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Wave Particle Duality

The Copenhagen interpretation of quantum mechanics invokes the notion of complementarity, or wave-particle duality, according to which the fundamental building blocks of matter are neither wave nor particle, but exhibit the properties of both. When we measure the position of a particle it appears as a point-like object with a precise position in space, but when left to its own devices, it evolves according to the laws of wave mechanics. This raises serious conceptual problems. We understand what a wave is, and we understand what a particle is, but it is difficult to conceive that something can be both wave and particle depending on what an experimental physicist does with it.

Young’s Slits

The laws of quantum mechanics and of the issues contained in wave particle duality are best illustrated by the Young's slits experiment, originally performed by Thomas Young in 1801 to resolve the long standing question of whether light was composed of particles, as Newton had believed, or whether it was a wave, as proposed by Huygens.Young made a point light source by shining sunlight through a single slit. This produces coherent light which passes through a pair of slits and illuminates a screen (in modern versions of the experiment, it is usual to use a laser light source, in which case the single slit is not required). Since the wave theory and the particle theory predict different patterns on the screen, the experiment should determine which is correct. If light consists of particles there should be a bright area in the centre of the screen, getting darker to either side. But if light is a wave then a circular wave pattern emanates from each slit. Where wave crests (red) meet crests and troughs (cyan) meet troughs, the amplitude of the wave increases creating a bright area on the screen. Where crests meet troughs, the waves cancel out (grey), leading to a dark region. These bright and dark bands are called interference fringes. Interference fringes are found, so Young concluded that light is a wave. Now imagine a reduction in the intensity of the light emitted from the source. At first the interference fringes merely grow dim, but if the intensity is reduced enough, light starts to behave like particles (photons). For a sufficiently dim light source, only one photon at a time passes through the slits. One photon does not produce interference fringes on screen. Instead it arrives at a precise point on the screen, behaving like a particle. A second photon arrives at a second point. If, over a period of time, a large number of photons pass through the slits, one at a time, the cumulative effect is the interference pattern. There is a large chance that each photon lands on the screen in one of the bright areas, and a very slim chance that it lands in a dark region. This is a most peculiar result, because the photon, which behaves like a particle when it leaves the source and when it arrives at the screen, seems to have the behaviour of a wave when travelling between the two.

Electrons as Waves

The Young’s slits experiment with single photons was not carried out until modern times, but in 1905 Einstein had shown that the photoelectric effect could be explained by hypothesising that light comes in quanta, now known as photons. In 1923 de Broglie reasoned that if a wave (light) turns out to be composed of particles, then particles might also behave like waves. This turned out to be correct. If the Young's slit experiment is performed for electrons instead of light, exactly the same result is obtained – electrons arrive at the screen as particles, each one at a point, but more of them arrive in specific areas. Again, the cumulative effect is an interference pattern.

This raises the questions “Which slit did the particle come through?” and “If it came through a particular slit, how can there be interference in a wave pattern from both slits?”. It is possible to test which slit the electron comes through, for example by shining a light behind the two slits, so that it scatters off the electron just after it passes through them. The electron now behaves like a particle as it comes through the slits. It is always seen to come through one or other slit. But the interference fringes disappear. The measurement to decide which slit the electron came through has changed the overall result. It is easy to see why. Light bounces off each electron as it comes through the slit, effectively kicking it off course and changing the pattern on the screen.

To minimise the effect of shining a light to decide which slit the electron came through, a very dim light might be tried. Now, sure enough, interference fringes start to reappear. But light is composed of photons. If an electron is hit by a photon as it passes through the slit, we can tell which slit the electron came through. The cumulative effect of electrons seen coming through the slits is fringes. But some of the electrons are not hit by a photon, and are not seen at all. The cumulative effect of unseen electrons is the interference pattern.

The Delayed Choice Quantum Eraser

Because light travels faster than electrons, in principle, the electron can pass through the slits before the decision is made, whether to switch on the light or leave it off. If we leave the light off, the electron apparently passes through the slits as a wave. If we switch it on, we find that the electron has passed through one or other slit, as a particle. We can apparently decide what type of behaviour the electron had at the slits after it has passed through them. This simple version of the experiment illustrates the principle, but is not viable in practice. The delayed choice quantum eraser experiment has been performed, and shows that we actually can determine behaviour at the slits after the particle passes through them.

The Collapse of the Wave Function

Just before the electron hits the screen it apparently takes the form of a wave spread over the region in front of the screen. On the instant it hits the screen, the wave ceases to exist, and the electron is detected at a single point, as though it is a particle. This process is known as the collapse of the wave function, or the reduction of the wave packet.

There are two parts to motion as described in quantum theory. The first is a determinist, continuous evolution following laws of wave mechanics. The second is a discontinuous, probabilistic change brought about by observation and measurement. This description summarises the whole of quantum theory, so that we may understand the principles of quantum mechanics by understanding the Young’s slits experiment.

The collapse of the wave function takes place instantaneously. As a consequence, special relativity implies that, if the wave is physically real, then according to a moving scientist, part of the wave collapses before the electron hits the screen, and, likewise, the electron becomes a particle before another part of the wave has started to collapse.

The Measurement Problem

The inherent conflict between determinist wave motion and probabilistic collapse has come to be known as the measurement problem. It has been suggested that probabilities in the results of measurement might arise from unknowns within the microscopic structure of a measurement apparatus and that the underlying physical processes in measurement are also governed by a wave equation, but there is no way to reconcile the linear process of wave evolution with the non-linear outcome of measurement. Decoherence shows how a macroscopic system interacting with a lot of microscopic systems (e.g. the individual light sensitive molecules of a photographic plate) can move from being in a pure quantum state to being in an incoherent mixture of quantum states, but it does not explain how the system comes to being in a particular one of these states.

Schrödinger’s Cat

Schrödinger put a cat in a box with a capsule of cyanide, triggered to break with a 50% chance by a quantum mechanical process killing the cat (oh, he didn’t actually do it, but he thought about it). A physicist looking at the box does not know whether the quantum process has broken the capsule or not, so he describes it with a quantum state, that is to say a wave function in which the process has part broken the cyanide capsule, and part not. If the wave function collapses when the observation takes place, then, prior to openning the box, he should describe the cat with a quantum state as well, in which the cat is part alive and desperately trying to get out of the box before the cyanide gets him, and part dead and lying in a heap on the floor. Mouse-over the image to open the box and observe the cat.

Wigner’s Friend

Wigner thought about putting his friend in the box, in place of the cat. If the collapse of the wave function does not take place until Wigner opens the box, then what happens to the friend? Is he now a wave function like the cat? If the friend is a physicist, does he not observe the capsule? Why should he not cause the wave function to collapse? What if he is not a physicist? Does anyone have the power to collapse a wave function, even if they don’t know what a wave function is? Can the cat cause the wave function to collapse? Can a beetle in the box collapse the wave function? Or a computer, or a ticker tape timer? Does a physicist outside the door of Wigner’s laboratory describe Wigner as a wave function who has part murdered his friend and part rescued him from the cyanide? Or do we each live in physically different universes, with wave functions collapsing at different times for each of us? These are just some of the issues raised if the wave function is part of the description of the physical properties of matter.

Relational Quantum Gravity

Relational quantum gravity is one of a number of what I call information theoretic interpretations. These interpretations have their roots in the original discussions between Bohr, Heisenberg, and others, which led to the Copenhagen interpretation, but they discard the notion of complementarity. The wave function is not conceived as describing a fundamental property of matter, but rather it describes what we can say about measurement. In these interpretations, the wave function is not real but is simply a way of calculating the probability for the outcome of an experiment. Information theoretic interpretations invert the measurement problem. Collapse is simply the change in a probability once the outcome of a measurement is known, but wave evolution requires explanation.

In my view, the problem with information theoretic interpretations is that they fall short of being complete interpretations of nature. If the wave function describes what we can know about reality, not reality itself, then we are still lacking a description of the underlying physics, and we do not have clear explanations as to why the laws of quantum mechanics yield correct probabilities or why evolution should obey the laws of wave mechanics. These are the issues addressed in relational quantum gravity.

There is no simple explanation of these issues. Rather, we must put together the mathematical treatments of relativity and quantum theory leading to quantum electrodynamics as described in this site. At the root of the explanation is the idea that we should take relativity one step further, into full blooded Cartesian relationism. Not only is motion relative, but position is relative too. Matter is described in terms of fundamental particles. Space and spacetime are not fundamental. They do not apply to the description of an individual particle, but emerge from interactions between many particles. Historically, relationism failed because it could not find a mathematical way in which to describe a universe in which only relative position is possible. Mathematics and physics are now a few generations more advanced. I have sought to show that quantum logic is the natural mathematical language in which we can describe measurement in a relationist universe and that wave evolution is imposed by special relativity.

If spacetime is an emergent quantity, it can only be used to describe the behaviour of matter when sufficient contact relationships (interactions) exist in the process under study. We can only say which slit a particle comes through if the particle has sufficient contact relationships with other matter to define position with respect to the slits. In special relativity we will define time and space coordinates by the radar method, using two way photon exchange. Later photon exchange will be seen in Feynman diagrams as the process which gives rise to the electromagnetic force and all the structures of matter in our immediate environment. Spacetime structure will be understood in the general case as emergent from the process of photon exchange. Using the radar method, the position coordinate of an event cannot be defined at the time of the event, but only afterwards, when the signal returns. Similarly, the spacial relationship of a particle passing through the slits is not determined at the time at which it passes through the slits, but only later, when the final form of its spacial relationships becomes established in the process of measurement.

The Einstein Podolsky Rosen Paradox (EPR)

We observe interference fringes which can be calculated from waves, but there is no direct observation of the wave function or of the infinite speed implicit in collapse. In order to highlight the very deep conflict between relativity and quantum mechanics, Einstein, Rosen and Podolsky imagined that a quantum mechanical process generates two particles flying in opposite directions with equal momenta. The momenta of the particles is not known, so the rules of quantum mechanics dictate that it is governed by a wave function. The two particles become separated. Alice measures the momentum of one particle, and Bob will measure the momentum of the second particle, at a distance remote from Alice. According to conservation of momentum, at the precise time at which Alice does her measurement, the outcome of Bob’s measurement is determined. So, the quantum state of a particle can be instantaneously changed by the remote action of an observer, in apparent conflict with relativity which prevents the instantanteous transmission of an effect.

Einstein believed that some unknown process, such as a hidden variable (a quantity which can be defined but cannot be known), must dictate the experimental result, but Von Neumann furnished a proof showing that local hidden variables cannot lead to the result (Bohmian mechanics seeks to circumvent the problem by postulating non-local hidden variables, but this simply means that instantaneous non-local effects are built into the interpretation from the outset, in defiance of both relativity and common sense).

Bell’s Inequality

John Bell adapted the EPR experiment to a form which is easier to test experimentally and demonstrated Bell’s inequality, by which the experimental predictions of quantum theory can be tested against theories of local hidden variables. He proposed using a process which emits two particles with equal and opposite spin. Initially spin is not aligned, but it can be measured in any axis. When spin is measured, it aligns with the axis chosen for the measurement. This implies that the other particle must be aligned on the same axis, with opposite spin. It appears that the fact of a spin measurement on one particle not only affects the result of measurement spin of the other, but actually determines the axis on which the spin of the second particle is aligned. Bell’s inequality shows that quantum theory and local hidden variables theories predict different correlations between the results of measurements on different axes, and enables us to experimentally determine which is correct. As stated by Bell, the implication is that, if quantum mechanics is correct, we must sacrifice at least one locality, causality, and realism.

The Aspect Experiment

Bell test experiments had been carried out a number of times and it had been found that Bell’s inequality is violated; the predictions of quantum mechanics supported. This left the possibility that the wave functions for both particles collapsed at the time of the decision of which axes to use, and that as this took place before the experiment, nothing need to travel faster than the speed of light. Alain Aspect and his colleagues in Paris set up the experiment in such a way that the decision on which axes were used to measure spin was made by a pseudorandom generator, after the particles were emitted. They still found that Bell’s inequality was violated. Improved versions of the experiment have confirmed the result. The decision on which direction to measure spin of one particle affects the measurement of the other, even though a message from the point of decision to the second particle would have to travel faster than the speed of light.

In spite of this result, no information travels from the results of one measurement to the other. At the time when Bob measures the spin of the second particle, there is no way he can say that his result is affected by Alice’s measurement of the first, because he does not yet know Alice’s result. Alice and Bob’s results must be brought together before a correlation can be found establishing that Bell’s ine quality is violated. The question, however, remains. If nothing travels faster than light, how can the correlation come about?

Locality and Causality

In practice, quantum mechanics is overwhelming supported by experiment. Physics makes no sense if we sacrifice realism. It seems we must have a problem with either locality, causality, or both. In relational quantum gravity we do not have to sacrifice either locality or causality, but we do have to be careful about how we state them. We have to dismiss naive statements based on an assumption of background spacetime. Bell's theorem does not lead us to reject locality or causality, but rather to reject the notion of a fundamental spacetime.


The reasons for this definition, and the meaning of proper time, will become clear in the treatment of special relativity in the next section. This Cartesian definition reflects the locality condition in qed, and allows that entangled particles in Bell's theorem are separated, in accordance with our intuitive ideas.


By this definition there is no causal relationship between the measurements of the entangled particles in Bell's theorem. The measurement of one particle does not alter the probabilities for the results of measurement of the other. Only when the two experimenters get together and compare results do they find a correlation. This can only be done at a later time, showing that the correlation is causally related to the measurements, but not that the measurements are causally related to each other.

Emergence of Spacetime

In relational quantum gravity, the resolution of Bell's theorem is not that we must reject realism, locality or causality, but rather we must recognise that spacetime is an emergent concept. It will be found in quantum electrodynamics that the process of photon exchange is responsible for the electromagnetic force, and all the structures we observe in our immediate environment. In relational quantum gravity we interpret spacetime as emerging as from photon exchange. An electron passing through the slits does not interact with the environment, and does not participate in the structure of space time created by other matter in the environment. It is therefore impossible to say which slit the electron passes through. It remains to understand interference effects which arise from quantum theory.

The notion of separation can only be said to hold when spacetime exists, that is to say *after* the required physical processes have taken place for the emergence of spacetime. This has not happened at the time of Alice and Bob’s measurements in the Bell tests, but it has happened when Alice and Bob get together and determine the correlation. There can be no exchange of photons between the immediate environments of Alice and Bob at the time of their measurements, because this would require that photons travel faster than the speed of light. Therefore, while Alice and Bob each observe spacetime structure in their immediate environment, the structure connecting those two regions is not yet complete. At the time when Alice and Bob bring their measurement results together, there will have been many more billions of interactions exchanging photons, and a single spacetime structure containing the regions of spacetime in which Alice and Bob carry out their measurements is then completed.

We cannot say that the outcome of one measurement has effected the other, because this presupposes the existence of spacetime, and puts the logical cart before the horse. We can only discuss the relative orientation of Alice & Bob's measurements in the context of a spacetime structure which contains both. In special relativity the structure of spacetime emerges from two way photon exchange in radar. In relational quantum gravity it emerges from photon exchange in the fundamental structures of matter. We can only talk of spacetime after two way photon exchange has taken place in such a way that spacetime structure has emerged. At the time the measurements take place, spacetime structure is not yet complete.

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