Uncertainty in the mesurements of a meter and the speed of light

[tiredryan]

I was reading that a meter is the length of the path traveled by light in a vacuum in 1⁄299,792,458 of a second. So the speed of light is exactly 299,792,458 m/s. I am wondering what is the uncertainty in our most accurate measurement of the speed of light.

For example say I had a machine that measured the speed of light with 1% uncertainty that I used as a meter reference. The speed of light will still be exactly 299,792,458 m/s, but my meter measurements will have a level of uncertainty.

What is the current lowest uncertainty in our measurements of the speed of light?

Thanks.

 

[russ_watters]

According to the wiki on the speed of light, it has been measured to an accuracy of +-1 m/sec.

 

[tiredryan]

According to the wiki on the speed of light, it has been measured to an accuracy of +-1 m/sec.

If I understand this right, then the uncertainty in our meter measurements is:
~1/299,792,458 = ~3.33564095 × 10-9 meters or ~3 nm.

Does this mean that any measurements under 3nm will have a high level of uncertainty when we relate it back to our meter standard?

 

[Vanadium 50]

Of course not. It means that any length measurement that needs an absolute accuracy better than 3 parts per billion is in trouble.

 

[f95toli]

What is the current lowest uncertainty in our measurements of the speed of light?

Zero. The speed of light is per definition exactly 299,792,458 m/s. All measurements of length refer back to this value (even from a practical point of view, since precison measurements are done using intereferometry).

It does not make sense to talk about the uncertainty in a definition, but what you can do is to state the uncertainty in the measurement of length and this is what is done in practice:
if you ask an NMI to measure the length of something (say a length bar of the type used to calibrate machinery) they will state the uncertainty in the calibration certificate: for commercial services this will be about +-50nm for a typical length bar 1m long.

Note that the currently accepted value for the largest uncertainty we can tolerate in the realization of a standard is about 1 part in 10^8; and before they defined the value for c they measured it with an accuray much better than this.

 

[tiredryan]

Thanks.

What is the lowest uncertainty we can obtain when we measure things on the small scale, for example nanometers? For example I see people say they have made transistors at 10 nm or measured proteins at 3 nm. Is it really 10 +/- 1 nm or 10.0 +/- 0.1 nm or lower (10.000000 +/- 0.0000001 nm) ?

 

[Rap]

Thanks.

What is the lowest uncertainty we can obtain when we measure things on the small scale, for example nanometers? For example I see people say they have made transistors at 10 nm or measured proteins at 3 nm. Is it really 10 +/- 1 nm or 10.0 +/- 0.1 nm or lower (10.000000 +/- 0.0000001 nm) ?

Well, I can give you a theoretical answer. Given that the speed of light is absolutely certain (299,792,458 meters/sec), the meter is defined as exactly the distance light travels in 299,792,458 sec, so our distance measurements are limited only by our inability to measure the second accurately. Looking at the Wikipedia article on the second, it looks like the uncertainty in the second is about 1 part in 10^15. So the lower limit on our ability to measure a nanometer is 1 part in 10^15. Any practical limit must be equal to or higher than this. The practical limit will depend upon the particular experimental setup, but I have no experience with this.

The speed of light is for light in a vacuum, with no gravitational fields. There is a practical error in the measurement of distance to the extent that we cannot obtain a perfect, gravity free vacuum. This will increase the amount of error in our measurement of distances, but I don't know what that new number would be. Maybe someone else can fill in the blanks?

 

[tiredryan]

Thanks for all your responses.

What got me to this question was how through the ages people have been racing to reach the "extremes" of mathematics and science. For example in mathematics we know pi past 2.6 trillion digits and our largest known prime number is 12,978,189 digits long. In physics we have reached temperatures below 100 pK. I was wonder if there was a similar competition in measuring distances with the least amount of uncertainty/highest amount of precision.