange wavelike behavior of quantum objects, such as interference…

All this has always struck me as fanciful. Why not just see how far we can get with conventional quantum mechanics? If we can explain how a unique classical world arises out of quantum mechanics using just the formal, mathematical framework of the theory, we can dispense with both the unsatisfactory and artificial cut of Bohr’s “Copenhagen interpretation” and the arcane paraphernalia of the others.“

Ball apparently finds the idea of a pilot wave as “mysterious” and “arcane” while seeming rather sanguine about the empirically baseless idea that a particle can be in a “superposition of states”. An absurd metaphysical proposition like that is somehow more palatable than a “mysterious” but physically plausible one.

Like Siegel, Ball makes no reference to the fact that PWT is not simply a different interpretation of the wavefunction-only model, like Many-Worlds, but constitutes a separate and distinct qualitative and quantitative model of quantum reality, one that produces the exact same statistical outcomes as the standard, reality-challenged version preferred by both authors. PWT does this while providing a plausible physical mechanism that is consistent with the physics of larger scales.

What is most striking about these rather casual dismissals is the seeming preference for mathematical mysticism over the open-ended nature of the scientific endeavor which seeks to understand the physical cause of observations that might at first seem inconsistent and mysterious. Modern theoretical physicists prefer to explain “mysterious” observations with imaginary things that cannot be observed, measured, or detected, rather than do the hard work of investigating the physical cause of those observations that only seem, at first encounter, to be mysterious.

Which brings us to the elephant in the room. The elephant in the room is indicated by a straightforward scientific question, Does the pilot wave of PWT refer to something physical as well as mathematical? A reasonable answer to that question is that there is a good deal of theoretical and observational evidence indicating that the pilot wave is a real physical entity that arises at the interface between a charged particle and the Ambient Electromagnetic Radiation that permeates the Cosmos. There is AER present in every laboratory in which quantum experiments are performed.

Modern Theoretical Physics pays no attention to the AER it swims in. MTP knows that the mass-energy content of an electron is equivalent to the energy of gamma radiation. MTP knows that a charged particle has a polarizing effect on nearby radiation. Despite this MTP does not incorporate the AER present in a typical laboratory environment into its analysis of the quantum behaviors it observes. Instead we get metaphysical prattling about superposition of states and wave-particle duality

MTP knows all about the individual frequencies and the linear rays of light by which we observe distant cosmological objects. The totality of that omnidirectionally emitted radiation, however, makes no appearance in the standard model of cosmology. In its place MTP has substituted the scientifically inert concept of a substantival spacetime. The resulting Big Bang model bears no resemblance to empirical reality.

An elucidation then, of the Pilot Wave Theory beyond its mathematical formalisms to a robust qualitative description of quantum scale behavior points directly at the AER as a causally interacting physical component of physical reality — and that analysis holds on all scales. The pilot wave of the theory is produced, in this conception, by the interaction of a charged particle (electron) with the AER of the laboratory. This qualitative description is made visually compelling by the work on Pilot Wave Hydrodynamics done at MIT by John Bush and his colleagues.

All of these considerations lead inexorably back to a question raised forty years ago by John S. Bell:

“Why is the pilot wave picture ignored in text books? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show us that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice?“

—— Quoted in the Stanford Encyclopedia of Philosophy article Bohmian Mechanics.

A Brief Defense of Pilot Wave Theory

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(Note: parts of this post appear in the comment section of the article being discussed. In that article the author uses the term Bohmian mechanics or just Bohm to refer to Pilot Wave Theory which is a more illustrative name for what is also sometimes called de Broglie-Bohm Pilot Wave Theory. I opt for Pilot Wave Theory (PWT) throughout this post. No matter the name it is the same theory that is being discussed.)

This recent article (Bohmian mechanics has a big problem) published by Tim Andersen, Ph.D. at The Infinite Universe presents an excellent illustration of a simple fact:

Math + Philosophy ≠ Physics

What is on display in Andersen’s article is a painfully contorted effort to dismiss Pilot Wave Theory on mathematical and philosophical grounds. But PWT is at root a phenomenological assertion about the physical nature of quantum systems. It is a physical description with ontologically relevant math. That math may have some shortcomings, though they are hardly as damning as the author would have you believe but the physical description it provides stands head and shoulders above the metaphysical nonsense generated by the standard Wavefunction-Only interpretation.

The author also displays considerable confusion about the nature of PWT, saying correctly at one point with regard to the status of a particle in the theory, “The particle itself is what we measure, and it is always there, whether we measure it or not.” A few paragraphs later, in the context of discussing locality he describes the status of the particle quite differently saying, “This is the price you pay for giving up locality. Because particles are not localized, they cannot be treated as free agents.” But then again we are told, “Bohm’s mechanics accepted nonlocality as the price to have definite particles (realism).”

The only thing that can be pointed out here is that in PWT particles always have a definite “local” position while in the standard WO interpretation particles are not localized, but smeared out. Andersen, for some reason, appears to be confused about this distinction which suggests his critique here is not based on a clear understanding of the Pilot Wave Theory.

The author also asserts that PWT “gives up” locality. It does not. What PWT does is add a non-local component explicitly to the model with it’s invocation of a pilot wave. It is the pilot (or guiding) wave that is, like all waves, a non-local phenomenon. The pilot wave is also distinct from the Schrodinger wavefunction which is another point that Andersen seems confused about:

“Bohm’s theory has a downside in that the wavefunction can guide as many particles as you like, and it does so instantaneously, allowing one particle to influence another also instantaneously.”

On the subject of non-locality, the author admits to being philosophically indisposed to the idea. This despite the clear evidence, that non-local effects are part of the phenomenological world. The problem seems to be an inclination to see it as matter of having to choose between mutually exclusive possibilities — either the world is local or it is non-local. That is, however, a false dichotomy.

Physical reality has both local (particle) and non-local (electromagnetic wave) components. Another way to say this is, particles are 3-dimensional (local) and electromagnetic waves are 4-dimensional (non-local) phenomena. That is typical of the complementary dualities often found in nature; it is a fundamental aspect of physical reality that the common reductionist viewpoint tends to obscure in its search for the One. It’s not a case of either/or; it’s both. Complementary dualities are the engines of physical reality.

In PWT the statistical outcomes of quantum experiments are attributed to the interaction of particles with waves. This is consistent with the rest of physical reality where waves and particles can be observed as distinct, interacting phenomena.

In contrast the, standard Wavefunction-Only interpretation of QM attributes the outcome of quantum experiments to a superposition of states, wherein a particle is said to be “smeared out” with no definite location until it is observed, at which point it is always found at a specific, though only statistically predicted, position. This miraculous turn of events, from smeared out to definite location is attributed to a “collapse of the wavefunction”. That miraculous and inexplicable and unobservable collapse is then said to present a “measurement problem”. It could also be thought of as a credibility problem.

So this strained, empirically baseless account of quantum behavior requires a non-local event, the “wavefunction collapse” which happens instantly at the moment the particle is detected. The author criticizes PWT for its explicit non-locality while failing to note that non-locality is also prominent in the standard WO interpretation. The reason non-locality is unavoidable is that non-local phenomena (waves) are as much a part of physical reality as local phenomena (particles). The standard interpretation does not acknowledge that duality and consequently it has a problem when non-locality makes its unwelcome appearance in a model that only recognizes locality.

PWT is consistent with the observed wave and particle nature of physical reality on all other scales, whereas the WO model produces a borderline irrational account of particles being spread out like waves only to become particles when you look at them.

Interestingly there are tabletop experiments conducted at MIT that produce directly observable quantum-like effects that are visually quite striking. The images produced in these clever experiments can be helpful to visualize and understand the mechanics of PWT: https://thales.mit.edu/bush/index.php/4801-2/

Throughout his diatribe Andersen teases a “Fatal Flaw” that will be revealed eventually, as if it were some thrilling conclusion to a schlock horror movie. When the momentous revelation arrives it doesn’t fail to disappoint. The Fatal Flaw requires taking this extravagant mathematicist-fantasyland conceit into consideration:

“This is relativity, but not in ordinary 4D spacetime like Einstein’s relativity. It is relativity in an infinite-dimensional space called a Hilbert space. Hilbert space is where the wavefunction actually lives and moves.”

Apparently the Fatal Flaw is that the PWT math is not mathematically equivalent to Heisenberg’s math which is equivalent to Schrodinger’s math somewhere over there in Hilbert space (in all its infinite glory). Unfortunately, for this FF theory, PWT has an additional guiding equation which describes a particle’s interaction with a pilot wave. 

So the criticism that PWT isn’t equivalent mathematically to the Heisenberg formalism that is equivalent to Schrodinger’s math is a fatuous mathematicist argument that has nothing to do with physics. Not being equivalent to S&H is a feature not a bug.

PWT does what the Schrodinger’s and Heisenberg’s math doesn’t do, describe a physical system in physical and mathematical terms that are consistent with empirical reality. Implying as Andersen does that a plausible, coherent, physical and mathematical model like PWT should be set aside because it doesn’t fit well with some arbitrary mathematicist conventions does not constitute a reasonable scientific argument.

PWT is not equivalent to those models – because it is more mathematically complete than either of them. What makes it more complete is the fact that it actually describes the physical interaction that produces the observed results — WO does not do that.

PWT provides a plausible physical account of a quantum physical process, with mathematics, that produces the observed outcomes of this type of quantum experiment while neither Heisenberg nor Schrodinger describe a process that is coherent or rational in scientific terms. All you get is statistics and absurd metaphysical handwaving. It is the Wavefunction-Only version of Quantum Mechanics that has a big problem: the model doesn’t make physical sense — it’s just some math. It gets the right answers on the test but it doesn’t know why the answers are right.

The ALER And Quantum Theory (revised)

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Note to Subscribers: This is a substantial modification of yesterday’s post. I’ve published it separately so that subscribers would receive a notification of the revision. I also substantially revised the preceding post on the ACER but directly modified the original which did not produce a notification to subscribers. I apologize for any confusion and will henceforth publish all substantive revisions to existing posts separately. Thank you for your patience.

The preceding post discussed the ACER (Ambient Cosmic Electromagnetic Radiation) and some of its implications. The ACER is present and detectable, at least in part, at the surface of the Earth. The Cosmic Microwave Background was discovered by a ground based antenna and in fact all pre-satellite-era cosmological observations were made at the surface of the Earth and involved the detection of various component frequencies of the ACER.

The situation is somewhat different in a closed room. Most of the ACER that does penetrate the atmosphere will not penetrate the walls and ceiling of the room. There will nonetheless be considerable ambient electromagnetic radiation some of it internally generated (artificial lighting, thermal radiation) and some measure of externally sourced penetrating radiation like radio frequencies. So in an enclosed room there will be an Ambient Local Electromagnetic Radiation (ALER) analogous to the ACER but having a somewhat different frequency distribution.

Some measure of ALER is present in every room humans might typically occupy including rooms dedicated to scientific experiments. Consider the room you are in as you read this. Not only is it suffused with visible light, there are also thermal radiation, radio frequencies and possibly some stray high energy UV and X, and gamma rays. 

We live our lives immersed in a sea of electromagnetic radiation whether sitting in a room or sitting out under a clear/cloudy, day/night sky. In the aggregate electromagnetic radiation provides the underlying 4-Dimensional framework of the Cosmos — at all scales.

Of particular interest with regard to Quantum Theory are the rooms where quantum experiments such as the double-slit are performed. Those rooms are also steeped in electromagnetic radiation, the ALER. 

In one version of the double-slit experiment electrons are slowly fired at the double slit screen and are subsequently detected at a second screen. As the electrons accumulate they form an interference pattern which is said to prove or at least demonstrate that electrons are both waves and particles. This would be a reasonable conclusion except this explanation takes no notice of the ALER through which the electron is traveling.

An electron affects an electromagnetic field and and is in turn affected by the field. This is not news; it is well established physics. Standard quantum theory pays no attention to the presence of the ALER and its interaction with the free electrons that are the subject of the experiment. 

The ALER is a chaotic field, streaming from all directions and comprised of many frequencies and yet the theoretical explanation of the double-slit experiment takes no account of the inescapable fact of the ALER’s presence and its unavoidable interaction with the electrons. Instead we get a feckless story about a wave-particle duality state that cannot be verified by observation, only believed in.

Such is the state of Quantum Theory — belief is obligatory because reality is irrelevant. In this it is of a piece with the rest of Modern Theoretical Physics. It presents an absurd, incoherent and at root irrational account of physical reality, one that bears almost no resemblance to the physical reality our lying eyes and instruments actually reveal to us. As with Ptolemaic cosmology, the math can be said to “work” but the physics is simply wrong.

Surprisingly this inability to grapple with the nature of physical reality is a matter of choice. There has been an alternate mathematical treatment of quantum mechanics known for more than 70 years. Bohmian mechanics models the double-slit experiment as an interaction between a particle and a guiding or pilot wave.

The mathematics of Bohmian mechanics does not explicitly describe the ALER only an abstract mathematical wave but the implications are clear. It is entirely within the reach of current mathematics to model physical reality without veering off into unrealistic metaphysical conjectures about wave-particle duality or particles that exist in a “superposition of states”. 

The price of this realistic framework is that the math is a bit more complicated than the “wavefunction only” model preferred by a “consensus” of the members of the scientific academy. The high priests of this consensus are quite obviously willing to sacrifice a coherent, logical and realistic account of quantum phenomena on the altar of mathematical convenience. Such is the state of Modern Theoretical Physics.

The ALER and Quantum Theory

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The preceding post discussed the ACER (Ambient Cosmic Electromagnetic Radiation) and some of its implications. The ACER is present and detectable, at least in part, at the surface of the Earth. The CMB was discovered by a ground based antenna and in fact all pre-satellite-era cosmological observations were made at the surface of the Earth and involved the detection of various component frequencies of the ACER.

The situation is somewhat different in a closed room. Most of the ACER that does penetrate the atmosphere will not penetrate the walls and ceiling of the room. There will nonetheless be considerable ambient electromagnetic radiation some of it internally generated (artificial lighting, thermal radiation) and some measure of externally sourced penetrating radiation like radio frequencies. So in an enclosed room there will be an Ambient Local Electromagnetic Radiation (ALER) analogous to the ACER but having a somewhat different frequency distribution.

Some measure of ALER is present in every room humans might typically occupy including rooms dedicated to scientific experiments. Consider the room you are in as you read this. Not only is it suffused with visible light, there are also thermal radiation, radio frequencies and possibly some stray high energy UV and X, and gamma rays. We live our lives immersed in a sea of electromagnetic radiation whether sitting in a room or sitting out under a clear or cloudy, day or night, sky.

Of particular interest in this regard are the rooms where quantum experiments such as the double-slit are performed. They also are bathed in electromagnetic radiation. In one version of the double-slit experiment electrons are slowly fired at the double slit screen and are subsequently detected at a second screen. As the electrons accumulate they form an interference pattern which is said to prove or at least demonstrate that electrons are both waves and particles. This would be a reasonable conclusion except this explanation takes no note of the ALER through which the electron is traveling.

An electron affects an electromagnetic field and and is in turn affected by the field. This is not news; it is well established physics. Standard quantum theory pays no attention to the presence of the ALER and its interaction with the free electrons that are the subject of the experiment. The ALER is a chaotic field, streaming from all directions and comprised of many frequencies and yet the theoretical explanation of the double-slit experiment takes no account of the inescapable fact of the ALER’s presence and its unavoidable interaction with the electrons. Instead we get a dubious story about a wave-particle duality state that cannot be verified by observation, only believed in.

Such is the state of Quantum Theory – belief is obligatory because reality is irrelevant. In this it is of a piece with the rest of Modern Theoretical Physics – presenting an absurd, incoherent and at root irrational account of physical reality, one that bears almost no resemblance to the physical reality our lying eyes and instruments actually reveal to us. As with Ptolemaic cosmology, the math can be said to “work” but the physics is simply wrong.

Bohmian Mechanics & A Mathematicism Rant

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26JUN22 Posted as a comment to this Quanta article. Probably won’t be published there until tomorrow.

Contextuality says that properties of particles, such as their position or polarization, exist only within the context of a measurement.

This is just the usual Copenhagen mush, that substitutes a feckless by-product of the pseudo-philosophy of mathematicism for scientific rigor. The rather irrational, anthropocentric view that a particle doesn’t have a position until it is measured is entirely dependent on the belief that the Schrodinger wavefunction is a complete and sufficient description of physical reality at the quantum scale. It is not.

The Schrodinger equation only provides a statistical distribution of the possible outcomes of a measurement without specifying the underlying physical processes that cause the observed outcomes. The only scientifically reasonable conclusion would seem to be that the equation constitutes an incomplete description of physical reality. The Copenhagen interpretation of QM – that the wavefunction is all that can be known is not a rational scientific viewpoint. In physical reality things exist whether humans observe them or not, or have models of them or not.

There has long been a known alternative to the wavefunction only version of QM that was championed by John Bell himself. In Bohmian mechanics, in addition to the wavefunction, there is a particle and and a guiding wave. In that context the wavefunction provides the outcome probabilities for the particle/guiding-wave interactions. Bohmian mechanics constitutes a sound scientific hypothesis; the Copenhagen interpretation (however defined) offers nothing but incoherent metaphysical posturing. As in:

The physicists showed that, although making a measurement on one ion does not physically affect the other, it changes the context and hence the outcome of the second ion’s measurement.

So what is that supposed to mean exactly, in physical terms? The measurement of one ion doesn’t affect the second ion but it does alter the outcome of the second ion’s measurement? But what is being measured if not the state of the second ion? The measurement of the second ion has changed but the ion itself is unaltered, because the “context” changed? What does that mean in terms of physics? Did the measurement apparatus change but not the second particle? It’s all incoherent and illogical, which is consistent with the Copenhagen interpretation I suppose, but that’s not saying much.

Bohmian mechanics makes short work of this matter. There are two charged particles, each with a guiding wave; those guiding waves interact in typical wave-like fashion in the 4 dimensional frame of electromagnetic radiation. The charged particles are connected in, by, and across that 4D frame. By common understanding, such a 4D frame has no time dimension. That is what accounts for the seemingly instantaneous behavior. That’s physics, it could be wrong, but it is physics. Contextuality is math; math is not physics.

Theoretical physics in its current guise is an unscientific mess because physical reality has been subordinated to mathematical and metaphysical considerations. And so we have the ongoing crises in physics in which the standard models are so discordant with physical reality in so many different ways that it seems difficult to say what precisely is wrong.

The simple answer is that you can’t do science that way. Attempting to build physics models outward from the mathematical and metaphysical realms of the human imagination is wrong. Basing those models on 100 year old assumptions and holding those outdated assumptions functionally inviolable is wrong.

Science has to be rooted in observation (direct detection) and measurement. Mathematics is an essential modeling tool of science but it is only a tool; it is not, of itself, science.

Theoretical physics, over the course of the 20th century, devolved into the study of ever more elaborate mathematical models, invoking ever more elaborate metaphysical conjectures of an invisible realm knowable only through the distorted lenses of those standard models.

Physical reality has to determine the structure of our theoretical models. Currently theorists with elaborate models dictate to scientists (those who observe, measure, and experiment) that they must search for the theoretical components of their models, or at least some signs and portents thereof. Failure to find the required entities and events does not constitute a failure of the model however, only a failure, thus far, of detection (dark matter, etc.) or the impossibility of detection (quarks, etc.). In any event the models cannot be falsified; they need only be modified.

Modern theoretical physics is an exercise in mathematicism and it has come to a dead end. That is the crisis in physics and it will continue until the math first approach is abandoned. It is anybody’s guess when that will happen. The last dark age of western science persisted for a millennium.