Higher-Dimensional Spacetime Viewed Through Systemic Functional Linguistics [2]

Penrose (2004: 881):

Before we dismiss this idea as a total fantasy we must recall the ingenious scheme, put forward in 1919 by the (at that time) little-known Polish mathematician Theodor Kaluza, and then further taken up by that same Swedish mathematical physicist Oskar Klein. Provided that the extra dimensions (in excess of 4, that is) are taken as small dimensions, in some appropriate sense, then we might not be directly aware of them. What does ‘small’ mean in this context? 

Recall the ‘hosepipe’ analogy of Fig. 15.1. When looked at from a great distance, the hosepipe appears to be 1-dimensional, but if we examine it more closely, we find a 2-dimensional surface. 

The idea is that some being, inhabiting the hosepipe universe, would not ‘know’ that the extra dimension wrapping around the pipe is actually ‘there’, provided that the physical dimensions of that being are much larger than the circumference of the hosepipe. Similar remarks would apply to a higher-dimensional ‘hosepipe universe’ of 4 + d dimensions, where d of the dimensions are ‘small’ and not directly perceived by a much larger being inhabiting this universe, who perceives only the 4 ‘large’ dimensions; see Fig. 31.3.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the hosepipe analogy confuses phenomena in spacetime with the spacetime in which phenomena are located. A 2-dimensional surface is a thing which extends in two spatial dimensions. A 3-dimensional hosepipe is a thing which extends in three spatial dimensions. The trajectory around the circumference of the hosepipe is here misconstrued as a spatial dimension.

Higher-Dimensional Spacetime Viewed Through Systemic Functional Linguistics [1]

Penrose (2004: 880-1, 882):

How is it that physicists could take seriously the possibility that the dimensionality of spacetime might be other than the four that we directly experience (one time and three space)? As mathematical exercises, such higher-dimensional things seem fine, but this is supposed to be a physical theory where ‘spacetime’ really means the combination of actual space with time. Indeed, as we shall be seeing, string theory (as it is currently understood) requires that spacetime must indeed have more than four dimensions. In the early theory the dimension number was taken to be 26, but later innovations (which involved the ideas of supersymmetry) led to this spacetime dimensionality being reduced to 10. … 

Whatever the status of these newer ideas, this suggestion of a higher-dimensionality for spacetime has, at this stage in our deliberations, a status no more compelling than that of a ‘cute idea’ — which the original Kaluza–Klein suggestion certainly was. Whatever may be the mathematical attractiveness of this idea, we have to address the question of whether there are good physical reasons for believing in such a scheme.

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, physical theories that propose higher-dimensional spacetime, such as the variants of String Theory, mistake geodesic trajectories in space over time for the spatiotemporal dimensions in which these are located.

A Viable Ontology For Quantum Mechanics Viewed Through Systemic Functional Linguistics

Penrose (2004: 865):

It is clear that we are far from a theory which can reliably address all these issues. But I hope, at least, that I have been able to persuade the reader of the fundamental importance of having a quantum mechanics with a viable ontology. The issues that are addressed in Chapters 29 and 30 of this book are not just matters of philosophical interest. The importance of having an ontologically coherent (improved) quantum mechanics cannot, in my view, be over-estimated. In this section, I have touched upon just one of the foundational issues that could be deeply affected by knowledge of such a theory. There are many more, including situations in biology, where as with the early universe, the present-day ‘Copenhagen’ viewpoint cannot really be applied — there being no clear division into a quantum system and a classical measuring device.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, it is a viable epistemology that quantum mechanics requires. Quantum mechanics has invalidated the epistemological assumption that meaning transcends semiotic systems. The ontology that follows from the epistemological assumption that meaning is immanent, and does not transcend semiotic systems, merely requires the additional distinction between potential and instance to make it coherent and viable. This makes the distinction between 'a quantum system' (potential and instance) and 'a classical measuring device' (instance of potential) perfectly clear.

Perspectives On The Very Early Universe Viewed Through Systemic Functional Linguistics

Penrose (2004: 863, 868n):

We should bear in mind that we are here concerned with the very early universe, where the temperature would have been perhaps some 10³²K. There were no experimenters around at that time performing ‘measurements’, so it is hard to see how the standard ‘Copenhagen’ perspective can be applied. 

What about the many-worlds view? In that picture, there is no actual R, and the Friedmann–Lemaître–Robertson–Walker-symmetric state of the universe would be maintained until the present day, this state being representable as a grand superposition of many constituent spacetime geometries. Only when conscious observers try to make sense of the world, according to this view, would the resolution into alternative spacetime geometries be deemed appropriate — there now being a superposition of conscious observers, each one perceiving a single ‘world’.⁴⁶

On the ‘For All Practical Purposes’ view, the presence of (sufficient) environmental decoherence is regarded as the signal, whereby our quantum superposition of different geometries is permitted to be regarded as a probability mixture of different geometries.

⁴⁶ On Wheeler’s own variant, the ‘participatory universe’, see Wheeler (1983), it would be the ultimate presence of conscious observers who somehow (teleologically) determine the particular selection of spacetime geometry that occurred in the early universe.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the Copenhagen interpretation is concerned with the construal of experience as first-order meaning, through perception, whereas (a model of) the very early universe is a reconstrual of first-order meaning as second-order meaning that realises theory, through cognition.

From the same perspective, the notion of 'a grand superposition of many constituent spacetime geometries' confuses potential construals of experience as meaning (superpositions) with instances of that potential (actual construals), and confuses spacetime with states of phenomena in spacetime. The notion of 'a superposition of conscious observers' misapplies the notion of alternative potential construals of meaning to the observer who construes experience as meaning. 

In this view, it is not that conscious observers '(teleologically) determine the particular selection of spacetime geometry that occurred in the early universe' but that this is second-order meaning construed by conscious processing.

The Quantum Description Of Spacetime Viewed Through Systemic Functional Linguistics

Penrose (2004: 862):

Similarly, in standard quantum mechanics, all the variables defining a spacetime state cannot be determined together. The quantum description of spacetime should nevertheless be perfectly well defined. But the Heisenberg principle tells us that this description cannot resemble a classical (pseudo-)Riemannian manifold, as different spacetime geometric quantities do not commute with one another. Instead, according to Wheeler’s picture, the state would consist of a vast superposition of different geometries, most of which would deviate wildly from flatness and so have the ‘foamlike’ character that he envisages.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, this confuses what is located in spacetime with the spacetime in which phenomena are located. For example, 'all the variables defining a spacetime state' are the variables of phenomena at a specified location in spacetime.

Moreover, the superposition of variables is the superposition of potential variables, not the superposition of actual variables that instantiate that potential, and the 'foamlike' character is concerned with instantiations of this potential, not with the spatiotemporal dimensions in which such instantiations are located.

The Unmeasured State Of A Particle Viewed Through Systemic Functional Linguistics

Penrose (2004: 861-2):

To clarify this picture, we must recall carefully what Heisenberg’s uncertainty relations actually state. They do not tell us that there is something inherently ‘fuzzy’ or ‘incoherent’ in the way that nature behaves at the tiniest scales. Instead, Heisenberg uncertainty restricts the precision whereby two non-commuting measurements can be carried out. We recall that, for a single particle, both its position and momentum in some direction, being non-commuting, cannot be determined precisely at the same time, the product of their respective errors being not less than ½ħ. There is a perfectly well-defined quantum state, however, and if no actual measurement is performed, the state of the particle will evolve precisely, according to Schrödinger’s equation.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, if no actual measurement is performed, then no construal of experience as a particle occurs. It is the potential state of the particle that evolves precisely according to Schrödinger’s equation.

Quantum Fluctuations Viewed Through Systemic Functional Linguistics

Penrose (2004: 861):

But what are quantum fluctuations? It is a feature of Heisenberg’s uncertainty relations, as applied to field quantities, that, if one tries to measure the value of a quantum field in some very small region to great accuracy, this will lead to a very large uncertainty in other (canonically) related field quantities, and hence to a very rapidly changing expected value of the quantity being measured. Thus, the very act of ascertaining the precise value of some field quantity will result in that quantity fluctuating wildly. This quantity could be some component of the spacetime metric, so we see that any attempt at measuring the metric precisely will result in enormous changes in that metric. It was considerations such as these that led John Wheeler, in the 1950s, to argue that the nature of spacetime at the Planck scale of 10⁻¹³ cm would be a wildly fluctuating ‘foam’.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, this confuses instantiations of potential (field quantities) with spatiotemporal locations in which such instantiations occur. That is, it is the instantiations of field quantities that constitute a 'fluctuating foam', not the spacetime in which they are located.

The Claim That Quantum Mechanics Has No Credible Ontology Viewed Through Systemic Functional Linguistics

Penrose (2004: 860):

My own bewilderment would arise primarily from a conviction that present-day quantum mechanics has no credible ontology, so that it must be seriously modified in order for the physics of the world to make sense.

Blogger Comments:

To be clear, ontology follows from epistemology. The reason for bewilderment is the fact that quantum theory successfully invalidates the 'transcendence' epistemology assumed by physicists, namely: that there are meanings outside semiotic systems that physicists will eventually discover in a final theory of everything. Quantum Theory supports the opposite view, the 'immanence' epistemology, whereby all meaning is within semiotic systems, and so supports the view that 'reality' is the meaning that is construed of experience which, in the case of experiments, happens when an observation is made.

And from the perspective of Systemic Functional Linguistic Theory, Quantum Theory makes the important — but insufficiently understood — distinction between potential construals of experience as meaning and actual construals of experience as meaning that instantiate that potential.

In short it is not the ontology of Quantum mechanics that must be seriously modified, but the epistemology that the physics community inherited from Galileo, and continues to assume without question, despite its disconfirmation.

Gravitational Objective Reduction Viewed Through Systemic Functional Linguistics

Penrose (2004: 853, 854-5):

The upshot of the above argument seems to be that a quantum superposition of two states ought indeed to decay into one or the other of its constituents in a time scale of the order ħ/EG. …

We now have what appears to be a plausible proposal for an objective state reduction which applies, at least, in situations when a quantum state is a superposition of two other states, each of which is stationary (in the aforementioned Schrödinger–Newton sense). According to this proposal, such a superposed state will spontaneously reduce into one or the other of its stationary constituents in an average timescale of about ħ/EG, where EG is the gravitational self-energy of the difference between the two mass distributions. I refer to this proposal as gravitational OR (where OR stands for the ‘objective reduction’ of the quantum state). …

It is my own standpoint, with regard to quantum state reduction, that it is indeed an objective process, and that it is always a gravitational phenomenon. …

A full theory is certainly lacking, and I have provided no actual dynamics for the reduction of the state, according to this OR process, even in the case of the particular superpositions that I have been considering.

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the process here is not one of decay or reduction, and the two states are not constituents. The 'constituents' of a quantum superposition are alternative potentials, and the 'decay' of a quantum superposition of two states into one of the two states is the instantiation of potential construals of experience as meaning as one actual construal of experience as meaning.

In this view, the problem here lies in treating potential as actual, and in excluding the construal of experience as meaning from the explanation.

Schrödinger’s Lump Viewed Through Systemic Functional Linguistics

Penrose (2004: 846, 847):

Let us return to the kind of situation referred to as ‘Schrödinger’s cat’. I illustrated how one might set up a quantum superposition of a live cat and a dead cat by using a beam splitter to put a photon’s state into a superposition, where the transmitted part of the photon’s state triggers a device to kill the cat, while the reflected part leaves the cat alive. Use of an actual cat would, of course, be not only inhumane, but taking an unnecessarily complicated physical system. So let us, instead, consider that the transmitted photon state simply activates a device which moves a lump of material horizontally by a small amount, whereas the reflected part leaves the lump alone; see Fig. 30.20. 

The superposed lump now plays the role of the Schrödinger’s cat — though not so dramatically as before! The question that I now want to raise is the following: is the quantum superposition of the two lump locations a stationary state? In conventional quantum mechanics, this would certainly be the case if we consider that each lump location separately represents a stationary state and that the energy in each case is the same (so the resting place of the displaced lump is neither raised nor lowered in relation to its original location). …

Now let us start to bring in the lessons that Einstein has taught us with his superb and now excellently confirmed general theory of relativity. In the first place, we might consider it important to bring in the gravitational field expressed in the background spacetime geometry. We can imagine that the experiment is being performed on the Earth, with the two instances of the lump sitting on a horizontal platform.

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the superposition of the two lumps is the superposition of two potential construals of experience of meaning, not two instances of potential. Observation will instantiate the potential as one of the two lumps in one location, but not both lumps in both locations.

The Destruction Of Material In A Black Hole Singularity Viewed Through Systemic Functional Linguistics

Penrose (2004: 840-1):

… the collapsing physical material simply falls across the horizon, taking all its ‘information’ with it, to be finally destroyed at the singularity. Nothing particular, of local physical importance, should happen at the horizon. The matter does not even ‘know’ when it crosses the horizon. We should bear in mind that we could be considering an initially very large black hole, perhaps like the holes that are believed to inhabit galactic centres, which could be of a million solar masses or more. As the horizon is crossed, nothing particular happens. The spacetime curvature and density of material is not large: only of the kind that we find in our own solar system. Even the location of the horizon is not determined by local considerations, since that location depends upon how much material later falls into the hole. If more material falls in later, then the horizon would actually been crossed earlier! 

I find it inconceivable that somehow ‘at the moment just before the horizon is crossed’ some sort of signal is emitted to the outside world conveying outwards the full details of all information contained in the collapsing material. In fact, simply a signal would by itself not be enough, since the material itself is, in a sense, really the ‘information’ that one is concerned with. Once it has fallen through the horizon, the material is trapped, and is inevitably destroyed in the singularity itself. … According to this picture, the material in the collapse is destroyed (and its ‘information’ is destroyed) only when it enters the singularity, not when it crosses the horizon.

Blogger Comments:

The event horizon of a black hole, according to the General Theory of Relativity, is circumference around a singularity at which the curvature of spacetime is such that light cannot escape. As physical material falls with the event horizon, therefore, it ceases to be observable.

From the perspective of Systemic Functional Linguistic Theory, it is the geodesic that is curved, not spacetime. This curved trajectory results from the relative contraction of space intervals in the direction of the singularity.

In this view, just as gravity is the relative contraction of space intervals, it is also the relative expansion of time intervals. This means that processes take longer and longer to unfold in the direction of the singularity. If the time intervals near the singularity approach infinity, then, relative to observers outside the event horizon, physical material falling towards a singularity, as space intervals contract towards zero, never actually reaches it.

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

Penrose (2004: 811):

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

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

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

Blogger Comments:

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

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

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

The Consistent-Histories Approach Viewed Through Systemic Functional Linguistics

Penrose (2004: 810-1):

If the ‘extravagant’ ontology for the consistent-histories approach (d) is adopted, in which reality is represented as a totality of maximally refined consistent-history sets, then a criticism can be raised which is somewhat similar to that of the many-worlds case (b). As with (b), a detailed and precise theory of conscious perceivers seems to be needed in order that (d) can conjure up a picture that is consistent with the physical world that we know. … Alternatively, one might prefer something like the more economical ontology in which a single maximally refined consistent history set might be considered as a plausible candidate for a ‘real-world’ ontology. …

In my own view, a major drawback with (d) is that … it does not seem to get us any closer to an understanding of what a physical measurement actually is than do the more conventional ontologies of (a) or (b). … 

Why, according to (d), do we not actually witness things like Schrödinger cats, in superposed limbo between life and death? The theory does not seem to give any improvement on the standard Copenhagen position (a) in explaining which systems (such as pieces of physical apparatus or cats) should behave classically, whereas neutrons or photons do not. 

… the criteria that have so far been put forward do not do enough to narrow down the model’s behaviour so that an unambiguous picture of something resembling the world we know can arise. This seems to be true both at the macroscopic ‘classical-like’ level … and also at the ‘quantum level’ at which one would hope to see undisturbed unitary evolution. Since the measurement paradox is concerned with the seeming conflict between physical behaviour at these two different levels, it is hard to see how the consistent-history viewpoint (d) is yet in a position to shed much light on this paradox.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the consistent histories approach mistakes potential (a consistent set of histories) for actual instances of that potential. Conscious perceivers are needed because it is a conscious act of perception that instantiates one of the potential construals of experience as meaning (pieces of physical apparatus and a dead cat or a live cat).

The Need For A Theory Of Perception Viewed Through Systemic Functional Linguistics

Penrose (2004: 809):

Since the mathematics alone will not single out the ‘|live cat⟩’ and ‘|dead cat⟩’ states as being in any way ‘preferred’, we still need a theory of perception before we can make sense of (b) [the 'many worlds' interpretation], and such a theory is lacking. Moreover, the onus on such a theory would be not only to explain why superpositions of dead and live cats (or of anything else macroscopic) do not occur in the perceived world, but also why the wondrous and extraordinarily precise squared-modulus rule actually gives the right answers for probabilities in quantum mechanics! A theory of perception that could do this would itself need to be as precise as quantum theory. Supporters of (b) have come nowhere close to suggesting such a scheme.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, it is not a theory of perception that is required but merely an understanding of the distinction between potential and instance. This distinction explains that superpositions of dead and live cats are not perceived because they are each potential construals of experience as meaning, only one of which is instantiated as an actual perception. It also explains the squared-modulus rule as modelling the potential of a quantum system, with probabilities as the quantification of that potential.

Superposed Perception States Viewed Through Systemic Functional Linguistics

Penrose (2004: 807, 808):

I wish to make clear that, as it stands, this [the 'many worlds' interpretation] is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat. … 

Why do we not permit these superposed perception states? Until we know exactly what it is about a quantum state that allows it to be considered as a ‘perception’, and consequently see that such superpositions are ‘not allowed’, we have really got nowhere in explaining why the real world of our experiences cannot involve superpositions of live and dead cats.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the superposition of live cat and dead cat is not a superposition of perception states, but a superposition of potential "perception states" (construals of experience as meaning). Perception involves the instantiation of one of these two potential meanings.

The Many-Worlds Standpoint On Schrödinger's Cat Viewed Through Systemic Functional Linguistics

Penrose (2004: 806-7):

What about the many-worlds standpoint (b), then? Here the ‘reality’ of the quantum superposition of a dead and a live cat is simply accepted (as would the quantum-superposed weather patterns of the previous paragraph); but this does not tell us what an observer, looking at the cat (or the weather), actually ‘perceives’. The state of the observer’s perception is considered to be entangled with the state of the cat. The perception state ‘I perceive a live cat’ accompanies the ‘live-cat’ state and the perception state ‘I perceive a dead cat’ accompanies the ‘dead-cat’ state. … It is then assumed that a perceiving being always finds his/her perception state to be in one of these two; accordingly, the cat is, in the perceived world, either alive or dead. These two possibilities coexist in ‘reality’ in the entangled superposition …

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the quantum-superposition of a dead cat and a live cat is the superposition of potential construals of experience as meaning, and so the 'many worlds' interpretation mistakes potential construals for actual construals. What an observer looking at the cat actually perceives is an instance of potential: either a dead cat or a live cat.

The state of the observer's perception is entangled with the state of the cat in the sense that the state of the cat is a construal of experience as meaning by the observer. Importantly, the assumption that the meaning 'the state of the cat' transcends the meaning of semiotic systems is precisely what this experiment, and Quantum Theory generally, invalidates.

'Wigner Reality' Viewed Through Systemic Functional Linguistics

Penrose (2004: 806):

It seems to me, however, that any theory that demands the presence of a conscious observer, in order that R be effected, leads to a very lop-sided (and, I would argue, highly implausible) picture of the universe. Imagine some distant Earth-like planet without conscious life, and for which there is no consciousness for many many light years in all directions. What is the weather like on that planet? 

Weather patterns have the property that they are ‘chaotic systems’, in the sense that any particular pattern which develops will depend critically on the tiniest details of what happened before. Indeed, it is probable that, in a month, say, tiny quantum effects will become so magnified that the entire pattern of weather on the planet would depend upon them. 

The absence of consciousness, according to the particular version of (f) (or perhaps (a)) under discussion, would imply that R never occurs on such a planet, so that the weather is, in reality, just some quantum superposed mess that does not resemble an actual weather in the sense that we know it. 

Yet if a spacecraft containing conscious travellers, or a probe with the capacity to transmit a signal to a conscious being, is able to train its sensors on that planet, then immediately — and only at that point — its weather suddenly becomes an ordinary weather, just as though it had been ordinary weather all the time! There is no actual contradiction with experience here, but is this ‘Wigner reality’ a believable picture for the behaviour of an actual physical universe? It is not, to me; but I can (just about) understand others giving it more credence.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the observation of weather is the construal of experience as meaning. If the weather on some distant Earth-like planet is not observed, then there is no construal of experience as meaning. If the weather on some distant Earth-like planet is observed, as by conscious travellers on a spacecraft or through the use of a sensor beam, then there is a construal of experience as meaning. Any superposition of weather patterns is a superposition of potential observations: of potential construals of experience as meaning.

Another Variant Of The Copenhagen Interpretation Viewed Through Systemic Functional Linguistics

Penrose (2004: 805-6):

Another variant of (a) would demand, in effect, that the ‘classical measuring apparatus’ is ultimately the observer’s consciousness. Accordingly (if we discount the consciousness of the cat itself), it is only when a conscious experimenter examines the cat that classicality has been achieved. It seems to me that, once we have arrived at this level, we are driven to take a position that is more in line with (b) or with (f). If we take the view that the U rules of quantum linear superposition continue to hold right up to the level of a conscious being, then we are in the realm of the many-worlds perspective (b), but if we take the stand that U fails for conscious beings, then we are driven to a version of (f) according to which some new type of behaviour, outside the ordinary predictions of quantum mechanics, comes into play with beings who possess consciousness. A suggestion along this line was actually put forward by the distinguished quantum physicist Eugene Wigner in 1961.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the 'classical measuring apparatus' is meaning that is the content of the observer's consciousness (and of any other linguate being who imagines or speaks or writes of it). The 'classical measuring apparatus', as such, is not the content of the cat's consciousness, because the cat cannot construe experience as linguistic meaning — though the cat can construe experience as perceptual meaning, and it is this construal that is the content of its consciousness.

The laws of quantum linear superposition continue to hold right up to when a conscious experimenter examines the cat because it is only then that the potential that the wavefunction probabilistically quantifies is construed as an actual instance of meaning. As previously argued, this does not entail a many worlds interpretation.

The Copenhagen Viewpoint On Schrödinger's Cat Viewed Through Systemic Functional Linguistics

Penrose (2004: 805):

Consider the Copenhagen viewpoint (a). As far as I can make out, this interpretation would simply regard the photon detector to be a ‘classical measuring device’, to which the rules of quantum superposition are not applied. The photon state between its emission and its detection (or non-detection) by the device is described by a wavefunction (state-vector), but no ‘physical reality’ is assigned to that. The wavefunction is used merely as a mathematical expression to be used for calculating probabilities. If the beam splitter is such that the photon amplitude is divided equally into two, then the calculation tells us that there is a 50% chance for the detector to register reception of the photon and a 50% chance that it will not. Therefore there is a 50% chance that the cat will be killed and a 50% chance that it will remain alive. 

This is physically the correct answer, where ‘physically’ refers to the behaviour of the world that we actually experience. Yet this description provides us with a very unsatisfactory picture of things if we wish to pursue the physical events in greater detail. What actually goes on inside a detector? Why are we allowed to treat it as a ‘classical device’ when, after all, it is constructed from the same quantum ingredients (protons, electrons, neutrons, virtual photons, etc.) as any other piece of physical material, large or small? I can well appreciate that, in the early days of quantum mechanics, something of the nature of Niels Bohr’s perspective on the subject was almost a necessity, so that the theory could actually be used, and progress in quantum physics could be made. Yet, as far as I can see, such a perspective can only be a temporary one, and it does not resolve the question of why, and at what stage, ‘classical behaviour’ might arise for large and complicated structures like ‘detectors’. Since viewpoint (a) requires such ‘classical structures’ for its interpretation of quantum mechanics, it can only be a ‘stop-gap’ position, in which the deeper issues concerning what actually constitutes a measurement are not addressed at all.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the rules of quantum superposition do not apply to the (observed) photon detector because quantum superposition applies only to potential meaning.

The photon state when it is not observed, as described by the wavefunction, is potential 'physical reality', and probability is the quantification of that potential meaning.

What goes on inside the detector, like the detector itself, is potential meaning until it is observed, and thereby construed as an instance of meaning.

The problems of quantum physics are solved by taking an immanence view of meaning and by distinguishing potential meaning from instances of that potential.

Schrödinger’s Cat As Both Dead And Alive Viewed Through Systemic Functional Linguistics

Penrose (2004: 804-5):

We suppose that there is a photon source S which emits a single photon in the direction of a beam splitter (‘half-silvered’ mirror), at which point the photon’s state is split into two parts. In one of the two emerging beams, the photon encounters a detector that is coupled to some murderous device for killing the poor cat, while in the other, the photon escapes, and the cat remains alive. See Fig. 29.7. …

Since these two alternatives for the photon must co-exist in quantum linear superposition, and since the linearity of Schrödinger’s equation demands that the two subsequent time-evolutions must persist in constant complex-number-weighted superposition, as time passes, the quantum state must ultimately involve such a complex-number superposition of a dead cat and a live cat: so the cat is both dead and alive at the same time!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the superposition of states is potential only. The cat is either alive or dead, depending on which photon state is instantiated. The absurd notion of the cat being both dead and alive at the same time simply arises from confusing potential with actual.

'Quantum Fluctuations In The Gravitational Field' Viewed Through Systemic Functional Linguistics

Penrose (2004: 803):

Sometimes the idea of ‘quantum fluctuations in the gravitational field’ might be appealed to, according to which the very structure of spacetime would become ‘foamlike’, rather than resembling a smooth manifold (Fig. 29.6) at the ‘Planck scale’ of some 10⁻³⁵m.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the notion of 'quantum fluctuations in the gravitational field' confuses the instantiation of quantum potential (fluctuations) with the spatiotemporal dimensions of the instances. That is, it confuses mediated processes with their circumstances.

The ‘Bohmian’ Interpretation Viewed Through Systemic Functional Linguistics

Penrose (2004: 789):

In the ‘Bohmian’ (pilot wave) case, the ontological position is, refreshingly, much more down to Earth, although even here there are some considerable subtleties — for there are, in a sense, two levels of reality, one of which is firmer than the other. It is simplest to put the case first for a system consisting of just a single spinless particle. Then this firmer level of reality is given by the particle’s actual position. In a two-slit experiment, since the particle’s location is ontologically real, it actually goes through one slit or it goes through the other, but its motion is ‘guided’, in effect, by ψ, so this provides a secondary, but nevertheless ontologically still ‘real’ status to the ψ also. … the picture is a very non-local one, where ψ is a highly ‘holistic’ entity (as it must be, in order to accord with the holistic nature of wavefunctions … ).

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the two levels of reality in the 'Bohmian' interpretation correspond to potential (meaning) and actual (meaning), with the secondary reality of the holistic 'guiding' wavefunction corresponding to probabilistic potential of the quantum system, as a whole, and the 'firmer' level of reality corresponding to actual instances of potential, such as a particle actually passing through one slit or the other.

The 'Environmental Decoherence' Interpretation Viewed Through Systemic Functional Linguistics

Penrose (2004: 785, 802):

… I should mention a further possibility for interpreting conventional quantum mechanics. This, as far as I can make out, is the most prevalent of the quantum-mechanical standpoints — that of environmental decoherence (c) — although it is perhaps more of a pragmatic than an ontological stance. 

The idea of (c) is that in any measurement process, the quantum system under consideration cannot be taken in isolation from its surroundings. Thus, when a measurement is performed, each different outcome does not constitute a quantum state on its own, but must be considered as part of an entangled state, where each alternative outcome is entangled with a different state of the environment. Now, the environment will consist of a great many particles, effectively in random motion, and the complete details of their locations and motions must be taken to be totally unobservable in practice. …

Holders of viewpoint (c) tend to regard themselves as ‘positivists’ who have no truck with ‘wishy-washy’ issues of ontology in any case, claiming to believe that they have no concern with what is ‘real’ and what is ‘not real’. As Stephen Hawking has said: 

I don’t demand that a theory correspond to reality because I don’t know what it is. Reality is not a quality you can test with litmus paper. All I’m concerned with is that the theory should predict the results of measurements.

My own position, on the other hand, is that the issue of ontology is crucial to quantum mechanics, though it raises some matters that are far from being resolved at the present time.

… the environmental-decoherence viewpoint (c) … maintains that state reduction R [the collapse of the wave function] can be understood as coming about because the quantum system under consideration becomes inextricably entangled with its environment.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the 'Environmental Decoherence' interpretation of Quantum Theory misconstrues the interdependence of potential as an entanglement of instances (states of the environment).

The Collapse Of The Wave Function As ‘All In The Mind’ Viewed Through Systemic Functional Linguistics

Penrose (2004: 784):

Despite their diametrically opposing natures, the viewpoints (a) and (b) have some significant points in common, with regard to how |ψ⟩ [the wave function] is taken to relate to our observed ‘reality’ — by which I mean to the seemingly real world that, on a macroscopic scale, we all experience. In this observed world, only one result of an experiment is taken to occur, and we may justly regard it as the job of physics to explain or to model the thing that we indeed normally refer to as ‘reality’. 

Neither according to (a) nor according to (b) is the state vector |ψ⟩ taken to describe that reality. And in each case, we must bring in the perceptions of some human experimenter to make sense of how the formalism relates to this observed real world. 

In case (a) it is the state vector |ψ⟩ itself that is taken to be an artefact of that human experimenter’s perceptions, whereas in case (b), it is ‘ordinary reality’ that is somehow delineated in terms of the perceptions of the experimenter, the state vector |ψ⟩ now representing some kind of deeper overriding reality (the omnium) that is not directly perceived. 

In both cases the ‘jumping’ of R [the collapse of the wave function] is taken to be not physically real, being, in a sense, ‘all in the mind’!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the wave function specifies potential 'observed reality', where 'reality' is the meaning construed of experience in the process of making an observation. The one result of an experiment is the one observation that instantiates one of the potential meanings as actual.

The Copenhagen Interpretation (a) acknowledges that the wave function involves the meaning of an observer, and in the Many Worlds Interpretation (b), the potential construed by the wave function is misunderstood as actual: as a 'deeper, overriding reality'.

From the perspective of Systemic Functional Linguistic Theory, the collapse of wave function is physically real, because physical reality is meaning construed of experience, as through mental processes of perception and cognition. The mind is the process of construing experience as meaning.

Everett's Many Worlds Interpretation Viewed Through Systemic Functional Linguistics

Penrose (2004: 784):

Why, according to (b), is the omnium not perceived as actual ‘reality’ by an experimenter? The idea is that the experimenter’s states of mind also coexist in the quantum superposition, these different individual mind states being entangled with the different possible results of the measurement being performed. 

The view is that, accordingly, there is effectively a ‘different world’ for each different possible result of the measurement, there being a separate ‘copy’ of the experimenter in each of these different worlds, all these worlds co-existing in quantum superposition. Each copy of the experimenter experiences a different outcome for the experiment, but since these ‘copies’ inhabit different worlds, there is no communication between them, and each thinks that only one result has occurred. 

Proponents of (b) often maintain that it is the requirement that an experimenter have a consistent ‘awareness state’ that forces the impression that there is just ‘one world’ in which R [the collapse of the wave function] appears to take place. Such a viewpoint was first explicitly put forward by Hugh Everett III in 1957 (although I suspect that many others had, not always with conviction, privately entertained this kind of view earlier — as I had myself in the mid-1950s — without daring to be open about it!).

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the experimenter's states of mind are meanings, and the quantum superposition of mind states is the superposition of meanings that constitute the potential of the quantum system. In this formulation, potential construals of experience as meaning are mistaken for actual construals of experience as meaning.

The Multiverse Interpretation Viewed Through Systemic Functional Linguistics

Penrose (2004: 783-4):

The supporters of alternative (b), on the other hand, do take |ψ⟩ [the wave function] to represent reality, but they deny that R [the collapse of the wave function] happens at all. They would argue that when a measurement takes place, all the alternative outcomes actually coexist in reality, in a grand quantum linear superposition of alternative universes. This grand superposition is described by a wavefunction |ψ⟩ for the entire universe. It is sometimes referred to as the ‘multiverse’, but I believe that a more appropriate term is the omnium. For although this viewpoint is commonly colloquially expressed as a belief in the parallel co-existence of different alternative worlds, this is misleading. The alternative worlds do not really ‘exist’ separately, in this view; only the vast particular superposition expressed by |ψ⟩ is taken as real.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the wave function construes potential, and its superpositions are the superposition of potential, not actual. It is only with the collapse of the wavefunction, when an observation is made, that the actual is instantiated. Supporters of the multiverse interpretation mistake potential universes for the actual universe that we experience as meaning.

The Copenhagen Interpretation Viewed Through Systemic Functional Linguistics

Penrose (2004: 783):

The viewpoint (a) is basically the ontology of the Copenhagen interpretation as expressed specifically by Niels Bohr, who regarded |ψ⟩ [i.e. the wave function] as not representing a quantum-level reality, but as something to be taken as merely describing the experimenter’s ‘knowledge’ of a quantum system.  

The ‘jumping’, according to R, [i.e. the collapse of the wave function] would then be understood as the experimenter’s simply acquiring more knowledge about the system, so it is the knowledge that jumps, not the physics of the system. 

According to (a), one should not ask that any ‘reality’ be assigned to quantum-level phenomena, the only acknowledged reality being that of the classical world within which the experimenter’s apparatus finds its home. 

As a variant of (a), one might take the view that this ‘classical world’ comes in not at the level of some piece of ‘macroscopic machinery’ that constitutes the observer’s measuring apparatus, but at the level of the observer’s own consciousness.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the Copenhagen interpretation takes an 'immanent' view of meaning, where meaning is a property of semiotic systems, rather than a 'transcendent' view of meaning, where meaning exists beyond semiotic systems. This is borne out by the distinction between 'knowledge' of the experimenter (immanent) and the physics of the system (transcendent).

However, the collapse of the wave function is not a matter of acquiring more knowledge (meaning), but a matter of construing the actual meaning (particle) that instantiates the potential meaning (wave). The contrast between 'quantum level phenomena' and the 'classical world' is the contrast between potential and actual 'reality' (meaning), both of which constitute the content of consciousness.

Quantum Physicists’ Ontologies Viewed Through Systemic Functional Linguistics

Penrose (2004: 782):

It is a common view among many of today’s physicists that quantum mechanics provides us with no picture of ‘reality’ at all! The formalism of quantum mechanics, on this view, is to be taken as just that: a mathematical formalism. This formalism, as many quantum physicists would argue, tells us essentially nothing about an actual quantum reality of the world, but merely allows us to compute probabilities for alternative realities that might occur. Such quantum physicists’ ontology — to the extent that they would be worried by matters of ‘ontology’ at all — would be the view (a): that there is simply no reality expressed in the quantum formalism. 

At the other extreme, there are many quantum physicists who take the (seemingly) diametrically opposite view (b): that the unitarily evolving quantum state completely describes actual reality, with the alarming implication that practically all quantum alternatives must always continue to coexist (in superposition).

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, 'reality' is meaning construed of experience, whether as the first-order phenomenal meanings of the material domain, or their reconstrual as the second-order metaphenomenal meanings that realise theories.

The 'reality' that is expressed in the quantum formalism is that actual reality is a probabilistic instantiation of potential reality ("alternative realities"). Quantum alternatives only co-exist in superposition as potential, not as actual.

A Quantum Superposition Of Spacetimes Viewed Through Systemic Functional Linguistics

Penrose (2004: 770):

In the Hartle–Hawking scheme, it is necessary to use Hawking’s ingenious modification of the Wick idea, in which the ‘rotation’ is applied not to a space which is a background to the paths, in a path integral — which is the usual idea — but to the individual spacetimes which themselves constitute each path of the path integral. …

Hartle and Hawking’s striking proposal was that this path-integral approach of Hawking’s could describe the relevant quantum theory for the Big Bang itself, and that in place of an actual singular spacetime there would be a quantum superposition (i.e. ‘path integral’) of ‘spacetimes’…

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, paths are trajectories though spacetime, whereas spacetime constitutes the dimensions in which such trajectories are measured. On this basis, an individual path is not an individual spacetime.

From this perspective, each path of a path integral is a potential path of a particle through spacetime. On this basis, there is no superposition of spacetimes in Hartle and Hawking’s proposal, only a superposition of potential trajectories through spacetime.

Naked Singularities Viewed Through Systemic Functional Linguistics

Penrose (2004: 767-8):

This observation should be taken in conjunction with another conjectured feature of spacetime singularities, referred to as cosmic censorship. This is a (currently unproved) assertion that, roughly speaking, in unstoppable gravitational collapse, a black hole will be the result, rather than something worse, known as a naked singularity. A naked singularity would be a spacetime singularity, resulting from a gravitational collapse, which is visible to outside observers, so it is not ‘clothed’ by an event horizon. There are various slightly different technical ways of specifying what is meant by the term ‘naked singularity’, and I do not propose to enter into the distinctions here. Sufficient for our purposes would be to say that a naked singularity is ‘timelike’, in the sense that signals can both enter and leave the singularity. Cosmic censorship would forbid such things (except possibly in certain highly contrived or ‘special’ situations that would not occur in a realistic gravitational collapse).

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, according to General Relativity, a singularity is a point with no spatial dimensions, since space intervals have contracted to zero. Importantly, a singularity is not a point in space, but space reduced to a point.

Since a singularity has no spatial dimensions, there is no space that a signal can enter or leave. Moreover, the notion of a naked singularity rests on the possibility that the singularity itself can be its own event horizon.

A Quantum Approach To The Big Bang Viewed Through Systemic Functional Linguistics

Penrose (2004: 765):

We have become used to mathematical laws — laws of extraordinary precision — controlling the physical behaviour of the world. It appears that we again require something of exceptional precision, a law that determines the very nature of the Big Bang. But the Big Bang is a spacetime singularity, and our present-day theories are not able to handle this kind of thing. Our expectations, however, are that what is required is some appropriate form of quantum gravity, where the rules of general relativity, of quantum mechanics, and perhaps also of some other unknown physical ingredients, must come together appropriately.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, mathematical laws neither control nor determine the physical behaviour it models, just as a map neither controls nor determines the territory it models. In terms of modality, mathematical laws are laws in the sense of modalisation (probability/usuality), not modulation (obligation/inclination).  In terms of construing experience, physical behaviour is first-order meaning (phenomenal), and mathematical laws are reconstruals of first-order meaning as second-order meaning (metaphenomenal).

From this perspective, according to General Relativity, a singularity is a mathematical point with no spatial dimensions: the point at which space intervals have contracted to zero due to the effects of mass. Since Quantum Theory models the instantiation of potential, its application to the Big Bang is to model the beginning of the Universe as the instantiation of potential, with space-time as the dimensions of the instantiations.

Apparent Cosmic Good Fortune Viewed Through Systemic Functional Linguistics

Penrose (2004: 759):

It is remarkable that the constants of Nature are so adjusted that such an energy level should be in just the right place, so life, as we know it, could come about. Another example of apparent cosmic good fortune is the fact that the neutron’s mass is just slightly greater than that of the proton (1838 and 1836 electron masses, respectively). The existence of an appropriate family of stable nuclei, on which almost the whole of chemistry depends, rests upon this seemingly fortuitous fact.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, this misconstrues result (life, stable nuclei) as purpose, since the word 'adjusted' implies intention.

An analogous proposition would be that Einstein's ancestors all slightly adjusted their behaviours to fortuitously produce Albert.

The Weak And Strong Forms Of The Anthropic Principle Viewed Through Systemic Functional Linguistics

Penrose (2004: 759):

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, this weak form of the Anthropic Principle simply locates a consequent (sentient life) with its necessary conditions (conditions suitable for sentient life).

From the same perspective, this strong form of the Anthropic Principle also locates a consequent (sentient life) with its necessary conditions (fundamental constants of Nature suitable for sentient life in one of many universes). This version proposes universes that cannot be scientifically investigated, drawing on the misunderstanding of potential as actual in the interpretation of quantum physics.

The Strong Anthropic Principle Viewed Through Systemic Functional Linguistics

Penrose (2004: 758):

Much more problematic are versions of the strong anthropic principle, according to which we try to extend the anthropic argument to determine actual constants of nature (such as the ratio of the mass of the electron to that of the proton, or the value of the fine structure constant). Some people might regard the strong anthropic principle as leading us to a belief in a ‘Divine Purpose’, whereby the Creator of the universe made sure that the fundamental physical constants were pre-ordained so as to have specific values that enable sentient life to be possible. 

On the other hand we may think of the strong principle as being an extension of the weak one where we broaden our questions of ‘where’ and ‘when’, so that they apply not just to a single spacetime, but to the whole ensemble of possible spacetimes. Different members of the ensemble might be expected to possess different values for the basic physical constants. The where/when question now also involves a choice of universe within the ensemble, so again we must find ourselves in a universe which permits sentience to come about.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the first interpretation of the strong anthropic principle, above, misconstrues sentient life as the purpose, rather than the result, of the fundamental physical constants, and then misconstrues this purpose as the reason for the fundamental physical constants.

The second interpretation, above, draws on the 'many worlds' interpretation of quantum physics, which misconstrues potential (possible) as actual. 

The Weak Anthropic Principle

Penrose (2004: 758):

It should be evident to the reader that arguments from the anthropic principle are fraught with uncertainties, although they are not without genuine significance. We do not have much idea, for example, what conditions are actually necessary for the production of sentient life. Nevertheless, the situation is not so bad when used with examples, such as given above, where we are taking the laws of physics and the overall spacetime structure of the universe as given, and we ask merely questions like where or when in the universe are conditions likely to be so-and-so, in order to be conducive to sentient life. This version of the anthropic principle is referred to, by Carter, as the weak anthropic principle.

Blogger Comments:

To be clear, this principle is so weak as to be neither anthropic nor a principle. It is merely an anthropocentric view of the search for extra-terrestrial intelligence.

The Anthropic Principle Viewed Through Systemic Functional Linguistics

Penrose (2004: 757):

Roughly speaking, the anthropic argument takes as its starting point the fact that the universe we perceive about us must be of such a nature as will produce and accommodate beings who can perceive it. We could use this argument to explain why the planet upon which we live has such a congenial range of temperatures, atmosphere, abundance of water, etc. etc. If conditions were not so congenial on this particular planet, then we would not be here, but somewhere else!

Blogger Comments:

To be clear, this fact misconstrues a past event as a future certainty. The fact is simply:

the universe we perceive about us is of such a nature as did produce and accommodate beings who can perceive it.

Systemic Functional Linguistic Theory distinguishes two general types of cause: reason/result and purpose. The fact, then, proposes that humans are the result of how the universe is. The anthropic argument, thus, tries to explain the reason (the conditions) by the result (humans), instead of explaining the result (humans) by the reason (the conditions). That is, it mistakes the result for the reason.

By a further step, the anthropic principle mistakes result for purpose, so that it explains the reason (the conditions) by the purpose (humans). In this view, humans are misconstrued as the purpose of the universe.

The Special Status Of Gravitational Fields Viewed Through Systemic Functional Linguistics

Penrose (2004: 731):

Gravity seems to have a very special status, different from that of any other field.

Blogger Comments:

To be clear, a physical field is a region of spacetime under the influence of some agency. From the perspective of Systemic Functional Linguistic Theory, a gravitational field is different from other types of field in as much as it is the dimensions of spacetime itself that are affected, since the agency (mass) causes the relative contraction of space intervals, and the relative expansion of time intervals, with increasing proximity to its centre.

Closed vs Open Universes Viewed Through Systemic Functional Linguistics

Penrose (2004: 721):

The usual K > 0 case is called a closed universe, which means spatially closed (i.e. contains a compact spacelike hypersurface). Frequently cosmologists refer to K < 0 as the ‘open’ case, whereas technically the K = 0 case is also spatially open.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, a spatially closed or open universe is one in which geodesic trajectories through space are 'closed' or 'open'.

Spatial Curvatures In The Evolution Of The Universe Viewed Through Systemic Functional Linguistics

Penrose (2004: 719-20):

In Fig. 27.13a,b,c, I have tried to depict the time-evolution of the universe, according to Friedmann’s original analysis of the Einstein equation, for the different alternative choices of spatial curvature [K]. In each case, the universe starts from a singularity — the so-called Big Bang — where spacetime curvatures become infinite and then it expands rapidly outwards. 

The ultimate behaviour depends critically on the value of K. If K > 0 (Fig. 27.13a), the expansion eventually reverses, and the universe returns to a singularity, often referred to as the Big Crunch, which is a precise time-reverse of the initial Big Bang in the exact Friedmann model. If K = 0 (Fig. 27.13b), then the expansion just manages to hang on and a collapse phase does not take place. If K < 0 (Fig. 27.13c), then there is no prospect of collapse, as the expansion ultimately approaches a constant rate. 

(There is an analogy, here, with the stone thrown upwards from the ground. If the stone’s initial speed is less than escape velocity, then it eventually falls back to the ground, like Friedmann’s universe for K > 0; if equal to escape velocity, then it just fails to fall back, like K = 0; if greater than escape velocity, then it continues and approaches a limiting rate which does not slow down, like K < 0.)

 

Blogger Comments:

For reasons previously given, from the perspective of Systemic Functional Linguistic Theory, 'spatial curvature' is not the curvature of space, but the curvature of geodesic trajectories (processes) in space. (This is borne out by the explanatory analogy, which is concerned with the trajectories of stones in space.)

Cosmic Censorship Viewed Through Systemic Functional Linguistics

Penrose (2004: 714):

It is generally believed that the spacetime singularities of gravitational collapse will necessarily always lie within an event horizon, so that whatever happen to be the extraordinary physical effects at such a singularity, these will be hidden from view of any external observer. This is not a mathematically established property of general relativity, however. The assumption that the singularities will always be so hidden is referred to as cosmic censorship…

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, not only are events near the singularity unobservable because the means of observation, light, is contained within the event horizon, but because of the expansion of time intervals there, such processes would take virtually forever to unfold, relative to the unfolding of processes outside the black hole, such as the process of observation.

Quantum Gravity Viewed Through Systemic Functional Linguistics

 Penrose (2004: 713):

In fact, it seems unavoidable that the realm of quantum gravity (or whatever is the appropriate term) will be entered, so that these expectations of the classical theory will have to be modified in accordance with this. We do not yet know what the correct ‘quantum-gravitational’ theory must be, but these black-hole considerations supply us with an important input; and this input should be guiding us in the appropriate directions in our search for the correct ‘quantum gravity’.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the search for a 'quantum gravitational' theory is a wild goose chase. Where Quantum Theory is concerned with the instantiation of potential, General Relativity is concerned with the interrelation of (instantiated) mass and spacetime.

The motivation for a 'quantum gravitational' theory is the desire to unify the four forces, but according to General Relativity, gravity is not a force between particles, but a geometrical effect of mass on spacetime.

The Unavoidability Of A Spacetime Singularity Viewed Through Systemic Functional Linguistics

Penrose (2004: 713):

At least, what we do know is that, so long as Einstein’s picture of a classical spacetime can be maintained, acting in accordance with Einstein’s equation (with non-negative energy densities and some other mild and ‘reasonable’ assumptions), then a spacetime singularity will be encountered within the hole. The expectation is that Einstein’s equation will tell us that this singularity cannot be avoided by any of the matter in the hole and that the ‘tidal forces’ (i.e. Weyl curvature) will diverge to infinity — very possibly in a wildly quasi-oscillatory fashion, in the general case.

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, General Relativity construes gravity as the contraction of space intervals in the direction of a centre of mass. If the singularity at the centre of a black hole is the contraction of space intervals to zero, then the spatial dimensions of matter that "encounters" it will be zero. This self-contradiction suggests that either the spatial intervals do not contract all the way to zero, a mathematical point, or that matter-energy falls short of the singularity.

Falling Into Black Holes — Viewed Through Systemic Functional Linguistics

Penrose (2004: 713):

For a black hole of a few solar masses, the tidal forces would be easily enough to kill a person long before the horizon is even reached, let alone crossed, but for the large black holes of 10⁶M⊙, or more, that are believed to inhabit galactic centres, there would be no particular problem from tidal effects as the horizon is crossed (the horizon being some millions of kilometres across). In fact, for our own galaxy, the curvature at the horizon of its central black hole is only about twenty times the spacetime curvature here at the surface of the Earth — which we don’t even notice! Yet, the relentless dragging of the observer inwards to the singularity at the centre would subsequently cause tidal effects to mount very rapidly to infinity, totally destroying the observer in less than a minute! Destruction by rapidly mounting tidal forces is, indeed, what awaits any physical material as it plunges inwards towards the centre of a black hole. Recall our concern about the fate of the material of our 10M⊙ collapsing star. Even the individual particles of which it is composed will, in short order, encounter tidal forces so strong that they will be torn apart — to what, no-one knows!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the curvature of spacetime at the event horizon of a black hole is actually the curvature of the shortest trajectory through spacetime, the geodesic, at the event horizon of a black hole.

The dragging of an observer (material) inwards towards the singularity at the centre of a black hole is due to the shortest trajectory being in that direction, since space intervals are relatively contracted in that direction. But since time intervals are relatively expanded in that direction, the time it takes for material to fall to the centre of a black hole approaches infinity, relative to the time intervals outside the black hole. That is, even if events inside a black hole could be observed from outside the black hole, they would appear to take forever.

Since space intervals contract with proximity to the singularity, material falling into a black hole has less and less space to occupy. But since the spacetime of black holes is due to the effects of mass, and matter can be neither created nor destroyed, a reasonable assumption is that individual particles will eventually be converted to energy at some point before the space intervals contract (theoretically) to zero at the singularity.

Crossing The Event Horizon Of A Black Hole Viewed Through Systemic Functional Linguistics

Penrose (2004: 711, 712-3):

The event horizon is not made of any material substance. It is merely a particular (hyper)surface in spacetime, separating those places from which signals can escape to external infinity from those places from which all signals would inevitably be trapped by the black hole. A hapless observer who falls through the event horizon, from the outside to the inside, would not notice anything locally peculiar just as the horizon is crossed. Moreover, the black hole itself is not a ponderable body; we think of it merely as a gravitating region of spacetime from within which no signal can escape. …

As noted above, an observer in a space ship would notice nothing particular happening as the horizon is crossed from the outside to the inside. Yet, as soon as that perilous journey has been undertaken, there is no return … there is no escape, and the observer would encounter rapidly increasing tidal effects (spacetime curvature) that diverge to infinity at the spacetime singularity at the centre (r = 0).

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the curvature of spacetime is actually the curvature of the geodesic, the shortest trajectory through space, due to the relative contraction of space intervals in the direction of the centre of a massive body. So the event horizon of a black hole is the outermost distance from the centre of a black hole at which the geodesic is so curved that the trajectory of light remains within that distance from the black hole centre. Because of this, no events within this horizon can be observed from outside the horizon, so as an observer crosses the event horizon, they cease to be observable to those outside the event horizon.

In this view of General Relativity, the singularity at the centre of a black hole is the point at which space intervals theoretically contract to zero and time intervals theoretically expand to infinity, though the space contraction may be physically limited to the Planck length, and the time expansion to its correlate.

According to General Relativity, a black hole must include a concentration of mass, since it is mass that contracts the space, and since energy can be neither created nor destroyed, it must also include all the energy that flows into it.

The Second Law Of Thermodynamics Viewed Through Systemic Functional Linguistics

Penrose (2004: 690):

Whereas the first law is an equality, the second law is an inequality. It tells us that a different quantity, known as the entropy has a larger (or, at least, not smaller) value after some process takes place than it had before. Entropy is, very roughly speaking, a measure of the ‘randomness’ in the system. Our body moving through the air starts with its energy in an organised form (its kinetic energy of motion) but when it slows down from air resistance, this energy gets distributed in the random motions of air particles and individual particles in the body. The ‘randomness has increased’; more specifically, the entropy has increased.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, energy can be understood as the ability of a process to unfold, and entropy can be understood as the decrease in that ability. In this view, the second law of thermodynamics says that the unfolding of a process has the effect of decreasing the ability of that process to unfold, therefore making the unfolding less probable in the future.

The First Law Of Thermodynamics Viewed Through Systemic Functional Linguistics

Penrose (2004: 690):

The First Law is simply the statement that the total energy is conserved in any isolated system. … The first law makes it explicit that the total energy is not lost when, say, a body loses its kinetic energy as it slows down because of air resistance. For this energy is simply taken up in heating the air and the body. This heat energy is understood as (primarily) kinetic energy in the motions of air molecules and vibrations of particles composing the body. Moreover, temperature is simply a measure of energy per degree of freedom, so the thermodynamic notions of heat and temperature are basically the same as previously understood dynamical notions, but applied at the level of the individual constituents of materials and treated in a statistical way. The First Law has the kind of precision that we are familiar with: the value of something, namely the total energy, remains constant despite the fact that all kinds of complicated processes may be taking place. The total energy after the process is equal to the total energy before the process.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, potential energy is the capacity of a process to unfold, and kinetic energy, for example, is the instantiation of that potential. In this view, the First Law of thermodynamics states that the total capacity for processes to unfold is conserved in any isolated system.

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.