The previous section of this review has attempted to provide an initial outline of some of the broad issues associated with the quantum model. This section will now try to consider some further causal issues associated with this model, which have arisen over the last 100 years. Again, while recognizing that the entirety of the quantum model is beyond the scope of this review, it will attempt to highlight some possible issues of concern. We might start with a basic characterisation of some of these issues:
- The quantum model is predicated on many mathematical abstractions.
- The model often lacks a coherent explanation of its causal mechanisms.
- Many explanations appear to rest on epistemological assumptions.
- Many assumptions extend beyond the ability of science to empirically verify.
The issue of the wave-particle duality was cited as a primary example of an assumption, which leads to causal contradictions. This situation can then be compounded when descriptions simply switch between the semantics of particles and waves, such that causality is lost in mathematical abstraction and multiple assumptions, which cannot be verify. Many times, it seems the unexplained is simply avoided by citing ‘ quantum weirdness ’, such that this assumption is now sufficient for science to stop looking for better models and answers. As already outlined, it might be argued that the historic development of the quantum model was first anchored to the Bohr model of the atom, forwarded in 1913. However, this model was quickly questioned as it did not account for a growing number of observations, such as the fine structure spectra of hydrogen. Equally, Bohr's model had initially suggested that that there could only be one electron per orbital, while in 1925 Pauli proposed a limit of two. However, Pauli’s resolution of this problem required the idea of quantum spin to be associated with an electron particle, as it moved within its orbital, although the nature of both ‘spin’ and ‘orbit’ are both questionable as physical concepts. Later, in 1926, Dirac’s equation suggested a ‘remedy’ to the non-relativistic nature of the Schrödinger equation in the form of the missing spin quantum number.
Note: Based on Pauli’s Exclusion Principle, two electrons can only occupy a single orbital if they have different spin. As such, the spin quantum number was assumed to provide two possible values [↑↓] to differentiate the electrons in the same orbital.
However, Dirac’s equation was not without its own set of issues, not only in terms of the requirement for negative energy states and the idea of virtual particles in quantum electrodynamics, which did not explain the anomaly of the Lamb shift or the magnetic moment of the electron. Dirac also tried to solve the issue as to why a bound electron does not emit radiation according to Maxwell’s equations by imposing the constraint of relativistic invariance.
Note: Within the Bohr model, an electron had an orbital velocity, such that it also has angular acceleration. If so, it was initially assumed that the electron should emit EM radiation, i.e. lose energy, and collapse into the nucleus. While this was obviously not the case, explaining why a bound electron did not emit EM radiation, as predicted by Maxwell’s equations, proved to be problematic within the particle concept. Of course, if the electron is described in terms of some form of standing wave structure with a wavelength defined by its orbital position, we then might question whether a bound electron has any velocity, such that Maxwell’s equations might only be applied to free electrons. However, we might also question how two electrons with opposite ‘spin’ within a single orbital are explained by a wave model.
So, to recap with the benefit of hindsight, the Schrödinger equation originally only provided a limited solution for the Bohr hydrogen atom and only referenced three quantum numbers, not four. Later, it was recognised that this solution did not account for a relativistic frame of reference. It also failed to predict the Lamb shift or the fine spectral structures or explain why bound electrons do not radiate energy. As such, there was an ever-growing conflict between predictions and observations, especially associated with larger atoms. Equally, the time-dependent solution of Schrodinger’s equation leads to the idea of a dispersive function in which different frequency components ‘propagate’ at different velocities, at least within the confines of its mathematical abstraction, such that the wave function disperses spatially and only unifies as a ‘particle’ based on the assumption of a ‘wave function collapse’. Within this wave-particle duality description, an electron can be effectively everywhere at some instance in time, while having no volume, but then able to collapse back into a point particle in zero time. As such, we might see the progression from Bohr’s original model towards increasing abstraction, which is decoupled from any obvious causality, i.e. we have a mathematical model not a physical description.
Note: It might also be highlighted that beyond a one-electron atom, the equations of the quantum model can still only be solved using approximation methods. For, in more complex configurations, the Schrödinger equation takes a differential form for which there is no analytical solution. Therefore, mathematical methods are used to approximate solutions of the eigenvalues using the variational method and perturbation theory.
However, some argue that these methods cannot be physically tested and often appear inconsistent with physical laws, such that we might justify the description of these methods as only approximations. So, in many cases, the success of the quantum model appears to required non-physical assumptions, e.g. probability wave functions or the renormalization of infinities, which even after decades of development have not been explained in terms of causality and only served to expand the assumptions underpinning a mathematical model, which often has little to say about physical reality.
Note: The behaviour of free electrons in superfluid helium might also question the quantum interpretation of the wavefunction as it suggests that the wave function does have a physical position, not a dispersed distribution, such that we might also question the need for the wave function collapse.
In the context of this outline, we might possibly understand why so many continue to question some aspects of the quantum model, because its foundations often appear to conflict with physical laws and suggest only probability outcomes. From the epistemological perspective of the Copenhagen interpretation, any speculation about the physical reality of an electron or photon, when not being observed must remain speculation. So, within the concept of the quantum model, it may only seek to correlate probability outcomes with experimental observation without necessarily providing any causal mechanisms. Of course, free from the need to explain how or why a quantum probability outcome occurs also gives it the freedom to simply justify its mathematical assumptions on the same basis that Ptolemy’s solar model made positional predictions of the planets on an entirely false assumption of physical reality. For, if a model is decoupled from physical causality, it is also able to speculate on all manner of things, which might be described as ‘unobservable’, such as virtual particles, multiple dimensions, the nature of charge and spin, along with many other esoteric speculations, such as worm holes, spooky action at a distance, infinities, faster than light signalling and even parallel universes.
Note: Today, after 100 years of research and development, quantum
theory still persists with the semantics of a wave-particle duality.
In addition, there remain unresolved measurement issues associated with
decoherence, wave function collapse, nonlocality, uncertainty and even
the reality of what exists between the initial and final quantum state.
In this context, the following discussions simply question whether all
of the issues raised against the quantum model can be answered based
on the claim of epistemological knowledge without providing the necessary
explanation of ontological causality. It might also be suggested that
such issues cannot be resolved by a show of hands to signify a preference
of some scientific consensus.