Friday 15 July 2011

practical effects of finiteness

The finiteness of the speed of light has implications for various sciences and technologies. In some cases, it is a hindrance: for example, c, being the upper limit of the speed with which signals can be sent, provides a theoretical upper limit for the operating speed of microprocessors.[66] On the other hand, some techniques depend on it, for example in distance measurements.
The speed of light is of relevance to communications. For example, given the equatorial circumference of the Earth is about 40,075 km and c about 300,000 km/s, the theoretical shortest time for a piece of information to travel half the globe along the surface is about 67 milliseconds. When light is travelling around the globe in an optical fibre, the actual transit time is longer, in part because the speed of light is slower by about 35% in an optical fibre, depending on its refractive index n.[67] Furthermore, straight lines rarely occur in global communications situations, and delays are created when the signal passes through an electronic switch or signal regenerator.[68]
The diameter of the moon is about one quarter of that of Earth, and their distance is about thirty times the diameter of Earth. A beam of light starts from the Earth and reaches the Moon in about a second and a quarter.
A beam of light is depicted travelling between the Earth and the Moon in the time it takes a light pulse to move between them: 1.255 seconds at their mean orbital (surface-to-surface) distance. The relative sizes and separation of the Earth–Moon system are shown to scale.
Another consequence of the finite speed of light is that communications between the Earth and spacecraft are not instantaneous. There is a brief delay from the source to the receiver, which becomes more noticeable as distances increase. This delay was significant for communications between ground control and Apollo 8 when it became the first manned spacecraft to orbit the Moon: for every question, the ground control station had to wait at least three seconds for the answer to arrive.[69] The communications delay between Earth and Mars can vary between five and twenty minutes depending upon the relative positions of the two planets. As a consequence of this, if a robot on the surface of Mars were to encounter a problem, its human controllers would not be aware of it until at least five minutes, and possibly up to twenty minutes, later; it would then take a further five to twenty minutes for instructions to travel from Earth to Mars.
The speed of light can also be of concern over very short distances. In supercomputers, the speed of light imposes a limit on how quickly data can be sent between processors. If a processor operates at 1 gigahertz, a signal can only travel a maximum of about 30 centimetres (1 ft) in a single cycle. Processors must therefore be placed close to each other to minimize communication latencies; this can cause difficulty with cooling. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single chips.[66]

[edit] Distance measurement

Radar systems measure the distance to a target by the time it takes a radio-wave pulse to return to the radar antenna after being reflected by the target: the distance to the target is half the round-trip transit time multiplied by the speed of light. A Global Positioning System (GPS) receiver measures its distance to GPS satellites based on how long it takes for a radio signal to arrive from each satellite, and from these distances calculates the receiver's position. Because light travels about 300,000 kilometres (186,000 miles) in one second, these measurements of small fractions of a second must be very precise. The Lunar Laser Ranging Experiment, radar astronomy and the Deep Space Network determine distances to the Moon,[70] planets[71] and spacecraft,[72] respectively, by measuring round-trip transit times.

No comments:

Post a Comment