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%.