# Why is the speed of light not 3 x $10^{8}$ m/s, or why not a round figure for the meter [duplicate]

This question is not about why the speed of light is not greater than 299,792,458 m/s. It's about why it's that exact value. This was a question from a book(I know homework questions are frowned upon here :P), and after almost 5 years, this has occurred back to me.

Is there any specific reason for that value? If it were, say, a scale at the International Bureau of Weights and Measures of exactly one meter length(as the cylinder of the kilogram), it would make sense. But I haven't heard of such a thing.

• That doesn't answer my question, unfortunately. All answers start with 'they came up with a number', and then continue to justify the number. Also, the accepted answer could be a joke answer. – cst1992 Jan 23 '16 at 12:49
• No, it really does answer your question: it is because it was originally a derived value and not a postulated one. – Kyle Kanos Jan 23 '16 at 12:59
• The speed of light depends on the units we choose, there is nothing particularly interesting about 299,792,458 m/s. In another units it could have been 3x10^8 but not in SI units. – SaudiBombsYemen Jan 23 '16 at 13:30
• I see what you mean about a joke answer. But it is serious. The Earth was hit my many big things around the time it was being formed, including one whose debris formed the moon. The Earth is about 4.5 billion years old, so 4.7 billion years is reasonable. But none of them were named Megapluto. The highly exact time and shift in rotation rate are made up. The point they illustrate would be the same if you used correct numbers from some real ancient collision. – mmesser314 Jan 23 '16 at 14:23
• for me, c = 1 ly / y – user46925 Jan 23 '16 at 15:02

Although the metre is now defined as the length travelled by light in a certain time interval, the unit has a historic origin (one ten millionth of a quarter of the earth's circumference) and more importantly, historic usage.

We can't suddenly say that a metre is the length travelled by light in 1/300,000,000s of a second, because then the new metre would be shorter than all pre-existing metres (and the same goes for cms, kms, etc etc).

However, light-seconds and light-years are units based on the speed of light and used by astronomers to measure very large distances

The reasons are compatibility with older definition based on the prototype bar. The meter is a widely used unit of measurement and it's better if the new definition would reproduce with enough precision the old one or it's will be huge pain in the neck for everyone to adapt new unit. It's ok if the difference is very small. However the "round speed of light meter" is 0.69mm larger. That's enormous difference and would present incompabilities even for some precision technology of 1900s!

People did pick a round number when they defined the meter. It was defined so the distance from the equator, through Paris, to the north pole was exactly 10000 meters. They also defined the kilometer, centimeter, and millimeter as round number multiples and fractions of the meter.

Roundness was a theme. The gram is the mass of a cubic centimeter of water. They also defined kilogram, microgram, and so on.

All the roundness was put into the units of measurement. They were tired of units like inches, feet, furlongs, and miles in England, a similar but different system in France, and something else in Germany.

After meters and seconds were defined, the speed of light was measured. It did not turn out to be round.

Over the years, the original definitions turned out to have shortcomings. They were replaced with new definitions. The goal of the new definitions was to match the old ones as closely as possible. The value for any measurement should be the same as closely as possible when using new and old definitions.

• On calculation, I was able to devise that it makes a difference of 1 meter per 1445.5 meters(around 0.06%). When this definition came into being, was that considered a significant fraction? – cst1992 Jan 23 '16 at 15:52
• Today 0.06% would be huge for many precision measurements. The meter was defined in 1791. I don't know how precise the best measurements were then, but I would not at all be surprised if it was noticeable. See physics.nist.gov/cuu/Units/meter.html for more information – mmesser314 Jan 23 '16 at 18:37