# Interpretations of Quantum Mechanics: Back to First Philosophy

If you believe in the power of mathematics to describe the universe, as the language of God so to speak, in its theoretical as well as predictive power in describing the nature of the physical universe at the cosmic as well as subatomic scale, you must in turn admit to or adhere to Bell’s Theorem that posits that there can be no local hidden variables that explain the EPR Paradox, which means that from a mathematical perspective, there must exist some sort of non-local force, some connecting principle, that sits behind the behavior and complex relationship of these subatomic “particles” that are being measured and interact with each other to form the basis of those things which we consider to be “real”, or are said to exist in some way, shape or form.

And if we as human beings, and all animals or physical objects for that matter, that consist of these subatomic particles, must adhere at some level to these very same principles, i.e. that there is some non-local underlying force that drives interconnectedness that is inconsistent with Einstein’s fundamental premise of Relativity, namely that nothing can travel at speeds faster than the speed of light, then we are left with the task of trying to make sense of what Quantum Theory actually implies, or means, and what those implications are for existence and life itself and how we are to live. It is in this spirit that Charlie ventured into the next level of modern day theoretical physics, what present day physicists call Interpretations of Quantum Mechanics, or from a philosophical perspective the metaphysical implications of Quantum Theory.

Although at first glance the exercise might seem to be a purely intellectual one, and to be clear Charlie had no desire to do more research or homework than required to wrap up his thesis, he did feel that before embarking on what he thought the metaphysical and philosophical implications of what Quantum Theory was, and how it might help him understand the basis, or lack of merit, of this underlying materialistic and objective view of reality, it was important that he cover at least some of the prevailing interpretations of the theory from within the physics community itself, a group of academics that were much brighter than he, and people that actually understood the underlying mathematics, something that Charlie could only do at a theoretical level, mostly relying on the physicists and other scientific authors’ interpretations of the underlying math in forming his understanding of Quantum Theory and what it implied about the nature of these subatomic “things”, and in turn what it implied about the nature of the bigger things that consisted of these smaller subatomic “things” that in turn make up what we consider to be “physical reality”.

There are many Interpretations of Quantum Theory but there are three in particular that Charlie thought deserved attention due either to their prevalence or acceptance in the academic community and/or their impact on scientific or philosophical inquiry into the limits of Quantum Theory’s implications from a mathematical, theoretical, or metaphysical, perspective. The first was the standard orthodox interpretation, the one most often compared to or cited in reference to when differing interpretations are put forth and explained. This is most commonly referred to as the *Copenhagen Interpretation* and it basically renders the theoretical boundaries of interpretation of Quantum Theory to the results of the experiment itself and no further. This point of view can be looked at as a pure mathematical and physical behavioral modelling view of Quantum Mechanics and fundamental rejects any philosophical or metaphysical implications.

The second Charlie wanted to look at was definitely a little out there but still held some prevalence in the academic community and was mathematically and theoretically sound as far as he could gather, and intellectually interesting, so he thought he should study it and understand what it said about Quantum Theory’s potential metaphysical implications in the somewhat extreme, abstract theoretically mathematical case. This interpretation has a few variants but is mostly referred to in the literature as the *Many-worlds*, or *Many-minds*, interpretation and it expands upon the theoretical boundaries of Quantum Mechanics by explaining its stochastic nature by proposing the existence of multiple universes, or at least multiple possible universes.

The last interpretation that at some level Charlie found the most appealing intellectually, particularly given the metaphysical extensions which it included explicitly, was referred to as the *Causal Interpretation,* also sometimes referred to as *de Broglie-Bohm* theory or simply *Bohmian mechanics*. It extends Quantum Mechanics to include a principle it refers to as *quantum potential, *and while it abandons the classical notion of locality it still preserves objective realism and determinism to a large extent. In most academic circles this theory is viewed as a hidden variable theory within the context of the EPR Paradox and Bell’s Theorem.

The most well established and most commonly accepted interpretation of Quantum Theory, the one that is most often taught in schools and textbooks and the one that most alternative interpretations are compared against, is the *Copenhagen Interpretation.* This interpretation is most often associated with Niels Bohr and Werner Heisenberg, stemming from their collaboration in Copenhagen in 1927, hence the name. The term was further crystallized in writings by Heisenberg in the 1950s when expressing his views on contradictory interpretations of Quantum Theory.

The Copenhagen interpretation holds that the Quantum Theory does not and cannot yield a description of an *objective reality*, but deals only with sets of probabilistic outcomes of experimental values borne from experiments observing or measuring various aspects of energy quanta, entities that do not fit neatly into classical interpretations of mechanics. The underlying tenet here is that the* act of measurement itself*, the observer (or by extension the apparatus of observation) *causes* the set of probabilistic outcomes to converge on a single outcome, a feature of Quantum Mechanics commonly referred to as *wave function collapse**,* and that any additional interpretation of what might actually be going on, i.e. the underlying “reality”, defies explanation and the interpretation of which is in fact inconsistent with the fundamental mathematical tenets of the theory itself.

In this interpretation of Quantum Theory, *reality *(used here in the classical sense of the term as existing independent of the observer) is *a function of the experiment*, and is defined as a result of the *act of observation* and has no meaning independent of the yielding of some measurement value. In other words, reality in the quantum world from this point of view does not exist independent of observation. Or put somewhat differently, the manifestation of what we think of or define as “real” is intrinsically *tied to and related to* the act of observation of the system itself.

Niels Bohr has been one of the strongest proponents of this interpretation, an interpretation which refuses to associate any metaphysical implications with the underlying theoretical model. His position is that given this proven interdependence between that which was being observed and the act of observation, no metaphysical interpretation can, or should, in fact be extrapolated from the theory, it is and can only be a tool to describe and measure states and particle/wave behavior in the subatomic realm that are made as a result of some well-defined experiment. In other words, in Bohr’s view, attempting to make some determination as to what Quantum Theory actually *meant*, beyond the results of a given experiment, violated the fundamental tenets of the theory itself. From Bohr’s perspective, the inability to draw conclusions beyond the results of the experiments which the mathematical models predict and measure was a necessary conclusion of the theorem’s basic tenets and that was the end of the matter. This view can be seen as the logical conclusion of the principle of *complementarity**, *one of the fundamental and intrinsic features of Quantum Mechanics that makes it so mysterious and hard to understand in classical terms.

Complementarity, which is closely tied to the Copenhagen interpretation, expresses the notion that in the quantum domain the results of the experiments, the values yielded (or observables) were fundamentally tied to the act of measurement itself and that in order to obtain a complete picture of the state of any given system, as bound by the uncertainty principle, one would need to run multiple experiments across a given system, each result in turn rounding out the notion of the state, or reality of said system. These combinatorial and uncertainty features of the domain which were intrinsic to Quantum Theory said something profound about the underlying uncertainty of the theory itself from a classical realist perspective. Perhaps complementarity can be viewed as the twin of uncertainty, or its inverse postulate.

Bohr summarized this very subtle and yet at the same time very profound notion of complementarity in 1949 as follows:

…however far the [quantum physical] phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word “experiment” we refer to a situation where we can tell others what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.

This crucial point…implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear…. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects.

[1]

Complementarity was in fact the core underlying principle which drove the existence of the uncertainty principle from Bohr’s perspective. It was the underlying characteristic and property of the quantum world that captured at some level its very essence. And complementarity, taken to its logical and theoretical limits, did not allow or provide any framework for describing any definition of the real world outside of the domain within which it dealt with, namely the measurement values or results of a given experiment, the measurement instruments themselves that were part of a given experiment, and the act of measurement itself.

Another interpretation or possible question to be asked given the uncertainty implicit in Quantum Mechanics was that perhaps all possible outcomes as described in the wave function did in some respect manifest, even if they call could not be *seen* or *perceived *in our objective reality. Although on the surface it seemed like a rather outlandish premise, this interpretation of Quantum Theory has gained some prominence in the last few decades, especially within the Computer Science and Computational Complexity fields (which Charlie was schooled in), and has come to be known in the literature as the *Many-Worlds interpretation *of Quantum Theory.

This original formulation of this theory was laid out by Hugh Everett in his PHD thesis in 1957 in a paper entitled *The Theory of the Universal Wave Function *wherein he referred to the interpretation not as Many-worlds but, much more aptly and more accurately given his initial formulation of the theoretical extensions of Quantum Mechanics that he proposed, as the *Relative-State formulation *of Quantum Mechanics. Almost completely ignored by the broader scientific community for several decades after he published his work, the theory was subsequently developed and expanded upon by several authors in the last decade or two and has come to be known, along with its variants that have cropped up, as the Many-worlds interpretation.

Everett was a graduate student at Princeton at the time that he authored *The Theory of the Universal Wave Function* and his advisor was John Wheeler, one of the most respected theoretical physicists of the latter half of the twentieth century. After writing his thesis, Everett did not in fact continue a career in academia and therefore subsequent interpretations and expansions upon his theory were left to later authors and researchers, most notably by Bryce Dewitt who coined the term “many-worlds”, and David Deutsch among others. DeWitt’s book on the topic published in 1973 entitled *The Many-Worlds Interpretation of Quantum Mechanics *in many respects popularized this interpretation and brought it back into mainstream physics and it included a reprint of Everett’s thesis. Deutsch’s seminal work on the topic is a book entitled *The Fabric of Reality* published in 1997 where he expands and extends the Many-worlds interpretation to other academic disciplines outside of physics such as philosophy and epistemology, computer science and quantum computing, and even Biology and theories of evolution.

In Everett’s original exposition of the theory, he begins by calling out some of the problems with the original, or classic, interpretation of Quantum Mechanics, specifically what he and other members of the physics community believed to be the artificial creation of the notion of *wave function collapse* to explain the quantum uncertain to deterministic behavior transitions, as well as the difficulty that standard interpretations of the theory had in dealing with systems that consisted of more than one observer. These he considered to be the main drivers behind his search for an alternative view, interpretation, or theoretical extension even of Quantum Theory. He actually referred to his Relative State formulation of Quantum Mechanics as a *metatheory* given that the standard interpretation could be derived from it.

Although Bohr, and presumably Heisenberg and von Neumann as well, whose collective views Quantum Theory’s philosophical implications make up the Copenhagen Interpretation, would no doubt explain away these strange and seemingly arbitrary assumptions as out of scope of the theory itself (i.e. Quantum Theory is intellectually and epistemologically bound by the experimental apparatus and their associated experimental results), Everett finds this view philosophically limiting and at the very least worth exploring tweaks and extensions to the theory to see if these shortcomings can be removed, and in turn what the implications are theoretically speaking when some of the more standard and orthodox assumptions of Quantum Mechanics are relaxed in some sense.

Because to Everett, and this view that has become more common in the last decade or two in fact, the standard interpretation of Quantum Theory (read Copenhagen Interpretation) fundamentally prevents us from any true *explanation* as to what the theory says about the nature of “reality” itself, or the real world as it were, a world considered to be governed by the laws of classic physics where things and objects exists independent of observers and where “objects” or “particles” have real, static measurable and definable qualities that exist independently of the act of measurement or observation, a world fundamentally incompatible with the stochastic and uncertain characteristics that governed the behavior of “things” in the subatomic or quantum realm. In Everett’s own words, his intent in defining a Relative State formulation of Quantum Mechanics is:

The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced.

[2]

Everett’s starts by making the following two basic assumptions from which he devises his somewhat counter intuitive but yet now relatively widely accepted interpretations of Quantum Theory. Firstly he assumes that all physical systems large or small can be described as states within Hilbert space, the fundamental geometric framework upon which Quantum Mechanics is constructed. Secondly he abstracts the notion of observer as a machine like entity with access to unlimited memory, which stores a history of previous states, or previous observations, and also has the ability to make simple deductions, or associations, regarding actions and behavior of system states solely based upon this memory and deductive reasoning.

His second assumption represents a marked distinction between it and Quantum Theory proper and incorporates observers and acts of observation (i.e. measurement) completely into the theoretical model. Furthermore, Everett proposes, and this is the core part of his thesis, that if you yield to assumptions 1 and 2, you can come up with an extension to Quantum Mechanics that describes the entire state of the universe, which includes the observers and objects of observation, that can be described in a completely mathematically consistent, coherent and fully deterministic manner without the need of the notion of wave function collapse or any additional assumptions for that matter.

Everett makes what he calls a *simplifying* assumption to Quantum Theory, i.e. removing the need for or notion of wave function collapse, and assumes the existence of a *universal wave function* (which is the title of his thesis in fact) which accounts for and describes the behavior of all physical systems and their interaction in the universe, completely including the observer and the act of observation into the model, observers being viewed as simply another form of a quantum state that interacts with the environment. Once these assumptions are made, he can then abstract the notion of measurement, which is the source of much of the oddity and complexity surrounding Quantum Theory, as simply interactions between quantum systems that are all governed by this same universal wave function.

In Everett’s metatheory, the notion of what an observer means and how they fit into the overall model are fully defined, and what he views as the seemingly arbitrary notion of wave function collapse is circumvented. His metatheory is defined by the assumption of the existence of a *universal wave function* which corresponds to the existence of a fully deterministic multi-verse based reality whereby the notion of wave function collapse represents not a collapse so to speak, but represents a *manifestation* of the realization of one possible outcome of measurement that exists in our “reality”, or our specific multi-verse, i.e. the one which we observe during our act of measurement.

But in Everett’s theoretical description of the universe, if you take what can be described as a literal interpretation of this universal wave function as the overarching description of reality, the other, unobserved, possible states reflected in the wave function of any system in question do not cease to exist with the act of observation. The act of observation of a given system does not represent a collapse of the quantum mechanical wave that describes said system state in Copenhagen quantum mechanical nomenclature, but that these other states that do not manifest in our act of observation of said system do have some existence that persists (to what degree and level of reality they persist is a somewhat open ended question and the subject of much debate in subsequent interpretations of Everett’s metatheory) but are simply not *perceived* by us.

In his own words, and this is a subtle yet important distinction between Everett’s view and the view of subsequent proponents of the Many-worlds interpretation, these unmanifest and unobserved states exist but remain *uncorrelated* with the observer in question, an observer that is incorporated and abstracted into the universal wave function model of reality.

We now consider the question of measurement in quantum mechanics, which we desire to treat as a natural process within the theory of pure wave mechanics. From our point of view there is no fundamental distinction between “measuring apparata” and other physical systems. For us, therefore, a measurement is simply a special case of interaction between physical systems – an interaction which has the property of correlating a quantity in one subsystem with a quantity in another.

[3]

This implies of course that these unperceived states do have some semblance of reality, that they do in fact exists as possible realities, realities that are thought to have varying levels of “existence” depending upon which version of the Many-worlds interpretation you adhere to. With DeWitt and Deutsch for example, a more literal, or “actual” you might say, interpretation of Everett’s original theory is taken, where these other states, these other realities or multi-verses, do in fact *physically* exist even though they cannot be perceived or validated by experiment.*[4]*

This is a more literal interpretation of Everett’s thesis however, and certainly nowhere does Everett explicitly state that these other potential uncorrelated states as he calls them actually physically exist. What he does say on the matter seems to imply some form of existence of these “possible” or potential universes that reflect non-measured or non-actualized states of physical systems, but not necessarily that these unrealized outcomes actually exist in some physical universe.

In reply to a preprint of this article some correspondents have raised the question of the “transition from possible to actual,” arguing that in “reality” there is—as our experience testifies—no such splitting of observer states, so that only one branch can ever actually exist. Since this point may occur to other readers the following is offered in explanation.

The whole issue of the transition from “possible” to “actual” is taken care of in the theory in a very simple way—there is no such transition, nor is such a transition necessary for the theory to be in accord with our experience. From the viewpoint of the theory all elements of a superposition (all “branches”) are “actual,” none any more “real” than the rest. It is unnecessary to suppose that all but one are somehow destroyed, since all the separate elements of a superposition individually obey the wave equation with complete indifference to the presence or absence (“actuality” or not) of any other elements. This total lack of effect of one branch on another also implies that no observer will ever be aware of any “splitting” process.

Arguments that the world picture presented by this theory is contradicted by experience, because we are unaware of any branching process, are like the criticism of the Copernican theory that the mobility of the earth as a real physical fact is incompatible with the common sense interpretation of nature because we feel no such motion. In both cases the argument fails when it is shown that the theory itself predicts that our experience will be what it in fact is. (In the Copernican case the addition of Newtonian physics was required to be able to show that the earth’s inhabitants would be unaware of any motion of the earth.)

[5]

According to Everett’s view then, the act of measurement of a quantum system, and its associated principles of *uncertainty* and *entanglement*, is simply the reflection of this splitting off of the *observable* universe from a higher order notion of a *multiverse* where all possible outcomes and alternate histories have the potential to exist. The radical form of the Many-worlds view is that these potential, unmanifest realities *do in fact exist*, whereas Everett seems to only go so far as to imply that they “could” exist and that conceptually their existence should not be ignored.

As hard as this Many-worlds or Many-minds interpretation of Quantum Mechanics might be to wrap your head around, it does represent a somewhat elegant theoretically and mathematically sound solution to some of the criticisms and challenges raised by the broader physics community against Quantum Theory, namely the EPR paradox and the Schrodinger’s cat problem. It does also raise some significant questions however as to the validity of his underlying theory of mind and subjective experience in general, notions which Everett somewhat glosses over (albeit intentionally, he is not constructing a theory of mind nor does he ever state that he intends to in any way) by making the simple assumption that observers can be incorporated into his universal wave function view of reality by abstracting them into simple deductive reasoning and memory based machines. Nonetheless this aspect of Everett’s interpretation of Quantum Theory, his implicit and simplified theory of observation and the role of mind, remains one of the most hotly debated and widely criticized aspect of his metatheory, and one upon which arguably his entire theoretical model rests and therefore calls the validity of the metatheory itself into question in some sense.*[6]*

The question of these varying interpretations, or approaches if you will, of Quantum Theory is what does the underlying theory, given that we can almost certainly guarantee its certitude, given that its backed up by very sound empirical evidence, really say about what it is that is going on? What is it that is happening in this quantum world and how does that affect, or does it affect, how we should understand what is happening at the human scale, or at the cosmic scale even. David Bohm, the main architect of what has come to be known as *Bohmian Mechanics*, an alternative viewpoint on Quantum Theory that although not taught in standard physics courses is at least becoming more widely accepted as a theoretically possible alternative, would say definitively yes.*[7]*

The theoretical foundations for Bohmian Mechanics were laid by Louis De Broglie in 1927 when he originally proposed that Schrodinger’s wave function could be interpreted as describing the existence a central physical particle accompanied by a *pilot wave* that governed its behavior, thereby explaining why these subatomic “particles” behaved like waves and particles depending upon the experiment. David Bohm then picked up on de Broglie’s work in 1952 to expand it to encompass more complex, multi-body physical systems, an original criticism of the work which, along with a subsequently proved incorrect proof that all hidden variable theories were impossible by John von Neumann in 1932, led to the abandonment of the theory by de Broglie and the physics community for some twenty years.

Bohmian Mechanics is most fully developed in Bohm and Basil Hiley’s book entitled *The Undivided Universe* which was first published in 1993 although much of its contents and the underlying theory had been thought out and published in previous papers on the topic since the 1950s. In their book they refer to their interpretation not as the Causal Interpretation, or even as De Broglie-Bohm Theory, but as the *Ontological Interpretation *of Quantum Theory given that from their perspective its gives the only complete *causal* and *deterministic* theoretical model of Quantum Theory where it is the actual position and location of the particle within the pilot-wave that determines the statistical outcome of the experiment that is governed by the wave function.

David Bohm was an American born British physicist of the twentieth century who made a variety of contributions to theoretical physics, but who also invested much time and thought into the metaphysical implications of Quantum Mechanics, and in metaphysics and philosophy in general, a topic that most theoretical physicists have steered away from. In this respect Bohm was a bit of a rebel relative to his peers in the academic community because he extended the hard science of theoretical physics into the more abstract realm of the descriptions of reality as a whole, incorporating *first philosophy* back into the discussion in many respects, but doing so with the tool of hard mathematics, making his theories very hard, if not impossible to ignore by the physics community at large, establishing a scientific foothold for some very Eastern philosophical metaphysical assumptions, namely what he called *undivided wholeness*.

Bohm was, like Everett, was dissatisfied with the mainstream interpretations of Quantum Mechanics which basically said its just a model, try not to think about it. This led him, apparently with some prodding by Einstein with whom he had ongoing dialogue toward the end of Einstein’s life, particularly with respect to the metaphysical implications and/or the completeness of Quantum Theory, to look for an alternative approach to Quantum Theory that might actually a) prove that hidden variable theories were actually possible (something that still remained in doubt well into the 70s and 80s even decades after Bohm first published his adaptation of de Broglie’s pilot-wave theory which supported multi-bodied systems) and b) actually try and explain what the heck was going on, which was wholly absent from Bohr’s, von Neumann and Heisenberg’s interpretations of Quantum Mechanics, whose views collectively gave weight to the orthodox view that it was simply a set of equations to predict results and had certain fundamental limitations to it, that were inherent in the model itself, and there was no point trying to further describe or explain what was actually going on.

Bohm then in the early 1950s (re)discovered, and subsequently expanded upon, the pilot-wave theory put forth by de Broglie in the 1920s, developing a more robust theoretical and mathematical foundation to de Broglie’s work which had been previously lacking, specifically extending the model to support multi-body systems. He then further extended the underlying mathematics of Quantum Theory to include a fundamentally non-local force called *quantum potential* which provided the basis for non-local correlations between subatomic particles and their associated measurements.

Furthermore, in Bohmian Mechanics, which is a hidden variable theory as defined in the context of the EPR Paradox and Bell’s Theorem many respects, Bohm posits that it is the actual position and momentum of the underlying particle(s) in question that were the so called *hidden variables,* values which governed, along with the quantum potential, how a quantum wave-particle would behave, thereby not only proving that hidden variable theories were possible (non-local ones specifically which was consistent with Bell’s Theorem), but also fundamentally sidestepping the measurement problem – there was no need conceptually for the notion of wave function collapse if in fact you could have a fully deterministic model of quantum behavior, behavior mapped by the Schrodinger equation with an addition term to account for the quantum potential of a given system, mapped out both for single particle as well as many particle systems through time and space which is effectively what Bohmian Mechanics provides.

De-Broglie’s pilot-wave theory from 1927 affirms the *existence* of subatomic particles, or corpuscles as they were called back then, but viewed these particles not as independent existing entities but as integrated into an undercurrent, or wave, which was fully described by Schrodinger’s wave function and gave these subatomic particles their wave-like characteristics of diffraction and interference while at the same time explained their particle like behavior as illustrated in certain experiments. This represented a significant divergence from standard interpretations of Quantum Theory at the time. From his original 1927 paper on the topic, De Broglie describes pilot-wave theory as follows:

One will assume the existence, as distinct realities, of the material point and of the continuous wave represented by the [wave function], and one will take it as a postulate that the motion of the point is determined as a function of the phase of the wave by the equation. One then conceives the continuous wave as guiding the motion of the particle. It is a pilot wave.

[8]

De Broglie’s pilot-wave theory was dismissed by the broader academic community when it was presented at the time however due to the fact that the model as presented by de Broglie was only understood to describe only single-body systems, combined with the then very strong belief that any variant of hidden variable theories were theoretically impossible as put forth by von Neumann in 1932.*[9]* Pilot-wave theoretical research wasn’t further pursued until Bohm picked the theory back up some thirty years later, where driven primarily by the desire to illustrate that hidden variable theories were in fact possible, expanded the theory to apply it to multi-body systems, giving the theory a more solid scientific ground and providing a fully developed framework for further consideration by the broader physics community.

*Bohmian Mechanics*, as Bohm’s exposition of de Broglie’s pilot-wave theory later evolved into its more mature form, provides a mathematical framework within which subatomic reality can indeed be thought of as actually existing independent of an observer or an act of measurement, a significant departure from standard interpretations of the theory that were prevalent for most of the twentieth century (in philosophic terms it’s a fully *realist* interpretation). The theory was consistent with Bell’s Theorem as it abandoned the notion of locality (Bohm’s pilot-wave theory actually inspired Bell in his work on Bell’s Theorem in fact) and also was also fully *deterministic*, positing that once the value of these hidden variables was known, all future states, and even past states, could be calculated and known as well, consistent in this sense with classical physics.*[10]* As John Stewart Bell, a proponent of pilot-wave theory puts it:

That the guiding wave, in the general case, propagates not in ordinary three-space but in a multidimensional-configuration space is the origin of the notorious ‘nonlocality’ of quantum mechanics. It is a merit of the de Broglie-Bohm version to bring this out so explicitly that it cannot be ignored.

[11]

Bohmian Mechanics falls into the category of *hidden variable* theories. It lays out a description of quantum reality where the Schrodinger wave function, along with the notion of quantum potential, is the guiding model of subatomic behavior, the position and momentum of said particle being the so-called “hidden variable” which in turn *determine* the result of a given experiment or observable result. Bohmian Mechanics is not only explicitly non-local, but its also fundamentally *realistic* and *deterministic*, although at the same time it flies in the face of some of the basic assumptions of classical physics, not brushing these features aside as in the more standard, orthodox view of Quantum Theory, but calling attention to them directly. No wonder his work was not that well received during his lifetime.

One of the distinguishing features of Bohmian Mechanics, and one that provides the basis for his metaphysical interpretations of Quantum Theory, is his notion of *quantum potential, *a force which, unlike the classical physics notion of force where the effect is a function of intensity or magnitude, is not only fundamentally non-local in a classical physics sense, but also, along with the Schrodinger wave equation, governs the behavior of a quantum system and determines its future and past states, irrespective of whether or not the quantum system is observed or measured. It’s the glue that keeps Bohmian Mechanics together and, along with the establishment of the actual position and momentum of a given particle (or set of particles) as being fundamentally real, is the mathematical (and metaphysical) tool that he uses to explain what’s actually going on in the quantum realm.

Quantum potential in Bohm’s view is a force that is universally present not only in the quantum realm but underlying all of physics, a force that effectively becomes negligent as the quantum system becomes sufficiently large and complex and is transformed from a system that exhibits both wave and particle like behavior to a system governed by classical physics as described by Newton.

It provides us with an explanation for wave function collapse and quantum measurement uncertainty as put forth by Heisenberg, von Neumann and others by positing that the Schrodinger’s wave function does in fact fully describe quantum system behavior, that the actual position and momentum of a given quantum state does in fact exist even if it is not measured or observed, and that there exists some element of non-local *active information *within the environment which explains the observable and experimentally verifiable existence of the correlation of classically separated (quantum) entities.. In other words, in Bohmian Mechanics, the quantum system not only has some definitive initial state, but it also *knows* about its environment to a certain extent, information that is embedded in the underlying quantum potential of a given system and can be mathematically modeled by adding the notion of quantum potential to Quantum Theory.

According to Bohm, one of the motivations for exploring the possibility of a fully deterministic/causal extension of Quantum Theory was not necessarily because he believed it to be the *right* interpretation, the correct one, but to show the *possibility* of such theories, the existence of which was cast into serious doubt after the development of von Neumann’s mathematical work in the 1930s, and even after Bell’s continuation of these theoretical constraints on Quantum Theory, which did in fact allow for non-local hidden variable theories, in the 1960s.

… it should be kept in mind that before this proposal was made there had existed the widespread impression that no conceptions of hidden variables at all, not even if they were abstract, and hypothetical, could possibly be consistent with the quantum theory.

[12]

Bohmian mechanics is consistent with Bell’s Theorem, which rules out hidden variables *only* in theories which assume *local realism*, i.e. that all objects or things are governed by and behave according to the principles of classical physics which are bound by the constraints of Relativity and the fixed speed of light, principles which have been demonstrated to be wholly inconsistent with Quantum Mechanics, causing of course much consternation in the physics community and calling into question classical realism in general.*[13]*

Bohmian Mechanics agrees with all of the mathematical predictions of standard interpretations of Quantum Theory, i.e. its mathematically equivalent, but extends the theoretical model to try and explain what is actually going on, what is driving the non-local behavior of these subatomic “things” and what in fact can be said to be “known” about the state of quantum systems independent of the act of measurement or observation. With this notion of *quantum potential, *Bohm provides a mathematical as well as metaphysical principle which “guides” subatomic particle(s), gives them some sense of environmental *awareness*, and is inherently nonlocal (in the classical sense).

With respect to the importance of Bohm’s work in Quantum Mechanics, Bell himself, albeit some 30 years after Bohm originally published his extension of de Broglie’s pilot-wave theory, had this to say:

But in 1952 I saw the impossible done. It was in papers by David Bohm. Bohm showed explicitly how parameters could indeed be introduced, into nonrelativistic wave mechanics, with the help of which the indeterministic description could be transformed into a deterministic one. More importantly, in my opinion, the subjectivity of the orthodox version, the necessary reference to the ‘observer,’ could be eliminated. …

But why then had Born not told me of this ‘pilot wave’? If only to point out what was wrong with it? Why did von Neumann not consider it? More extraordinarily, why did people go on producing ‘‘impossibility’’ proofs, after 1952, and as recently as 1978? … 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?

[14]

Bohmian Mechanics contribution to Quantum Mechanics, and physics as a whole in fact, is not only that it calls into question the presumption of local realism specifically, what Einstein referred to as “spooky action at a distance”,* *but also in that it proved unequivocally that hidden variable theories are in fact theoretically and mathematically possible and still consistent with the basic tenets of Quantum Mechanics. Bohm in fact “completes” Quantum Mechanics in the true sense that EPR (EPR Paradox) initially called into question.

What Bohmian Mechanics calls our attention to quite directly, and in a very uncomfortable way from a classical physics perspective, is that there are metaphysical assumptions about reality in general that are fully baked into classical physics that must be relaxed in order to understand, and in fact explain, Quantum Mechanics. Furthermore, it was these same subatomic particles (and/or waves) whose behavior which was modeled so successfully with Quantum Mechanics, that in some shape or form constituted the basic building blocks of the entire “classically” physical world. This fact could not be denied. And yet the laws and theorems that have been developed to describe this behavior, i.e. classical physics, were and still are fundamentally incompatible with the laws that govern the subatomic realm, specifically the underlying assumptions about what is “real” and how these objects of reality behave and are related to each other.*[15]*

While the standard interpretation of Quantum Theory holds that the model is simply a calculation tool and is bound by certain metaphysical constraints that are inherent to the theoretical model itself, Bohmian Mechanics and Everett’s Relative State formulation of Quantum Theory (and by association the various Many-World Interpretations that stemmed from it by DeWitt, Deutsch and others) intend to try and explain what is really going on in a manner that’s at least consistent with the underlying mathematics of Quantum Theory, albeit drawing very different conclusions about the nature of the reality that is being described. In order to do this, some adventure into metaphysics, Aristotle’s first philosophy, is required.

Although the orthodox interpretation of Quantum Theory would have us believe that we can draw no metaphysical conclusions based upon what quantum mechanics tells us, that it is simply a tool for deriving values or observables from experimental results, Bohmian Mechanics, along with Everett’s Relative State formulation, tell us that there do exist, can exist, alternative theoretical models of quantum behavior which give at least an explanation of what “might” be going on, despite requiring an altogether different perspective on what we think of as “real”, and/or the nature of existence itself, requiring us to reconsider the underlying assumptions that sit at the very foundation of classical physics.

One can put it quite succinctly by observing that no matter what interpretation of Quantum Theory you find most attractive, at the very least the classical notion of *local realism *must be abandoned in order to make sense of what is going on. One would be hard pressed to find someone with a good understanding of Quantum Theory who would dispute this.

*[1]* Niels Bohr (1949),”Discussions with Einstein on Epistemological Problems in Atomic Physics”. In P. Schilpp. Albert Einstein: Philosopher-Scientist. Open Court.

*[2]* From the Introduction of Everett’s thesis in 1957 *“Relative State” Formulation of Quantum Mechanics*.

*[3]* Hugh Everett, III. *Theory of the Universal Wave Function*, 1957. Pg 53.

*[4]* Deutsch actually posits that proof of the “existence” of these other multi-verses is given by the wave interference pattern displayed in even the single split version of the classic double slit experiment as well as the some of the running time algorithm enhancements driven by quantum computing, namely Shor’s algorithm which finds the polynomial factors of a given number which runs an order of magnitude faster on quantum computers than it does on classical, 1 or 0 but based machines. This claim is controversial to say the least, or at least remains an open point of contention among the broader physics community. See http://daviddeutsch.physics.ox.ac.uk/Articles/Frontiers.html for a summary of his views on the matter.

*[5]* Everett’s thesis in 1957 *“Relative State” Formulation of Quantum Mechanics*, Note on Page 15, presumably in response to criticisms he received upon publishing the draft of his thesis to various distinguished members of the physics community, one of who was Niels Bohr.

*[6]* See Bohm and Hiley’s Chapter on Many-Worlds in their 1993 book entitled *The Undivided Universe: An Ontological Interpretation of Quantum Theory *for a good overview of the strengths and weaknesses mathematical and otherwise of Everett and DeWitt’s different perspectives on the Many-Worlds interpretation of Quantum Theory.

*[7]* Bohmian Mechanics is also sometimes referred to as *De Broglie-Bohm Theory* or the *Causal Interpretation* of Quantum Theory. Its authors however prefer *Ontological Interpretation*.

*[8]* Louis De Broglie `Wave mechanics and the atomic structure of matter and of radiation’, Le Journal de Physique et le Radium, 8, 225 (1927)

*[9]* John von Neumann was instrumental in not only laying the mathematical foundations of Quantum Mechanics but also establishing the mathematical boundaries within which interpretations of the theory could be made, which included as it turned out a fairly comprehensive proof that ruled out (certain) classes of hidden variable theories to explain the underlying mathematics, a line of research that was followed by Bell which of course led to an expansion of the theoretical limitations of hidden variable theories, i.e. Bell’s Theorem, which depending on which source you read proved von Neumann’s assumptions to be false, or at best misleading. Von Neumann also interestingly enough posited the idea of consciousness as an explanation for wave function collapse, a notion that of course was not addressed or picked up by the broader physics community given its philosophical implications.

*[10]* These features are why it is sometimes referred to as the *Causal Interpretation *due to the fact that that it outlined a fully causal description of the universe and its contents.

*[11]* From Stanford Encyclopedia entry on Bohmian Mechanics by Sheldon Goldstein, quote from Bell, *Speakable and Unspeakable in Quantum Mechanics*, Cambridge: Cambridge University Press; 1987, p. 115.

*[12]* David Bohm, Wholeness and the Implicate Order, London: Routledge 1980 pg. 81.

*[13]* In fact, it was Bohm’s extension of De Broglie’s work on pilot-wave theory that provided at least to some degree the motivation for Bell to come up with his theorem to begin with; see Bell’s paper entitled *On the Einstein Podolsky Rosen Paradox* in 1964, published some 12 years after Bohm published his adaption of De Broglie’s pilot-wave theory.

*[14]* From Stanford Encyclopedia entry on *Bohmian Mechanics*, 2001 by Sheldon Goldstein; taken from Bell 1987, “Speakable and Unspeakable in Quantum Mechanics”, Cambridge University Press.

*[15]* There has been significant progress in the last decade or two in reconciling quantum theory and classical mechanics, most notably with respect to Newtonian trajectory behavior, what is described in the literature as accounting for the classical limit. For a good review of the topic see the article *The Emergence of Classical Dynamics in a Quantum World* by Tanmoy Bhattacharya, Salman Habib, and Kurt Jacobs published in Las Alamos Science in 2002.

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