We can't, it's a triangle. Locally you use something that moves to define your units, then when you say something else is moving at some speed, all you're doing is saying how fast it moves compared to first thing. When both things are light, you always get the same answer.
So... there's no way to measure vacuum impedance except by measuring the speed of light? In that case, why did you even bring up the subject of vacuum impedance way back in post 290?
You don't already know the cycles per second. Because you don't have your second defined yet.
YOU SAID:
You can't see any nearby stars, but you can detect the 21cm hydrogen line. This electromagnetic radiation "is at the precise frequency of 1420.40575177 MHz". You detect it, and find it to be isotropic. [...] So if your master clock suffers some breakdown, you know that you can recalibrate it by counting the hydrogen-line microwaves passing you by.
In
your scenario we
start off with a clock. The second has
already been defined,
that's how we know what the frequency is.
If the clock breaks down, we still know what the frequency was. We wrote it down on a piece of paper. (You might not have, but I did.)
So back to my original question, what do we care what the speed of light was, or what the wavelength is? All we need to know if the cycles per second, and measure how long it takes that many cycles to pass.
No you don't. You're in a boat with some waves passing you by. You sit there counting how many times you bob up and down, and then you say I declare the duration of x waves passing me by to be one minute. You don't already know their frequency, if you did you would already have your minute, so there wouldn't be any point counting those waves to define it.
Unless everybody in the world was on the boat, and they had no reliable way of precisely measuring the time, and those waves happen to be passing at a remarkably constant and unchanging rate.
Then you could just make up a number, any number you wanted, and as long as everyone else in the boat used the same number, that would
be a minute.
If there was already a different way of measuring a minute, such as 1/1440 of the time between one dawn and another, but was unsatisfactory for some reason, you could pick a number that would give about the same length of time so that your almanacs and cookbooks which give time in minutes won't need to be updated.
That's pretty much what was done with the second, only the boat is the entire world.
If you're trying to determine the duration of a second, there'd be no point counting the cycles of the signal unless you knew the frequency, because it's the frequency that determines how many cycles you need to count.
And if you already know their frequency, you already know how many cycles per second you're talking about, so you already know what the second is so there's no point defining it.
Just because you know the frequency doesn't necessarily mean that you know the duration of the second. Somebody else, who happened to know the duration of the second, might have sent you a letter telling you what the frequency is. Or you might have worked out what the frequency was while you knew the duration of the second, but no longer know what the second is because your clock broke down. Or an international standards organization might have published a document telling you what the frequency of the microwaves that have a certain effect on a specific atom is.
In these cases, you know the frequency but not the second. So you can use the frequency to work out the second, without knowing or caring what the speed of light is.
You can't use frequency to define the second. Because frequency is cycles per second.
You've got that backwards. You
can use frequency to define the second
because frequency is
cycles per second
Yes it is.
I didn't actually say that. What I'm trying to get across is that regardless of how fast those waves are coming at you, you count x bobs then say that's a second. Then you watch how far a wave moves during the same fraction of a second and say that's a metre. So regardless of how I vary the wave speed with my magic button, when you repeat your exercise you always end up saying that the waves are moving at 299,458,792 metres per second, and you always assign them the same wavelength and frequency.
I see where you're making your mistake. You think the speed of light is analogous to the distance traveled by waves on the sea. Not true. That's
wavelength. The speed of light is analogous to the current of the water on which the waves propagate, which can be a completely different speed to the frequency at which the waves are passing you.
The
frequency of light is the
side to side "motion" of the photon. (Light is a transverse wave, remember?) The
speed of light is the
forward motion of the photon.
The speed of light is
NOT dependent on it's frequency. It could be oscillating at a thousand cycles per second, or a million, or a billion. This has no effect on how far it travels in that time.
If we were defining the meter by
wavelength, you'd have a valid point. But we're not, so you don't.
Groan, the irony. RC, do not accuse me of ignorance. Photons do not annihilate one another. Shine a light beam, now shine another light beam through it. See that fireball of annihilating photons where the light beams intersect? Er, no.
Oh my
[Insert fictitious deity here].
This one
literally made me laugh out loud.
(The humor lies in the fact that you begin by claiming it's ironic that he should be accusing you of ignorance... and then unwittingly and indisputably prove him right while attempting to prove the opposite.)
Farsight, I'm done wasting my time on you.
(You might want to look up some information on interference patterns, and the double slit experiment, before you make yourself appear even more foolish.)