[Physics] Why wasn’t the meter defined using a round-number fraction (like 1/300 000 000) of the distance travelled by light in 1 second


We know that 1 meter is the distance travelled by light in vacuum within a time interval of 1/299,792,458 second. My question is why we didn't take a simpler number like 1/300,000.000 or why not just 1?

Best Answer

Because it would have been incredibly expensive.

The current definition of the meter, based on a fixed value of the speed of light, was adopted on 1983, and it replaced the 1960 definition which was based on the wavelength of a krypton emission line. In essence, the light-based precision length metrology methods had become so accurate that the main source of uncertainty in length measurements was the uncertainty in the speed of light. That is, the speed of light was already determined to be $299\,792\,458\:\rm m/s$, with an uncertainty on the $\pm 1\:\rm m/s$ range and with a large established body of measurements that used it to that precision.

Now, if you're doing a change to a fixed speed of light, it is indeed tempting to change the number from $299\,792\,458$ to a nice round $300\,000\,000$, since after all they're very close - the ratio $$ \frac{300\,000\,000}{299\,792\,458} \approx 1.00069 $$ is pretty close to unity. So, why didn't we? In short, because the ratio $$ \frac{300\,000\,000}{299\,792\,458} \approx 1.00069 $$ is not close to unity at all. The two definitions differ by $7$ parts in $10^{4}$ (just short of 0.1%), and that means that every length measurement that involved more than three significant figures would've had to be re-calibrated, both in pure science as well as in industry. This would have required an enormous effort to re-write a huge fraction of the scientific and engineering literature (including technical manuals and software implementations), as well as actual physical changes to hardware to return their measurements back to round numbers (i.e. if you manufactured $5\:\rm mm$-long bolts to a $10^{-3}$ relative tolerance, then you would need to change your standards or maintain off-by-0.1% non-round-number lengths for your parts).

The change would also have similarly affected all measurements of quantities (like force, energy, pressure, and all of electrical metrology) with a nonzero length dimension that involve more than three significant figures. All told, you're talking about a significant fraction (more than half?) of all measurements.

The role of metrology is to provide a common currency in measurements that can be used for science, engineering, industry and commerce, and to be as transparent as possible. Changing standards is extremely expensive (just ask the countries that switched from imperial to metric, or the ones that haven't because it's too onerous) and the gains need to be clearly worthwhile. Rounding out the speed of light does not come anywhere close to meeting that standard.

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