The de-Broglie–Bohm Approach Viewed Through Systemic Functional Linguistics

Penrose (2004: 1032):

As far as I can make out, the only interpretations that do not necessarily depend upon some notion of ‘conscious observer’ are that of de-Broglie–Bohm that require some fundamental change in the rules of quantum mechanics, according to which U and R are both taken to be approximations to some kind of objectively real physical evolution.

As I have stated in many places in this book, I am an adherent of this last view, where it is with gravitational phenomena that an objective R (i.e. OR) takes over from U. This gravitational OR would take place spontaneously, and requires no conscious observer to be part of the process. In usual circumstances, there would be frequent manifestations of OR occurring all the time, and these would lead to a classical world emerging on a large scale, as an excellent approximation. Accordingly, there is no need to invoke any conscious observer in order to achieve the reduction of the quantum state (R) when a measurement takes place. 

On the other hand, I envisage that the phenomenon of consciousness — which I take to be a real physical process, arising ‘out there’ in the physical world — fundamentally makes use of the actual OR process. Thus, my own position is basically the reverse of those referred to above, in which, in one way or another, it is envisaged that consciousness is responsible for the R process. In my own view, it is a physically real R process that is (partly) responsible for consciousness!

Blogger Comments:

To be clear, the de-Broglie–Bohm 'pilot wave' interpretation of quantum mechanics posits two levels of reality:

a firmer ‘particle’ level of the reality of the configuration of the system, as well as a secondary ‘wave’ level of reality, defined by the wavefunction ψ, whose role is to guide the behaviour of the firmer level.

From the perspective of Systemic Functional Linguistic Theory, the 'wave' level identifies the range of potential construals of experience as meaning, and the 'particle' level constitutes an instance of those potential construals. From this perspective, both levels are intersubjectively real.

The 'taking over' of R from U — the collapse of the wavefunction — is the instantiation of potential when a conscious observer takes a measurement, and the wavefunction 'guides' the 'behaviour of the firmer level' in the sense that is delimits the range of potential that can be instantiated and grades it in terms of probability.

Consciousness, in this view, is mental and verbal symbolic processing, rather than a physical process, but it is realised by physical processes of the brain, the observation or thought of which is an instance of a construal of experience as meaning.

The ‘Pilot-Wave’ Approach Viewed Through Systemic Functional Linguistics

Penrose (2004: 811):

… the de Broglie–Bohm ‘pilot-wave’ viewpoint (e) appears to have the clearest ontology among all those which do not actually alter the predictions of quantum theory. Yet, it does not, in my opinion, really address the measurement paradox in a clearly more satisfactory way than the others do. As I see it, (e) may indeed gain conceptual benefit from its two levels of reality — having a firmer ‘particle’ level of the reality of the configuration of the system, as well as a secondary ‘wave’ level of reality, defined by the wavefunction ψ, whose role is to guide the behaviour of the firmer level. But it is not clear to me how we can be sure, in any situation of actual experiment, which level we should be appealing to.

My difficulty is that there is no parameter defining which systems are, in an appropriate sense, ‘big’, so that they accord with a more classical ‘particle-like’ or ‘configuration-like’ pictures, and which systems are ‘small’, so that the ‘wavefunction-like’ behaviour becomes important (and this criticism applies also to (d) ). We know that quantum behaviour can stretch over distances of tens of kilometres at least, so that it is not just physical distance that tells us when a system ceases to look quantum mechanical and begins to behave like a classical entity. But nevertheless there is a sense in which a large object (like a cat) seems not to accord with the small-scale unitary quantum laws. …

But whether or not one believes that any particular such measure is appropriate, it seems to me that some measure of scale is indeed needed, for defining when classical-like behaviour begins to take over from small-scale quantum activity. In common with the other quantum ontologies in which no measurable deviations from standard quantum mechanics is expected, the point of view (e) does not possess such a scale measure, so I do not see that it can adequately address the paradox of Schrödinger’s cat.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the two levels of reality in the de Broglie–Bohm ‘pilot-wave’ viewpoint are the two poles of instantiation: potential and instance. The secondary 'wave' level of reality constitutes the range of potential construals of experience as meaning, and the firmer 'particle' constitutes an instance of that potential: an actual construal of experience as meaning. So, since an actual experiment involves an actual construal of potential, 'we should be appealing to' both levels, instance and potential.

In this view, 'classical' phenomena, such as large-scale objects like cats, do accord with small-scale quantum laws, because an observation of a cat is an actual construal of experience of meaning: the most probable instance of potential construals. The improbability of other potential construals accounts for their non-instantiation at scales within the range of immediate human perception.

The thought experiment of Schrödinger's cat ceases to be a paradox when it is understood that 'classical-like' behaviour is an actual construal of experience as meaning, and that the notion of 'small-scale quantum activity' fails to distinguish between such a construal and the probabilistic potential construals of which it is an instance.

Wavelike Particles And Particulate Waves Viewed Through Systemic Functional Linguistics

Penrose (2004: 500-1):

The upshot is that a particle of momentum p seems to be a periodic thing, like a wave, where there is a universal relationship between the wavelength λ and the magnitude p of its momentum … 

The wavelength λ, associated with a particle of momentum p, is called its de Broglie wavelength, after the highly insightful French aristocrat and physicist Prince Louis de Broglie, who first suggested, in 1923, that all material particles have a wavelike nature with a wavelength given by the above formula. Moreover, in accordance with the requirements of relativity, the particle should also have a frequency ν … 

These kinds of consideration led to the conclusion that an ordinary particle displays wavelike behaviour, this having a universal relationship to the particle’s rest-mass as determined by the Planck and de Broglie formulae.  

But, in the previous two decades, a converse to this had already been established, demonstrating that entities previously thought of as purely wavelike — basically Maxwell’s oscillating electric and magnetic fields as the constituents of light — had also to be viewed as having a particulate nature, again consistent with the Planck and de Broglie formulae.

 

Blogger Comments:

If wave-particle complementarity is viewed from the perspective of Systemic Functional Linguistic Theory, then a wave constitutes quantum potential and a particle constitutes an actual instance of that potential. The crest of a wave measures the most probable location of a particle, the frequency measures the number of probability peaks per time interval, and the wavelength measures the time interval between probability peaks. It is in this sense that wavelength is 'associated' with the momentum (mass x velocity) of a particle.

Matter Waves Viewed Through Systemic Functional Linguistics

Davies & Gribbin (1992: 196):

A French student, Louis de Broglie, came up with a bold idea. If light waves can behave like particles, perhaps electrons, which everyone then thought of as material particles, could also behave like waves? Developing this idea, de Broglie produced a simple formula showing how the wavelength of such a particle might be related to the momentum of the particle. Momentum is the product of mass and velocity; de Broglie suggested that converting momentum into wavelength involved, once again, Planck's constant. 

Although de Broglie did not provide a detailed theory of matter waves (that was achieved by the Austrian physicist Erwin Schrödinger), his idea provided a graphic model for the way that electrons might occupy only certain energy levels around the nucleus of an atom. If an electron is in some sense a wave, then in order to make the wave "fit'' into an orbit around the nucleus, the size of the orbit must correspond to a whole number of wavelengths, so that when the wave is wrapped around the nucleus it will join together smoothly. Only certain discrete energy levels are allowed because only at certain distances from the nucleus will the wave patterns join up consistently.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, wave-particle duality is the duality of potential and instance. The wave of an electron is, for example, a measure of the probable locations of electrons, and wavelength is the distance between equiprobable locations.

On this basis, the discrete energy levels at certain distances from the nucleus of an atom correspond to those orbits that accommodate a whole number of equiprobable locations of electrons.

Heisenberg's Uncertainty Principle Viewed Through Systemic Functional Linguistics

Robinson (2005: 92-3):

In 1924 de Broglie proposed that all matter has a wave associated with it, and this was quickly confirmed for electrons by diffraction experiments. In 1926 Schrödinger, in his classic wave equation — aided importantly by Born — replaced the picture of an electron as a particle having a precise position and momentum as it orbits a nucleus with a wave function that predicted stationary waves of electron probability around the nucleus. Schrödinger's equation enables physicists to calculate not the location of an electron at any given moment but its probability of being at any particular point in space. … the electron becomes a probability wave in the Schrödinger/Born model.

Then in 1927 Heisenberg, in his far-reaching uncertainty principle, proved that the position and momentum of any elementary particle such as an electron can never be measured simultaneously with unlimited accuracy. The more an experimenter tries to pin down the position in space, the greater will be the uncertainty in momentum, and vice versa, because the very act of observing the particle (say by firing a photon at it) will inevitably disturb its position and momentum. 

The Heisenberg uncertainty principle states that the uncertainty in the position multiplied by the uncertainty in momentum will always exceed a constant based on Planck's constant h. Other kinds of uncertainty principle may also be derived, such as one which relates the uncertainty in the energy of a particle to the time interval in which one measures the energy.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the wave of a particle is its potential, measured in terms of probability, and the particle is the instantiation of that potential, measured in terms of frequency.

Heisenberg's uncertainty principle is the probability measure of the meaning being construed viewed from the perspective of the observer who is doing the construing.