The definition of the SI base unit "metre" [1] doesn't seem to rule out explicitly that a certain value of "length, in meters" could be attributed to a pair of ends which are rigid to each other, but not at rest to each other.

Consider, therefore, two such ends, $A$ and $B$, which both find constant but unequal ping durations between each other, i.e. in the notation of [2]$\! {\,}^{(\ast)}$:

$[ \, A \, B \, A \, ] \ne [ \, B \, A \, B \, ]$.

Is there a value of "length, in meters" attributable to this pair of ends, $A$ and $B$ ?

If so, what is that value?,

i.e. if the SI definition allowed to express the value of "the lenght $AB$" as "$x \, \text{m}$", for some positive real number $x$, then how should $x$ be expressed in terms of the two (given) unequal ping duration values $[ \, A \, B \, A \, ]$ and $[ \, B \, A \, B \, ]$, and the SI base unit "second" ("$ \text{s}$")?

(Is perhaps: "$x := \left( \frac{[ \, A \, B \, A \, ]}{2 \, \text{s}} + \frac{[ \, B \, A \, B \, ]}{2 \, \text{s}} \right) \times \frac{299 \, 792 \, 458}{2}$"?

Or perhaps: "$x := \sqrt{ \frac{[ \, A \, B \, A \, ]}{2 \, \text{s}} \times \frac{[ \, B \, A \, B \, ]}{2 \, \text{s}} } \times 299 \, 792 \, 458$"? ...)

References:

[1] SI brochure (8th edition, 2006), Section 2.1.1.1; http://www.bipm.org/en/si/base_units/metre.html ("*The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.*"). Together with "the mise en pratique of the definition of the metre"; http://www.bipm.org/en/publications/mep.html

[2] J.L.Synge, "Relativity. The general Theory", North-Holland, 1960; p.409:

"* [...] light signals passing between a source $0$ and mirrors $1$, $2$, [...]*

Trip-times such as $[ \, 0 \, 1 \, 0 \, ]$ [...] are measureable [...]"

$(\ast$: Suggestions for more standard and/or expressive notation for ping durations are welcome.$)$

This post imported from StackExchange Physics at 2014-04-24 07:32 (UCT), posted by SE-user user12262