söndag 2 februari 2014

Stars and Planets Find Their Way Without GPS

The Universe within 50.000 lightyears works fine without GPS

In his annus mirabilis 1905 Einstein presents his special theory of relativity in the article On the Electrodynamics of Moving Bodies, starting out with a discussion of the concept of simultaneity:
• We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events.
• Thus with the help of certain imaginary physical experiments (clock synchronization) we have settled what is to be understood by synchronous stationary clocks located at different places, and have evidently obtained a definition of “simultaneous” or “synchronous,” and of “time.”
• In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.
• According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York.
• The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first.
• A mathematical form of the relativity of simultaneity ("local time") was introduced by Hendrik Lorentz in 1892, and physically interpreted (to first order in v/c) as the result of a synchronization using light signals by Henri Poincaré in 1900.
• However, both Lorentz and Poincaré based their conceptions on the aether as a preferred but undetectable frame of reference, and continued to distinguish between "true time" (in the aether) and "apparent" times for moving observers.
• It was Albert Einstein in 1905 who abandoned the (classical) aether and emphasized the significance of relativity of simultaneity to our understanding of space and time.
We see that relativity theory springs from a perceived theoretical difficulty of synchronizing very distant clocks traveling at speeds close to the speed of light. But so what? Who cares about simultaneity in such an extreme situation? Why did Lorentz and Poincare ask this question, followed by Einstein?

The answer is that the question of time and simultaneity was central to navigation in order to determine longitude from Sun elevation, which stimulated the development of marine clocks usable on rocking ships peaking with the chronometers by John Harrison (1693-1776) with an accuracy of seconds over weeks.

The next step was taken with the discovery of electromagnetic waves in the late 19th century allowing precise clock synchronization over long distance by signals traveling with the speed of light. This stimulated theoretical questions on synchronization of distant clocks moving with respect to each other and then the possible dependence of the speed of light on the velocities of source and receiver.

From these speculations initiated by Lorentz and Poincare and followed by Einstein, relativity theory was born as an extreme thought experiment of synchronization over very long distance between clocks traveling at very high speeds, indeed a very extreme situation beyond any practical reality. Reality is limited but thought experiments face no limits as intellectual games.

The GPS system is based on synchronization of clocks on satellites moving around the Earth with a stationary master clock on the Earth. Although satellite clock rate is offset with a few nano-seconds with the intention to compensate for estimated effects of both the special and the general theory of relativity,  the synchronization is continuously updated and thus the offset could as well be zero.
In other words, GPS does not rely on relativity theory, and shows that accurate synchronization of clocks in the near-field of the Earth not moving very fast, is possible. Absolute simultaneity can be established in the near-field of the Earth without any need of relativity theory.

One way of describing the role of relativity theory is to say that might be useful for setting up a GPS system for the Universe with very distant clocks moving at speeds close to the speed of light requiring simultaneity and synchronization to work as a system.

But there is no need for such a system, not even the European Union is contemplating setting up such system. Money is definitely lacking and so there is no need of relativity and large scale/speed simultaneity  either.

In the next post I will argue that simultaneity is a concept used by humans to construct a GPS system covering the Earth to be used by humans, but it is not a concept which is needed to describe physics because the World goes around without any use of GPS. Humans have use of GPS, but not stars and planets.

PS: The common formulation of Newton's law of gravitational force between two material bodies involves the instantaneous positions of the bodies, and so appears to require absolute simultaneity. But there is another way of viewing Newton's law without thus requirement.