Scientific measurement standards

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This is not a question about relativity per se, but relates to it sufficiently I hope. Standard values for many scientific constants are defined, and ideally in the most universal way possible. For example, the standard length unit, a meter, is defined with respect to the distance light travels in certain amount of time, that being defined by a certain number of oscillations of an atomic "clock". By relativity, the speed of light is constant in a vacuum, however distance and time are affected by relative movement and gravitational fields. So my question is, is the standard meter defined with respect to a particular location on earth, with the understanding that it will vary according to relative position of another location either moving or under different gravitational influences (like further away from the center of the earth, or on the moon)? Or are the necessary corrections beyond the requirements of most practical scientific or engineering applications?
 
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An observer who is "traveling" or under a gravitational influence cannot tell that his distances or time or speed of light measurements are affected by those factors as long as he is not accelerating (changing his speed or direction). For example, the atomic clocks at Greenwich, England run at a different rate than identical ones at Boulder, CO, but everything is consistent at each location. Meter sticks made at each location based on a clock and the speed of light at each location will be the same length when brought together. But we can tell that the clocks are running at different speeds and corrections need to be made so that we all use a common interval for a second independent of our elevation. GPS is the modern solution to this problem.
 
That does indeed make sense. As long as the 'internal physics' of the clocks is constant (whatever that means) meters generated at different locations will be the same when brought together. That's the 'best' one can do. Thanks for clarifying.
 
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