Quantum Mechanics

Introduction | Quantum Mechanics | Whitehead and Bell's Inequality | Whitehead and the Copenhagen Interpretation
Conclusion | Footnotes | Bibliography

Although quantum mechanics burst onto the scientific scene in the mid 1920's, the theory was not considered 'complete' until after World War II, 2 and Whitehead had at his disposal only information about quantum mechanics in its infancy. Yet it is the highly metaphysical consequences of modern quantum mechanics that Whitehead would most readily engage with today, were he here. This paper explores what would happen if Whitehead were to appear today and find out that his metaphysical theory was quite 'out of date', and in need of rethinking. This is no small task by any means, and thus I will focus mainly on the consequences of the crucial experiment performed recently by A. Aspect which violates the Bell Inequality before considering a few features of the 'standard' interpretation of quantum mechanics and the ways in which Whitehead might be able to deal with them. I hope to bring to light some aspects of the symbiotic nature of the relationship between physics and metaphysics by examining quantum mechanics in the context of Whitehead's metaphysical scheme--an approach that at least provides an interesting way in which to scrutinize the problems of quantum mechanics, even if it is sure that Whitehead will not be able to solve any of the problems (the reasons for this shall become apparent). In order to make it slightly less taxing to the reader unfamiliar with quantum mechanics, some explanatory background material is provided, but by no means do I present a complete introduction, as a sufficient literature exists for this particular purpose. However, I do assume that the reader has at least a basic understanding of Whitehead's metaphysical scheme.

Background to Bell's Theorem

In 1935, Einstein, Podolsky, and Rosen published a paper in the Physical Review which questioned the completeness of quantum mechanics. It seems that if one accepts that there can be no action-at-a-distance (i.e. no signal or information that can travel faster than light), and that properties of any physical system exist independently of our choice to observe them (both of which are plausible assumptions), then quantum mechanics is actually incomplete--it does not make predictions that are in accord with our observation of physical facts. Einstein, Podolsky, and Rosen (EPR) formulated a clever thought experiment3 which showed that quantum mechanics would predict results which could not be explained if the assumptions of locality (no action-at-a-distance) and reality (the definiteness of properties of a quantum object regardless of experimental apparatus or individual measurements of such properties) were accepted.

A reply to this claim of incompleteness was quickly offered by Neils Bohr, the prime defender of quantum mechanics at the time. Most physicists accepted Bohr's refutation of the EPR argument (the specifics of which are not important here), but debate continued. However, what debate that did exist remained entirely theoretical, and as a result of the general acceptance of Bohr's ideas along with this inability to form physical experiments that could test the theories, the issue was placed on the back burner--until further notice.

Further notice came in 1965, when John Bell provided the possibility for experimentally testing the arguments of the EPR thought experiment. Bell determined a limit for certain kinds of empirical predictions made by any theory that accepts the assumptions 'locality' and 'reality', and from this formulated an inequality4 that he subsequently showed all 'locally real' theories are absolutely required to obey. In particular, and for the purposes of this paper, this means that in certain experiments where measurements of a property of a quantum system (like spin or polarization) are correlated with each other, all locally real theories must predict correlations that fall within certain well defined limits--an upper limit of possible correlation between empirical measurements of properties of a quantum system is established. Since I deal with the idea of locally real theories throughout this paper, allow me to briefly summarize their major characteristics. First, such theories assume that physical phenomenon are produced by interactions between physical entities which have definite properties at all times, and which are independent of our knowledge of them. Thus, when the tree falls in the forest and there is no one around to hear, it does make a sound. Second, such theories assume that there is always some sort of definite physical property that can account for any observed phenomenon. This results in the assumption that a complete state-description of a system consists in the accurate specification of the physical properties that make up the system (what is physically the case). Lastly, it is assumed that there is no possibility for faster than light signaling, a principle central to relativity theory. Although such locally real theories do not necessarily require a deterministic universe, the derivation of such a universe is quite natural given these basic assumptions.

Quantum mechanics, however, does not satisfy Bell's Inequality5; it predicts correlations that cross the boundaries delineated by the structure of the inequality. It has long been known that quantum mechanics predicts 'strange' correlations that seem to defy a common, classical6 conception of reality, and in fact it is for basically this type of reason that Einstein, Podolsky, and Rosen argued in 1935 that it was incomplete. The formulation of Bell's Inequality, however, allowed the possibility for determining, experimentally, who was right: quantum mechanics or a locally real theory of the sort Einstein postulated, because it stated what must be the case in our experiments if a locally real theory is correct.

It is important to note that Bell's Theorem does not in any way depend upon quantum mechanics itself, but instead arises from a set of logical premises independent of any physical theory. This is crucial because in effect it allowed Bell to set up a situation in which the entire class of 'locally real' theories could be tested, without having to consider each 'locally real' theory individually. This type of phenomenon has been accurately dubbed 'experimental metaphysics' and is significant in that a set of metaphysical assumptions can be adequately tested through experiments that fall entirely in the realm of physics.

Aspect's Experiment

The experiment that is generally regarded as the most successful test of Bell's Inequality was conducted by A. Aspect, J. Dalibard, and G. Roger in 1982. In the experiment an 'excited' atom decays and emits two photons in opposite directions. Detectors placed on opposite sides of the room then record the polarization of the photons. There are two detectors on each side, one of which detects for polarization in one direction (say +45 degrees from horizontal), and another which detects for polarization in another direction (say -45 degrees from horizontal). The photon is directed to either of the two detectors by a switch through which the photon must pass. The experimenters can change at random how the switch is set, and therefore to which detector a photon will go, and therefore what type of measurement will be made in a particular run of the experiment (+45 or -45 polarization).

Interestingly, however, the setting of the switch, and thus the subsequent path of the photons, can be left until just before the photon arrives at the switch, long after the photons have been emitted. This feature is extremely significant, because it is impossible for a signal, even a signal traveling at the speed of light, to travel from one side of the experiment to the other (conceivably in order to 'tell' the other photon how the switch was set across the room) before the switch could be changed.

Einstein, Podolsky, and Rosen argued that quantum mechanics requires that a property, like polarization of the photon (P1) in a certain direction, could be measured at a distance by measuring the polarization of another photon (P2) that had previously interacted with it--that is, quantum mechanics predicts that there will be a certain level of correlation between the measurements of the polarization of the two photons. They argued that since it is impossible for the measurement of P2 to actually interfere with P1 (no action-at-a-distance), it follows that P1 must have had its particular polarization before the measurement of P2 was taken, and that our measurement is merely conforming with the independent and enduring reality of the actual polarization of P1.

This idea is strengthened by the fact that because the particular direction of polarization being measured can be changed by the experimenter after the photons are long separated (we can switch the setup of our apparatus just before the photon arrives and instead measure for polarization in a different direction), it must be the case that all properties must be 'real' before they are measured, for otherwise the measurement itself (and by implication the experimenter's choice of what property to measure) must have some impact on the determination of the property of a quantum system.7

Aspect's experiment is important in the sense that it does much more than just resolve a technical point between two contending theories; it forces us to reconsider our conception of the structure of the universe and the nature of reality--it leads us into metaphysics. Before the advent of quantum mechanics, most scientists believed that objects had an independent existence, that things (tables, chairs, your mother-in-law) existed 'out there' whether or not anyone observed them. It was also thought that each object enjoyed a complete set of attributes, such as position, momentum, energy, and spin both before and after our observation of it. According to this conception, atoms and electrons (little things) would differ from bowling balls and watermelons (big things) only in scale and not in kind.

When Aspect's experiment was performed, the results were clear: Bell's Inequality was violated--the correlations exceeded the limits set by the inequality. Physicists expected this result, for otherwise the most successful theory in scientific history would be wrong! However, even though it was known that quantum mechanics disagreed with the common sense, Newtonian view of reality, Aspect's experiment has definitely and completely confirmed this in a repeatable experimental situation--to the best of our knowledge quantum mechanics remains a perfectly good theory, just as it is.

The problem is that quantum mechanics doesn't provide its own interpretation. As a theory, quantum mechanics is essentially a number crunching exercise: plug a few numbers into some equations and other numbers result, and it just so happens that the resulting numbers always seem to fit with actual observations of the world. Various theories try to explain what is 'actually happening' in the universe such that these particular numbers, and not other numbers result, but they do not originate in quantum mechanical theory itself, but instead exist in the form of supplementary, essentially ad hoc explanations.

Today, much of the debate about quantum mechanics is not about quantum mechanical theory as much as it is about the theory of quantum mechanics, or rather, the philosophy of quantum mechanics: what must be the case metaphysically assuming quantum mechanics is "correct". There exist many different "interpretations" of quantum theory, which provide explanations of one sort or another for observed phenomenon. Unfortunately, all these metaphysical theories are in perfect agreement with the predictions of quantum mechanics--each theory gives the same observed results! Their differences lie in the way in which they answer the question: "What must be the case metaphysically in order to satisfactorily account for observed phenomenon?". Note that the question is not "What must be the case metaphysically in order to account for observed phenomenon?". The key lies in the word "satisfactorily"--if physicists were only concerned about the probability of predicting any particular quantum event, then all questioning ceases, as this is exactly what quantum mechanics does best;8 but if physicists question why it is that our universe seems to be one in which quantum mechanics is a good theory, suddenly metaphysics enters the scene, center stage. Most contemporary debate concerning quantum theory tends to focus on the relative advantages and disadvantages of competing interpretations.9 However, since they are all equal in the realm of prediction, it is impossible to determine which theory is "right". Aspect's experiment is one (rare!) instance in which definitive metaphysical consequences arise from an entirely physical experiment.

Consequences of Aspect's Experiment and the Violation of Bell's Inequality

The most immediate and important consequence of the violation of Bell's Inequality is the seemingly final rejection of all locally real theories. Even though it was known that quantum mechanics was basically incompatible with a locally real view of reality since the 1920's, the major evidence for this rested only in the awesome predictive power of quantum mechanics--the fact that it just seemed to work. The locally real Newtonian view, dominant among scientists10 in the pre-quantum mechanical era, although discredited, was not actually disproved, and many scientists (Einstein among them) tried desperately to find a way to save what their common sense intuition knew to be true about reality.

The rejection of locally real theories means that at least one of the assumptions of the Bell Inequality must be false. As discussed above, Bell's initial assumptions were 'reality' and 'locality', but later it was shown by J. Jarrett that the assumption of 'locality' is really a combination of two other assumptions. He called these premises 'locality' and 'completeness', but I shall adopt Shimony's terminology and use 'parameter independence' and 'outcome independence' instead, so as not to confuse Bell's assumption of locality with Jarrett's slightly different version. Parameter independence states that the probability of an outcome of an observation on one particle is independent of the parameter chosen for the analyzer of the other particle. In terms of the Aspect experiment, this merely means that the particular direction of polarization that we set up the apparatus to detect on one side of the room can in no way effect the actual outcome of the measurement of the polarization of the photon on the other side of the room. Outcome independence states that the probability of an outcome of an observation on one particle is independent of the outcome of the observation of the other particle. Which is to say in our example that the fact of detecting the polarization of one photon to be +45 on one side of the room can in no way influence the actual outcome of the measurement of the photon on the other side of the room.

We now have a few options: we can get rid of any one of these three assumptions11, or any two, or perhaps even all three. No matter which assumption we throw out, however, our view of reality must change significantly. If we abolish parameter independence, then it seems that the mere fact of the experimenter's choice to detect for polarization in a certain direction on one side of the room will effect the actual outcome of the measurement occurring on the other side of the room. This fact is too bizarre for all but a few physicists to accept--most feel that parameter independence seems to be an important feature of reality.

Getting rid of the reality assumption flies in the face of all common sense, for the answer to the 'tree question' would then be that no, when a tree falls in the forest and there's no one around to hear it, it doesn't make a sound. This question, however, brings up an important point, the elucidation of which has allowed the majority of physicists today to accept that reality is not a necessary assumption.

In the tree example, the objects (the tree, the forest, even the vibrations of the air caused by the falling tree) are all 'macroscopic'. That is, it seems to be a definite feature of reality that objects of sufficient size can be treated classically (with standard, locally real Newtonian mechanics), and that quantum mechanical effects on such objects are statistically negligible and can be ignored. Apparently the strange properties predicted by quantum mechanics only take noticeable effect when the systems considered are small enough. Thus, both locality and reality can be said to exist simultaneously for non-quantum systems in a perfectly ordinary way that corresponds to our common sense intuition. The problem is that on a quantum level, these effects still do exist even in large objects. Therefore, it can be said of the Moon, for example, that it can be treated as actually existing when we are not looking, even though its quantum constituents cannot individually be said to exist (in the full sense of the term)! How could an actually existing object like the Moon be built up out of objects in a quantum realm that have no reality apart from our observation of them? Yet this is one consequence of rejecting the reality assumption, and thus is one of the major issues which physicists are trying to come to grips with today.

Our last choice is to discard outcome independence. It is generally agreed among physicists that this is the best candidate for rejection, but getting rid of this assumption has its own problems. To reject outcome independence means that even though the configuration of the distant apparatus cannot affect the outcome of a measurement here, there still exists a strange type of correlation between the results that physicists are hard pressed to explain. It seems that somehow the actual outcome of the measurement here can effect the outcome of the measurement across the room.

Interestingly, the most commonly accepted view of quantum mechanics (called the Copenhagen interpretation after the city in which its inventor, Neils Bohr, worked) rejects both outcome independence and reality. For Bohr, the only way to obtain information about a quantum system is to measure it, but the act of measurement always has some sort of effect on the system being measured. It is therefore pointless to think of an isolated quantum system as having definite properties, because we can never know what these properties are without measurement. But since the act of measurement turns the system into a non-isolated one that includes the measuring devices themselves, it seems that we must determine that definite physical properties are possessed only by the combination of the system plus the measuring apparatus. Until we have measured some property of a quantum object, it is meaningless to even talk about the independent exi