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

Hawking (1988: 85-7):

Eventually, when the star has shrunk to a certain critical radius, the gravitational field at the surface becomes so strong that the light cones are bent inward so much that light can no longer escape (Fig. 6.1). According to the theory of relativity, nothing can travel faster than light. Thus if light cannot escape, neither can anything else; everything is dragged back by the gravitational field. So one has a set of events, a region of space-time, from which it is not possible to escape to reach a distant observer. This region is what we now call a black hole. Its boundary is called the event horizon and it coincides with the paths of light rays that just fail to escape from the black hole. 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, according to General Relativity, the event horizon of a black hole is the distance from the gravitational singularity where the intervals of the three spatial dimensions have contracted to such an extent that the trajectory of light is curved to remain within the space between it and the singularity. 

Gravitational Redshift Viewed Through Systemic Functional Linguistics

Hawking (1988: 85):

The gravitational field of the star changes the paths of light rays in space-time from what they would have been had the star not been present. The light cones, which indicate the paths followed in space and time by flashes of light emitted from their tips, are bent slightly inward near the surface of the star. This can be seen in the bending of light from distant stars observed during an eclipse of the sun. As the star contracts, the gravitational field at its surface gets stronger and the light cones get bent inward more. This makes it more difficult for light from the star to escape, and the light appears dimmer and redder to an observer at a distance.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, according to General Relativity, the gravitational field of a star is the relative contraction of space intervals around the centre of its mass.  It is this contraction of space intervals that accounts for the geodesic trajectory of light from distant stars curving towards the star it is passing.

The redshift of the light from distant stars passing through the star's gravitational field is due to the light's passage from the relatively contracted space intervals near the star to the relatively expanded space intervals further from the star.  The relative expansion of space intervals means relatively more space between photons of a given frequency, and so relatively longer wavelengths, and so a relative shift towards the red end of the visible spectrum.

The Formation Of White Dwarf Stars And Neutron Stars Viewed Through Systemic Functional Linguistics

Hawking (1988: 84):

If a star’s mass is less than the Chandrasekhar limit, it can eventually stop contracting and settle down to a possible final state as a “white dwarf” with a radius of a few thousand miles and a density of hundreds of tons per cubic inch. A white dwarf is supported by the exclusion principle repulsion between the electrons in its matter. …

Landau pointed out that there was another possible final state for a star, also with a limiting mass of about one or two times the mass of the sun but much smaller even than a white dwarf. These stars would be supported by the exclusion principle repulsion between neutrons and protons, rather than between electrons. They were therefore called neutron stars. They would have a radius of only ten miles or so and a density of hundreds of millions of tons per cubic inch.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, according to General Relativity and Quantum Mechanics, a white dwarf star is the balance of the gravitational contraction of space-intervals and the expanded volume of matter-energy due to the repulsion of electrons, as described by the Pauli exclusion principle; whereas a neutron star is the balance of the gravitational contraction of space-intervals and the expanded volume of matter-energy due to the repulsion of nucleons (neutrons and protons), as described by the Pauli exclusion principle.

The Gravitational Collapse Of Stars Viewed Through Systemic Functional Linguistics

Hawking (1988: 83-4):

Chandrasekhar worked out how big a star could be and still support itself against its own gravity after it had used up all its fuel. The idea was this: when the star becomes small, the matter particles get very near each other, and so according to the Pauli exclusion principle, they must have very different velocities. This makes them move away from each other and so tends to make the star expand. A star can therefore maintain itself at a constant radius by a balance between the attraction of gravity and the repulsion that arises from the exclusion principle, just as earlier in its life gravity was balanced by the heat. 

Chandrasekhar realised, however, that there is a limit to the repulsion that the exclusion principle can provide. The theory of relativity limits the maximum difference in the velocities of the matter particles in the star to the speed of light. This means that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than the attraction of gravity. Chandrasekhar calculated that a cold star of more than about one and a half times the mass of the sun would not be able to support itself against its own gravity. (This mass is now known as the Chandrasekhar limit.)

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, according to General Relativity, the star "becoming small" under gravity is actually the contraction of the space occupied by the star, and it is this that brings the matter particles closer together. 

On the other hand, the expansion of the star due to the repulsion of particles, as described by the Pauli exclusion principle, is the expansion of the volume of the matter-energy occupying the space, not the expansion of space itself.

That is, the balance that is achieved is between the gravitational contraction of space intervals and the expansion of the volume of the matter-energy (the star itself). 

When the density of a star reduces the amount of particle repulsion, the volume of the star no longer counterbalances the gravitational contraction of the space it occupies, and the star is no longer 'able to support itself against its own gravity'.

Star Formation Viewed Through Systemic Functional Linguistics

Hawking (1988: 82-3):

A star is formed when a large amount of gas (mostly hydrogen) starts to collapse in on itself due to its gravitational attraction. As it contracts, the atoms of the gas collide with each other more and more frequently and at greater and greater speeds — the gas heats up. Eventually, the gas will be so hot that when the hydrogen atoms collide they no longer bounce off each other, but instead coalesce to form helium. The heat released in this reaction, which is like a controlled hydrogen bomb explosion, is what makes the star shine. This additional heat also increases the pressure of the gas until it is sufficient to balance the gravitational attraction, and the gas stops contracting. … When a star runs out of fuel, it starts to cool off and so to contract.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, according to General Relativity, the collapse of the hydrogen gas is actually the contraction of the space occupied by gas cloud. Because the contraction of space brings the atoms closer together, it increases the probability of them colliding and coalescing (via deuterium) to form helium atoms.

On this basis, the balance that is achieved is between the gravitational contraction of space intervals and the expansion of the volume of matter-energy (the star itself). When a star runs out of fuel, it no longer expands to counterbalance the gravitational contraction of the space it occupies.

The Notion Of Time Running Backwards (Or Forwards) Through Systemic Functional Linguistics

Hawking (1988: 77-8):

Up to 1956 it was believed that the laws of physics obeyed each of three separate symmetries called C, P, and T. …The symmetry T means that if you reverse the direction of motion of all particles and antiparticles, the system should go back to what it was at earlier times; in other words, the laws are the same in the forward and backward directions of time. … 

There is a mathematical theorem that says that any theory that obeys quantum mechanics and relativity must always obey the combined symmetry CPT. In other words, the universe would have to behave the same if one replaced particles by antiparticles, took the mirror image, and also reversed the direction of time. But Cronin and Fitch showed that if one replaces particles by antiparticles and takes the mirror image, but does not reverse the direction of time, then the universe does not behave the same. The laws of physics, therefore, must change if one reverses the direction of time— they do not obey the symmetry T. Certainly the early universe does not obey the symmetry T: as time runs forward the universe expands — if it ran backward, the universe would be contracting.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the universe does not obey physical models of it, just as a landscape does not obey a map.  Like a landscape, the universe is a construal of experience as meaning, and, like a map of a landscape, a physical model of the universe is a reconstrual of meaning.

Importantly, (conceptually) reversing the direction of motion of particles through space does not reverse the direction of time.  This is because time is the dimension of the unfolding of processes, and this is independent of the direction of motion through space.  The locomotion of particles only occurs along spatial dimensions, not through time; time is a measurement of location and extent of the unfolding of the process of locomotion. A process extends from one location on the time dimension to another.

Moreover, the mistaken notion of time "running" forward or backward arises from confusing the circumstantial dimension (time) with the process that is used as the standard of measurement (the ticking of a clock).

In this interpretation, time does not run either forward or backward, whether the spatial intervals of the universe are expanding or contracting.

Quantum Gravity And Gravitational Waves Through Systemic Functional Linguistics

Hawking (1988: 70):

In the quantum mechanical way of looking at the gravitational field, the force between two matter particles is pictured as being carried by a particle of spin 2 called the graviton. This has no mass of its own, so the force that it carries is long range. The gravitational force between the sun and the earth is ascribed to the exchange of gravitons between the particles that make up these two bodies. Although the exchanged particles are virtual, they certainly do produce a measurable effect — they make the earth orbit the sun! Real gravitons make up what classical physicists would call gravitational waves, which are very weak—and so difficult to detect that they have not yet been observed.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the attempt to model gravity in terms of quantum mechanics is an attempt to model a relation between matter and space-time as interactions between matter particles.  Gravitons are still undetected and remain "hypothetical".

Gravitational waves, on the other hand, are propagations of relative space interval contractions and time interval expansions through space; that is, the spatial propagation of the effects of matter on space-time.  Gravitational waves have been detected and are no longer "hypothetical".

Comparing Gravity To The Other Physical Forces Using Systemic Functional Linguistics

Hawking (1988: 70):

The first category is the gravitational force. This force is universal, that is, every particle feels the force of gravity, according to its mass or energy. Gravity is the weakest of the four forces by a long way; it is so weak that we would not notice it at all were it not for two special properties that it has: it can act over large distances, and it is always attractive. This means that the very weak gravitational forces between the individual particles in two large bodies, such as the earth and the sun, can all add up to produce a significant force. The other three forces are either short range, or are sometimes attractive and sometimes repulsive, so they tend to cancel out.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, gravity and the cosmological expansion are the attractive and repulsive aspects of the same phenomenon.  In gravity, intervals of space are relatively contracted, and intervals of time are relatively expanded, whereas, in the cosmological expansion, intervals of space are relatively expanded, and intervals of time are relatively contracted.  Taken together, they resemble the other forces in this respect.

On the other hand, this unity differs from the other forces, in as much as gravity and the cosmological expansion are concerned with the interaction of matter-energy and space-time, whereas the other forces — the electromagnetic, and the strong and weak nuclear forces — are concerned with interactions of matter-energy only.

The Quantum Mechanics Of A Singularity Through Systemic Functional Linguistics

Hawking (1988: 60-1):

Einstein’s general theory of relativity seems to govern the large-scale structure of the universe. It is what is called a classical theory; that is, it does not take account of the uncertainty principle of quantum mechanics, as it should for consistency with other theories. The reason that this does not lead to any discrepancy with observation is that all the gravitational fields that we normally experience are very weak. However, the singularity theorems discussed earlier indicate that the gravitational field should get very strong in at least two situations, black holes and the big bang. In such strong fields the effects of quantum mechanics should be important.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, general relativity is concerned with the relation between space-time and matter-energy, and construes it geometrically: in terms of contracted and expanded space-time dimensions and curved trajectories of matter-energy along those dimensions.  A gravitational field demarcates the extent of space-time altered by the presence of matter-energy: the contraction of space-intervals, inversely proportional to the expansion of time intervals.

Quantum mechanics, on the other hand, is concerned with the instantiation of matter-energy properties, with quantum fields demarcating the extent of space-time in which quantum instantiations potentially occur.

On this basis, the strong gravitational field around a black hole contracts the spatial intervals of a quantum field, thereby reducing the relative spatial extent of potential instantiations of matter-energy, while expanding its time intervals, such that quantum processes unfold relatively more slowly along spatial dimensions.

At the singularity itself, then, where spatial intervals contract to 0, the field of potential quantum instantiations contracts to 0.  As a consequence, there are no processes to unfold, and so: there are no processes by which to measure time, and so: there is no time dimension (time intervals expand to ∞).

Feynman's 'Sum Over Histories' Through Systemic Functional Linguistics

Hawking (1988: 59-60):

A nice way of visualising the wave/particle duality is the so-called sum over histories introduced by the American scientist Richard Feynman. In this approach the particle is not supposed to have a single history or path in space-time, as it would in a classical, non-quantum theory. Instead it is supposed to go from A to B by every possible path. With each path there are associated a couple of numbers: one represents the size of a wave and the other represents the position in the cycle (i.e., whether it is at a crest or a trough). The probability of going from A to B is found by adding up the waves for all the paths.

Blogger Comments:

From the perspective of Systemic Functional Linguistic theory, Feynman's 'sum over histories' approach — taking into account of every possible trajectory — is the reconstrual of experience as quantum system potential, which is quantified as probability.  The actual paths taken by particles are instances of that potential, whose different frequencies instantiate the different system probabilities.

The Double-Slit Experiment Of Quantum Theory Through Systemic Functional Linguistics [19]

Hawking (1988: 58-9):

Interference can also occur for particles, because of the duality introduced by quantum mechanics. A famous example is the so-called two-slit experiment (Fig. 4.2). Consider a partition with two narrow parallel slits in it. On one side of the partition one places a source of light of a particular colour (that is, of a particular wavelength). Most of the light will hit the partition, but a small amount will go through the slits. Now suppose one places a screen on the far side of the partition from the light. Any point on the screen will receive waves from the two slits. However, in general, the distance the light has to travel from the source to the screen via the two slits will be different. This will mean that the waves from the slits will not be in phase with each other when they arrive at the screen: in some places the waves will cancel each other out, and in others they will reinforce each other. The result is a characteristic pattern of light and dark fringes.

 

The remarkable thing is that one gets exactly the same kind of fringes if one replaces the source of light by a source of particles such as electrons with a definite speed (this means that the corresponding waves have a definite length). It seems the more peculiar because if one only has one slit, one does not get any fringes, just a uniform distribution of electrons across the screen. One might therefore think that opening another slit would just increase the number of electrons hitting each point of the screen, but, because of interference, it actually decreases it in some places. If electrons are sent through the slits one at a time, one would expect each to pass through one slit or the other, and so behave just as if the slit it passed through were the only one there—giving a uniform distribution on the screen. In reality, however, even when the electrons are sent one at a time, the fringes still appear. Each electron, therefore, must be passing through both slits at the same time!

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, wave-particle duality is the complementarity of potential and instance.  On this view, it is particles, not waves, that pass through the slits.

Importantly, if only one particle is emitted in the double-slit experiment, there is no interference pattern recorded on the detector screen. The interference patterns only begin to appear as more and more particles are detected. This means that the interference cannot be a property of each single instance. And this means that each detected particle only goes through one slit or the other, not both.

Instead, the "interference" is a property of the quantum system as potential, as described by the wave function, with the different frequencies of particle impacts instantiating the different probabilities of the quantum system potential.

Wave-Particle Duality Through Systemic Functional Linguistics [9]

Hawking (1988: 56):

Although light is made up of waves, Planck’s quantum hypothesis tells us that in some ways it behaves as if it were composed of particles: it can be emitted or absorbed only in packets, or quanta. Equally, Heisenberg’s uncertainty principle implies that particles behave in some respects like waves: they do not have a definite position but are “smeared out” with a certain probability distribution. The theory of quantum mechanics is based on an entirely new type of mathematics that no longer describes the real world in terms of particles and waves; it is only the observations of the world that may be described in those terms.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, particles do have a definite position, as demonstrated when an observation is made.  They are not "smeared out" because the probability distribution quantifies their potential positions, not their actual (instantial) positions.

The mathematics of quantum mechanics does describe the "real world" in terms of particles and waves, but with the following qualifications:

1. the "real world" is the identity relation of perceptual and linguistic meaning, construed of experience of the non-semiotic domain;
2. the mathematics of waves quantifies quantum systems as potential; and
3. the mathematics of particles quantifies instances of quantum potential.

The "Unpredictability Or Randomness" Of Quantum Mechanics Through Systemic Functional Linguistics

Hawking (1988: 55-6):

In general, quantum mechanics does not predict a single definite result for an observation. Instead, it predicts a number of different possible outcomes and tells us how likely each of these is. That is to say, if one made the same measurement on a large number of similar systems, each of which started off in the same way, one would find that the result of the measurement would be A in a certain number of cases, B in a different number, and so on. One could predict the approximate number of times that the result would be A or B, but one could not predict the specific result of an individual measurement. Quantum mechanics therefore introduces an unavoidable element of unpredictability or randomness into science.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the possible outcomes predicted by (the wave function of) quantum mechanics constitute the potential meanings of a given system that can be construed of experience, and the likelihood of each outcome constitutes the quantification of such potential as probability.  The specific results of individual measurements are instances of that potential, whose frequencies are in line with the probabilities of the system potential.

What this actually demonstrates is that the construal experience of the non-semiotic domain as meaning, by consciousness, is itself probabilistic.