New Philosophy for a New Millennium

(A series of notes prepared as part of an informal research

 project between 2000 and 2005)

By Mike Holliday


Appendix: Realism and the Physical World

I want to look at the relationship between physics (especially quantum mechanics and cosmology) and the themes of emergence, existence, and explanation that I discussed in the main text. My purpose here is to see how these themes might affect our understanding of what modern physics is telling us about the nature of the universe. This is still an area of considerable puzzlement and debate; after all, the physicist Richard Feynman (1967, p. 129) once famously wrote 'I think it is safe to say that no one understands quantum mechanics.' So I don't pretend that I can present a clear picture of these notoriously murky waters. Nevertheless, there are some interesting similarities between the philosophical issues that I have been considering and the answers that physics is giving us to the question 'what is the universe really like?', and these similarities should make us wary of being led astray, led away from a clearer understanding of what physics can tell us, by our underlying philosophical assumptions. I shall consider this topic in an Appendix so as not to break up the flow of the main text.

1 The Quantum World

Let's start by considering the two-slit experiment that is frequently used to illustrate the peculiar nature of quantum theory. If we shine a light source at a barrier containing two slits with a wall positioned behind it, then we obtain a series of light and dark stripes on the wall - an interference pattern. This has been known since Thomas Young's first two-slit experiment in 1801, and was taken as being proof of the wave nature of light since the light stripes represent areas where the wave peaks arriving from each of the two slits coincide and the dark patches represent areas where the waves cancel each other out. Of course, we have subsequently learned that light consists of particles that we call photons: so we can suppose that we slow down the emission of light from the source until it emits single photons, one at a time, and that the wall consists of a series of photoelectric cells that can measure the impact of a single photon. Now we find that one photoelectric cell will fire at a time, indicating the position that an individual photon has hit on the wall. If we let the experiment run over a period of time, we find that the pattern of individual hits on the wall builds up to recreate the striped interference pattern.1 But this seems impossible - surely each photon of light can only go through one of the slits? After all, we know that any individual photon hits a particular point on the wall, because only one photoelectric cell fires. And there doesn't seem to be anything else that might affect the photon's path; so how is it that we still get an interference pattern rather than a couple of bright stripes directly behind each slit? Even more puzzling is what happens when we vary the experiment by trying to detect which slit the particle passes through. Now the interference pattern disappears, replaced by a pattern consistent with only one slit being open at a time.

Despite the strangeness of these results, they are in fact exactly as predicted by quantum theory. This is possible because the theory's formalism is such that it relates to the whole experimental set-up rather than separately to each individual path that the photon might follow.2 More specifically, the formalism describes the position of the photon as being a superposition of all its possible positions. This superposition differs from each of what we might otherwise consider the four possibilities - that the photon passes through the left slit; that it passes through the right slit; that it passes through neither slit; or that it passes through both slits.

But I have not been quite right here. Quantum theory is in fact a mathematical formalism that relates future observations to earlier observations,3 and it therefore says nothing about the position of the photon until it is observed. The theory is simply an algorithm for calculating the probability that we will get a particular result when we make a measurement, in this case the position of the photon when it arrives at the wall of photoelectric cells. Given this, and the fact that we never actually observe a superposition (each photon hits a specific spot on the wall behind the slits), one obvious interpretation of what quantum theory is telling us is that position in space is not an inherent property belonging to all entities at all times, but is perhaps a form of emergent property - in this case a property of the photon that emerges from its interaction with the experimental apparatus.

It is interesting to note, however, that not all properties of sub-atomic particles are like this. Each particle has certain static attributes, such as mass, charge, and spin magnitude, which are the same for every such particle under any measurement situation. It is only a particle's dynamic attributes, such as position, momentum, and spin orientation, that vary according to the measurement situation. The static attributes can be thought of as defining a kind of particle, for example a photon, an electron, or a neutrino, whereas the dynamic attributes seem to distinguish one individual particle of a particular type from another individual particle of the same type. Instead of thinking of individual particles with two different types of properties, it may be more helpful to consider the static attributes as being in some way universals,4 and the dynamic attributes as being emergent properties that allow us to attribute individuality to particles, and hence to objects more generally. This would be taking seriously a warning from Omnes (1999, p. 195) that 'It would be vain for [common sense] to pretend to impose on the atomic scale philosophical "principles" that are simply the inordinate worship and unjustified hypostatizing of our thought habits and language tics.'5 The question 'in what sense are the dynamic properties emergent?' is one that I will return to later (see section 4, below). However, this account still leaves a number of other puzzling aspects of quantum mechanics unexplained, and I want to consider these before returning to the question of emergence.

One such puzzle is encountered in what are described as quantum eraser experiments. Variations on the two-slit experiment show that quantum interference effects can be destroyed by the availability of 'which way information', i.e. the ability to ascertain which path a particle actually followed. The idea behind quantum eraser experiments is that the effect of which way information can be reversed at a later stage in the experiment ('erased'), thereby bringing back the interference effects. For example, in the experiment described above, we can tell which slit a photon went through by inserting polarizing filters in front of each slit; the filters then effectively mark the photons by only allowing through particles polarized in a particular direction, for example 'horizontal' for the right slit and 'vertical' for the left slit. We now no longer obtain an interference pattern at the detection screen. But if we put a third polarizing filter in front of the detection screen, and set this filter at 45° to the other two filters, then the which way information is scrambled and we can't tell the polarization of the light when it hits the detection screen. The interference effect now reappears!

Delayed choice experiments have some similarity to the quantum eraser. For example, imagine that we could insert or remove the 45° polarizing filter very quickly, such that a decision as to whether to include it in the experimental set-up could be made after a photon had passed through the barrier but before it hit the detection screen: this would be a case of a delayed choice experiment - we are able to force the experiment to show an interference behavior (or not) by our actions after the part of the experiment that we believe produces the interference.6

What such results seem to count against is the idea that each photon starts off in a delocalized state, and that its position only becomes definite when it interacts with the experimental apparatus. This doesn't seem to be a coherent account of what happens in the quantum eraser experiment, because in that case we add further measuring apparatus (the 45° polarizing filter), yet the result returns to what it was before we put in place the first set of filters; that is, we once again see an interference pattern. In a sense, this is not entirely surprising; thus far, I have been treating a particle's location in space as something that emerges in time, but this would seem at odds with notions that have been commonplace in physics since Einstein introduced his Special Theory of Relativity in 1905, in particular that space and time need to be considered as two aspects of a single space-time. Therefore, what I need to do next is consider the notion of time as it appears in modern physics.

2 Time and Quantum Theory

There are two major reasons for believing that the way we think about time, in the everyday sense of the word, is not consonant with the world of modern physics. Firstly, special relativity strongly suggests that simultaneity is not a concept that reflects an underlying physical reality (see, for example, Saunders 2002). The effect of Einstein's theory on our conception of time can be seen from a recent poll of physicists, who were asked if they thought time was a fundamental concept, or whether it was derivative of something else - as, for example, is temperature. The result showed that around half believed that time would eventually be interpreted in terms of other physical variables (reported in Rees 1999, p. 139). This is one reason why many physicists view the cosmos as a 'block universe' consisting of three dimensions of space and one of time:7

On this view there is no more an objective division of the world into the past, the present, and the future than there is an objective division of a region of space into here and there. Not surprisingly, then, supporters of this view deny that there is any ontological difference - any difference concerning simply existence - between the past, the present, and the future. ... it regards reality as a single entity of which time is an ingredient, rather than as a changeable entity set in time (Price 1996a, p. 12).

There is no 'present', 'past', or 'future' in such a universe except relative to the frame of reference of an observer in that universe. I shall return to relativity, and more specifically general relativity, in a later section, but for now I want to discuss (at somewhat greater length) the second consideration that leads us to question our common conception of time, a consideration which is related to our perception that time is asymmetric in nature, in other words that the future is somehow radically different from the past. Much of the discussion in this and the following section derives from Huw Price's book Time's Arrow and Archimedes' Point (1996a), which contains a thorough analysis of the issues that are involved in trying to understand the true nature of this asymmetry.

The difficulty with taking time to be a fundamental element of the physical fabric of the universe is that it seems to be the case that physical processes are, at a micro level, time symmetric; that is, we cannot tell from observing such physical processes which way they are oriented in time. Consider two elementary particles colliding, and then view what happens in reverse - rewind the film, so to speak. Nothing unusual appears to occur in the reversed viewing. Furthermore, the equations that describe particle physics are time symmetric and can in principle be used to derive an initial state from a final state just as easily as they can a final state from an initial state (Penrose 1989, p. 392).8 This is completely different from what we see in everyday life, where we certainly can determine time orientation: a glass can topple from a table and smash into pieces, and if we watched a film of the glass reassembling itself and flying upwards to land on the edge of the table then we would know that we were watching a film backwards. The usual explanation given for this is that processes at the macro-level are subject to the second law of thermodynamics, which says that the entropy (i.e. the extent of disorder) of a closed system must always increase. The underlying reason for the second law is statistical: there are many more possible disordered micro-states than there are ordered micro-states. For example, if we have a room where all the air has been confined to one corner and then released, the air molecules move so as to eventually disperse throughout the room. This happens because the number of combinations of positions of the individual molecules that represent an even spread throughout the room is very much larger than the number of combinations of positions that represent all the molecules in one corner. It would be a major miracle if the random movements of the molecules moved them all back into the corner after the air has dispersed. But if we consider the matter carefully, we can see that this explanation of the asymmetry of time simply displaces the puzzle, since it implies that the early universe must have been exceptionally ordered. If we ask the question 'Why should it be the past that is more ordered than the future, and not vice versa?', we can see that the real mystery is why the early universe should have been in such an unlikely state of low entropy (Price 1996a). I'll consider this question shortly, but for now the important point to take on board is that the asymmetry that we perceive in the macro universe seems to derive from cosmological considerations, rather than being part of the essential structure of the universe. 

I want to link this discussion of the asymmetry of time to two strands of thought that we encountered earlier. Firstly, Price's analysis shows the importance of not hypostasizing time as a metaphysical entity. Once we hypostasize time, then we make the asymmetry of time a fundamental feature of the universe. By doing so, we are unable to appreciate how this asymmetry may arise from other factors, and hence we block some of the possibilities for making progress in our understanding of the physical universe. Secondly, our discussion reveals once again the importance of an active observer (or more correctly, an active participant) in describing what we consider to be external reality. Huw Price has pointed out that, despite the tendency of physicists to think in terms of a block universe, there still seems to be a presumption that there is a sense in which the past is always determined and the future always undetermined. But, suggests Price, this could well be a view that we arrive at because of our existence at the macro level and the effect that the one-way direction of entropy change has on the way we view the world:

Perhaps causal asymmetry isn't really in the world at all, but the appearance that it is is a product of our own standpoint. ... The difference between the fixity of the inputs from the past and the openness of the outputs to the future is a feature of the experience from the inside - a feature of what it feels like to be an agent (Price 1996a, pp. 155, 169).

Now we can return to some of the puzzles of quantum theory. The asymmetry of time does not seem to be built into physical processes at the micro level, but instead appears to be due to the boundary condition of the early state of the universe. Accordingly, we seem to have no prima facie reason to think that events involving particles at the micro level will be correlated with past interactions but will not be correlated with future interactions. Indeed, quantum theory, and more specifically the experiments undertaken in connection with Bell's Theorem,9 suggest strongly that in some experimental situations the best explanation of the results is that physical variables (such as momentum, or spin) are correlated with measurements that we will perform on them in the future (Price 1996a, chapter 9).10

Huw Price describes this possibility by means of the phrase 'advanced action', which can be easily misunderstood as somehow involving causation directed backwards in time. But in the context of Price's earlier comments about the block universe, it seems more correct to understand the phrase as simply referring to the dependence of the present on the future (Price 1996a, p. 180). In a later article (1996b), Price clarifies his position:

The work done by [the advanced action] hypothesis in [quantum mechanics] does not require that these correlations be objectively causal. It simply requires that the correlations display certain distinctive patterns, the possibility of which has been overlooked by other approaches to [quantum mechanics]. (In particular, it requires that there be significant correlations between measurement settings and earlier states of measured systems.) 

I interpret Price in general terms as holding that (i) time-asymmetric causation is not a fundamental element in the structure of the universe; (ii) events in time are correlated with one another; (iii) there is an objective, cosmological asymmetry in the universe which gives rise at the macro level to agents and a concept in them of 'causation'; and (iv) in specially designed experimental situations it is possible to obtain a set of results where a correlation with a future measurement setting seems to be a good explanation of an earlier state of the system being measured. This result is not too counter-intuitive, once we appreciate that a correlation is not directional in time, and that the appearance of causation appears to be a 'macro' process that is ultimately dependent on the cosmological structure of the universe. Indeed, it is only by making sure our experimental set-up excludes outside influences that might disturb the correlation between an individual particle and a particular measurement (i.e. that it excludes the effect of 'macro' processes) that we find a correlation between the present and the future that can be explained by what Price terms 'advanced action' (and all other measurement attempts can constitute such an 'outside influence').

3 Entropy and Gravity

A few paragraphs ago, I left hanging the question why is the universe such that entropy always increases? After all, it is this fact that appears to lead to the asymmetry that we perceive in the universe at the macro level. Cosmologists are agreed that the very early state of the universe was exceptionally evenly distributed. As Price (1996a, p. 79) points out, we might think that there is nothing unusual in this; for example, we expect a gas to spread itself out evenly throughout a container. However, this is because the most important force in this case is the pressure caused by the movement of the gas molecules. In the case of the universe as a whole, gravity has a much more significant effect, causing matter to gather together; hence, we should expect a universe such as ours to be 'clumpy'. Price concludes (1996a, p. 101) that a smooth early universe is therefore a rather improbable state: if gravity provides a reason for the end state of the universe to be clumpy, then we have to explain why it doesn't provide a reason for the early universe to be clumpy also. One suggested solution to the puzzle of the smooth Big Bang is the possibility that, even if the universe starts at maximum entropy (i.e. complete disorder), its expansion allows increasing room for disorder and hence for pockets of structured order (see, for example, Stenger 1995, pp. 226-229). In effect, maximum entropy is considered for the size of the universe at that point in time, and entropy can increase as the universe inflates following the Big Bang. This makes many more particle states accessible and thereby increases the maximum entropy of the universe. Hence structure and order can form in some parts of the universe at the expense of increased disorder or entropy elsewhere. Thus differences in the size of the universe may create, on their own, a direction for time (Stenger, forthcoming).

This type of suggestion has been criticized by both Price (1996a, pp. 81-82) and Penrose (1989, pp, 426, 440-447) on the ground that the homogeneous nature of the very early universe has to be 'special' to an unbelievable degree (Penrose arrives at a figure of 1 in 10000000000123), and hence that its low entropy cannot not depend on the limited possibilities of a small universe. Part of the case made by Price and Penrose is to note that any argument about the reasonableness of a smooth Big Bang would also apply (other things being equal) to a universe collapsing under gravity into what would effectively be a massive black hole. Price (1996a, pp. 81-86) argues that even if we believe that a contracting end to the universe is unlikely, an adherent to the 'smooth start' must have some way of dealing with the (counterfactual) argument that if the universe were to collapse in the future under the effect of gravity, then it would be a clumpy universe, and temporal symmetry suggests that the early universe should therefore also have been clumpy.

This argument would be negated by a theory which provided an explanation as to why a smooth boundary at one end is reasonable and which also implied that there is only one such temporal boundary, i.e. that the universe does not contract.11 Unfortunately at this point I can offer nothing except outright speculation. A smooth universe is one where all the distances between particles are (nearly) identical. So I suggest that one possible way to identify a reason for the low level of entropy associated with the Big Bang is to consider a relational account of physical reality. We would ask ourselves the question 'what does it actually mean in a relational universe to say that distances are "different" or "the same"?' One implication might be that the separation between particles is definable in terms of other properties. If this were so, then the smoothness of the universe could be determined by properties that we associate with its age. So whether a stage of the universe is considered 'small' or 'smooth' may be closely related to other factors that belong to a universe that is in an 'early state', for example high temperature, whereas a 'later state' would tie together other aspects such as 'large' / high entropy / low temperature; (of course, this is only consistent with a universe that doesn't reverse its expansion and end in a so-called Big Crunch). We would also need to develop a specific account of why the 'larger' states appear to us as being 'later' than the 'smaller' states - for example, by utilizing Price's suggestion that time has a statistical origin.12

4 The Emergence of Space and Time

One of the most intractable problems in modern-day physics is the attempt to reconcile the two major revolutions that occurred at the start of the twentieth century, namely quantum mechanics and relativity. Although both theories are supported by a wealth of experimental data, evidence so strong that very few physicists seriously entertain the idea that either theory is radically mistaken, they involve background assumptions that are flatly incompatible. In particular, quantum mechanics assumes a Newtonian view as to the nature of space and time, a view that general relativity rejects, and it also incorporates a form of indeterminism that seems inconsistent with the determinist dynamics by means of which general relativity describes the behavior of the gravitational field and the geometry of space and time. This inconsistency between the two theories is masked by the fact that they were initially developed to describe domains of a radically different scale. General relativity is a theory of gravitation, a force so weak that we normally only see its effect through large accumulations of matter, principally on a cosmological scale. Quantum mechanics, on the other hand, describes the domain of the very small, at the level of sub-atomic particles. However, the situation changes once physicists attempt to describe what happens at the so-called Planck scale, a scale so small that it is as far removed from the size of a proton as a proton is from the size of the earth. General relativity describes the very structure of space and time, as well as gravity (indeed it equates gravity with the structure of space-time). Therefore at the Planck scale, physicists need to take account of both relativity and quantum theory. Yet so far, all attempts to utilize both theories in their existing forms have given nonsensical answers.

If general relativity is our modern-day theory of gravity, then the search to reconcile it with quantum mechanics is effectively an attempt to construct a theory of quantum gravity. One of the most promising attempts is loop quantum gravity, of which two of the leading proponents are Lee Smolin and Carlo Rovelli.13 In his book Three Roads to Quantum Gravity (2000), Smolin takes as his starting point the notion that 'there is nothing outside the universe' and hence that anything in the universe can only be described by referring to other things in the universe. From the very start, therefore, Smolin's is a relational physics, where the world consists of a network of relationships. Indeed, general relativity is itself a theory that describes gravity, space, and time in terms of such a network:14 

Neither space nor time has any existence outside the system of evolving relationships that comprises the universe. Physicists refer to this feature of general relativity as background independence. By this we mean that there is no fixed background, or stage, that remains fixed for all time. In contrast, a theory such as Newtonian mechanics or electromagnetism is background dependent because it assumes that there exists a fixed, unchanging background that provides the ultimate answer to all questions about where and when (Smolin 2000, pp. 24-25; see also Rovelli 1997).

Since space-time and the gravitational field are identical, the space-time metric that was central to Newtonian dynamics and to special relativity drops away, and we are left with a set of interacting fields, one of which is the gravitational field. In general relativity, motion is simply the displacement of these dynamical objects with respect to each other. Rovelli notes the way in which this completes a return to a relational understanding of physics:

To describe the motion of a dynamical object, Newton had to assume that acceleration is absolute, namely it is not relative to this or that other dynamical object. Rather, it is relative to a background space. Faraday, Maxwell and Einstein extended the notion of 'dynamical object': the stuff of the world is fields, not just bodies. Finally, [general relativity] tells us that the background space is itself one of these fields. Thus, the circle is closed, and we are back to relationalism: Newton's motion with respect to space is indeed motion with respect to a dynamical object: the gravitational field (Rovelli 2001).

We can now perhaps obtain a clearer idea of the way in which the dynamic properties of particles can be considered 'emergent'. On Smolin's and Rovelli's account, there is no inherent background to the universe, and therefore it is not just position in space, but space itself which emerges from the relationships that constitute the universe. Similarly, general relativity also implies a relational account of time; it tells us about the way in which a number of variables evolve with respect to one another, but no single one of these variables is preferred in the sense that it represents 'proper time' (Rovelli 2000). Rovelli suggests that we instead consider time as having a statistical and thermodynamical origin, much as described by Huw Price.

Smolin views causality as the key relationship between the events that form the universe, but he is referring to causality not as some sort of metaphysical relationship but as a connection determined by the light cones that specify which events are in the past of certain other events. So described, causality is a structural feature of the relationships that comprise the universe. General relativity tells us that our universe is indeed a 'causal universe' in this sense, because no information or effect can travel faster than the speed of light, and it is this fact which restricts the size of the light cones of an event and hence determines that certain other events are in its 'past' and can be causally related to it:

So in our universe, specifying the paths of all the light rays or, equivalently, drawing the light cones around every event, is a way to describe the structure of all possible causal relations. Together, these relations comprise what we call the causal structure of a universe (Smolin 2000, p. 59).

In general relativity, the causal structure is itself dynamical in the sense that it is influenced by the events that it describes, evolving in accordance with equations formulated by Einstein. It is these equations that describe, inter alia, the curvature of space-time near massive objects, an effect that we perceive as gravity. The picture that Smolin gives us is therefore one in which space, time, causality, and gravity all arise from the network of relationships at the quantum scale. 

5 A Relational Interpretation of Quantum Theory

Another of the major mysteries of modern physics is the search for an intelligible interpretation of quantum theory; in other words, an answer to the question what does the universe have to be like for quantum theory to be correct?

The principal difficulty with quantum theory is that it does not appear possible to interpret it in a 'realistic' manner, such that atomic particles always have determinate properties such as position and momentum. It seems that these properties do not become definite until we try to measure them. An important distinction here is between the formal theory of quantum mechanics and its interpretation. Quantum theory is a methodology, an algorithm if you like, for generating various possible measurement results from an initial measurement(s); but the theory still needs to be interpreted, if we are to get beyond a description of sets of measurements. For example, suppose I have a source that emits an electron every minute, and I have a number of detectors set up in line to make measurements of the spin of the electrons in various directions. Then quantum theory simply provides a way of generating the probabilities of various spin measurements from detectors further down the line, based on the readings that I obtain from detectors nearer the source. Strictly speaking, all I am dealing with is measurements. Of course, there is a sense in which I have to make a minimal degree of interpretation when I say that these measurements relate to something called 'spin of an electron'. But interpretation proper is whatever takes me beyond the language of measurements; when I claim, for example, that after I make a measurement a particle has a spin of '1' in direction x. And a complete interpretation of quantum theory attempts to provide a coherent understanding of how all these measurements might relate to entities in the world, for example to properties of particles. But such an interpretation does not appear to be achievable .

The argument between Einstein and Bohr in the 1930s centered on whether it was actually possible to provide a realistic interpretation to quantum theory. Einstein argued that it was not possible to give such an interpretation and that quantum theory must therefore be incomplete. It was generally thought that Bohr had the better of Einstein in this debate, and the 'Copenhagen Interpretation' advanced by Bohr and others became the consensus opinion of physicists. However, there has been continuing dissatisfaction with Copenhagen, which is derided by some as merely an invocation to 'shut up and calculate', and the last fifty years have seen an increasing number of alternative interpretations.15

The difficulties seem to occur when we suppose that there are definite entities, e.g. 'electrons,' that have certain properties, e.g. 'spin of 1 in direction x'. The language that is used here is that of the world of 'medium-sized, dry goods', of objects and of continuing properties that belong to those objects and that produce certain effects. But quantum theory strongly suggests that particles cannot have definite properties in-between measurements. Our examination of objectification and hypostatization suggests that a successful interpretation might well be one that eschews the language of objecthood and definite properties, whilst still trying to say something that assists our understanding of the world of the very small (and in this sense going beyond the Copenhagen Interpretation). There have recently surfaced a few suggested interpretations along these lines, interpretations that stress the relative nature of the physical variables that are described by quantum theory. The common thread to this type of interpretation is that any description of what is happening in a specific situation, such as a particular experiment, is relative to something or other. To hark back to Putnam, we may say that any single quantum description is not the one and only correct description of an underlying reality, since we also need to take account of some sort of background to the description. This type of approach to the interpretation of quantum mechanics can, I think, be seen most clearly in a paper by Carlo Rovelli (1996).

Rovelli aims to derive the formalism of quantum theory from a small number of postulates that are motivated primarily from experimental results. Quantum mechanics, says Rovelli,

will cease to look puzzling only when we will be able to derive the formalism of the theory from a set of simple physical assertions ... about the world. Therefore, we should not try to append a reasonable interpretation to the quantum mechanics formalism, but rather to derive the formalism from a set of experimentally motivated postulates.

This methodology leads Rovelli to suggest that we reject something that is normally taken for granted - the concept of observer-independent properties: 'The notion rejected ... is the notion of absolute, or observer-independent, state of a system; equivalently, the notion of observer-independent values of physical quantities.' (To avoid any misunderstanding here, we should note that Rovelli is not using the term 'observer' to refer specifically to conscious or animate objects, but instead to any physical system that can register information, for example a pointer dial.)

The following example is used by Rovelli to show how we can more easily understand quantum mechanics once we have rejected this assumption. Suppose we have an observer, O, who makes a measurement of a system, S, the result of which can be either 1 or 2; also suppose that, when O actually makes the measurement, the result obtained is 1. Now assume another observer, P, who does not make a measurement of S, but who knows the initial states of both O and S. Once the measurement is made, O's description of S is that it is in state |1>, whilst P can only say that the combined system O plus S (i.e. the original observer and the original system) is in a superposition of two states, namely (i) S is in state |1> and O measures 1, and (ii) S is in state |2> and O measures 2. Recall from our earlier discussion of superpositions that this is most definitely not the same as saying that the combined system is either in state (i) or in state (ii). As Rovelli points out, this means that P's description does not include a specific statement that S is in the state |1>, which certainly does form an element of O's description. Therefore O and S have different descriptions of the state of S, and Rovelli thereby arrives at his main observation: 'In quantum mechanics different observers may give different accounts of the same sequence of events.'

Rovelli then considers the view that quantum mechanics is incomplete and that there is a 'deeper reality' that accounts for the relative nature of the descriptions made by O and by P. In fact, we see no experimental evidence suggesting that quantum mechanics is incomplete, and Rovelli's methodological suggestion is that we therefore accept that it is complete. This would imply that there is nothing in a complete description of the world beyond the information that systems have about other systems, and hence that physics is entirely relational. But of course, we anticipate that the descriptions given by O and P will be related to each other in some way. And we do indeed find that there is a relationship, but that this relationship is itself governed by the formalism of quantum theory: 'It is possible to compare different views, but the process of comparison is always a physical interaction, and all physical interactions are quantum mechanical in nature' (Rovelli 1996).

As an example, Rovelli considers one of the more intractable aspects of the interpretation of quantum theory, namely how to make sense of what is referred to as 'the collapse of the wave function'. The function that describes the probabilities of future measurement results evolves in a deterministic manner, except when a measurement is actually made, at which point it instantly changes so as to take account of the fact that this measurement must have had a definite result; the function now has to show that this actual result has a probability of 100%. So if the spin of an electron in a particular direction can be 1 or 0, then the function initially shows the state of the electron evolving (as, for example, it interacts with other entities or moves around in space) as a superposition of the two states, 1 and 0. However, once we actually measure the spin in that particular direction, we get a definite result, either 1 or 0. Suppose the result is 1: now the function suddenly changes so as to show that the result '1' has a 100% probability and the result '0' a zero probability. But there seems to be no way to account for this radical change in the function if the whole world is quantum mechanical in nature. The relational interpretation resolves this puzzle quite straightforwardly because the evolution of the state of a system assumes that it is isolated, an assumption that no longer holds once a measurement is made:

The unitary evolution does not break down for mysterious physical quantum jumps, or due to unknown effects, but simply because O is not giving a full dynamical description of the interaction. O cannot have a full description of the interaction of S with himself (O), because his information is correlation, and there is no meaning in being correlated with oneself. ... There is no way a system P may get information about a system O without physically interacting with it, and therefore without breaking down (at the time of the interaction) the unitary evolution description of O (Rovelli 1996).

But how are we to understand the 'physical meaning' of something having a value of a property only relative to something else? Rovelli says that it is possible to understand what is involved here if we consider how the matter looks to P, the second observer. Considering her description in quantum mechanical terms, we say that there is a correlation between the measurement expressed by O and the variable q that belongs to the system S. Suppose, for example, that the original 'observer', O, is a dial with a pointer. If the second observer, P, were to look at O and then take her own measurement of S, then the two results would be correlated. If P finds that S is in state |1>, then she finds that O's reading is 1; and if she finds that S is in state |2>, then she finds that O's reading is 2. The combined state of O plus S therefore contains information - in the information-theoretic sense described by Shannon (1949) - because the number of possible configurations of the pointer and of q are reduced from four to two. 'Information expresses the fact that a system is in a certain configuration, which is correlated to the configuration of another system (information source). ... any physical system may contain information about another physical system' (Rovelli 1996).

The existence of Planck's constant is interpreted by Rovelli as implying that the amount of information that can be extracted from a system is limited. When we combine this with a second postulate, that it is always possible to acquire new information from a system, then we can (almost) derive the formalism of quantum mechanics, thereby achieving the aim that Rovelli stated at the outset. Both these postulates are experimentally derived; they formalize what we have learned about the micro-world from experimental setups such as those that I described earlier.

Rovelli notes that his views are closely linked to arguments made by Mermin to the effect that 'correlations have physical reality; that which they correlate does not'. If we stay with the correlations themselves, says Mermin (1998), then quantum mechanics is unproblematical: in order to fully describe the quantum state of a complex system, we only require the correlations between its subsystems:

It is a remarkable ... feature of the quantum mechanical formalism that all the joint distributions associated with any of the possible resolutions of a system into subsystems and any of the possible choices of observable within each subsystem, are mutually compatible: they all assign identical probabilities within any sets of subsystems to which they can all be applied. The physical reality of subsystem correlations need therefore not be restricted to any particular resolution of a system into subsystems or to particular choices of observable within each subsystem, even though different observables for a given subsystem fail, in general to commute. It is only when one tries to go beyond their inter-subsystem correlations to actual correlata - particular values for the subsystem observables - that non-commuting observables are incapable of sharing simultaneous physical reality. 

Although all the correlations can be correct, they cannot all reflect determinate values of underlying properties since this produces inconsistencies. 'The correlata cannot all have physical reality because ... it is impossible to construct, in the standard way, a full and mutually consistent set of conditional distributions from the joint and individual subsystem distributions' (Mermin 1998). The distributions of probabilities referred to here are conditional because they refer to mutually exclusive situations; for example, we carry out experiment 1 or we carry out experiment 2, and we never get to carry out both experiment 1 and experiment 2 (at the same time on the same system).16

The relational interpretation of quantum mechanics displays the benefits that can be obtained by not assuming an ontology derived from our everyday existence. Rovelli's key move is to drop the assumption that there are such things as absolute properties of microphysical entities:

The core idea is to read [quantum] theory as a theoretical account of the way distinct physical systems affect each other when they interact (and not of the way physical systems 'are'), and the idea that this account exhausts all that can be said about the physical world. The physical world is thus seen as a net of interacting components, where there is no meaning to the state of an isolated system. A physical system (or, more precisely, its contingent state) is reduced to the net of relations it entertains with the surrounding systems, and the physical structure of the world is identified as this net of relationships (Laudisa & Rovelli 2002).

It is interesting that Rovelli's relational account accords an essential theoretical position to observers (in the sense of the term noted above) that is similar to that of Maturana and Varela as described in An Alternative Metaphor:

... states [of a system] have no absolute meaning, and must be interpreted as the content of the information that [another] system has about [them]. ... Thus, the properties of the systems are to be described by an interrelated net of observations and information collected from observations. ... There is no way to 'exit' from the observer-observed global system: 'Any observation requires an observer' (The expression is freely taken from [Maturana and Varela]) (Rovelli 1996).

Mike Holliday (July 2005)

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[1] This is not simply a property of light; in the last twenty years similar experiments have been carried out involving electrons and even whole atoms (see Gribbin 1995, pp. 7-9, for a few of the technical details).

[2] Quantum theory describes the the state of a system, where the term 'state' is to be understood in a technical sense and not simply as a list of the values of all the properties of the system and/or the system's individual elements.

[3] For a good, basic introduction to the formalism of quantum mechanics, see Ismael 2004.

[4] I have some reservations about my use of the word 'universal' here. My philosophic instincts are too anti-Platonist to accept some form of general entity; what I have in mind is rather a form of particular that does not have its existence defined in terms of a location in space and time. However, I do not pretend to have an account of the relationship between such particulars and those entities that we do think of as having an existence in space and time.

One advantage of thinking about the physical world in this manner is that we might be able to finesse the issue as to whether causation contains an element of necessity, an element that appears to be intimately involved in our understanding of causation and yet difficult to identify in the world. There seems to be a problem in thinking of causation as involving both a regularity of several sets of similar events (whenever A, then B) and a set of singular events (a causes b). This may appear less troublesome if the underlying similarity comes down to multiple manifestations (if this is the right word to use here) of a single physical constant in a space-time arena which is itself emergent.

[5] The way in which our everyday concepts such as identity, objects, and space do not really apply at the level of the micro-world is emphasized in a number of the papers collected in Castellani 1998, especially those by di Francia, Reichenbach, and Aerts .

[6] Because of practical issues, actual experiments often utilize a beam splitter that separates light into two beams, rather than a single beam that then passes through two slits. The two resulting beams are then brought back together to display interference effects. In a delayed choice experiment, detectors are positioned in each of the two possible routes, and these can be switched on or off very quickly, quicker than the time it takes the beam to travel from the splitter. The idea is that we can choose to obtain an interference pattern (or not) after each photon has emerged from the beam splitter (see Baggott 2004, pp. 182-184). An interesting account of an experiment with a two-slit setup and both quantum eraser and delayed choice effects is available at; this site describes an experiment originally reported in Walborn et al. 2002.

[7] For a review of the philosophical support for the block-universe view, see Price 1996a (pp. 12-16).

[8] With one minor exception relating to the behavior of particles known as neutral kaons.

[9] Bell's Theorem is normally taken as proving that, given a small number of assumptions, any theory that reproduces the statistical predictions of quantum theory must be non-local. For good introductions to Bell's Theorem, see Stenger 1995 (pp. 110-123) and Herbert 1985 (pp. 215-227). Bell himself recognized that his Theorem depended upon the assumption that there is no correlation between the state of a particle and the settings of future measuring instruments, see Price 1996a (pp. 231-233, 241-242).

[10] For a similar attempt to explain some of the difficulties of quantum theory by reference to the time-symmetrical nature of physics at the micro-level, and the existence of correlations with the settings of experimental apparatus in the future, see Stenger 1995 and Stenger 2000 (chapter 8). Stenger stresses the contextuality of quantum theory, by which he means that the theory's predictions depend upon the entire experimental set-up, and not just a single detecting device:

Changing a detector off in another corner changes the experiment. Contextuality can be shown to be a natural feature that follows directly from a fundamental fact about quantum phenomena - the apparent symmetry of time. When no distinction is made between past and future, the future experimental arrangement of detection devices, such as polarizer orientations, must have as much effect on the system as any initial conditions. Final and initial conditions are conceptually equivalent (1995, p. 204).

[11]  Stephen Hawking once believed that he had proved a conclusion to this effect. Discussing the implications of his 'no boundary condition' cosmological theory, he says that that the theory itself can generate a direction in time: 'The universe is nearly homogeneous and isotropic when it is small. But it is more irregular, when it is large. In other words, disorder increases, as the universe expands' (Hawking 1994; quoted in Price 1996, p. 90). However, he now believes that his conclusion was mistaken; see Price 1996a (pp. 86-93). 

[12] It is worth noting that Price (1996a, pp. 95-96) suggests that any such theory would have a difficulty because black holes in a non-collapsing universe also have exceedingly high entropy, whereas a time-symmetric physics suggests that they should be similar to the Big Bang and therefore low entropy. Personally, I think that it isn't clear that a singularity can be described as 'clumpy' rather then 'smooth' (particularly given a relational account of distance and therefore of the separation between particles) which is what I think it would take to defeat the sort of move that I have suggested. I have a feeling that arguments such as Price's tend to hypostatize entropy (rather than seeing it as a statistical measure), thereby making the Second Law of Thermodynamics an iron-clad law that must be obeyed by a part of the universe that collapses towards a singularity. But I believe that at this point our arguments are beginning to outrun our understanding of the universe.

[13] For non-technical accounts of the search for a theory of quantum gravity, and loop quantum gravity in particular, see Rovelli 1998 and 2001, and Smolin 2000. Rovelli 2004 is a recent comprehensive textbook at a more technical level.

[14] It is true that general relativity is not generally held to support a relational view of physics. In particular, the development of field theory has strongly mitigated against traditional relational accounts of physical reality, such as those of Leibniz and Mach. Matter is now usually conceived of in terms of fields that range over a space (or space-time) metric - in a sense space and time are seen as more basic entities than matter (Butterfield 2001). On the other hand, there are serious interpretive issues as to the ontological status of space-time points in a theory such as general relativity. One such problem is that the space-time metric in general relativity is dynamic: it depends on the gravitational field itself and cannot therefore be thought of as a fixed background. A second difficulty, described in Butterfield & Isham 1999, lies with general relativity's diffeomorphism invariance:

... the physical content is wholly unaffected by applying any smooth, invertible transformation (called a 'diffeomorphism') between spacetime points, which thus function as mere 'pegs' on which to 'hang' the fields ...  This feature suggests that ... spacetime points should not be taken as real objects, even in interpreting classical general relativity: rather they are an artefact of the way we have formulated the theory. ... [The lesson is that] we should be wary of taking as the basic objects of our ontology (according to some theory) those items that are postulated as the initial elements in a mathematical presentation of the theory.

[15] These alternative interpretations include hidden variables (Bohm), many worlds (initially suggested by Hugh Everett), many minds, Cramer's transactional interpretation, decoherence (Zurek, Omnes), and proposals for adding to quantum dynamics (Ghirardi-Rimini-Weber). The literature on the interpretation of quantum theory is immense, and this is not the place to review the various interpretations that have been suggested. For useful summaries, try Herbert 1985 and Baggot 2004.

[16] Mermin's discussion (1998) does, unfortunately in my opinion, confuse the issue by attributing some aspects of the problem of the interpretation of quantum theory to human consciousness. For example, he says that '... physics can only (correctly) assert that photomultiplier #n firing is perfectly correlated with my knowing that photomultiplier #n fired for either value of n. The question that physics does not answer is how it can be that I know that it is #1 and is not #2. This is indeed a problem. It is part of the problem of consciousness.' I don't feel that this emphasis on consciousness is a particularly promising direction to take, although there are others who would disagree, for example Lockwood (1989) and Stapp (2004).