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yuiop
yuiop is offline
#53
Jan4-08, 07:40 PM
P: 3,966
Quote Quote by dbecker215 View Post
It's a bit more complicated than that. Distance, or length, doesn't change with relativity. Distance itself is defined as being a scalar quantity. Scalar quantities do not require direction therefore do not change in a coordinate system. (see Wikipedia for distance, scalar, and magnitude) This means that it is space that warps, b/c space and time are viewed as being inseparable therefore if time warps space must also warp. When you add in space distortion this changes your displacement and your vector, but not distance.
The poster was talking about distances as measured by observers in different reference frames, and Doc Al is right in saying they are not invarient. In the example a person at rest with the Earth would say the distance to the planet if 7 light years and the rocket traveler would measure the distance as 1 light year. Neither can prove the other is wrong, as neither can prove they are at rest with some absolute reference frame.

Whether distances are classed as scalar or vector quantities is not really relevent in this context but for the record the distance refered to by x in the Lorentz transformation t = y(t' +vx') and x = y(x' +vt') is a vector quantiy as it can take a + or - sign according to which direction from the origin of the reference frame that the distance x is measured. Perhaps you meant that proper distances (distances that are measured by an observer at rest with the endpoints of the distance being measured) are invarient?

Bell's spaceship paradox provides a good insight into the nature of length contraction and distances in special relativity. I think Bell once said that if you do not understand that the string between the rockets will snap then you do not really undersand relativity. Interestingly, in a straw poll of scientists at CERN theory division, most of the scientists got the paradox wrong!

http://en.wikipedia.org/wiki/Bell's_spaceship_paradox