Spacetime

From the preceding reflections on time dilation, we learn that Albert Einstein has overthrown commonsense assumptions about space and time that were valid for centuries. Relative to the observer, distances appear to contract while clocks tick more slowly when moving at velocities close to the speed of light. These are the practical consequences of Special Relativity, the work for which Einstein became famous. Einstein did not stop at this point. In 1916, he published his General Relativity, which further challenged conventional wisdom. The paper proposed that matter causes spacetime to curve. Gravitation is understood as the warping of spacetime, not a force acting at a distance, as Newton had suggested.

A massive object causes spacetime to curve, which is often illustrated with the picture of a bowling ball lying on a stretched rubber sheet:

Gravity

Contrary to appearance, the diagram does not depict the three-dimensional space of everyday experience. Instead it shows how a 2-D slice through familiar 3-D space is curved downwards when embedded in flattened hyperspace. We cannot fully envision this hyperspace. Flattening it to 3-D allows us to represent the curvature and helps us visualise the implications of Einstein's General Theory of Relativity.

Gravitation bends light rays.

Since light has no mass, it is not subject to Newton's law of gravity, and hence, in Newtonian physics gravity has no effect on light. If space is curved, however, it follows that a ray of light seemingly moving in a straight line really travels in a curved line following the curvature of space. This is comparable, in some way, to the itinerary of a plane. Because the earth is a sphere, the shortest path between two points on earth is described by a geodesic, a curved line. While moving along the geodesic it would appear to the passengers of the plane that they are moving in a straight line, although they are not. Similarly, the light of distant stars travels through the curved geometry of space before it reaches Earth. This proposition is supported by observation.

When the light of a star passes close to the Sun, it is deflected by the Sun's gravitational field, which causes it to appear slightly displaced. The star appears to be farther from the Sun than it should be. The displacement has been measured by photographing the apparent position of stars during a solar eclipse and comparing these positions with those observed in the night some time later. Apparent shifts of less than 2 seconds per arc have been measured this way, in close agreement with the predictions of General Relativity. Likewise, the mentioned deviation in the orbit of Mercury when the planet reaches its perihelion (=closest position to the Sun), which is in contradiction with the laws of Newton, can be explained with Einstein's model of curved space.

Gravitation is not a force, but a property of spacetime.

According to Einstein, not only are time and space relative, but the geometry of space is different from what we experience in daily life. Hyperspace is a mathematical construct that we can use to describe gravitational effects in terms of geometry, rather than by the postulation of attracting and repelling forces.

Einstein arrived at this idea by looking at gravity and acceleration. He thought that a falling object does not "feel" any gravitational force, while an object being accelerated does. For this reason, he suggested to equate gravitational mass with inertial mass. He postulated that if a frame of reference is uniformly accelerated relative to a Galilean one, then we can consider it to be at rest by introducing the presence of uniform gravitational field relative to it. This is known as the principle of equivalence.

The principle says that a uniform acceleration is equivalent to a uniform gravitational field, like the one on Earth.

Elevator PrincipleSuppose the elevator in picture (1) is located in space and is accelerated upwards by exactly 32 feet per second squared. The person feels a downward pull that is equivalent to the pull of the gravitational field on Earth.

Suppose the elevator in picture (2) is located on Earth and is in the state of free fall. The person in the cabin feels no gravity, because the gravitational field of the Earth is cancelled by the opposite acceleration of the elevator.

In both cases, the person cannot tell the difference between the pull of acceleration and gravity, or respectively the weightlessness felt in space and on Earth.

Time dilated by matter.

If acceleration is equivalent to gravitation, it follows that the predictions of Special Relativity must also be valid for very strong gravitational fields. The curvature of spacetime by matter therefore not only stretches or shrinks distances, depending on their direction with respect to the gravitational field, but also appears to slow down the flow of time. This effect is called gravitational time dilation. In most circumstances, such gravitational time dilation is minuscule and hardly observable, but it can become very significant when spacetime is curved by a massive object, such as a black hole.

A black hole is the most compact matter imaginable. It is an extremely massive and dense object in space that is thought to be formed by a star collapsing under its own gravity. Black holes are black, because nothing, not even light, can escape from its extreme gravity. The existence of black holes is not yet firmly established. Major advances in computation are only now enabling scientists to simulate how black holes form, evolve, and interact. They are betting on powerful instruments now under construction to confirm that these exotic objects actually exist.

What happens if an astronaut falls into a black hole?

The gravitational time dilation effect a black hole produces is equal to that of an object moving near the speed of light. For example, an observer far from a black hole would observe time passing extremely slowly for an astronaut falling through the hole's boundary. In fact, the distant observer would never see the hapless victim actually fall in. His or her time, as measured by the observer, would appear to stand still.

From the perspective of the unlucky astronaut, things would, of course, look quite different. After having passed the black hole's event horizon, the point in space from which nothing can escape its pull, there is no way back. While approaching the centre, the gravitational pull on the astronaut's head and feet differs so strongly that the body would be stretched out "like spaghetti" (Stephen Hawking). Hence, it may be a good idea to stay away from black holes, should they actually exist.

Relativity supersedes Aristotle and Newton.

What are the philosophical consequences of Einstein's Relativity Theory? Around 350 BC, Aristotle put forward the view that mechanical objects prefer the state of rest. This proposition was derived from the observation that mechanical systems come to rest if there is no external force sustaining motion. Relativity proves this wrong. The motion of all objects is relative to each other, and it is really a matter of convention to define one reference frame as being at rest. Though this insight comes from Galilean relativity alone, Einstein added that the same applies to the time dimension. Therefore, commonsense notions of congruity and simultaneity do not apply to the processes and events taking place in the large-scale structure of the universe. A lifespan on Earth may be just one second in another galaxy and vice versa. There is a multitude of spacetime reference frames, and a multitude of realities throughout the universe.

Does relativity disprove empiricism?

The four-dimensional, non-Euclidean spacetime used in relativistic computations defies visualisation and lies beyond human perception. We cannot imagine three-dimensional space being curved, or moving around in a four-dimensional coordinate system. In fact, contemporary physics is only intelligible with the help of mathematics. It cannot be visualised, and it looks as if we have to accept the limitations of our own mind in this regard. This raises an interesting question in epistemology. How do the findings of Relativity fit with David Hume's (1711-1776) famous proposition that all contents of mind, all ideas, concepts, and thoughts are derived from sense experiences? Would Hume be able to uphold his radical empiricism?

Perhaps not. The notion of spacetime in Special and General Relativity is obviously not derived from sense experience. One would also be hard-pressed to explain the making of Relativity merely in terms of derived and recombined sense impressions and associations. Relativity cannot be deduced from empirical judgements, but it is derived from mathematical propositions, or respectively from what Kant had coined "synthetic a priori judgements". Relativity marks a turn in science away from practical laboratory and field study towards purely theoretical fields.

Heraclitus prevails.

Finally, the findings of Einstein may also have put an end to classical controversy between the Greek schools of Heraclitus and Parmenides. The latter philosopher held that all is One and that motion is an illusion, while Heraclitus stated just the opposite, namely that motionlessness is an illusion and that everything is always in a permanent state of motion and change. While the Parmenidean argument may be given some credit for using clever metaphors (from an arrow's perspective the archer is moving away), it is now firmly established that the physical world looks much more Heraclitean than Parmenidean. Even if an object appears to be at rest in a designated reference frame, it still travels through time.

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