The Laws Of Dynamics That Shape The Universe Viewed Through Systemic Functional Linguistics

Penrose (2004: 686):

What sorts of laws shape the universe with all its contents? The answer provided by practically all successful physical theories, from the time of Galileo onwards, would be given in the form of a dynamics — that is, a specification of how a physical system will develop with time, given the physical state of the system at one particular time. These theories do not tell us what the world is like; they say, instead: ‘if the world was like such-and-such at one time, then it will be like so-and-so at some later time’. Such a theory will not tell us how the world is shaped unless we tell it how the world was shaped.

 Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, laws don't shape the universe, just as a map doesn't shape the terrain it models. Instead, the physical universe is the construal of experience as first-order (phenomenal) meanings, and the laws of physics are reconstruals of first-order meanings as second-order (metaphenomenal) meanings that realise theory.

Importantly, the laws reconstrue the Universe in terms of modalisation (probability), not modulation (obligation).

The "Deeper ‘Platonic’ Meaning" In The Path-Integral Approach Viewed Through Systemic Functional Linguistics

Penrose (2004: 670-1):

Indeed, the path-integral approach is, it seems, almost wholly dependent upon a faith that the wildly divergent expressions that we are presented with (like the divergent series above) actually have a deeper ‘Platonic’ meaning that we may not yet properly perceive. We appear to be forced to admit that something of this nature must be the case because, on the physical side, we are not infrequently presented with answers of uncanny physical accuracy when (if I may be permitted to conjure up an improbable-sounding metaphor) we bulldoze our way through the mathematics with great sensitivity and precision!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the "deeper ‘Platonic’ meaning" of wildly divergent expressions in the path-integral approach is that the meaning they construe is potential.

An Illustration Of A Path Integral Viewed Through Systemic Functional Linguistics

Penrose (2004: 668):

The most accessible illustration of a path integral is the case of a single point particle moving in some field of force (so the configuration space is now space itself). Here, we consider all the various histories, starting at some spacetime point a and finishing at some other spacetime point b as in Fig. 26.3a. These histories are taken to be continuous spacetime paths winding their way from a to b. We do not require that the path be a ‘legal’ one, according to the rules of special relativity (i.e. that it be constrained to lie within the light cones, as required by classical relativity), nor do we even require that the path proceed entirely into the future. The ‘history’ can wiggle up and down in time if it wants to (Fig. 26.3b)!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, 'all the various histories' constitute the potential of the quantum system. And from this perspective, there is no travelling in time. Time is dimension of the unfolding of processes, such as travelling. A process, and so a particle mediating the process, extends from one location in time to another. Travelling from 1pm to 2pm is extending from 1pm to 2pm, so duration, not motion.

Feynman 'Path Integrals' Or 'Sum Over Histories' Viewed Through Systemic Functional Linguistics

Penrose (2004: 666-7):

The basic idea is a different perspective on the fundamental quantum-mechanical principle of complex linear superposition that we encountered earlier. Here, we think of that principle as applied, not just to specific quantum states, but to entire spacetime histories. We tend to think of these histories as ‘possible alternative classical trajectories’ (in configuration space). The idea is that in the quantum world, instead of there being just one classical ‘reality’, represented by one such trajectory (one history), there is a great complex superposition of all these ‘alternative realities’ (superposed alternative histories).

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, a great complex superposition of all these 'alternative realities' represented as ‘possible alternative classical trajectories’ constitutes the potential of the quantum system, whereas the one classical 'reality' represented by one trajectory is one instance of that quantum potential.

Travelling In Time Viewed Through Systemic Functional Linguistics

Penrose (2004: 639):

Assuming CPT, we can regard C — the interchange of particles with their antiparticles — as equivalent to PT, so we can regard the antiparticle of some particle as being the ‘space–time reflection’ (PT) of that particle. Ignoring the space-reflection aspect of this, we obtain the interpretation of an antiparticle as being the particle travelling backwards in time. This, indeed, is the way that Richard Feynman liked to interpret anti-particles. It provides a very convenient and consistent way of treating antiparticles within the context of Feynman graphs.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, there is no travelling in time. Time is dimension of the unfolding of processes, such as travelling. A process, and so a particle mediating the process, extends from one location in time to another. Travelling from 1pm to 2pm is extending from 1pm to 2pm, so duration, not motion.

The Reality Of Mathematical Descriptions Viewed Through Systemic Functional Linguistics

Penrose (2004: 631-2):

Bearing this in mind, let us raise the question as to whether these zig and zag particles are ‘real’. Or are they perhaps artefacts of the particular mathematical formalism that I have been adopting here for the description of the Dirac equation for the electron? This raises a more general question: what is the physical justification in allowing oneself to be carried along by the elegance of some mathematical description and then trying to regard that description as describing a ‘reality’? … 

So are these zigs and zags real? For my own part, I would say so; they are as real as the ‘Dirac electron’ is itself real — as a highly appropriate idealised mathematical description of one of the most fundamental ingredients of the universe. But is this real ‘reality’?

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, 'reality' is meaning construed of experience: the phenomena construed by language and their reconstrual as metaphenomena, the meanings of meanings that realise theory. In this view, the 'zig and zag' particles are real, as metaphenomena, but whether they are interpersonally assessed as valid is a separate matter.

The Actual Perceived Motion Of An Electron Viewed Through Systemic Functional Linguistics

Penrose (2004: 631):

Accordingly, my above description of the electron’s motion as consisting of this jiggling back and forth, where a zig is continually being converted into a zag and back again, must be taken appropriately in this spirit. The actual motion is composed of a vast number of such individual processes (in fact infinitely many of them) all superposed, and we may think of the electron’s perceived motion as being some sort of ‘average’ (though strictly a quantum superposition) of these. Even this describes merely the free electron. An actual electron will be continually undergoing interactions with other particles (such as photons, the quanta of the electromagnetic field). All such interaction processes should also be included in the overall superposition.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the actual perceived motion of an electron is an instantiation of its system of quantum potential: the superposition of all potential individual or interaction processes.

The Quantum Interpretation Of Feynman Graphs Viewed Through Systemic Functional Linguistics

Penrose (2004: 631):

There is a word of warning that I must give, however, about how we are to interpret Feyman-graph diagrams. We can legitimately think of the process that is being depicted as a spacetime description of what is going on; but at the quantum level of things, we must take the view that, even for a single particle, there are a great many such processes going on simultaneously. Each individual one of these processes is to be viewed as taking part in some enormous quantum superposition of vast numbers of different processes. The actual quantum state of the system consists of the entire superposition. An individual Feynman graph represents merely one component of it.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the entire superposition of simultaneous processes is potential, not actual, and an individual Feynman graph represents one instantiation, not component, of that potential.

A Spacetime Diagram Of An EPR Situation Viewed Through Systemic Functional Linguistics

Penrose (2004: 606, 607):

What is the quanglement perspective on these matters? On this picture, it is not correct to think of either measurement (mine or my colleague’s) as effecting the reduction and the other (my colleague’s or mine) as measuring the reduced state. The two measurement events are on an equal footing with one another, and we think of the quanglement as providing a connection between these events which correlates the two. It makes no difference which event is viewed as being to the past of the other, for quanglement can equally be thought of as propagating into the past as propagating into the future. Not being capable directly of carrying information, quanglement does not respect the normal restrictions of relativistic causality. It merely effects constraints on the joint probabilities of the results of different measurements.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, entanglement refers to the interdependency of instantiation probabilities in the system of quantum potential. This means that the instantiation of one state, through observation, affects the instantiation probabilities of other potential states, but importantly, the instantiation of the affected state only occurs when an observation is made. In the thought experiment, this occurs only at B on Titan and at A on Earth. 

Accordingly, B' is the time on Earth at which the first state is observed on Titan (B), and A' is the time on Titan at which the second state is observed on Earth (A).

B" and A" are a different matter, since they are concerned with information flow between Titan and Earth. B" is earliest time on Earth that news of B on Titan can arrive. A" is the latest time on Titan that information can arrive on Earth at the time of A.

Because entanglement is a feature of quantum potential, there is no actual propagation of entanglement, since it is instances that propagate, not potential.

The Flitting Back And Forth In Time Of Quanglement Viewed Through Systemic Functional Linguistics

Penrose (2004: 604, 605):

One of the most direct uses of the idea of quanglement is in certain experiments where a pair of entangled photons is produced according to the process referred to as parametric down-conversion (see Fig. 23.8). …

In one particularly striking experiment, one of the photons (photon A) passes through hole of a particular shape as it speeds towards its detector DA. The other photon (photon B) passes through a lens that is positioned so as to focus it, appropriately, at its detector DB. The position of detector DB is moved around slightly as each photon pair is emitted. The situation is illustrated schematically in Fig. 23.9a.

Whenever DA registers reception of photon A and DB also registers reception of B, the position of DB is noted. This is repeated many times, and gradually an image is built up by the detector DB, where only the positions of B are counted when simultaneously DA registers. The shape of the hole that A encounters is gradually built up at DB, even though photon B never directly encounters the hole at all! It is as though DB ‘sees’ the shape of the hole by looking backwards in time to the emission point C at the crystal, and then forwards in time in the guise of photon A. It can do this because the ‘seeing’ process in this situation is achieved by quanglement. This flitting back and forth in time is precisely the kind of thing that quanglement is allowed to do.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, there is no flitting back and forward in time in this experiment, and it is only the experimenter that 'sees'. The correlations of observations at the detectors DA  and DB is due to probability dependencies in the instantiation quantum potential, not to interactions between the detections of instances (photons).

Zig-zagging Backwards And Forwards In Time Viewed Through Systemic Functional Linguistics

Penrose (2004: 603):

At least in this book, I shall refer to what is commonly called ‘quantum information’ as quanglement. The term suggests ‘quantum mechanics’ and it suggests ‘entanglement’. This is very appropriate. This is what quanglement is all about. Quanglement also does have something very much to do with information, but it is not information. There is no way to send an ordinary signal by means of quanglement alone. This much is made clear from the fact that past-directed channels of quanglement can be used just as well as future-directed channels. If quanglement were transmittable information, then it would be possible to send messages into the past, which it isn’t. … 

As far as I can make out, quanglement links are always constrained by the light cones, just as are ordinary information links, but quanglement links have the novel feature that they can zig-zag backwards and forwards in time, so as to achieve an effective ‘spacelike propagation’. Since quanglement is not information, this does not allow actual signals to be sent faster than light.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, time is the dimension along which processes unfold. In this view, processes extend in time, maximally from initial to final temporal locations. That is, time is endured, not moved through, whether backwards or forwards.

Faster Than Light Signalling Between Entangled Particles Viewed Through Systemic Functional Linguistics

Penrose (2004: 598):

Most particularly, we recall the seeming conflict with special relativity: that the ‘communication’ between EPR pairs seems to pay no respect to Einstein’s own requirements that signalling faster than light should not be allowed.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, there is no signalling between entangled particles (EPR pairs) because their properties are instances of interdependent quantum potential. That is, it is the instantiation of potential as the properties of one particle that selects the instantiated properties of the other. The relation is between potential and instance, not between instance and instance.

Relativity And The Simultaneity Of Entanglement Viewed Through Systemic Functional Linguistics

Penrose (2004: 593):

I have not yet finished with the other puzzles presented to us by entanglement. Some of these have to do with the way that the measurement of an entangled system sits extremely uncomfortably with the requirements of relativity, since a measurement of one part of an entangled pair would seem to have to affect the other simultaneously which, as we have seen, is not a notion that we ought to countenance if we are to remain true to relativistic principles.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, there is no inconsistency between the measurement of an entangled system and the requirements of relativity. This is because the measurement of an entangled system is the construal of simultaneous instances of the same interdependent quantum potential, and so concerns the relation between instance and potential, not the simultaneous effect of instance on instance, whereas relativity concerns the relation between instances and their spatiotemporal dimensions, not the relation between instance and potential.

The 'Conventional' View Of Entanglements Viewed Through Systemic Functional Linguistics

Penrose (2004: 593):

But how is the matter dealt with in ‘conventional’ quantum mechanics? It seems that ‘in practice’ physicists always assume that these supposed entanglements with the outside world can be ignored. Otherwise neither classical mechanics nor conventional quantum mechanics could ever be trusted. The view seems to be that all the entanglements will somehow ‘average out’ so that they do not need to be considered in practice, in any actual situation. Yet I am unaware of any remotely convincing demonstration that this is likely to be the case. Rather than averaging out, it would appear to be the case that everything just gets less and less like the universe we know, with individual objects not even having approximately defined locations that are not conditional on vastly many other occurrences elsewhere in the universe. I do not see any way out of this conundrum …

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, entanglements are not with the outside world but within quantum potential. The way out of this conundrum is to apply the distinction between potential and instance to Quantum Theory, with interdependent probabilities as the quantification of potential, and to not confuse potential with instance.

Quantum Measurement Viewed Through Systemic Functional Linguistics

Penrose (2004: 593):

It seems to me that something of the nature of a ‘measurement’ is always an essential part of the setting up of a quantum experiment, to ensure that the state is uncontaminated by swarms of these unwanted entanglements. In saying this, I do not mean to imply that the experimenter deliberately sets up a ‘measurement’ to achieve this. It is my own view that Nature herself is continually enacting R-process effects, without any deliberate intentions on the part of an experimenter or any intervention by a ‘conscious observer’.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the 'measurement' by a conscious observer is essential because it is only in the observation in a quantum experiment that experience is construed as meaning: as a particle that is an instance of 'entangled' quantum potential. It is only through the intervention of a conscious observer that experience is construed as meaning.

The Notion That Measurements Slash Through Entanglements Viewed Through Systemic Functional Linguistics

Penrose (2004: 592):

Recall that I envisaged performing a measurement on an EPR pair, the other member of which was approaching my colleague on the planet Titan. If I make my measurement first, then upon my performing this measurement, this very act would cut my colleague’s particle free of its entanglement with mine, and from then on (until it became measured by my colleague) it would possess a state vector of its own, unencumbered by any further responsibility to its partner, no matter what I might subsequently do to it. Thus, it seems, it is measurements that slash through these entanglements. Can this be true?

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the act of measurement is an act of observation, which is the construal of experience as meaning. In this case, the meaning that is construed is an instance of quantum system potential. Systems of potential are quantified in terms of probability. If probabilities in a system are interdependent ("entangled"), then the (observed) instantiation of variables of one particle depend on the (observed) instantiation of variables of another.

Why Particle Entanglement Is Not Directly Observed — Viewed Through Systemic Functional Linguistics

Penrose (2004: 591):

Let me begin by addressing this second mystery. I shall be returning to the first in due course. A puzzle that must be faced is the fact that entanglements tend to spread. It would seem that eventually every particle in the universe must become entangled with every other. Or are they already all entangled with each other? Why do we not just experience an entangled mess, with no resemblance whatsoever to the (almost) classical world that we actually perceive?

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the entanglement of particles is due to — and evidence of — the fact that they are instances of the same quantum potential.

As previously explained, from this perspective, the reason why entangled quantum states are not directly experienced, is explained by the fact that only instances can be observed; this is the construal of experience as first-order meaning. Potential, on the other hand, can only be theorised; this is the reconstrual of first-order meaning as second-order meaning. It is theory only that provides the means of thinking, not observing, that quantum states are entangled.

Two Mysteries Of Quantum Entanglement Viewed Through Systemic Functional Linguistics

Penrose (2004: 591):

It seems to me that there are two quite distinct mysteries presented by quantum entanglement, and I believe that the answer to each of them is something of a completely different (although interrelated) character. 

The first mystery is the phenomenon itself. How are we to come to terms with quantum entanglement and to make sense of it in terms of ideas that we can comprehend, so that we can manage to accept it as something that forms an important part of the workings of our actual universe? 

The second mystery is somewhat complementary to the first. Since, according to quantum mechanics, entanglement is such a ubiquitous phenomenon — and we recall that the stupendous majority of quantum states are actually entangled ones — why is it something that we barely notice in our direct experience of the world? Why do these ubiquitous effects of entanglement not confront us at every turn? I do not believe that this second mystery has received nearly the attention that it deserves, people’s puzzlement having been almost entirely concentrated on the first.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the first mystery, quantum entanglement, is explained by distinguishing potential from instance, and recognising that the probabilities of particle instantiations are interdependent.

From the same perspective, the second mystery, why entangled quantum states are not directly experienced, is explained by the fact that only instances can be observed (the construal of experience as first-order meaning). Potential, on the other hand, can only be theorised (the reconstrual of first-order meaning as second-order meaning). It is theory only that provides the means of recognising that quantum states are entangled.

'Mysterious' Quantum Entanglement Viewed Through Systemic Functional Linguistics

Penrose (2004: 589):

The key issue is that the particles have been assumed to behave independently of each other after they have left the source, and to give the correct joint quantum probabilities whatever combination of detector settings confronts them. The point is that the particles have to mimic the expectations of quantum mechanics. We have found that these cannot be split into separate expectations for the two particles individually. The only way that the particles can consistently provide the correct quantum-mechanical answers is by being, in some way, ‘connected’ to each other, right up until one or the other of them is actually measured. This mysterious ‘connection’ between them is quantum entanglement. … The expectations of quantum mechanics (rather than of common sense) have been consistently vindicated!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the mysterious connection between the two observed particles lies in the fact that both are instances of the same quantum potential, such that the instantiation probabilities ("expectations") of the particles are mutually dependent. 

Quantum Entanglement Viewed Through Systemic Functional Linguistics

Penrose (2004: 583-4):

So what is quantum entanglement? What are EPR effects? … The simplest EPR situation is that considered by David Bohm (1951). In this, we envisage a pair of spin ½ particles, let us say, particle PL and particle PR, which start together in a combined spin 0 state, and then travel away from each other to the left and right to respective detectors L and R at a great distance apart (see Fig. 23.2).

Let us suppose that each of the detectors is capable of measuring the spin of the approaching particle in some direction that is only decided upon when the two particles are well separated from each other. The problem is to see whether it is possible to reproduce the expectations of quantum mechanics using some model in which the particles are regarded as unconnected independent classical-like entities, each one being unable to communicate with the other after they have separated. 

It turns out, because of a remarkable theorem due to the Northern Irish physicist John S. Bell, that it is not possible to reproduce the predictions of quantum theory in this way. Bell derived inequalities relating the joint probabilities of the results of two physically separated measurements that are violated by the expectations of quantum mechanics, yet which are necessarily satisfied by any model in which the two particles behave as independent entities after they have become physically separated. Thus, Bell-inequality violation demonstrates the presence of essentially quantum-theoretic effects — these being effects of quantum entanglements between physically separated particles — which cannot be explained by any model according to which the particles are treated as unconnected and independent actual things.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, particles are actual, but they are instances of potential. Each observation of the spin of a particle is the instantiation of quantum potential, where the probability of each instance of spin depends on the probability of the other. In this view, there is no signalling or interaction between the instances (particles), since the relation here is between potential (wavefunction) and instances of that potential (particles).

The Hidden Basis Of Einstein–Podolski–Rosen Effects Viewed Through Systemic Functional Linguistics

Penrose (2004: 582-3):

Entanglements between particles, a notion first made explicit by Schrödinger (1935b), are what lead to the extremely puzzling but actually observed phenomena known as Einstein–Podolski–Rosen (EPR) effects. They are, however, rather subtle features of the quantum world which are quite hard to demonstrate experimentally in a convincing way. It is remarkable that we seem to have to turn to something so esoteric and hidden from view when, for many-particle systems, almost the entire ‘information’ in the wavefunction is concerned with such matters!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, it is because the wavefunction construes potential, rather than actual, that what underlies the observed (actual) EPR effects is 'hidden from view'.

The Wavefunction Of Many-Particle Systems Viewed Through Systemic Functional Linguistics

Penrose (2004: 580):

How, then, are we to treat many-particle systems according to the standard non-relativistic Schrödinger picture? As described [previously], we shall have a single Hamiltonian, in which all momentum variables must appear for all the particles in the system. Each of these momenta gets replaced, in the quantisation prescription of the position-space (Schrödinger) representation, by a partial differentiation operator with respect to the relevant position coordinate of that particular particle. All these operators have to act on something and, for consistency of their interpretation, they must all act on the same thing. This is the wavefunction. As stated above, we must indeed have one wavefunction Ψ for the entire system, and this wavefunction must indeed be a function of the different position coordinates of all the separate particles.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the wavefunction identifies the potential of a quantum system: all the probable locations of all the particles that are instances of that systemic potential.

Relativistic Quantum Theory Viewed Through Systemic Functional Linguistics

Penrose (2004: 579):

But this is not how ordinary quantum mechanics works. There is only one time for all the particles. 

When we think about physics in an ordinary ‘non-relativistic’ way, this may indeed seem sensible, since in non-relativistic physics, time is external and absolute, and it simply ‘ticks away’ in the background, independently of the particular contents of the universe at any one moment. 

But, since the introduction of relativity, we know that such a picture can only be an approximation. What is the ‘time’ for one observer is a mixture of space and time for another, and vice versa. 

Ordinary quantum theory demands that each particle individually must carry its own space coordinate. Accordingly, in a properly relativistic quantum theory, it should also individually carry its own time coordinate. 

Indeed, this viewpoint has been adopted from time to time by various authors, going back to the late 1920s, but it does not seem to have been developed into a full-blown relativistic theory. A basic difficulty with allowing each particle its own separate time is that then each particle seems to go on its merry way off into a separate time dimension, so further ingredients would be needed to get us back to reality.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, time does not "tick away". Instead, time is the dimension of the unfolding of processes, such as the ticking of a clock, and the duration between ticks of a clock serves as a standard by which to measure the unfolding of other processes.

From this same perspective, the notion of a relativistic quantum theory is mistaken. Quantum theory is concerned with the relation between potential and instance, but General Relativity is not. General Relativity is concerned with modelling the relation between instances (particles) and their spatiotemporal dimensions.

The reason why instances of the same potential do not have different time co-ordinates is that they are mediums of the one process of instantiation, and it is this one unfolding that is measured as the one time. Put simply, such instantiations are simultaneous.

The Non-Relativistic Time Of Quantum Theory Viewed Through Systemic Functional Linguistics

Penrose (2004: 579):

A noteworthy feature of standard quantum theory is that, for a system of many particles, there is only one time coordinate, whereas each of the independent particles involved in the quantum system has its own independent set of position coordinates. This is a curious feature of non-relativistic quantum mechanics if we like to think of it as some kind of limiting approximation to a ‘more complete’ relativistic theory. For, in a relativistic scheme, the way that we treat space is essentially the way that we should also treat time. Since each particle has its own space coordinates, it should also have its own time coordinate. But this is not how ordinary quantum mechanics works. There is only one time for all the particles.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, time is the dimension of the unfolding of processes. In this scenario, the single process that unfolds is the instantiation of potential, so accordingly, all particles that mediate that single process share the same time co-ordinate.

The Quantum-Hamiltonian Approach Viewed Through Systemic Functional Linguistics

Penrose (2004: 578):

Let us return to what has been set out in the preceding two chapters, for the mathematics of a quantum system. The quantum-Hamiltonian approach, which provides us with the Schrödinger equation for the evolution of the quantum state vector, still applies when there are many particles, possibly interacting, possibly spinning, just as well as it did with a single particle without spin. All we need is a suitable Hamiltonian to incorporate all these features. We do not have a separate wavefunction for each particle; instead, we have one state vector, which describes the entire system. In a position-space representation, this single state vector can still be thought of as a wavefunction Ψ, but it would be a function of all the position coordinates of all the particles — so it is really a function on the configuration space of the system of particles…

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, such a wavefunction identifies all the potential position co-ordinates of all the particles: the potential configuration space of particle instantiation.

Quantum Entanglement Viewed Through Systemic Functional Linguistics

Penrose (2004: 578):

It would not be unreasonable to expect that, since our formalism has described for us the quantum behaviour of individual particles or other isolated entities, so also should it have told us how to describe systems containing several separate particles, perhaps interacting with one another in various ways. In a sense this is true…, but some distinctly new features arise, when more than just one particle is present in a system. The underlying quality that is new is the phenomenon of quantum entanglement, whereby a system of more than one particle must nevertheless be treated as a single holistic unit, and different manifestations of this phenomenon present us with yet more mystery in quantum behaviour than we have encountered already. Moreover, particles that are identical to each other are always automatically entangled with one another, although we shall find that this can happen in two quite distinct ways, depending upon the nature of the particle.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the 'single holistic unit' is the system of quantum potential, and quantum entanglement refers to the fact that probabilities of instantiation in the system are interdependent, such that one instantiation affects the probabilities of other instantiations of the same system of potential.

Superposed ‘Quantum Orbits’ Viewed Through Systemic Functional Linguistics

Penrose (2004: 572, 573):

For example, a hydrogen atom consists of an electron in orbit around its proton nucleus … . But the rules of quantum mechanics tell us that the quantum-mechanical orbit will not involve just a single classical trajectory about the nucleus, but is basically a quantum superposition of many such. These superposed ‘quantum orbits’ will be stationary solutions of the Schrödinger equation, with a Hamiltonian that is basically the same as in the classical case, but ‘canonically quantised’ … . 

… Such ‘quantised orbits’ are sometimes referred to as orbitals;

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the superposition of electron orbits around a nucleus models the phenomenon as potential, not actual. An actual electron is an instance of this potential.

Quantum States vs Classical States Viewed Through Systemic Functional Linguistics

Penrose (2004: 566):

The answer is that almost all ‘large’ quantum states do not resemble classical ones. The most famous such example is Schrödinger’s hypothetical cat, which is in a quantum superposition of being alive and dead. Why do we not actually see things like this at a classical level? This is an aspect of the measurement paradox which will be discussed in Chapters 29 and 30.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, Classical physics provides a model of the actual only, whereas Quantum physics distinguishes between actual and potential, such that the actual are instances of potential. Quantum superposition states are potential states, not actual states, and as such, are not seen 'at the classical level' of actual states.

The 'Bomb Test' Thought Experiment Viewed Through Systemic Functional Linguistics

Penrose (2004: 545-6):

An impressive use of this kind of thing has been suggested by Avshalom Elitzur and Lev Vaidman. Let us think of our beam-splitter as being part of a Mach–Zehnder type of interferometer, but where we do not know whether a detector C has, or has not, been placed in the transmitted beam of the first beam splitter. Let us suppose that the detector C triggers a bomb, so that the bomb would explode if C were to receive the photon. There are two final detectors A and B, and we know that only A and not B can register receipt of the photon if C is absent. See Fig. 22.6.

We wish to ascertain the presence of C (and the bomb) in some circumstance where we do not actually lose it in an explosion. This is achieved when detector B actually does register the photon; for that can occur only if detector C makes the measurement that it does not receive the photon! For then the photon has actually taken the other route, so that now A and B each has probability ½ of receiving the photon (because there is now no interference between the two beams), whereas in the absence of C, only A can ever receive the photon. 

In the examples just given, there is no degeneracy, so the issue that was addressed above that the mere result of the measurement may not determine the state that the system ‘jumps’ into does not arise.

 

Blogger Comments:

To be clear, the claim for this experimental set-up is if detector C is absent, then the emitted proton has a 100% probability of being observed at detector A. However, if detector C is present and no photon is observed there, then there is a 100% probability that photon has been reflected at the first beam splitter, and then reflected to the second beam splitter, after which there is a 50% probability of observing the photon at detector A, and a 50% probability of observing the photon at detector B. So the observation of the photon at detector B guarantees the absence of detector C.

From the perspective of Systemic Functional Linguistic Theory, the experimental set-up affords a range of quantum system possibilities, each with interdependent probabilities from which actual instantial events can be reasoned.

'Null Measurement' Viewed Through Systemic Functional Linguistics

Penrose (2004: 545):

Let us consider a situation … where a single photon is aimed at a beam splitter, and its state is partially reflected and partially transmitted. After the encounter, the state is thus a sum of these two orthogonal parts, the transmitted part |τ⟩ and the reflected part |ρ⟩:

|ψ⟩ = |τ⟩ + |ρ⟩

(see Fig. 22.5). 

Suppose that a detector is placed in the transmitted beam where, for the purposes of argument, we assume that the detector has 100% detection efficiency. Moreover, the photon source is to be such that each photon emission event is recorded (at the source) with 100% efficiency. … If we find that, on some occasions, the source has emitted a photon but the detector has not received it, then we can be sure that on these occasions the photon has ‘gone the other way’, and its state is therefore the reflected one: |ρ⟩. The remarkable thing is that the measurement of non-detection of the photon has caused the photon’s state to undergo a quantum jump (from the superposition |ψ⟩ to the reflected state |ρ⟩), despite the fact that the photon has not interacted with the measuring apparatus at all! This is an example of a null measurement.

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, a single photon aimed at a beam splitter is not 'partially reflected and partially transmitted'. It is either reflected or transmitted, and only observation will resolve which alternative is the case. The 'sum of these two orthogonal parts' represents the potential of the quantum system, not any actual instance (photon) of that potential.

The reason why the observed absence (null measurement) of a photon at one detector guarantees its presence at the other is that the experimental set-up provides only two possibilities. If the probability of finding a proton at one detector is 0%, then the probability of finding a proton at the other detector is 100%.

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.

The Non-Locality Of The Wavefunction Viewed Through Systemic Functional Linguistics

Penrose (2004: 512):

So we have just got exactly nowhere in understanding wave/particles — some irate reader will surely object with increasingly justified impatience! But hold on please, we are not through with interpreting our wavefunctions. We have to think of the entire wave as describing (or ‘being’) just a single particle. Although it does, in a definite sense, determine the probability that a spot will occur at the various places on the screen, this probability refers to just the one particle. This interpretation will not work if we think of the wavefunction in a local way, as independently providing a probability of spot formation at each separate place on the screen. We must think of a wavefunction as one entire thing. If it causes a spot to appear at one place, then it has done its job, and this apparent act of creation forbids it from causing a spot to appear somewhere else as well. Wavefunctions are quite unlike the waves of classical physics in this important respect. The different parts of the wave cannot be thought of as local disturbances, each carrying on independently of what is happening in a remote region. Wavefunctions have a strongly non-local character; in this sense they are completely holistic entities.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the 'entire' wave neither describes nor is a single particle. Rather, the wave is a construal of the potential of a particle. The notion of the wave being local or non-local derives partly from misunderstanding the wave as construing the potential of a location rather than the potential of a particle.

Moreover, the wave function neither causes nor creates the appearance of a particle at a location on the screen. It is in the act of observation that experience is construed as meaning: a particle as an instance of quantum potential.

In this view, the important respect in which wavefunctions are quite unlike the waves of classical physics is that they are construals of experience as potential, whereas classical waves are construals of experience as actual. The non-locality of wavefunctions is the "non-locality" of potential.

'Self-Interference' In The Two-Slit Experiment Viewed Through Systemic Functional Linguistics

 Penrose (2004: 512):

The difficulty is made more manifest if we imagine that our particles are charged particles, such as electrons. For if the emission of a single electron at the source could result in a pair of electrons arriving at the screen, even if only very occasionally, then we should have a violation of the law of conservation of charge. The same would apply to any other conserved particle ‘quantum number’, such as baryon conservation, for example, if we were to use neutrons. Such non-conservation behaviour would be in gross contradiction with an enormous amount of experimental evidence. Yet, electrons and neutrons do exhibit the kind of self-interference that results in a two-slit-experiment behaviour as I have just described!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, this scenario confuses quantum potential with actual instances of that potential. In the two-slit experiment, one electron is emitted and one electron arrives at the screen. The 'self-interference' is not between two instances (particles) of the one potential (wave), but between two potentials (waves) of the one instance (particle).

The Probabilities Of The Wavefunction Viewed Through Systemic Functional Linguistics

Penrose (2004: 511-2):

There is something that should be emphasised here. One could imagine that a little spot on the screen comes about from time to time, when the local intensity of the wave reaches some critical value or, rather, that there is some probability of a little spot appearing on the screen, this probability increases as the intensity of the wave increases. Nice try! But as I have formulated the two-slit experiment (in its idealised form) above, this simply will not work. For if it were just a matter of individual probabilities at individual places, we should expect that sometimes two spots would appear on the screen, at widely separated locations where the intensity is appreciable, with just the one wavefunction describing the emission of a single particle at the source.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the wave grades the probable locations of a particle — not the probable particles of a location.