Relative Velocity And Space-Time

Davies & Gribbin (1992: 74):

To take a specific example, at 90 per cent of the speed of light lengths are shrunk by more than half, and clocks run at less than half speed. These effects are, however, entirely relative to the observers concerned. A 'superwitch' travelling with the broom handle at such a speed relative to the ground would notice nothing unusual about either its length or the rate of passage of time. For such an observer it would be the objects that are fixed to the ground that are contracted, with clocks on the ground seeming to run slow compared with a clock attached to the flying broomstick. Thus when observers are in relative motion each sees the other's length contracted and the other's clock running slow.

Blogger Comments:

To be clear, travelling at 90 per cent of the clocks run at less than half speed relative to the clocks on the ground. For the fast-moving observer, the clock appears to run normally, but it is the clock on the ground that appears to run faster by comparison. This is why the twin travelling at high speed ages more slowly than the twin on the ground; see the twin paradox.

In other words, in this thought experiment, the fast-moving observer sees the other's clock running fast — not slow — and it is only the observer on the ground who sees the other's clock running slow. And, a faster clock here means contracted time intervals, whereas a slower clock means expanded time intervals (between each 'tick').

By the same token, the fast-moving observer sees the other's length expanded — not contracted — and it is only the observer on the ground who sees the other's length contracted.

Relative Time And Space Intervals

Davies & Gribbin (1992: 70, 71, 73-4):

In other words, the simultaneity of events that are separated in space is relative. Different observers in different states of motion measure different durations between the same pair of events. In a similar fashion, it turns out that different observers in different states of motion will measure different distances between the same pair of events. …

When an observer changes his or her state of motion, the relationship between space and time is altered, so that distances and durations are perceived differently. …

To achieve a noticeable effect, the motion must be at a sizeable fraction of the speed of light. The effect is once again to alter the apparent length of the broom handle, making it appear shorter in the direction of motion. This is simply the length-contraction effect we mentioned earlier. Conversely, time intervals are stretched, or dilated by the motion. In a sense, an interval of space is traded for an interval of time. 

So how much space is each unit of time worth? Since the conversion factor is the speed of light, one second is worth the distance light travels in one second — about 300,000 km, or one light-second.

 

Blogger Comments:

To be clear, this is Special Relativity. Compared with a slower moving body, for a faster moving body, time intervals are relatively expanded and space intervals in the direction of motion are relatively contracted. This means that, for the faster moving body, processes unfold relatively more slowly — the interval between each tick of a clock is longer — and the body traverses more space intervals per unit of time in the direction of motion.

This is the same effect as gravity in General Relativity. Time intervals are relatively more expanded, and space intervals are relatively more contracted with proximity to the centre of mass. A falling body traverses increasingly more intervals of space per unit of time as it falls — i.e. accelerates — but the process itself unfolds increasingly more slowly — i.e. time units 'stretch' — as the body approaches the centre of mass.

To be clear, it is not so much that time and space intervals are "traded", but that the relative extent of time intervals and space intervals is inversely proportional.

The Notion Of The Universe 'Knowing', 'Predicting' And 'Computing' Its Own Behaviour Viewed Through Systemic Functional Linguistics

Davies & Gribbin (1992: 35, 36):

We stress that this [the unpredictability of chaotic systems] is not just a human limitation. The Universe itself cannot 'know' its own workings with absolute precision, and therefore cannot 'predict' what will happen next, in every detail. Some things really are random. … deterministic chaos seems random because we are necessarily ignorant of the ultra-fine detail of just a few degrees of freedom, and so is the Universe itself. …

Those systems that are chaotic have severely limited predictability, and even one such system would rapidly exhaust the capacity of the entire Universe to compute its behaviour. It seems, then, that the Universe is incapable of computing the future behaviour of even a small part of itself, let alone all of itself. Expressed more dramatically, the Universe is its own fastest simulator.

This is surely a profound conclusion. It means that, even accepting a strictly deterministic account of nature, the future states of the Universe are in some sense 'open'. Some people have seized on this openness to argue for the reality of human free will. Others claim that it bestows upon nature an element of creativity, an ability to bring forth that which is genuinely new, something not already implicit in earlier states of the Universe.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the notion that the Universe 'knows', 'predicts' and 'computes' its own behaviour, independently of the semiosis of humans, is a metaphor derived from the transcendent view of meaning: that meaning transcends semiotic systems and the aim of science is to match that meaning with theory. This view is invalidated by the finding of Quantum Physics that, in Wheeler's words, a phenomenon is not a real phenomenon until it is an observed phenomenon; that is, that meaning is immanent: a property of semiotic systems only.

The proposition that the future is 'open' is distinct from the proposal of free will. The proposition involves modalisation (probability and usuality), whereas the proposal involves modulation (inclination and obligation).

The Randomness And Determinism Of Quantum Theory Through Systemic Functional Linguistics

Davies & Gribbin (1992: 26-7):

At the heart of quantum mechanics lies Heisenberg's uncertainty principle, which states that everything we can measure is subject to truly random fluctuations. … the essential point is that quantum fluctuations are not the result of human limitations or hidden levels of mechanistic clockwork; they are inherent in the workings of nature on an atomic scale. For example, the exact moment of decay of a particular radioactive nucleus is intrinsically uncertain. An element of genuine unpredictability is thus an integral part of nature.

In spite of this uncertainty, there remains a sense in which quantum mechanics is still a deterministic theory. Although the outcome of a particular quantum process might be undetermined, the relative probabilities of different outcomes evolve in a deterministic manner. What this means is that although you cannot know in a particular case what will be the outcome of the 'throw of the quantum dice', you can know completely accurately how the betting odds vary from moment to moment. As a statistical theory, quantum mechanics remains deterministic.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, 'quantum fluctuations' are instantiations of quantum potential, whose random statistical properties are instantiations of the calculable probabilities of quantum potential.