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.