Can someone explain the following logic used to define the meter?

[sodium.dioxid]

"The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.Note that the effect of this definition is to fix the speed of light in vacuum at exactly 299,792,458 m/s."

I don't understand this because how can you use a number based on the meter to go back and define the meter? In other words, if light travels at x METERS / second. How can you use x METERS / second to define what a meter is?

 

[SpectraCat]

Imagine that you need to communicate our systems of weights and measures to an intelligent being from another planet ... the only common basis for comparison that you can use are the properties of the universe that we find ourselves in. So, the idea is to define SI units of measure in terms of physically observable phenomena, rather than marks on a bar in a museum somewhere. We know from relativity that the speed of light in a vacuum is a fundamental constant of nature. Its dimensions are length divided by time. So, once we decide on a fundamental unit of time or length, we can define the other in terms of the speed of light. In the case of SI units, it is the second which is arbitrarily defined as:

"the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom"

Now that you have the fundamental unit of time nailed down, you can choose to define your fundamental unit of length in terms of how far light travels in a certain time interval. For historical reasons (i.e. marks on a bar of platinum in a Paris museum), we chose to define the meter as indicated in your post.

 

[rcgldr]

How much of these definitions are affected by gravity under general reltivity, in terms of the ratio of the difference in magnitude between two environments, versus total magnitude of the defined constants, due to gravity, say between 0 to 10 g's?

 

[D H]

"The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second."

There's no circularity here. Just a bit of oddness with that magic time interval, 1/299,792,458 of a second.

"Note that the effect of this definition is to fix the speed of light in vacuum at exactly 299,792,458 m/s."

This is a direct consequence of the definition of a meter. The speed of light is a defined constant. The rationale is that the speed of light, as far as we can tell, is a universal constant. Almost 100 years past between the Michelson Morley experiment and the adoption of this definition of the meter. Physicists had had a century to find any evidence that the speed of light is not the same to all observers. No such evidence was found.

 

[Borek]

"Note that the effect of this definition is to fix the speed of light in vacuum at exactly 299,792,458 m/s."

This is a little bit twisted and I think I know where your confusion comes from. Note that speed of light is fixed at the cost of meter - with each more precise measurement of light speed length of meter can slightly change, even if the speed of light will be still constant at exactly 299,792,458 m/s.