Astronomy and Astrophysics – Astronomy
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009iau...261.0302g&link_type=abstract
American Astronomical Society, IAU Symposium #261. Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Ana
Astronomy and Astrophysics
Astronomy
Scientific paper
The units of measurements for the relativistic dynamics remain a controversial topic. The metric defines implicitly coordinates by a mathematical relation with proper time. It is postulated that atomic transitions provide a realization of the ideal proper time of the theory on the world line of the atoms. Proper time is thus measurable by standards in the usual sense of metrology. But coordinates are not. Some authors consider them as pure numbers, others as non-measurable quantities, but with the usual dimensions of time and length, with specific units. The problem of units is further complicated by scaling factors which minimize the deviation of coordinate times with respect to International Atomic Time.
After an attempt to define dimensionless "graduation units” for scales and discussions with metrologists, the author concluded that the simplest solution is to apply strictly the rules of the quantity calculus without trying to interpret them in terms of "concrete” measurements. In brief, these rules state that there is only one unit per physical dimension (the second for time, the metre for space), so that algebraic relations between quantities remain valid with their numerical values. In other terms a quantity is defined by its name, not by its unit. This "abstract” point of view may be seen as a convention.
The contact between concrete and abstract points of view raises difficulties, essentially of wording. An example is the expression of the duration in seconds of proper time between second markers of a coordinate time, without implying a specific unit for coordinate time. Suggestions to solve these difficulties will be made.
Astronomers are used to apply, let us say "blindly,” the abstract point of view, the second being the unit of all classical time scales, sidereal time, Universal Time, etc. The situation with relativistic coordinates is quite similar.
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