In Part-1: The Pre-War Years, we covered the development of a number of concepts, which appeared to contradict the established view of classical physics at that time. The implications of these quantum concepts would, over a period of some 20-30 years, come to be accepted in what is now known as the Copenhagen Interpretation. However, this acceptance was far from universal, even between the founders of quantum theory, and the debate surrounding its interpretation of objective reality continues to this day.
To allow this section of the discussion to continue without immediate reference to earlier discussions, we might try to summarise some of the more far reaching implications linked to the Copenhagen Interpretation. From a classical perspective, these implications would not only question the assumed deterministic nature of reality, but ultimately come to question whether it was possible for science to even describe any sort of objective reality:
|According to the original formalism of QM, there is no clear distinction between particles and waves, at least, as often perceived in terms of classical physics. However, where similar semantics are used in QM, they normally infer a description of point particles and wave functions, while in QFT these concepts become increasingly submerged within a description of a system defined in terms of states and observables, which are then collectively modelled as a virtual statistical ensemble. In this respect, deBroglie’s original description of a matter-wave appears to have become lost within a mathematical construct, which has no agreed objective existence.|
However, this interpretation was not, and is still not, universally accepted, such that we might identify a number of distinct philosophical positions that will initially be defined as ranging from ‘objective’ to ‘subjective’ descriptions of reality. However, this philosophical debate might be anchored to almost any number of starting points, which then lead to different conclusions about the quantum model, e.g.
- QM is incomplete/wrong, therefore cannot fully describe an objective reality.
- QM is complete/right, therefore it must describe a quantum reality.
- QM is only partially verified, therefore its description is still hypothetical.
- QM is a mathematical construct therefore can only describe a subjective reality.
In many respects, this scope of opinion appears to have gone hand-in-hand with the development of quantum mechanics from its inception, despite its obvious predictive successes along the way. However, while the actual issues that drive people to different opinions can be very complex, the basic problem might possibly be summarised in quite a simple question:
Based on known facts, what is quantum theory actually telling us?
Naturally, the development of quantum mechanics in the post-war era would have started out being influenced by earlier philosophical debate, but it would also have been guided by the growth of supportive experimental data, which suggested quantum reality was indeed fundamentally different to any description anchored in classical mechanics. However, as experimental data continued to grow in apparent support of the somewhat more ‘metaphysical’ interpretations of quantum mechanics, so the idea of a physical or objective reality appear to give way to a purely mathematical description of reality.
But what arguments supported such assumptions?
Possibly, at this point, we need to step back and widen the context of the discussion to consider our own perception of reality. As has been touched on in other discussions, what we, as human beings, perceive as physical is based on an internal construct within our brains derived from inputs from our senses. As such, our perception of reality is intrinsically ‘subjective’ based on evolutionary physiology and ever-changing worldviews, e.g. cultural beliefs. From this perspective, we might realise that it is possible for different people to have a different perception of reality, which must become increasingly obvious when the argument is extended to different life-forms, e.g. apes, mammals, fish, insects. However, returning to the domain of scientific knowledge, we might realise that developments over the last 2000 years have come to profoundly changed the way most of us understand the world around us, i.e. what constitutes our understanding of reality. As such, we have seen the solidity of our world give way to atoms, which might be described as point-particles in the vastness of the sub-atomic vacuum of space interconnected by fundamental forces. Now, within the scope of QFT, we are being asked to consider the ‘physicality’ of the sub-atomic structure, where the only tangible concepts left might be the idea of quantum waves within quantum fields.
But what are quantum waves and quantum fields?
In practice, the questions regarding the ‘real’ nature of a quantum wave appear to be seldom asked these days, possibly because the classical concept of a wave has become subsumed within the mathematical definition of the wave function. As such, the interpretation of the wave function has essentially become dependent on a mathematical construct of space, e.g. phase or momentum. When the discussion of quantum fields does occur, it is usually anchored in some initial perception of an electromagnetic fields, which can then quickly become lost in the extended description of static, scalar, vector and/or spinor fields. Likewise, while QFT still appears to use the semantics of particles in many of its descriptions, this usually only infer the mathematical construct of a point-particle, which does not necessarily have any implied physical existence, despite any initial misconceptions anchored in classical physics.
So what, if anything, physically transports energy and momentum from A to B?
While you might start to question the point of this discussion, it is simply trying to highlight the trend whereby theoretical physics has become increasingly dependent on mathematical constructs to the point where mathematics becomes our most fundamental description of reality. For example, in the first chapter of Roger Penrose’s book ‘The Road to Reality’ he provides the diagram shown below to illustrate the perception of reality in terms of a threefold relationship:
However, while most might accept the growing necessity of mathematical models, as a critical ‘tool’ of modern science, we might also need to consider a more profound question about the nature of reality, as described by the mathematics within quantum theory.
Does quantum theory question the existence of any physical objective reality?
The development of quantum theory represents a progression of scientific thinking, which we might initially anchor in Planck’s introduction of quantized energy and Einstein’s suggestion that light has a particle-like nature as well as a wave-like nature. Later, Compton’s work appeared to confirm Einstein’s idea about light photons having a particle-like nature, which deBroglie then extended to electrons having a wave-like nature, such that the whole wave-particle duality debate would be re-opened. Subsequently, Schrodinger developed a wave solution, which although still rooted in classical wave mechanics included a number of key changes. First, the switch to the complex form of the wave equation, developed by Euler, which allowed Schrodinger to create a solution that used the 1st differential with respect to time, while also replacing the physical concept of amplitude [A] with the abstracted symbol [Ψ]. By using the 1st differential form, Schrodinger was then able to directly substitute for the dispersive relationship between wave number [к] and angular frequency [ω] and replace these terms with equivalent energy [E] and momentum [p] expressions rooted in deBroglie hypothesis.
Note: See note following equation  in the discussion 'A Matter of Perspective' for a wider discussion of dispersion.
But how should such paradigm shifts be interpreted?
Based on classical wave mechanics, the square of the wave amplitude [A] corresponded to energy, but Max Born would interpreted the square of the amplitude [Ψ] as simply the mathematical probability density of finding a particle in a certain location in space.
Was this a pivotal change in scientific thinking?
The question is raised because, in some respects, Born’s interpretation of the probability amplitude might be seen as the point where mathematical reality started to take some precedence over the idea of physical reality. Of course, from a physical perspective, it is not unreasonable to assume that the probable location of a particle would coincide with the location of maximum energy. However, Dirac’s Equation would, in some ways, complete a mathematical transformation of a classical wave function, subject to relativistic energy consideration, into a purely mathematical description requiring 4x4 matrices in which complex numbers were needed to represent any notion of a quantum spin state.
But does this mathematical perspective really question the very nature of objective reality?
In the same timeframe, the Copenhagen Interpretation forwarded the idea that quantum waves were primarily a mathematical construct, which should not necessarily be interpreted as having any objective reality. However, at some level, quantum theory still appears able to predict the outcome of an apparently ‘physical’ process, at least, in the sense that there are processes involving energy [E] and momentum [p] that can be measured. As a simplification of the details, such issues might suggest why the Copenhagen Interpretation has never been fully accepted, even in the scientific community, and why alternatives have subsequently been sought. So, in many ways, we might summarise the following discussions in a single question:
Does mathematics simply model reality or does it become reality itself?