# What if we measure a physical constant to higher accuracy? [closed]

So, the SI system of units has the basic philosophy of defining all 7 of the base units in terms of universal constants such as the plank constant, the speed of light, etc. These are all measured, then defined to be that number. But what if we we to develop a more accurate measurement apparatus, and obtain higher accuracy. Would this effect the definition?

For example, the speed of light was defined to be exactly 299,792,458 m/s. Now imagine we develop some apparatus that measures it to be 299,792,458.6 m/s, with all experimental error accounted for, etc. How would this effect the definition of the meter, which is based upon the speed of light?

• You should look up the source definitions of the fundamental units, as well as which fundamental constants are measured directly and which are measured in terms of other fundamental constants. Nov 20, 2018 at 13:57
• I do know them; the second is a good one, because it is based only on one thing, the hyperfine transitions of that Cesium isotope, and the meter is next best, since it needs just light and the second. I have qualms with defining constants that were experimentally measured since accuracy can change over time. How does this practice effect things like high precision measurement and the like Nov 21, 2018 at 17:39
• This questions seems to be unrelated to the history of science. Maybe it is better suited for physics.stackexchange.com Nov 23, 2018 at 22:59

For example, the speed of light was defined to be exactly 299,792,458 m/s. Now imagine we develop some apparatus that measures it to be 299,792,458.6 m/s, with all experimental error accounted for, etc. How would this effect the definition of the meter, which is based upon the speed of light?

See the definition of the metre on Wikipedia:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 second.

So we'd change our definition of the metre to:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458.6 seconds.

I think the important thing to note here is that the speed of light is constant by definition. It's defined to be constant. See what John Moffat and João Magueijo said in their 2007 Comments on “Note on varying speed of light theories”

“Can c vary? Could such a variation be measured? As correctly pointed out by Ellis, within the current protocol for measuring time and space the answer is no. The unit of time is defined by an oscillating system or the frequency of an atomic transition, and the unit of space is defined in terms of the distance travelled by light in the unit of time. We therefore have a situation akin to saying that the speed of light is “one light-year per year”, i.e. its constancy has become a tautology or a definition”.

And it isn't constant. It varies in the room you're in. That's why optical clocks go slower when they're lower. Einstein said this in 1920:

“Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable”.

See my "physics detective" essay the speed of light is not constant for details and references.

• Except that all scientists understand that $c_0$ is constant and that any reference to "speed of light" that lacks "..in this medium..." or "..in this \$FIELD .." is taken as a reference to the vacuum speed of light. Nov 20, 2018 at 13:59
• @Carl Witthoft : the speed of light in vacuo is not constant. A lot of scientists think it is, but that's a modern-day myth. See en.wikipedia.org/wiki/Shapiro_time_delay and read the Shapiro quote. Nov 20, 2018 at 17:37
• SMH - clearly in vacuo also implies in the absence of mass! Don't be so pedantic! Nov 20, 2018 at 18:33
• @Carl Witthoft : in vacuo does not imply the absence of mass. It implies the absence of air. Get your spacesuit on whilst I evacuate the air from the room you're in. OK now look up. The speed of light up near the ceiling is greater than the speed of light down by the floor. That's why optical clocks go slower when they're lower. It's also why light curves and why your pencil falls down. See math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/… Nov 20, 2018 at 21:53
• See a good discussion of time dilation: The clock appears to go slower when lower only to an observer higher up relative to the gravitational mass: for an observer local to the same clock it appears to go at the normal rate, and for an observer lower down than the clock it appears to go faster than normal. Nov 20, 2018 at 22:23