Premise, Verification and Conclusion
As outlined in the previous discussion, the pre-war years established many of the foundation principles, along with an initial philosophical interpretation, which in many respects are still associated with quantum theory today. However, it might be argued that this initial era of quantum mechanics also brought about an equally significant change in the underlying methodology of science, as reflected in the title of this discussion. In this context, we should possibly clarify the scope of ‘hypothesis’ as being distinct from ‘theory’, as it will be suggested that a theory has to be subject to some experimental observation or verification, although not necessarily conclusive, before it becomes more widely accepted. In contrast, a hypothesis may be little more than a speculative assumption, possibly only sustained by the consistency of its mathematical argument.
So is quantum mechanics, hypothesis or theory?
While most might reasonably argue that QM/QFT is an accepted theory, subject to much experimental verification, there is clearly an aspect of quantum mechanics that still unsettles many people, such that we may wish to table another question:
If QM/QFT is a verified theory, why are there still so many different interpretations?
Clearly there is an aspect of uncertainty, not so much with the verified results, but rather with the premise of some of the assumptions that have not been verified. For example, we might cite the premise of the wave function collapse, which is a general assumption of the theory, which has not been verified and on which many of the interpretations differ. As such, it would appear that we might have to question this assumption and that of an entangled quantum state prior to the assumed collapse of a wave function. For if the wave function itself only exists as a mathematical construct, what reality do we assign to any subsequent description linked to this concept? In fact, it was this type of debate that led Schrodinger to question the physical or ‘ontological’ description of the wave function and, by 1935, he appears to have conceded the point in the following quote:
“I am long past the stage where I thought that one can consider the wave function as somehow a direct description of reality.”
For it seems that many were able to argue that Schrodinger’s wave function exists outside of what most people might initially assumed to be the objective reality of ‘physical spacetime’, but which mathematicians might describe in terms of ’configuration space’. Therefore, in order to understand how quantum mechanics continued to develop in the post-war years, we possibly also need to outline the nature of mathematical space, as opposed to what we might intuitively consider physical space. The following list is purely illustrative, and not exhaustive, of the apparently ever-expanding description of mathematical space:
- 3D Space to 4D Spacetime
- Configuration to Phase Space
- Hilbert to Fock Space
The idea of 3-dimensional space is a fairly intuitive concept for most people given that we have sensory capability to directly perceive space extending along one of 3 axes. However, the idea of 4-dimensional spacetime, as required by special relativity, might be said to be more of an abstract concept, although central to the ability of physics to describe the effects of relativistic motion within a mathematical framework. As such, we might immediately see a requirement that extends beyond the normal human perception of space and time. In this context, phase space is another coordinate system described in terms of position [q] and momentum [p] of the particles within the system. In practice, the motion of an ensemble of particles in phase space can be reduced in complexity by employing statistical mechanics. Through such concepts it is possible to calculate the state of a system, at any given time in the future or the past, using the ideas of Hamilton or Lagrange mechanics. Of course, we can still relate phase space back to a possibly more basic description of ‘physical space’ using a simple illustration in which two particles [p_{1}] and [p_{2}] are said to have independent trajectories in terms of 3-spatial dimensions and 1-time dimension, e.g.
[1]
However, while the transition into quantum mechanics often prefers to model a system of particles, as an ensemble system, similar in scope to statistical mechanics, it does so based on the probability density associated with Schrodinger's wave equation. As such, a two particle ensemble would conform to the following generic description:
[2]
We can see that the conceptual form of [2] now requires 7 parameters to define the probability of all possible combinations of location within the 2 particle example. However, for N-particles, the definition of configuration space requires 3N+1 dimensions, i.e. 3 spatial dimensions for each particle plus one for time. Equally, in quantum mechanics, it is said not to be possible to define the probability model for [p_{1}] and [p_{2}] in isolation, i.e. before the wave function collapse, because components of the system may exist in an entangled state. So, proceeding towards evermore abstraction, we might define Hilbert space as another mathematical concept that generalizes the notion of Euclidean (3D) space. As such, it extends the ideas of vector algebra and calculus in 2D/3D space to a conceptual space of possibly infinite dimensions. However, the idea of Hilbert space can be extended, yet further, by introducing the concept of Fock space as an algebraic construct of quantum states representing an unknown number or statistical ensemble of particles from a single particle Hilbert space. Within these different definitions of ‘space’, we might see one of the fundamental issues that has led to so many differing interpretations of quantum mechanics, which may be more reflective of a philosophical debate about the mathematics, than the actual physics, in the absence of any definitive empirical verification. Therefore, in the spirit of the philosophical debate to follow, it might not be totally inappropriate to precede the discussion of quantum interpretations with some possibly contentious, but thoughtful, quotes:
Physics is becoming so unbelievably complex that it is taking longer and longer to train a physicist. It is taking so long, in fact, to train a physicist to the place where he understands the nature of physical problems that he is already too old to solve them. Eugene Paul Wigner |
While those on the wrong side of the dividing line of experience might not like to admit it, they might still acknowledge the amount of time now required to come to any appreciable understanding of just one branch of modern physics may have already extended beyond a human lifetime. Of course, this then raises the question as to who is qualified to judge the totality of physics:
Nobody knows more than a tiny fragment of science well enough to judge its validity and value at first hand. For the rest he has to rely on views accepted at second hand on the authority of a community of people accredited as scientists. But this accrediting depends in its turn on a complex organization. For each member of the community can judge at first hand only a small number of his fellow members, and yet eventually each is accredited by all. What happens is that each recognizes as scientists a number of others by whom he is recognized as such in return, and these relations form chains which transmit these mutual recognitions at second hand through the whole community. This is how each member becomes directly or indirectly accredited by all. The system extends into the past. Its members recognize the same set of persons as their masters and derive from this allegiance a common tradition, of which each carries on a particular strand. Michael Polanyi |
In essence, the quote above suggests that there may no longer be much room for a polymath in modern science, even if they exist, as the complexity expands beyond that of any individual endeavour. As such, this might explain the institutional segregation of knowledge in which each branch of science establishes its own hierarchy of authority. Of course, if you accept that science is still subject to the human condition, then the implications of the next quote may not seem so contentious:
I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Count Leo Tolstoy |
While some may reject the suggestion that science can ever be deflected from its truthful endeavour, it may still be argued that science does not develop in isolation of the human condition. If so, then we might still reference Maslow’s hierarchy of human needs and recognise the influence of esteem and power at the apex of this hierarchy.
“Unwilling to confess their ignorance of the formula or unable to question its relevance to the question at hand, his opponents accepted his argument with a nod of profound approval” |
Clearly, by way of counter-argument, many may wish to point out that this position is far too cynical and simply point to the many important insights gained through quantum theory in the post-war era. With this counter-position tabled, we shall now turn our attention to the various interpretations of quantum mechanics to see if they help to refute the apparent accusation being made. However, before doing so, the following footnote might be seen as an example of where deductive premise can lead, for in the absence of verification, it may well be as valid an interpretation as any of those about to be reviewed!
Abstract: A
Cybernetic Interpretation of Quantum Mechanics
Ross Rhodes
This paper surveys evidence and arguments for the proposition that the universe as we know it is not a physical, material world but a computer-generated simulation, a kind of virtual reality. The evidence is drawn from the observations of natural phenomena in the realm of quantum mechanics. The arguments are drawn from philosophy and from the results of experiment. While the experiments discussed are not conclusive in this regard, they are found to be consistent with a computer model of the universe. Six categories of quantum puzzles are examined: quantum waves, the measurement effect (including the uncertainty principle), the equivalence of quantum units, discontinuity, non-locality, and the overall relationship of natural phenomena to the mathematical formalism. Many of the phenomena observed in the laboratory are puzzling because they are difficult to conceptualize as physical phenomena, yet they can be modeled exactly by mathematical manipulations. When we analogize to the operations of a digital computer, these same phenomena can be understood as logical and, in some cases, necessary features of computer programming designed to produce a virtual reality simulation for the benefit of the user.