Carsten Agger and Niels K. Petersen | THE TORCH

Observational Dependence and the Construction of Theories (on Modern Physics)

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Quantum physics has revolutionized the traditional conceptions of the relationship between the observer and the observed. The present article attempts to present the meaning and context of this revolution, as well as an analysis and refutation of some of the most common arguments against the so-called Copenhagen interpretations and its implications for our conception of reality.

PHYSICAL THEORY
The science of physics endeavours to explore the connections and interactions between the components of the world. In principle, its subject matter thus becomes the world and Nature as such, but in practice, physics is primarily concerned with non-living Nature, the movements in time and space of bodies and particles, and their interactions. Physics is therefore also concerned with the most fundamental issues regarding the nature and structure of matter, time and space.

Physics is a quantitative science in the sense that any prediction in a physical theory concerns the quantitative result of a specific measurement. Wherever possible, a successful physical theory is required not only to explain well-known empirical data, but must also predict the outcomes of future experiments or uncover hitherto unknown connections between physical phenomena.

In classical physics, space and time are absolute concepts in the sense that the description of a physical system is an account of the state of the system at any point in space and time. Thus the world described is formally assumed to exist in itself, as a reality independent of the observation, i.e. an objective reality.

This, however, does not mean that classical physics as such is based on nor leads to an epistemological realism. Most theories of classical physics are based on unscrupulously unrealistic simplifications, because the theories do not seek to establish a realistic picture of the physical phenomena as such, but rather supply a useful tool for handling the phenomena. The point is that if more realistic theories were constructed, the physicist would only gain a more complicated model, that might yield slightly better agreement with experiment, but there would still be no way of saying that the theory corresponded more closely with the world as it might be in itself. Objectivity is simply one of the rules for formulating theories in classical physics, and even though an epistemological realism seems to be assumed, in practice it is not.

EINSTEIN’S RELATIVITY & HEISENBERG’S INDETERMINACY
With the advent of Einstein’s theories of relativity, space and time could no longer be considered absolute. In fact, the definition of space and time in these theories can only be related to their observation from specific frames of reference. The theories of relativity therefore require that the description of a physical system must include a specification of a point of reference from which the system is to be observed. The physical system however is still assumed to exist independently of observation.

This is not the case in quantum theory, which is the theory used to describe miscroscopic systems. An important consequence of this theory are the Heisenberg’s relations of indeterminacy, which state that it is not possible to measure certain pairs of physical quantities with arbitrary precision. This indeterminacy has to do with the action of the experimental apparatus on the observed system, and implies that the observed phenomena not only depend on the type of system one chooses to observe but also on the specific experimental setup.

In order to illustrate what is meant by the statement that the observed phenomenon depends upon the chosen experimental setup we will consider the simplest possible mechanical system: a single partivle in movement.

Such a particle may in classical physics be adequately described by indicating its position and velocity at all times - it is normally more convenient, however, to describe its movement in terms of momentum, which is the produkt of the velocity and the particle’s mass. The importance of the momentum stems from the so-called law of conservation of momentum - the total momentum of a given, isolated system before and after some reaction occurs will always be the same. No violation of this rule has ever been observed.

For this system, Heisenberg’s indeterminacy relation states that the product of the uncertainty with which the particle’s momentum p and position x are known at least equals the half of Planck’s constant h divided by 2p:

Delta x Delta p >= h/2p

[Sorry about the typographical shortcoming -Eds ]
Planck’s constant is very small, and therefore no quantum uncertainty is usually observed in the macroscopic world of our daily life. We observe, however, that the relation limits the precision with which the two quantities can be known simultaneously. In principle we could make an infinitely accurate measurement of the particle’sm position, but then we would have to renounce from making any predictions regarding its movement. Such physical variables which cannot be defined simultaneously are often called complementary.

INTERACTION WITH THE EXPERIMENTAL APPARATUS
In the mathematical formalism of quantum mechanics, a system is described by its wave function. This wave function may be considered a probability density, because the square of it in a specific point in space represents the probability of finding the particle at this point in a specific measurement. The exact location of the particle or the exact outcome of the measurement are not given by the theory, as it only allows a calculation of probabilities. In fact, before the measurement has been carried out, the statement that the particle has a position cannot be attributed any meaning.

This can be realized without discussion of the mathematical formalism, by studying a Gedankenexperiment which analyses the consequences of the indeterminacy relation for the measurement of the complementary variables position and momentum. In this experiment, a particle is shot through a narrow slit in a diaphragm.

After the collision, the uncertainty on the position of the particle must be determined by the width of the slit and by the uncertainty on the position of the diaphragm. We assume that the momentum of the particle before the collision is well-defined (and known to us), and that the slit is very narrow, so that a measurement of the diaphragm’s position would give us an exact determination of the position of the particle. On the other hand: if we can measure the momentum of the diaphragm after the collision, we could use this knowledge and the already mentioned law of conservation of momentumto get an exact determination of the particle’s momentum. But how does the measurement of one of these quantities influence our possibilities of predicting the value of the other? In order to measure the position of the particle, the diaphragm is fastened to the foundation (which serves to define our system of reference, the laboratory system) in a certain heght, so that it is stationary. The interaction between the particle and the diaphragm leads to an absorption of an uncontrollable amount of momentum in the foundation from which we observe the particle. This naturally introduces an uncertainty in the momentum of the particle after collision, and it is therefore impossible to predict the momentum.

If on the other hand the momentum is to be determined, the diaphragm can be placed on a spring, so that it can move freely. To establish the momentum after the collision, the momentum of the diaphragm has be to determined in order to use the principle of conservation of momentum. According to the indeterminacy relation an uncertainty in the diaphragm’s position is therefore introduced, and it is no longer possible to predict the position of the particle.

In both cases, the determination of one quantity precludes the simultaneous determination of the other - if, for instance, we should wish also to know the momentum of the particle after having determined its position, this measurement would demand yet an interaction with our experimental apparatus which would destroy the position. No meaning can therefore be ascribed to the statement that the particle has a specific position and a specific momentum at the same time.

Another experimental setup, this diaphragm is used to determine the intitial conditions in a so-called double slit experiment. In this setup, a diaphragm with two slits is placed behind our »movable«diaphragm; the particle may then pass through the hole in the first diaphragm, subsequently pass through one of the two slits in the second diaphragm, and subsequently be registered on a photographic plate behind the second diaphragm.

If the diaphragm is allowed to move freely, the direction in which the particle moves after the collision can be determined by measuring the momentum of the diaphragm. When the direction is known, it can be determined which slit the particle passed through. This is a so-called welcher Weg experiment.

If the diaphragm is stationary, the momentum cannot be estimated (but its initial position is well-known), and therefore the direction in which the particle moves after the collision cannot be determined. It therefore has no meaning to say that the particle passed through either slit. Instead its wave function propagates through both slits, and if the experiment is carried out many times an interference pattern will appear on the wall. So if the initial position of the particle is known, the particle behaves like a wave phenomenon, and therefore in a sense passes through both slits and neither. On the other hand: if the initial momentum is known, it behaves as a particle and passes through only one of the two slits.

It should be noticed, howevere, that in the case where the first diaphragm is movable, we still have a choice, after the particle has passed through it, whether we want its position or its momentum to be well-defined. If we wish to determine its momentum, we may measure the momentum of the diaphragm after the collision, as discussed above. We might also, however, measure the position of the diaphragm immediately after the collision and thus get an exact determination of the particle’s initial position (but not, of course, of its momentum).

The choice between a stationary and a movable diaphragm thus can be made after the experiment has been carried out, i.e. when the experiment is all over, we can choose whether the particle passed through one or both slits. So if one insists on describing the phenomenon as something whixh exists independently of our experimental setup, one must accept that the effect comes before the cause. This however is no causal effect backwards in time, but follows from the fact that the phenomenon studied can not be said to exist independently of the measurement, as it is only defined by a specification of the whole experimental setup.

THE STANDARD INTERPRETATION
This standard interpretation of quantum mechanics was primarily formulated by Niels Bohr and his associates, and was coined the Copenhagen school by Werner Heisenberg. This is the most dominant of all interpretations of quantum mechanics, and most of its advocates consider it the only one.

The reproducible experimental situation is the fundament of physics as an empirical science, and physics therefore requires an unambiguous descriptive language in which experiments and their results can be communicated from one physicist to another. This language, according to Bohr, is our common language and its refinements, mathematics and classical physics.

The descriptive property implies a dualistic division between subject and object, whereas the unambiguity of the language implies the interchangeability of subjects. Furthermore the objects of the language are localised in time and space, and a determinism is implied.

As physics must be communicated in this common language, the phenomena of quantum physics can only be attributed any meaning within its conceptual frame. Furthermore, observations of quantum phenomena will always occur in experimental situations, where the apparatus leading to the final measurement can be described by classical physics alone.

If however one should wish to talk of phenomena not defined within the conceptual frame, the concepts must necessarily be used in a wrong way. The description therefore becomes paradoxical. An example of this paradoxical use of language is when people talk of a quantum phenomenon being both a particle and a wave while at the same time it is neither. Therefore it has no meaning to talk of what way the photon went in a double slit experiment, unless of course the experiment is a welcher Weg experiment designed to establish through which slit it went.

Several recent welcher Weg experiments have been carried out in cases where the Heisenberg uncertainty relation does not forbid the welcher Weg detection [1]. In some of these, slight modifications to the experimental setup can change the experimental result from an ordinary double slit situation to a welcher Weg measurement (termed quantum marker), and then back to the double slit situation (quantum eraser). In one particularly interesting experiment the choice between the setup being a quantum marker and an eraser type experiment was chosen at some time after the initiation of the experiment [2]. The idea behind this delayed choice experiment is to seek experimental evidence of a realistic interpretation of what happens ‘inside the experiment’. The results however fully follow standard quantum mechanic complementarity, and therefore can only be realistically interpreted by using a paradoxical use of language, in which the effect comes before the cause, i.e. causality breaks down.

This of course means that it is not possible to visualize quantum phenomena in the way known from classical physics. The physicist however still has to draw small waves or particles on the blackboard when reviewing an experimental situation, simply because we are “suspended in language”, as Bohr expressed it [3]. Even a paradoxical use of language can be helpful when considering an experimental situation, which strictly speaking can only be analysed through the mathematical formalism of quantum mechanics.

It is still however meaningful for a physicist to talk about where classical objects, like e.g. a planet, is at a given point in space and time, even though no one observes it, simply because this is a legal way of using our common language. Bohr’s semantic analysis therefore essentially is a specification of what physics is: “It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.” [4] This however does not imply that “nature” has an ontologically realistic status, as nature as such has no more ontological status than any other concept in our common language.

To Bohr the question of choosing between idealism and realism was meaningless, because either position is an attempt to talk of something beyond our common language. In fact, man is unable to ‘step outside’ the conceptual frame in order to communicate with other people about the world. In the sense that an observer is defined, he is part of the world.

Bohr’s view therefore concerns concepts in no other sense than the one given by the conceptual frame. From this point of view it is absurd to attribute to the dualism implicit in the conceptual frame any other meaning than that implied by the conceptual frame. This is also the case for classical phenomena. Even though it is meaningful to consider them as independent of observation within the context of common language, their definition is still inextricably connected to an observational situation.

THE CRITIQUE OF THE STANDARD INTERPRETATION
Quantum mechanics has been so tremendously succesful that we have no reason to consider it as erroneous. Potential opponents to the standard interpretation therefore must either show that quantum mechanics is not a complete theory, i.e. that there are quantum phenomena not described by the theory, or they must construct a new theory. There are as yet no empiricial results that allow us to suspect that quantum physics is not complete. Many attempts however have been made to formulate alternative theories, but none has convincingly surpassed the standard theory.

Characteristic of these attempts are that they try to ascribe ontological reality to either the quantum phenomena or to the mathematical formalism. Thus it has been tried to use so-called hidden variables, i.e. purely speculative physical quantities, that might allow for a realistic theory, which would yield a non-paradoxical description of the phenomena disjoined from the experimental observation. Most of these theories have been proven wrong or simply redundant.

In classical physics the mathematical formalism usually can be interpreted in a physical way. According to the standard interpretation the formalism of quantum mechanics is just an algorithm whose results alone can be interpreted as relating to physical phenomena. By definition the wave function cannot be observed. The statistical distribution of possible measurements of a specific physical quantity however are given by the square of the wave function.

In the measurement one possible outcome of the experiment becomes an actuality, a selection which is referred to as the collapse of the wave function. This ‘collapse’ however is not a physical phenomenon, though attempts have been made to consider it as such, but simply a formal way of saying that a measurement has taken place.

In order to get around this ‘measurement problem’ the so-called many worlds interpretation redefines the collapse as a branching of the universe into separate parallel universes [5]. Thus there exist universes in which each possible outcome of a measurement are observed. The ‘real’ phenomenon of this interpretation therefore is the wave function of the universe, whereas the observer and the measurement itself are only parts of the systems described by the wave function.

The many worlds view therefore postulates the paradoxical and unprovable existence of a multitude of necessarily disjoint parallel universes. From an epistemological point of view the theory therefore is highly metaphysical.

A specific kind of realism called local realism originating in a famous paper by Einstein, Podolsky and Rosen in 1935 has been of particular importance [6]. This is a realism that explicitly states the usual physical assumption of locality, i.e. that it is possible to make a measurement on one of two non-interacting systems without affecting the other. In 1964 J. S. Bell found a mathematical relation, Bell’s inequality, which in principle allows for a simple test of local realism versus quantum mechanics [7]. An experimental test was carried out in the early eighties by Alain Aspect and his associates [8], and it is fair to say, that there is a broad acceptance of the view that the local realism hereby was empirically refuted.

Many people then prefer to replace local realism by a non-local realism by saying that quantum phenomena are non-local. However even after excluding the most hypotetical theories, non-local realism remains a peculiar epistemological point of view, which hardly satisfies what Einstein, Podolsky and Rosen termed “a reasonable definition of reality.”

DEPENDENCE ON OBSERVATION
In any case one is inclined to ask what this realism is intended to be used for? What is the necessity of demanding such a bookkeeping by double entry that requires a one-to-one correspondence between the empirical data and an abstract world? As W. H. Zurek writes: ”The only ‘failure’ of quantum theory is its inability to provide a natural framework that can accomodate our prejudices about the workings of the universe.” [9] Are not these prejudices the main reason for upholding some kind of realism? Even if one is required to drop one of the basic assumptions of physics, namely locality? If furthermore realism is not required, why insist on it as an assumption?

Naturally there are unanswered questions. Is quantum mechanics complete? Will future empirical results change our understanding of the relation between observer and observed? There is of course no guarantee that we will not be forced to change our present conception, but as of the moment we have no reason to question the completeness of quantum mechanics, and it is indeed hard for us to see how further empirical results should challenge the purely semantic and conceptual analysis of the standard interpretation.

It must therefore be considered a purely metaphysical opinion to view physics as an exploration of a world distinct from the conceptual framework of our common language. When doing physics the physicist is required to work within this framework, obeying its internal laws and logic. What lies beyond this is either metaphysics or paradoxical statements required to help discussing experimental situations in quantum physics.

All experimentally plausible alternatives require a kind of non-local causal interaction and thereby assume either the possibility of propagation with speeds exceeding that of light or of time reversal. Such assumptions have no empirical basis and clearly depart from the most basic assumptions of ordinary physics, including quantum mechanics.

Such theories therefore are far removed from the naive realism that usually is the ideal of their makers. The realistic physicist would even have to admit that his theory is not an ultimate model of the world as it ‘really’ is, but simply yet another idealization, another model that will not have proved its worth until it has improved on the present theory, either by predicting new results and connections or by giving more precise predictions for already known results.

So there is not much reason to doubt the inevitable implication of the standard interpretation, that there is an insoluble connection between the observation and the observed, and that the observed can not be said to exist independently of the observation.

By Carsten K. Agger and Niels K. Petersen
Published in Faklen (The Torch) No. 4, 1997

References

[1] A. G. Zajonc, L. J. Wang, X. Y. Zou & L. Mandel. Nature 353, 507 (1991).
[2] T. J. Herzog, P. G. Kwiat, H. Weinfurter & A. Zeilinger. Physical Review Letters 75, 3034 (1995).
[3] N. Bohr quoted in A. Petersen. Bulletin of the Atomic Scientists XIX no. 7, 10-11 (1963).
[4] ibid. p. 12.
[5] H. Everett. Reviews of Modern Physics 29, 454 (1957).
[6] A. Einstein, B. Podolsky & N. Rosen. Physical Review 47, 777 (1935).
[7] J. S. Bell. Physics 1, 195 (1964).
[8] A. Aspect, P. Grangier & G. Roger. Physical Review Letters 47, 460 (1981). A. Aspect, J. Dalibard & G. Roger. Physcial Review Letters 49, 1804 (1982).
[9] W. H. Zurek. Physics Today (October 1991) p. 36.

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