The 'Convenience' View Of R Viewed Through Systemic Functional Linguistics

Penrose (2004: 532):

According to such a ‘convenience’ view of R, one imagines that R would emerge as some kind of approximation to a ‘true’ underlying U evolution. But this viewpoint leads to serious paradoxes. 

For example, let us recall the thought experiment where my two colleagues in space had individual detectors, and try to imagine that the response of each detector is simply the result of a Schrödinger evolution starting from its interaction with the wave-packet part that it receives. The quantum state before detection is actually a sum of the two individual wave-packet parts, one reaching one detector and the other part reaching the other detector; therefore, by linearity, the subsequent Schrödinger evolved response of each detector must coexist in superposition with a response in the other. The Schrödinger evolution leads to one detector response plus the other detector response (‘plus’ in the sense of quantum superposition of the two detector responses), not one detector response or the other detector response (the ‘or’ being what actually always happens in practice). It seems to me untenable to maintain that U tells the whole story (and the ‘conventional’ quantum mechanics of Niels Bohr’s ‘Copenhagen interpretation’ certainly does not try to do this; for it treats the detectors themselves as ‘classical entities’). 

As far as I can see, the only way to insist that U holds for all processes, including measurement, would be to pass to a ‘many-worlds’ type of view in which the two detector responses do actually coexist, but in what are referred to as ‘different worlds’. But even then, U cannot be ‘the whole story’, because we would need a theory to explain that aspect of our conscious perceptions which allows only individual detector responses to be consciously perceived, whereas superpositions of responses with non-responses are never consciously perceived! … I should register, at this point, that I do not myself believe that ‘many worlds’ is the right way to go; I am merely arguing that it seems to be where one is led if one insists on ‘U at all levels’.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the 'underlying U evolution' is quantum potential and the 'approximation' R is an instance of that potential, and this viewpoint does not lead to paradoxes.

In this view, the wave-packet is potential, not actual, so it does not actually travel, in the recalled thought experiment, and it is quantum potential that 'coexists in superposition, not actual instances of that potential. It is only when a detector screen is observed that the quantum potential "collapses" to an actual instance of construed meaning. 

Moreover, this view is consistent with the Copenhagen Interpretation, whereas the 'many-worlds' interpretation miscontrues superpositions of potential as superpositions of actual instances.

Quantum Entanglement Viewed Through Systemic Functional Linguistics

Penrose (2004: 532):

We shall come to the quantum-mechanical notion of ‘entanglement’ … . We shall see that quantum states are ‘holistic’ entities … where different parts of the system do not have separate quantum states of their own, but are parts of one entangled ‘whole’.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, 'entanglement' refers to the interdependencies within the 'holistic' system of quantum potential. One instantiation of potential has probabilistic consequences for related instantiations of potential.

Schrödinger Equation Determinism Vs Quantum Uncertainty Viewed Through Systemic Functional Linguistics

Penrose (2004: 530):

One thing that we note is that [the Schrödinger equation] is a deterministic equation (the time evolution being completely fixed once the state is known at any one time). This may come as a surprise to some people, who may well have heard of ‘quantum uncertainty’, and of the fact that quantum systems behave in nondeterministic ways. This lack of determinism comes about in the application of the R-process only. It is not to be found in the (U) time-evolution of the quantum state, as described by the Schrödinger equation.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the Schrödinger equation models a quantum system as potential, and it this that is deterministic. Quantum uncertainty, on the other hand, in this view, describes the probabilistic nature of the instantiation of quantum potential as actual particles. The distinction is between the deterministic nature of potential and the probabilistic nature of the instantiation of that potential.

The Apparent Contradiction Between The Unitary Evolution And State Reduction Viewed Through Systemic Functional Linguistics

Penrose (2004: 529-30):

[Most physicists'] reason for preferring not to contemplate altering the basic framework of quantum mechanics is (in addition to the great mathematical elegance of its U formalism) the tremendously impressive and precise agreement between quantum theory and experimental fact, where nothing is known that tells against quantum theory (in its present hybrid form) and many varied results confirm it to great accuracy. Accordingly, most quantum physicists would adopt a philosophical standpoint (or, rather, one of the various different alternative philosophical standpoints) which try to come to terms with the apparent contradiction between the U and R procedures, while not attempting to change the present-day quantum formalism in any significant way. … 

I think that it would be fair to say that a common thread in much of what might be called ‘conventional’ attitudes to quantum mechanics is that the U process is to be taken as an ‘underlying truth’ and that one must come to terms with R, in one way or another, as being some type of approximation, illusion, or convenience, and there are many accounts in the literature which pursue this kind of approach. Even those (myself included) who are of the opinion that some change in the quantum formalism is needed at some stage, would argue that the present-day scheme is at least a marvellous approximation, so it is necessary to understand it thoroughly if there is to be any hope of moving beyond it. Accordingly, we must try to see more deeply how it is that U operates and, moreover, how it is that it can dovetail so beautifully with R, whilst nevertheless being inconsistent with it!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the relation between the U and R procedures is not the relation between 'underlying truth' and approximation, but the relation between potential and an actualised instance of that potential. It is this that accounts for the 'apparent contradiction' between them.

The Alternation Between Unitary Evolution And State Reduction Viewed Through Systemic Functional Linguistics

Penrose (2004: 528-9):

I denote Schrödinger evolution by U and state reduction by R. This alternation between these two completely different-looking procedures would appear to be a distinctly odd type of way for a universe to behave! See Fig. 22.1. 

Indeed, we might imagine that, in actuality, this is an approximation to something else, as yet unknown. Perhaps there is a more general mathematical equation, or evolution principle of some coherent mathematical kind, which has both U and R as limiting approximations? My personal opinion is that this kind of change to quantum theory is very likely to be correct… . However most physicists appear not to believe that this kind of route is a fruitful one to follow.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the alternation between U and R is "an approximation to" the alternation between quantum potential (when no observation is made) and an instance or quantum potential (when an observation is made).

In this view, it is the interpretation of quantum theory that needs to be changed, not quantum theory itself.

The Evolution And Collapse Of The Wavefunction Viewed Through Systemic Functional Linguistics

Penrose (2004: 528):

Let us review the descriptions in the previous chapter, where we had to become accustomed to the (non-relativistic) quantum particle as being something described by what we have called a state vector (or wavefunction) whose evolution is, in a very precise way, provided by the Schrödinger equation — until some measurement is performed on the system. … 

The jumping of the quantum state to one of the eigenstates of Q is the process referred to as state-vector reduction or collapse of the wavefunction. It is one of quantum theory’s most puzzling features, and we shall be coming back to this issue many times in this book. I believe that most quantum physicists would not regard state-vector reduction as a real action of the physical world, but that it reflects the fact that we should not regard the state vector as describing an ‘actual’ quantum-level physical reality. 

Nevertheless, irrespective of whatever attitude we might happen to have about of the physical reality of the phenomenon, the way in which quantum mechanics is used in practice is to take the state indeed to jump in this curious way whenever a measurement is deemed to take place. Immediately after the measurement, Schrödinger evolution takes over again — until another measurement is performed on the system, and so on.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the evolution of the wavefunction is the evolution of potential and the collapse of the wavefunction, when some measurement is performed on the system, is the instantiation of potential, when experience is construed as meaning in an act of observation.

In this view, the collapse of the wavefunction is not a 'real action of the physical world' but an act of construing experience as an instance of meaning of the physical domain. The wavefunction does not describe actual reality but construes potential reality.

The Non-intuitive Nature of 'Nature' Viewed Through Systemic Functional Linguistics

Penrose (2004: 527):

The non-intuitive nature of quantum mechanics — or, rather, of Nature herself at the level of quantum-mechanical activity — leads many people to despair of finding any kind of trustworthy picture of quantum-level phenomena. Yet, there is much beautiful geometry associated with quantum mechanics in addition to its elegant algebraic structure, and it would be a pity to feel that one must necessarily rely merely upon a pictureless, unvisualisable formalism in order to make headway with the description of quantum actions. Although we have seen that even a single featureless ‘point particle’ appears to be a mysterious spread-out wavy thing in the quantum formalism, it is a ‘thing’ that can be pictured, having a fascinating mathematical structure in which many of the aspects of complex number magic start to show themselves.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, 'Nature' is first-order meaning construed of experience, whereas quantum mechanics is a reconstrual of first-order meaning as the second-order meaning of a scientific theory. If anything, it is second-order meaning of the theory that is 'non-intuitive', not the first-order meaning of Nature.

But the theory ceases to be non-intuitive if wave/particle complementarity is understood as potential/instance complementarity, and if meaning is understood as immanent within semiotic systems, rather than something transcendent and independent of them.

The 'Reality' Of A Probability Wave Viewed Through Systemic Functional Linguistics

Penrose (2004: 520):

It seems to me to be clear that the wavefunction must be something a good deal more ‘real’ than would be the case for merely ‘a probability wave’. The Schrödinger equation provides us with a precise evolution in time for this entity (whether it is charged or not), an evolution that depends critically upon how the phase indeed varies from place to place. But if we ask of a wavefunction ‘where is the particle?’, by performing upon it a position measurement, we must be prepared to lose this phase-distribution information. In fact, after the measurement, we have to start all over again with a new wavefunction. If the result of the measurement asserts ‘the particle is here’, then our new wavefunction has to be very strongly peaked at the position ‘here’, but then it rapidly disperses again, in accordance with Schrödinger evolution. If our position measurement were absolutely precise, then the new state would be ‘infinitely peaked’ at that location;

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, probability is an assessment of potential. So the 'reality' that a probability wave assesses is potential 'reality'.

The reason why 'performing a position measurement' loses the 'phase-distribution information' of the wavefunction is that making such an observation actualises just one instance of the total potential.

The reason why a new wavefunction is required after 'performing a position measurement' is that the potential of the quantum system has changed after making an observation.

In this view, the notion that a wavefunction "disperses" misconstrues potential as actual. It is only the particle that is actual, and 'actual' in the sense of being an instance of the potential specified by the wavefunction.

The Wavefunction As A ‘Probability Wave’ Viewed Through Systemic Functional Linguistics

Penrose (2004: 519, 504):

In accordance with this probability interpretation, it is not uncommon for the wavefunction to be called a ‘probability wave’. However, I think that this is a very unsatisfactory description. In the first place, ψ(x) itself is complex, and so it certainly cannot be a probability. Moreover, the phase of ψ (up to an overall constant multiplying factor) is an essential ingredient for the Schrödinger evolution. 

Even regarding |ψ|² (or |ψ|² / ||ψ||) as a ‘probability wave’ does not seem very sensible to me. Recall that for a momentum state, the modulus |ψ| of ψ is actually constant throughout the whole of spacetime. There is no information in |ψ| telling us even the direction of motion of the wave! It is the phase, alone, that gives this wave its ‘wavelike’ character. 

Moreover, probabilities are never negative, let alone complex. If the wavefunction were just a wave of probabilities, then there would never be any of the cancellations of destructive interference. This cancellation is a characteristic feature of quantum mechanics, so vividly portrayed (Fig. 21.4d) in the two-slit experiment!

Blogger Comments:

To be clear, it was the physicist Max Born who first interpreted the wavefunction as a probability wave, and this as giving the potential locations of a particle, not the direction of motion of an actual wave. 

From the perspective of Systemic Functional Linguistic Theory, the notion of a probability wave is entirely consistent with the bands of constructive and destructive interference on the detector screen in the two-slit experiment. This is because the experiment sets up two waves of probability, one for each possibility — passing through one slit or the other — so that it is the probability waves that overlap. The frequency of particle locations observed on the detector screen is in line with the probable locations of particles as modelled by the overlapping wavefunctions.

The Wavefunction As A Probability Distribution Viewed Through Systemic Functional Linguistics

Penrose (2004: 517):

Let us here address the more limited question of what the wavefunction ψ is supposed to be telling us about the particle’s position. The rules of quantum theory tell us that ψ’s squared modulus ψ² (= ψψ) is to be interpreted as the probability distribution, giving the likelihood of a position measurement finding the particle at the various possible spatial locations. Thus, wherever the wavefunction is largest in absolute value, the particle is most likely to be found. Wherever it is zero, the particle will not be found. Now, the total probability of finding the particle somewhere in space has to be 1;

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, probability is an assessment of potential. In giving a probability distribution, the wavefunction is a model of potential. The finding of a particle at a location is the construal of experience as an instance of that potential.

The Spreading Out Of The Wavefunction Viewed Through Systemic Functional Linguistics

Penrose (2004: 516-7):

For the moment, let us accept this curious description, at least as a mathematical model of the quantum world, whereby the quantum state evolves for a while in the form of a wavefunction, usually spreading out through space  (but possibly being focused in again to a more localised region); but then, when a measurement is performed, the state collapses down to something localised and specific. This instant localisation happens no matter how spread out the wavefunction may have been before the measurement, whereafter the state again evolves as a Schrödinger-guided wave, starting from this specific localised configuration, usually spreading out again until the next measurement is performed. From the above experimental (and ‘thought-experimental’) situations, the impression could be gained that the particle-like aspects of a wave/particle are what show up in a measurement, whereas it is the wavelike ones that show up between measurements.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the wavefunction does not 'spread out through space' before and after the taking of measurements. This is to misconstrue potential as actual. Instead, the wavefunction identifies the potential locations of a particle in terms of probability. It is only when an observation is made that an instance of this potential is actualised as a particle at a specific location. 

The ‘Reality’ Of The Wavefunction Viewed Through Systemic Functional Linguistics

Penrose (2004: 516):

But even if we accept that, at least at the level of formal mathematical description, we must adopt this curious ‘jumping’ procedure, there is the question of what this tells us about the ‘reality’ of the wavefunction. This ‘jumping’ of the quantum state — a process that does not seem to be covered by any continuous evolution in accordance with the Schrödinger equation — is what leads a great many physicists to doubt that the evolution of the state vector can possibly be taken seriously as an adequate description of physical reality. Schrödinger himself was extremely uncomfortable with ‘quantum jumps’, and he once remarked in a conversation with Niels Bohr:

If all this damned quantum jumping were really here to stay then I should be sorry I ever got involved with quantum theory.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the 'jumping' of the quantum state is the instantiation of potential when an observation construes experience as meaning. What this tells us about the 'reality' of the wavefunction is that it is a model of potential 'reality', not a model of actual 'reality'.

The problem here, for physicists, is that physics cannot provide an understanding of 'quantum jumps'. Understanding 'quantum jumps' requires (i) understanding the distinction between potential and actual, and the relation between them, and (ii) understanding the epistemological distinction between the 'transcendent' view of meaning, assumed in science since Galileo, and the 'immanent' view of meaning that the findings of quantum physics supports. In this latter view, meaning does not transcend semiotic systems.

'What Constitutes A Measurement’ Viewed Through Systemic Functional Linguistics

Penrose (2004: 516):

But now another question looms large. How do we know what physical circumstance it is that constitutes a ‘measurement’? Why, after we have been happily using this wavefunction description of a particle as a wave spread out in two quite different directions through the reaches of space, should we suddenly revert to a description of it as a localised particle as soon as the detection of it is performed? 

This same curious kind of picture of a quantum particle appears also to be appropriate for detection at the screen in our two-slit experiment, just as it was with the (unspecified) ‘detectors’ used by my far-flung colleagues. 

In my descriptions so far, it certainly seems that the wavelike aspects must be maintained right up until we choose to ‘perform a measurement’ to detect the particle, but then we suddenly revert to a particle-like description, where there is an awkward discontinuous (and non-local) change of the state — a quantum jump — as we pass from the wavefunction picture to the ‘reality’ presented by the measurement. Why? What is it about the detection process that demands that a different (and highly non-local) mathematical procedure should be adopted, in the event of a ‘measurement’, from the standard quantum-evolution procedure provided by Schrödinger’s equation?

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, a 'measurement' is an observation, and an observation is a mental process mediated by a Senser.

From this perspective, the wavefunction measures the potential meaning that can be construed of experience by the Senser. It is only when the Senser makes an observation that one instance of this potential is made actual as a particle. It is this process of instantiation that constitutes a 'quantum jump'.

In this view, the description above misconstrues the potential as actual, and misconstrues the potential–instance relation as an actual before–after relation.

The Non-Local Holistic Character Of A Wavefunction Viewed Through Systemic Functional Linguistics

Penrose (2004: 515):

The key puzzle is that somehow a photon (or other quantum particle) seems to have to ‘know’ what kind of experiment is going to be performed upon it well in advance of the actual performing of that experiment. How can it have the foresight to know whether to put itself into ‘particle mode’ or ‘wave mode’ as it leaves the (first) beam splitter? 

The way that quantum theory works is not to give the particle any such ‘foresight’ but simply to accept the non-local holistic character of a wavefunction. In both of the above experiments, we take the wavefunction to be split into two parts at the initial beam splitter, and the particle-like aspect of the wave/particle only shows up at the detector, when the measurement is finally performed. The measurement makes the holistic character of the wavefunction manifest, in the sense that the particle always shows up in just one place, its appearance at one location forbidding its simultaneous appearance anywhere else.

Blogger Comments:

 From the perspective of Systemic Functional Linguistic Theory, the 'non-local holistic character of a wavefunction' derives from the fact that it construes the probabilistic range of potential locations of the particle, rather than the actual location ('the one place') of the particle.

The wavefunction is not 'split into two parts' at the beam splitter because the wavefunction is not actual. Instead, the wavefunction construes the probability of a particle going one way or the other at the beam splitter. The reason that the particle is detected, rather than the wave, is that only the particle is actual.

The measurement 'makes the holistic character of the wavefunction manifest' in the sense that an observation construes one instance — one particle at one location — of the overall quantum potential.

The Further Splitting Of Wave Packets Viewed Through Systemic Functional Linguistics

Penrose (2004: 514-5):

But there are other experiments that might be performed on the photon after it emerges from the beam splitter. How can our poor little photon know, when it is about to emerge, that my colleagues do not plan a different type of fate for it? Suppose that, instead of each individually trying to detect the photon, they had concocted the following plan. They would separately reflect their parts of the wavefunction to a fourth location, where the two reflected parts would, say after a further year, simultaneously encounter a second beam splitter (Fig. 21.9). 

There, each arriving wave packet part would be individually split in two, so that one half emerges from this beam splitter in one direction to encounter a detector A, and where the other half emerges in another direction to go to another detector, B. (This applies separately for each of the two wave-packet parts, coming from the separate vicinities of each of my two colleagues.) If all the path lengths are accurately fixed appropriately (say all equal), then we find, remarkably, that the emerging photon can only activate one of the detectors, say A, and not B, because of constructive interference between the two parts of the wavefunction at A and destructive interference at B. 

No purely particulate picture of a photon can achieve this. The wavefunction is definitely needed, now, to explain the wave aspect of wave/particle duality. If the photon had already made its choice as to which of my colleagues to travel towards, when it left the first beam splitter, then the other route would become irrelevant. In that case, when the photon finally reaches the second beam splitter it comes from only one direction, and it could go either way, to reach either A or B. There is now no possibility of the needed destructive interference that prevents it from reaching the detector at B. Since A is always the detector that registers, it cannot just be the case that the photon has simply made its choice when it leaves the first beam splitter. It is necessary that both of the alternative routes that the photon might take are simultaneously felt out by the photon in its passage from the first to the second beam splitter.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, this again misconstrues the wavefunction as actual instead of potential. It is not the wavefunction, in the form of a wave packet, that encounters beam-splitters, but the particle as an instance of the potential specified by the wavefunction. Again, the 'splitting of the wave packet' is the superposition of quantum potentials, and it is this superposition that specifies the total potential. Again, only one detector is activated because only one photon is emitted, and only it can encounter a beam-splitter.

The metaphor of a photon knowing, choosing and 'feeling out alternative routes' is misleading. A photon is an instance of the potential specified by the wave function, and it only becomes actual when an observation is made.

The Splitting Of A Wave Packet Viewed Through Systemic Functional Linguistics

Penrose (2004: 512-4):

This point can be made even more forcefully in a somewhat different experimental situation. This has the additional advantage of making quite clear to us that the wave-packet picture of a wave/particle is, by itself, quite inadequate for explaining particle-like quantum behaviour. Let us imagine that there is a particle source, just as before, and we are going to suppose that it only emits a single particle. Instead of using a barrier with a pair of slits, we are going to suppose that there is what is called a beamsplitter in the particle’s path. 

It will help our imaginations if we think of our particle as a photon, and we can imagine that the beam-splitter is a kind of ‘half-silvered mirror’ which is to split our photon wave packet into two widely separated parts. For clarity of our conceptions, let us envisage our ‘experiment’ being carried out in interstellar space (and the reader should be warned that I am not proposing anything remotely practical here — our example will serve merely to exhibit some very basic predictions of quantum mechanics under extreme circumstances). 

If we choose, we can imagine the photon’s wavefunction to start out from the source in the form of a neat little wave packet, but, after encountering the beam-splitter, it will divide itself in two, with one wave-packet part reflected from the beam-splitter and the other wave-packet part transmitted through it, say in perpendicular directions (Fig. 21.8).

The entire wavefunction is the sum of these two parts. We could wait for a year, if we like, before choosing to intercept the photon’s wavefunction with a photographic plate or other kind of detector. The two parts will be a very long way away from each other by now, but we can imagine that I have two colleagues (in two different space laboratories), more than 1.4 light years separated from one another. Each of my colleagues has a separate detector, and although each of the two wave-packet parts may individually have dispersed considerably by now, each colleague has a large paraboidal reflecting mirror which collects the dispersed wave packet, focusing it on that particular colleague’s detector. 

What does quantum mechanics say will happen? It says that one or other of my colleagues will indeed detect the photon, but that they cannot both detect the photon. This is not the kind of thing that a classical wave does. Remember that my two colleagues are over 1.4 light years apart. Relativity insists that no signal can pass between them in less than 1.4 years; yet the fact that one wavepacket part yields up a photon prevents the other one, 1.4 light years away, from doing so, and vice versa. In only a year’s time, I learn from each of them what has happened, and I find that only one of them has received a photon. The part of the wavefunction that each colleague has access to seems to ‘know’ what the other part of the wavefunction is up to! 

Every time I perform this experiment, I find that one or other of them receives the photon, but not both. No classical type of wave effect could achieve this apparently ‘instantaneous communication’ between the two parts of the wavefunction. Quantum wavefunctions are just different from classical waves.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, this misconstrues potential as actual. It is a particle that either passes through the beam-splitter or is reflected by it, not the wavefunction in the form of a wavepacket. The 'splitting of the wave packet' is the superposition of two wavefunctions, one for each possible trajectory of the particle after it encounters the beam-splitter. It is this superposition of potential that constitutes the 'entire wavefunction'.

The reason why only one colleague detects the photon is that only one photon is emitted. There is no 'instantaneous communication' between the 'two parts of the wavefunction' because their superposition represents potential events, not actual events.