Quantum Interpretations

Over the years, considerable progress has been made based on experiments with individual quantum systems. Based primarily on technological progress, it is now possible to actually perform, in part, certain aspects of the earlier ‘gedanken’ thought experiments on which so much emphasis was originally placed. However, in many ways, this progress has only succeeded in drawing attention to the more fundamental problems of understanding, and interpreting, the full implications of quantum theory for which no definitive consensus has yet been reached.

In many respects, it might be argued that many of the interpretations, to be discussed, may well be based on the philosophical preference of its author. So while an interpretation may be underwritten by a certain amount of mathematical justification, each remains beyond any reasonable form of empirical verification and, as such, cannot be completely refuted, no matter how improbable. In this respect, it is important to note that nearly all of these interpretations are in full agreement with each other regarding theoretical predictions and experimental observations. As such, there may be no obvious way of deciding, at this time, which of these interpretations is right, or wrong, although this state of affairs might explain why so many interpretations persist.

So what purpose do these interpretations serve?

At one level, an interpretation might simply debate the formalism of quantum theory in terms of the premises that underpin its equations, which ultimately lead to the predictions on which it is quantitatively judged. Alternatively, other interpretations may focus more on the ‘ontological’ versus ‘epistemological’ debate centred on the underlying nature of reality. However, from the practical perspective of the following discussions, we might list a number of questions that many people might ask themselves along the way:

In what reality does quantum wave superposition exist?
In what reality does the collapse of the quantum wave take place?
Can entanglement be explained in any other way?
What is the role of the observer in the measurement process?
Why is the description of quantum processes so complex?

Again, it needs to be stressed that there is no overwhelming consensus that suggests any of the interpretations represent anything more than hypothesis, i.e. speculation, at this point in time. As indicated, in some respects, many are little more than philosophical conjecture on which further assumptions have been extrapolated, which ultimately lead to unverified or unverifiable conclusions. As such, we will only review a selection of the interpretations in the table below, primarily to reflect the scope of opinions that have existed and, to some extent, still exist in modern quantum theory.

In the context of the table above, it might be argued that the original Copenhagen Interpretation tried to restrict the scope of conjecture to that of quantum mechanics being a mathematical tool. As such, while it might be capable of accurately determining the probability of an event occurring in the quantum realm, it deferred from too much speculation as to why ‘quantum reality’ appears to work as it does. As a result, other interpretations were developed that tried to address this ‘missing piece’ in our understanding by attempting to explain how ‘mechanical determinism’  emerges from the description of 'mathematical probability. For the sake of brevity, the central aspects of discussion will be limited to just two experimental aspects, which have been previously discussed, i.e.

• Double slit experiment
• The EPR experiment

While most interpretations try to remain within the boundary of any accepted experimental results, it is clear that they are also attempting to address issues, which extend beyond any accepted explanation of verifiable science. Therefore, while the links above point to overviews of established positions, any discussion of the various  interpretation tends to expand the scope of the debate to include a wider perspective of the issues, e.g.

• Double-Slit Experiment:
  Intuition suggests that no wave interference pattern will occur when photons, as particles, pass through one or other of the two slits. However, in contradiction to this intuition, an interference pattern does emerge as successive photons seemingly passes through one or the other of the two slits. While we might make some general reference to the wave-particle duality of photons, there is no obvious ‘mechanical’ solution that can be visualised in terms of a Huygen’s wave front or how far this wave front  extends around the wave-particle. Basically, there is no accepted structural model of a photon. However, as a ‘mathematical’ solution, QM is free to define the photon as a probability amplitude associated with some given wave function, which is then able to pass through both slits, even though there is no obvious corresponding mechanical description. We might even extend the idea of a photon being represented as a probability amplitude, as discussed under Feynman’s QED model, such that the mathematical model of the photon not only ‘travels’ the two paths through the slits, but every conceivable path, i.e. the sum over all paths. However, again, we appear to be left with no obvious mechanical counterpart to this mathematical solution. This said, the discussion of coherence may offer up some physical rationale as to why the interference pattern disappears when measurement is involved.
  
  
• Bell’s Theorem:
  Bell’s theorem or inequalities relates to statistical measurements made by observers on pairs of particles that have interacted and then separated, such that they might be described as entangled. However, over time, a set of inequalities, similar to Bell's original inequality, have been defined that might now be generally referenced as Bell’s theorem. If Bell's theorem is correct it suggests the results predicted by quantum mechanics cannot be explained by any theory, which preserves locality, while supporting hidden variables. However, none of the tests to-date has met all the conditions required by the theorem, while many of the conditions imposed on local hidden variable theories have been criticized as overly restrictive. Therefore, many argue that results to-date cannot necessarily be cited as conclusive proof of non-locality. As such, we are left to consider whether this mathematical conjecture provides adequate grounds on which to reject the existence of an objective reality.
  
  
• EPR Experiment:
  Based on Bell’s inequality, it is often assumed that there can be no accepted quantum mechanical solution that can avoid the issue of non-locality, such that there is no obvious mechanical explanation of quantum entanglement. If we define an entangled state in terms of quantum spin, when a measurement causes the ‘assumed’ collapse of an entangled wave function, it immediately determines the spin of both particles, irrespective of the distance between them. As such, there is a suggestion of some quantum effects that travel faster than light, which have led to the description of ‘spooky action at a distance’ that have no obvious propagation mechanism.

The only point of raising these issues at this stage is to highlight the need to decide whether any of the following interpretations really provide an adequate, or probable, solution in terms of both its mathematical and mechanical description of reality.