03-03-2005, 02:15 AM
Directions are not important if you are floating in empty space. There all directions are equal. This is called isotropy.
On the surface of the earth isotropy doesn't hold. Earth's rotation about its axis clearly defines north-south and east-west directions. Other set of directions come from earth's rotation about the Sun. The plane of ecliptic and earth's direction of motion around sun give another set of directions. In planetary astronomy these two sets of coordinate systems are most widely used. Each coordinate system is based on clear-cut significance for the primary directions.
Even larger coordinate systems can be created. For example the milky-way galaxy has a spiral structure and is rotating about its center. It is easy to define a galactic north-south and galactic east-west direction this way.
So if someone says all directions are equal, then that is obviously not true in any of these coordinate systems.
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->in the Cosmic level, there are no directions, and what is east now has changed 1 second later (owing to earth's rotation.)<!--QuoteEnd--><!--QuoteEEnd-->
There is no preferred 'cosmic level'. Einstein's principle of relativity unambiguosly says that all coordinate frames are equivalent to each other. One fixed to a moving mosquito is as valid as one fixed to the galaxy.
For a person sitting in the ecliptic coordinate system, my 'east' direction vector would keep on changing both due to earth's rotation and due to earth's revolution around the Sun. But for a coordinate system fixed to the earth, north-south, east and west are defined by vectors that do not change direction. In this coordinate frame, sun etc move, but earth doesn't.
Post Copernicus, people have developed this misconception that a coordinate system fixed to earth is somehow 'wrong' and a coordinate system fixed to the ecliptic is more 'correct'. This thinking is wrong! As exemplified by the principle of relativity, all the coordinate systems are equally valid. Physics remains same, no matter which coordinate system is chosen. The advantage of heliocentric system is that, computation of planetary orbits is much more simple compared to one based on geocentric system. But there are other calculations for which a geocentric system is preferred. There are other cal;culations (in astronomy) where a coordinate system fixed relative to the galaxy is more convenient. The coordinates differ in their convenience, not in their validity.
It is natural to assume that 'dik' and 'dikpalas' were thought about in a coordinate system fixed to the earth (geocentric system). There is nothing wrong or invalid with this system. And just because the vectors representing these directions keep on changing when viewed from a heliocentric frame of reference doesn't imply that they are invalid. These vectors are fixed in the geocentric reference frame which is as valid a frame as any.
On the surface of the earth isotropy doesn't hold. Earth's rotation about its axis clearly defines north-south and east-west directions. Other set of directions come from earth's rotation about the Sun. The plane of ecliptic and earth's direction of motion around sun give another set of directions. In planetary astronomy these two sets of coordinate systems are most widely used. Each coordinate system is based on clear-cut significance for the primary directions.
Even larger coordinate systems can be created. For example the milky-way galaxy has a spiral structure and is rotating about its center. It is easy to define a galactic north-south and galactic east-west direction this way.
So if someone says all directions are equal, then that is obviously not true in any of these coordinate systems.
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->in the Cosmic level, there are no directions, and what is east now has changed 1 second later (owing to earth's rotation.)<!--QuoteEnd--><!--QuoteEEnd-->
There is no preferred 'cosmic level'. Einstein's principle of relativity unambiguosly says that all coordinate frames are equivalent to each other. One fixed to a moving mosquito is as valid as one fixed to the galaxy.
For a person sitting in the ecliptic coordinate system, my 'east' direction vector would keep on changing both due to earth's rotation and due to earth's revolution around the Sun. But for a coordinate system fixed to the earth, north-south, east and west are defined by vectors that do not change direction. In this coordinate frame, sun etc move, but earth doesn't.
Post Copernicus, people have developed this misconception that a coordinate system fixed to earth is somehow 'wrong' and a coordinate system fixed to the ecliptic is more 'correct'. This thinking is wrong! As exemplified by the principle of relativity, all the coordinate systems are equally valid. Physics remains same, no matter which coordinate system is chosen. The advantage of heliocentric system is that, computation of planetary orbits is much more simple compared to one based on geocentric system. But there are other calculations for which a geocentric system is preferred. There are other cal;culations (in astronomy) where a coordinate system fixed relative to the galaxy is more convenient. The coordinates differ in their convenience, not in their validity.
It is natural to assume that 'dik' and 'dikpalas' were thought about in a coordinate system fixed to the earth (geocentric system). There is nothing wrong or invalid with this system. And just because the vectors representing these directions keep on changing when viewed from a heliocentric frame of reference doesn't imply that they are invalid. These vectors are fixed in the geocentric reference frame which is as valid a frame as any.