The Astrophysics Spectator

Issue 2.15, April 20, 2005

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April 20, 2005

Special relativity, the theory of how our measurements of time and length change as we accelerate, cannot be ignored in astronomy. Its effects are seen in the jets of gas flowing out of compact binary star system and out of the centers of galaxies, they are seen in the gases in supernovae remnants, and they are seen in the cosmic rays striking Earth. This week we add pages discussing the theory of special relativity and its consequences for an observer experiencing constant acceleration.

Special relativity was developed by Albert Einstein to make our equations for electricity and magnetism complete and consistent. This theory states that our measurement of time and length are affected by our motion. This means that my clocks and rulers give different results for me than for someone traveling away from me. This startling theory is required if we accept the conclusion from Maxwell's equations that the speed of light is the same for all observers, regardless of their motion.

The assumption of a single speed for light was one that most scientists of the 19th century could not make; it contradicted all experience in Newtonian physics. In Newtonian mechanics, two people moving relative to each other sees the objects around them moving at different speeds. So passengers in a car see each other and the car as having no speed, and they see the pedestrians standing on the sidewalk moving with the speed of the car, but the standing pedestrians see themselves as having no speed, and they see the the passengers in a car as moving with the same speed as their car. Scientists of the 19th century wanted to apply this behavior to light by modifying Maxwell's equations.

If we assume that Maxwell's equations are complete, then we must modify Newtonian physics to create a complete and consistent mathematical theory for the motion of objects. The theory one obtains is special relativity.

Special relativity has several interesting implications for a passenger in a rocket accelerating at a constant rate. A passenger finds that a clock at his feet moves more slowly than a clock at his head. He sees that the light from a lamp becomes bluer when raised over his head, and it becomes redder when the lamp is lowered to his feet. Light no longer travels in straight lines, but instead travels in an arc. Finally, he finds that an event horizon has formed behind his spacecraft; objects that fall through the event horizon are incapable of communicating with our passenger. In a word, our passenger has created his own artificial black hole.

These pages on special relativity motivate this week's commentary on the distinction between the appearance of and the abstract theoretical description of an object.

Jim Brainerd


Knowledge from Appearance. Our theories of astronomical sources are not limited to the physics of the source, but include the physics of how radiation from the source reaches Earth and how that radiation interacts with our instruments. When we test a theory, we are testing whether the theory gives the correct appearance of an object. Can we reach a point where a theory correctly gives the appearance of an object without giving a true description of the object? (continue)


The Origin of Special Relativity. Maxwell's equations, which are the equations that describe electricity and magnetism, allows only a single speed for light. This means that an observer always measures a single value for the speed of a light wave regardless of how fast he is traveling. To make Maxwell's equations fit into a consistent theory of physics, our intuitive understanding of length and time must be modified so that changes in our own velocity do not change the speed we measure for a light wave. The theory of space and time that is consistent with Maxwell's equations is called special relativity. (continue)

Constant Acceleration in Special Relativity. When a traveler is accelerated at a constant rate, he creates a world that is indistinguishable from the region just above the event horizon of a black hole. For the accelerating traveler, time slows: the greater the acceleration, the greater the time dilation. The acceleration is strongest at the back of a traveler's spacecraft, and weakest at the nose. Time passes more slowly in the back of the rocket than in the nose, and light emitted above the traveler appears bluer than light emitted below the traveler. Light no longer travels in a straight line, and an event horizon follows the spacecraft. (continue)


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