Potentially Embarrassing ‘What?’ And ‘Why?’ Questions Viewed Through Systemic Functional Linguistics

Penrose (2004: 1028):

Modern science would be cautious in attempting answers to ‘why?’ questions as well as ‘what?’. Yet, questions as to ‘what?’ and ‘why?’ are frequently supplied with answers. It is considered acceptable to do so provided that the questions are not asking about reality at its deepest levels. One may expect an answer to such a question as the following. ‘What is a cholesterol molecule made of?’; ‘why does a match burst into flame when dragged rapidly across a suitable rough surface?’; ‘what is an aurora?’; ‘why does the sun shine?’; ‘what are the forces which hold a hydrogen atom or a hydrogen molecule together?’; and ‘why is a uranium nucleus unstable?’. Yet, some other questions that one might pose could cause more embarrassment, such as ‘what is an electron?’ or ‘why does space have just three dimensions?’. These questions can, however, find meaning within some more fundamental picture of physical reality.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, an electron is just what physics says it is. For example:

The electron is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ.

From this perspective, there are three dimensions of space because this number proved functional in the construal of experience as first-order meaning, and has since proved functional in reconstruals of first-order meaning as the second-order meaning of theory. String theorists are trying to demonstrate that what they think are additional spatial dimensions would be more functional in the second-order meaning of theory.

A Quantum Theory That Encompasses Gravity Viewed Through Systemic Functional Linguistics

Penrose (2004: 1013-4):

A general consensus seems indeed to have grown up that, in order for real progress to be made in our moving beyond the standard models of particle physics (and cosmology), and thereby obtaining a deeper understanding of the basic ingredients of the universe, it will be necessary to have a quantum theory that encompasses gravity in addition to the strong, weak, and electromagnetic forces.

Blogger Comments:

To be clear, the General Theory of Relativity construes gravity, not as a force, but as a mutual relation between mass and spacetime, whereas particle physics construes the three forces as types of particle exchange.

From the perspective of Systemic Functional Linguistic Theory, it is not necessary for quantum theory to encompass gravity because quantum theory is concerned with the instantiation of potential as particles, and general relativity is concerned with the mutual relation of particles and spacetime.

Physicists' Ideas Of Space And Time Viewed Through Systemic Functional Linguistics

Penrose (2004: 958):

Yet, some physicists would strongly argue that a far more radical overhaul of the ideas of space and time is needed, if the appropriately deeper insights are to be gained as to the nature of a ‘quantum spacetime’.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, in the General Theory of Relativity, the three dimensions of space measure the relative location and extent of phenomena, and the dimension of time measures the relative unfolding of processes.

As this blog demonstrates, in physics, phenomena in space, such as geodesic trajectories, are mistaken for space, the dimensions in which they are located and extend, and processes, such as the ticking of a clock, are mistaken for time, the dimension in which the unfolding of processes is located and extends.

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.

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 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.

'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.

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.

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.

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

Penrose (2004: 606, 607):

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

Blogger Comments:

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

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

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

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