I Definition of the Meter

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I'm reading a book from the authors Halliday and Resnick and it says that

Code:
The meter is the length of the path traveled by light in a vacuum 
during a time interval of 1/299 792 458 of a second.
This time interval was chosen so that the speed of light c is exactly
c = 299 792 458 m/s.
I understand that, and it also make sense if you plug in these values into the dx formula of motion (you get dx = 1m)

but how did we calculate the speed of light in m/s very precisely before redefining the meter? The calculation of the speed depends in the previous definition of the meter right? So how does this new definition of meter can use the speed of light which was calculated using another definition of the meter? It does not really make sense to me...
 

russ_watters

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but how did we calculate the speed of light in m/s very precisely before redefining the meter? The calculation of the speed depends in the previous definition of the meter right? So how does this new definition of meter can use the speed of light which was calculated using another definition of the meter? It does not really make sense to me...
You've correctly Identified the problem as being circular. Ultimately, units are arbitrary, so breaking the cycle simply meant making an arbitrary choice to fix one of the variables. The speed of light is the easier to deal with, so it was made the basis.

The wiki article on the definition of the meter describes some of that logic. For example, it immediately resulted in higher measurement accuracy for laser wavelength comparisons.
 

sophiecentaur

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It does not really make sense to me
That's a fair reaction until you look at the bigger picture.
All units are defined by referring them to each other but the best quantities to hang the system on are those which can be measured accurately and reliably. Time (and frequency) are the best ones to start with because we can use atomic transitions in repeatable, accurate experiments to 'define' the second in terms of EM waves. Distance (the metre) hangs directly on that because we have confirmed that c is the same everywhere. c is the third value which can be reliably used in the x=ct equation.
 

phyzguy

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I'm reading a book from the authors Halliday and Resnick and it says that

Code:
The meter is the length of the path traveled by light in a vacuum
during a time interval of 1/299 792 458 of a second.
This time interval was chosen so that the speed of light c is exactly
c = 299 792 458 m/s.
I understand that, and it also make sense if you plug in these values into the dx formula of motion (you get dx = 1m)

but how did we calculate the speed of light in m/s very precisely before redefining the meter? The calculation of the speed depends in the previous definition of the meter right? So how does this new definition of meter can use the speed of light which was calculated using another definition of the meter? It does not really make sense to me...
The meter was originally defined as 1/10,000,000 of the distance from the equator to the pole, and the second was defined as 1/86,400 of the length of the mean solar day. Given those, we can measure the speed of light in m/s. The meter was then changed to be the length of a bar of iridium that was stored somewhere in Europe. As the measurements got better and better, it was decided to use a certain frequency of light emitted in an atomic transition to define the second, and then fix the speed of light and use that to define the meter. So the meter is no longer defined by a physical object like the Earth or a metal bar.
 
Ohh I see. So the reason is that using the atomic measurement of time which is the most accurate measurement we have made, we use it with a less accurate measurement like the speed of light in order to redefine the meter more accurately. So the secret here is time, because we succeeded measuring it better we use it to redefine the meter better.

Did I got it right?
 

phyzguy

Science Advisor
4,101
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Ohh I see. So the reason is that using the atomic measurement of time which is the most accurate measurement we have made, we use it with a less accurate measurement like the speed of light in order to redefine the meter more accurately. So the secret here is time, because we succeeded measuring it better we use it to redefine the meter better.

Did I got it right?
I think so. Note that the speed of light is no longer measured, but is now defined, so it is known with no uncertainty. This web site has a lot more information and history.
 
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Ohh I see. So the reason is that using the atomic measurement of time which is the most accurate measurement we have made, we use it with a less accurate measurement like the speed of light in order to redefine the meter more accurately. So the secret here is time, because we succeeded measuring it better we use it to redefine the meter better.

Did I got it right?
Yes, that's how I've always understood it. But I went looking for the exact technical arguments for the change (which was made in 1983). The best detail I've found so far in that Google search is in the language of the actual 1983 resolution of the Bureau International des Poids et Mesures. Here are what I see as the key arguments in that resolution, though there are more (boldface is mine):
  • that progress made in the measurement of the frequency and wavelength of these radiations has resulted in concordant determinations of the speed of light whose accuracy is limited principally by the realization of the present definition of the metre,
  • that wavelengths determined from frequency measurements and a given value for the speed of light have a reproducibility superior to that which can be obtained by comparison with the wavelength of the standard radiation of krypton 86,
  • that a new definition of the metre has been envisaged in various forms all of which have the effect of giving the speed of light an exact value, equal to the recommended value, and that this introduces no appreciable discontinuity into the unit of length, taking into account the relative uncertainty of
    plusminus.gif
    4 ´ 10–9 of the best realizations of the present definition of the metre,
From 1960-1983 the standard was a wavelength emitted by a particular atomic transition of krypton.
 

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This is so awesome! I imagine myself hearing this in high school. When our teacher was saying something like that we where like "whaaat?" but now I get it.
 

sophiecentaur

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This is so awesome! I imagine myself hearing this in high school. When our teacher was saying something like that we where like "whaaat?" but now I get it.
This was always happening to me at school. I would get only half of a message (sometimes my fault and sometimes the fault of the teachers) and I would often get a wrong idea about things. That could stick with me for years until another input would put me right. This is where Forums like PF come in handy - we have time to chew things over and improve our own understanding - and that of others (hopefully).
 

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