Physics
Scientific paper
Jul 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994amjph..62..648f&link_type=abstract
American Journal of Physics, Volume 62, Issue 7, pp. 648-656 (1994).
Physics
3
Special Relativity
Scientific paper
The standard model of light exchange in the expanding universe is usually expressed in the Robertson-Walker (RW) proper distance as a function of RW cosmic time, a standard time which is the same for all points on the expanding spatial coordinates. In these coordinates, light like the cosmic microwave background emitted early in the universe close to the origin recedes before it approaches the earth, taking about one-third of the universe's age, t0, to achieve a maximum distance of about ct0/2, traveling outward an average velocity (maximum distance divided by elapsed cosmic time) about 50% greater than c, the normal speed of light in the absence of gravity. This paper examines this light exchange in fixed spatial coordinates rather than the RW comoving coordinates both because it provides a graceful transition from special relativity and because it is an interesting exercise by itself. For this the array of noninertial observers at fixed distances from the origin must have peculiar velocities, moving towards the origin from the inertial observers on the RW comoving coordinates in order to keep their distances fixed. This peculiar velocity, V, plays a very similar role to that of two inertial systems moving at a velocity of V with respect to each other.
When V approaches the velocity of light, the fixed observer encounters a singular point, earlier than which the time on her clock is not defined since she cannot move faster than light. This is the same point where the RW distance for approaching light is at a maximum. Near this point the fixed observer measurements show dilations of time and radial distance proportional to 1-(V/C)2, instead of the square root of this quantity which is characteristic of the Lorentz transform. This can be shown by a transform from RW coordinates to the fixed coordinates, using for radius any of three distance measures: the Euclidean distance, the RW proper distance, or the light distance (sometimes called the radar distance). In spite of the difficulties with the singularity occurring with these fixed coordinates, for all three assumptions of distance and for a range of densities from 0 to twice the critical density, a fairly simple picture of light exchange in fixed coordinates emerges; light arriving at the origin at the present time, t0, which was emitted early in the universe travels out to a maximum distance of close to ct0/2 in a time close to t0/2, and comes back to the origin, traveling in both directions close to the normal speed of light, c. For the last half of the universe's history, this is close to the picture derived from special relativity for zero gravity.
No associations
LandOfFree
Light exchange in an expanding universe in fixed coordinates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Light exchange in an expanding universe in fixed coordinates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Light exchange in an expanding universe in fixed coordinates will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1252670