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.

The Conflict Between The Wave And Particle Pictures Viewed Through Systemic Functional Linguistics

Penrose (2004: 511):

But the whole point of the two-slit experiment — so I was supposed to have been insisting — is that the experiment shows up a conflict between the wave picture and a particle picture. Indeed so; the most obvious manifestation of particle nature, in this experiment, occurs when these little fellows make their tiny marks on the screen: one at a time . . . !

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, there is no conflict between the wave picture and the particle picture, if the wave is understood as a picture of potential, and the particle is understood as a picture of an actual instance of that potential.

Wavefunction Peaks Viewed Through Systemic Functional Linguistics

Penrose (2004: 508):

What has happened to our ordinary picture of a particle, as something (at least approximately) localised at a single point? Well, we might say that a momentum state is only an idealisation. We can still get away with having a very well-defined (if not perfectly precisely defined) momentum if we pass to somewhat similar states referred to as ‘wave packets’. These are given by wavefunctions that peak sharply in magnitude at some position and are ‘almost’ eigenfunctions of momentum, in an appropriate sense. In one dimension such wave packets can be presented explicitly, …. This is the well-known ‘bell-shaped’ curve of statistics…

 

Blogger Comments:

According to Max Born, the wavefunction is a measure of probability. According to Systemic Functional Linguistic Theory, probability is an assessment of potential. On this basis, the peak in magnitude of a wavefunction marks the most probable instantiation of potential.

Quantum Reality Viewed Through Systemic Functional Linguistics

Penrose (2004: 507-8):

Let us step back from these detailed matters for a moment, and ask what all this is trying to tell us about ‘reality’. Are the dynamical variables ‘real things’? Are the states ‘real’? Or should we say that we have achieved reality only when we have arrived at the seemingly ‘classical’ quantities that arise as eigenvalues of the dynamical variables (or of other operators)? In fact, quantum physicists tend not to be very clear about this issue. Most of them are distinctly uncomfortable about addressing the issue of ‘reality’ at all. They may claim to take what they would call a ‘positivist’ stand, and refuse to consider what ‘reality’ is supposed to mean, regarding such an inquiry as ‘unscientific’. All that we should ask of our formalism, they might claim, would be that it give answers to appropriate questions that we may pose of a system, and that those answers agree with observational fact.

If we are to believe that any one thing in the quantum formalism is ‘actually’ real, for a quantum system, then I think that it has to be the wavefunction (or state vector) that describes quantum reality. My own viewpoint is that the question of ‘reality’ must be addressed in quantum mechanics — especially if one takes the view (as many physicists appear to) that the quantum formalism applies universally to the whole of physics — for then, if there is no quantum reality, there can be no reality at any level (all levels being quantum levels, on this view). To me, it makes no sense to deny reality altogether in this way. We need a notion of physical reality, even if only a provisional or approximate one, for without it our objective universe, and thence the whole of science, simply evaporates before our contemplative gaze!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, reality is meaning construed of experience. The wavefunction is a construal of experience as potential reality. In an observation, an instance of potential reality is construed as actual reality.

The Two-Slit Experiment Viewed Through Systemic Functional Linguistics

Penrose (2004: 504-5):

One of the most convincing (and best known) reasons for our having to face up to the fact that particles can behave as waves and waves as particles is the two-slit experiment. Here we have a source of particles and a detector screen, where there is a barrier with a pair of narrowly separated parallel slits in it, situated between source and screen; see Fig. 21.4a. 

We suppose that one particle at a time is emitted, aimed at the screen. If we start with one slit open and the other closed, then a haphazard pattern of dots will appear at the screen, forming one at a time as individual particles from the source hit it. The intensity of the pattern (in the sense of the greatest density of dots) is most extreme in a central strip close to the plane connecting source to slit, as is to be expected, and it falls off uniformly in both directions from this central strip (Fig. 21.4b). This pattern is effectively the same if the experiment is repeated with the other slit being the open one (Fig. 21.4c). No puzzle here. But if the experiment is run once more when both slits are now open, then something extraordinary happens; see Fig. 21.4d.  

The particles still make dots on the screen one at a time, but now there is a wavy interference pattern of parallel bands of intensity, where we even find that there are regions on the screen that are never reached by particles from the source, despite the fact that when just one or the other of the slits was open, then particles could reach those regions perfectly happily! Although the spots reach the screen one at a time at localised positions, and although each occurrence of a particle meeting the screen can be identified with a particular particle emission event at the source, the behaviour of the particle between source and screen, including its ambiguous encounter with the two slits in the barrier, is like a wave, where the wave/particle feels out both slits during this encounter.  Moreover … the spacing of the bands on the screen tells us what the wavelength of our wave/particle must be… 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, wave-particle duality is the complementarity of potential and instance. In this experiment, it is particles that are emitted at the source and detected on the screen, and so it is particles that are actual. The fact that waves are neither emitted at the source nor detected on the screen demonstrates that the wave aspect is not actual.

The wave, as quantum potential, measures the probability of a particle's location, and the actual locations of particles on the detector screen are instances of that probability, with the most frequent locations (highest densities) being instances of the highest probability.

When only one slit is open, quantum potential is measured by one wave of probability, so the pattern of particle detections reflects this. But when two slits are open, quantum potential is measured by two waves of probability, such that the actual locations of particles on the detector screen are in line with the constructive and destructive interference patterns of the two waves of probability.

In this view, then, the spacing of the bands on the detector screen manifests a wavelength of equiprobability, and to say that the behaviour of the particle between the source and the screen is like a wave is to mistake potential for actual. Moreover, as Richard Feynman explained to his BBC TV audience in 1965:

To conclude that it goes either through one hole or the other when you are not looking is to produce an error.

Wavelike Particles And Particulate Waves Viewed Through Systemic Functional Linguistics

Penrose (2004: 500-1):

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

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

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

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

 

Blogger Comments:

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

Frequency And Wave Number Viewed Through Systemic Functional Linguistics

Penrose (2004: 500):

Detailed experimental issues are not things that I can go into here, but the essential point that emerges from a vast amount of experimental evidence is that there is a direct association between frequency and energy, and a corresponding association between wave number (the reciprocal of wavelength) and momentum; moreover, these associations appear to be universal, in all phenomena.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the frequency of light is the number of photons per interval of time, and the wave number of light is the number of photons per interval of space. The number of photons per time unit is associated with energy, and the number of photons per space unit is associated with momentum. (The wave quantifies light as potential, with each wave crest as the most probable location of an actual particle.)

'What Quantum Theory Actually Tells Us To Believe About ‘Reality’ ' — Viewed Through Systemic Functional Linguistics

Penrose (2004: 493):

It is probable that most physicists would regard the changes in our picture of the world that quantum mechanics has wrought as being far more revolutionary even than the extraordinary curved spacetime of Einstein’s general relativity. Indeed, what quantum theory actually tells us to believe about ‘reality’ at the submicroscopic levels of atoms or of fundamental particles is, as we shall be seeing in this chapter and in the next two, so greatly removed from our ordinary classical pictures that we may choose simply to give up on quantum-level ‘pictures’ altogether. Indeed many physicists appear even to doubt the very existence of a true ‘reality’ at quantum scales and, instead, rely merely upon the quantum-mechanical mathematical formalism to obtain answers.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, 'what quantum theory actually tells us' is that meaning does not transcend semiotic systems, and that meaning is instantiated in the act of observation; that reality is the meaning construed of experience.

In this view, there is no need to 'give up on quantum level pictures' or to 'doubt the existence of a true reality at quantum scales'. What is needed is the abandonment of the epistemological assumption that experience is categorised independently of semiotic systems, and that the task of science is to discover those 'true' categories. Instead, science is concerned with reconstruing the phenomenal meaning construed by language as metaphenomenal meaning whose validity is decided by the assumptions, principles and methodologies of science.

Gravitational Waves Viewed Through Systemic Functional Linguistics

Penrose (2004: 465):

Now let us consider that the bodies [imagined planets] are in motion, in orbit about one another. It is a consequence of Einstein’s field equation that gravitational waves — ripples in the fabric of spacetime — will emanate from the system and carry (positive) energy away from it. In normal circumstances, this energy loss will be very small. For example, the largest such effect in our own solar system arises from the Jupiter–Sun system, and the rate of energy loss is only about that emitted by a 40-watt light bulb!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the construal of spacetime as a fabric mistakes circumstance for thing. Spacetime is not a thing, but where things are located.

If gravity is understood as the relative contraction of space intervals, and the relative expansion of time intervals, with proximity to a centre of mass, then gravitational waves are propagations of relatively contracted intervals of space, and relatively expanded intervals of time.

The Spacetime Curvature Of Gravitation Viewed Through Systemic Functional Linguistics

Penrose (2004: 459):

Gravitation [in Einstein’s model] is not to be regarded as a force; for, to an observer who is falling freely (such as our astronaut A), there is no gravitational force to be felt. Instead, gravitation manifests itself in the form of spacetime curvature.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, it is not spacetime (circumstance) that is curved, but the trajectory (process) of an orbiting body through spacetime. The curvature of the trajectory is due to the contraction of space intervals in the direction of the centre of mass, since this means that the geodesic, the shortest path between two points in three-dimensional space, is biased towards the centre of mass, relative to other directions.

'Disembodied' Fields Viewed Through Systemic Functional Linguistics

Penrose (2004: 441):

I referred, at the beginning of this chapter, to the fact that a profound shift in Newtonian foundations had already begun in the 19th century, before the revolutions of relativity and quantum theory in the 20th. The first hint that such a change might be needed came from the wonderful experimental findings of Michæl Faraday in about 1833, and from the pictures of reality that he found himself needing in order to accommodate these. Basically, the fundamental change was to consider that the ‘Newtonian particles’ and the ‘forces’ that act between them are not the only inhabitants of our universe. Instead, the idea of a ‘field’, with a disembodied existence of its own was now having to be taken seriously. It was the great Scottish physicist James Clark Maxwell who, in 1864, formulated the equations that this ‘disembodied field’ must satisfy, and he showed that these fields can carry energy from one place to another. These equations unified the behaviour of electric fields, magnetic fields, and even light, and they are now known simply as Maxwell’s equations, the first of the relativistic field equations.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the notion of a field as an 'inhabitant of our universe' misconstrues an extent as a thing. The characterisation of a field as 'disembodied' suggests a partial recognition of the fact that a field is not a thing, since physical things are "embodied".

On this basis, fields are the extents of spacetime in which specific 'behaviours' (e.g. the 'carrying of energy from place to place') unfold.

Physical Fields Viewed Through Systemic Functional Linguistics

Penrose (2004: 440):

In the period between the introduction of Newton’s superb dynamical scheme, which we can best date as the publication of his Principia in 1687, and the appearance of special relativity theory, which could reasonably be dated at Einstein’s first publication on the subject, in 1905, many important developments in our pictures of fundamental physics took place. The biggest shift that occurred in this period was the realisation, mainly through the 19th century work of Faraday and Maxwell, that some notion of physical field, permeating space, must coexist with the previously held ‘Newtonian reality’ of individual particles interacting via instantaneous forces. Later, this ‘field’ notion also became a crucial ingredient of Einstein’s 1915 curved-spacetime theory of gravity. What are now called the classical fields are, indeed, the electromagnetic field of Maxwell and the gravitational field of Einstein.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, a physical field is an extent, a circumstance of processes, not a thing. On this basis, a physical field does not 'permeate' space, it is space — an extent of space.

And as previously explained, from this perspective, in the Theory of General Relativity, it is not spacetime (circumstance) that is curved, but the motion (process) of bodies (things) — geodesic trajectories — through spacetime.

Newtonian Potential And Kinetic Energy Viewed Through Systemic Functional Linguistics

Penrose (2004: 431):

The energy of a system may be considered to be composed of two parts, namely the kinetic energy (i.e. energy of motion) and the potential energy (the energy stored in the forces between particles).

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, energy is the ability of processes to unfold. Potential energy is that ability as potential, and kinetic energy is an instantiation of that ability.