The meter was standardized much before the velocity of light was precisely determined. Long back the length of a meter was determined and every where this standard is already in use. Like in tailor shops, carpenters, schools, books etc. So, it is not possible to change the length of a meter.
It has been determined that light travels 299, 792, 458 meters/second experimentally and theoretically. Speed of Light is supposed to be the most invariant of the physical quantities in the universe. It does not change. Other standards like length of a rod or bar will vary depending on temperature. The measurement may depend on geographical location too. So a meter is defined as 1/299, 792, 458 of distance travelled by light in a second.
cube volume = a³ dimension = Length³ units = meter³ or cm³
sphere volume = 4π/3 a³, dimension = length³ units = meter³ or cm³
ratio = a³ / (4π/3 a³) = 3/4π
If length of everything changes to twice, then the length of meter bar or measuring tape also becomes twice. So it is not possible to detect the change. Because even human beings, the buildings etc. will change proportionately.
If we make the hypothesis that speed of light is constant, then we can test the change of lengths in universe. Then using our measurement techniques of time and length the speed of light will be found to be 1/2 of its original speed.
Clocks will show the same time as before. They will not change. Time is found as ratios of two physical quantities, so the doubling effect is cancelled.
All the terms in an equation must have the same dimensions and same units for proper addition or subtraction or to equate them. You have to convert all the terms in to one single unit.
You can write as 5 meters + 3 cm = 5, 030 mm
But to verify, compute you must convert them all into one unit, as in
5, 000 mm+ 30 mm = 5, 030 mm
two physical quantities have same dimensions, but they can have different units.
5 meters, 5 cm, 5 mm all have dimension as Length. [ L ]. But different units and different magnitude values.
foot - easily available. it is not invariable.. it is not indestructible. it is not easily reproducible, the length may change in time over years, as people grow and get diseases which can alter the length of foot.
1. by intensity of light from sun directly and that of light reflected by Moon.
2. At the time of eclipse, we can find the distance between Earth and Sun and distance between Earth and Moon. Then we subtract or add to get the distance.
3. using the lunar year, Earth's year and distance between earth and moon.