The Common Visualisation Of General Relativity

Robinson (2005: 75, 77):

Gravity would no longer be an interaction of bodies through a law of forces; it would be a field effect that emerged from the way in which mass curved space. When a marble is propelled across a flat, smooth trampoline on which sits a large and heavy ball, the marble follows a curved path around the depression caused by the ball (see Fig. 5).

In the Newtonian view a gravitational force emanates from the ball and somehow compels the marble to move in a curve. But according to general relativity it is the curvature of space — or rather space-time — that is responsible; there is no mysterious force. Matter tells space how to curve; space tells matter how to move — this is a grossly simplified summary of Einstein's general theory of relativity.

Blogger Comments:

If, according to Einstein's theory of General Relativity, gravity is the relative contraction of space intervals and expansion of time intervals, with increasing proximity to a centre of mass, then this very common representation of gravity is inconsistent with the theory, and thus a source of confusion. 

Specifically, the expansion of time intervals is not addressed, and space intervals are not shown as contracting with proximity to the ball, but rather as slightly expanding, as two dimensions of space are curved in a way to cause the curved trajectory of the marble.

The curved trajectory of the marble, however, actually corresponds to the geodesic that arises from space intervals being contracted in the direction of the ball.

Special Relativity On Space-Time — Through Systemic Functional Linguistics [2]

Robinson (2005: 62):

Thus the time of a person chasing the light wave and the time of the wave itself are not the same. Time flows for the person at a rate different from that of the wave. The faster the person goes, the slower his time flows, and therefore the less distance he covers (since distance travelled equals speed multiplied by duration of travel). As he approaches the speed of light, his watch gets slower and slower until it almost stops. …

For space there is a difference, too, between the person and the light wave. The faster the person goes, the more his space contracts, and therefore the less distance he covers. As he approaches the speed of light, he shrinks to almost nothing.

Depending on how close the person's speed is to the speed of light, he experiences a mixture of time slowing and space contracting, according to Einstein's equations of relativity.

 

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, time is the dimension of the unfolding of processes, and it is construed in terms of location and extent. According to the the Special Theory of Relativity, as the velocity of a body increases 

• its time intervals expand, so processes — like the ticking of a clock — unfold more slowly, and
• its space intervals contract in the direction of motion. 

Contrary to the above, the contraction of space intervals, as velocity of a body increases, actually means that the body covers more distance (space intervals) per time interval, not less. It is the space occupied by the body that 'shrinks' in the direction of motion.

This is equivalent to the gravitational contraction of space intervals towards the centre of mass, described by General Relativity, in which case a falling body covers increasingly more space intervals per time interval — accelerates — as it falls.

General Relativity On Black Holes — Through Systemic Functional Linguistics

Hawking (2005: 49):

Penrose and I showed that general relativity predicted that time would come to an end inside a black hole, both for the star and for any unfortunate astronaut who happened to fall into it.

 

Blogger Comments:

From the perspective of Systemic Functional linguistic Theory, the notion of time coming to an end corresponds to the relative expansion of time intervals to ∞ at the singularity of a black hole, where space intervals are relatively contracted to 0.

(Interestingly, both singularities (general relativity) and travelling at the speed of light (special relativity) have exactly the same effect on time and space intervals.)

But between the singularity and the event horizon, time intervals are less than ∞, so time has not quite come to an end, and space intervals are more than 0, suggesting that any matter–energy there is crushed into that space.

General Relativity On Space-Time — Through Systemic Functional Linguistics

 Hawking (2005: 46, 48):

But on his return to Zurich in 1912 Einstein had the brain wave of realising that the equivalence [of acceleration and gravity] would work if the geometry of space-time was curved and not flat, as had been assumed hitherto. His idea was that mass and energy would warp space-time in some manner yet to be determined. Objects such as apples or planets would try to move in straight lines through space-time, but their paths would appear to be bent by a gravitational field because space-time is curved. …

The new theory of curved space-time was called general relativity to distinguish it from the original theory without gravity, which was now known as special relativity. 

Blogger Comments:

SFL Theory construes space and time in terms of location and extent, the latter including the notion of interval. Physics construes space-time as four dimensions, and General Relativity construes intervals of time as relatively expanded in the direction of the centre of mass — a clock ticks more slowly — and intervals of space as relatively contracted in the direction of the centre of mass.

On this basis, bodies do not move in straight lines through curved space-time. Instead, bodies move in curved trajectories through space that is contracted in the direction of the centre of mass. That is, it is the geodesic — the shortest trajectory between two points in space — that is curved, not space-time.

Special Relativity On Space-Time — Through Systemic Functional Linguistics [1]

Hawking (2005: 43-4):

Based on the Michelson-Morley experiment, the Irish physicist George FitzGerald and the Dutch physicist Hendrik Lorentz suggested that bodies moving through the ether would contract and that clocks would slow down. This contraction and the slowing down of clocks would be such that all people would measure the same speed for light, no matter how they were moving with respect to the ether. … 

However, in a paper written in 1905, Einstein pointed out that if one could not detect whether or not one was moving through space, the notion of an ether was redundant. Instead, he started from the postulate that the laws of science should appear the same to all freely moving observers. In particular, they should all measure the same speed of light, no matter how fast they were moving. The speed of light is independent of their motion and is the same in all directions.

This required abandoning the idea that there is a universal quantity called time that all clocks would measure. Instead, everyone would have his or her own personal time. The times of two people would agree if the people were at rest with respect to each other, but not if they were moving. …

Einstein's postulate that the laws of nature should appear the same to all freely moving observers was the foundation of the theory of relativity, so called because it implied that only relative motion was important.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, time is the dimension of the unfolding of processes. The relative slowing down of the ticking of a clock, for a body moving more quickly through space, corresponds to a relative expansion of the time interval between each tick of the clock. That is, the Special Theory of Relativity holds that the dimension of time expands for a moving body as its velocity increases. At the speed of light, the time expands to infinity.

There is also a suggestion here, though not taken up by Hawking, that as a body moves more quickly, space relatively contracts along the dimension of motion. At the speed of light, this space dimension contracts to zero. This would suggest that a photon moving through a vacuum has relatively no extension along the dimension of motion.