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army1987 comments on Local truth - Less Wrong Discussion
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How would you distinguish an universe where the, ahem, King's lower extremities grow and everything else stays the same from one where the King's lower extremities stay the same and everything else shrinks? (This is essentially the same point as that of this post but for scaling rather than rototranslations.)
(Well, the last time I had this discussion IIRC I initially had John Baez on my side then the person I was arguing against managed to convert him via private e-mail, but I couldn't understand what he said she said to him.)
Why would I want to?
My point being, you are not under any obligation to define the meter in terms of the speed of light when you are discussing a possible change in the speed of light. You are attempting an argument by definition, and rather a silly one. Define the meter in a way that's convenient to what you're trying to do, and have done.
Like what?
Like using the King's foot, or the curvature of the Earth, or a platinum bar, or indeed anything that isn't defined in terms of the thing whose changes you are trying to talk about.
The fact is that platinum atoms are bound together by the electromagnetic force, so if c = 1/sqrt(mu_0 epsilon_0) changes their distance changes too. (Who the hell is downvoting the entire thread, anyway?)
Equally a problem with the fine structure constant, since it directly measures the strength of the electromagnetic force. However, while the length of a platinum bar would, as you say, change under a change in the speed of light, it would not change linearly; so you can measure ratios of lengths and presumably pinpoint the constant that changed. The curvature of the Earth, for example, presumably depends on the strength of gravity in addition to the electromagnetic repulsion of its constituent particles, so it should change more slowly than the platinum bar's length.
But the fine structure constant is dimensionless, so you don't need to find a standard to measure it which doesn't change when it changes.
Ah, now I see what you're saying. Good point.
One of the points is that different frames of reference have different ratios of the length of artifacts, when those artifacts are moving relative to each other.
Usually when defining lengths in terms of an artefact you use the rest frame of the artefact (i.e. the one in which the artefact is longest).
Doesn't the time required to traverse the rest length of an artifact vary between observers? Edit: Also, how does knowing the length some other observer sees useful at all?
So what? Stick to one frame of reference; thought it doesn't matter which one you use, that doesn't mean you're not allowed to use one. Every observer will see the same change in the speed of light using their own measure of distance; or at any rate can agree on the change by mathing out the frame-of-reference effects.
So, measuring distance in 'the average length of these two sticks' and time in 'how long it takes half of a stationary sample of this radioactive element to decay', various observers get radically different values for the speed of light.
That's without any changes to the current world, if the sticks are moving.
Then I suggest that your observers not go out of their way to be stupid. Put everything in the same frame of reference first.
Just because you can play nitwit games with picking silly units of measurement doesn't mean you have to. To do particle physics, for example, you often have to calculate away the frame-of-reference effects; so what? Just put everything in a convenient frame and then be consistent about it. You seem to be assuming some kind of idiot-savant observer who is informed enough to deliberately pick a unit that's vulnerable to frame-of-reference effects, but not bright enough to calculate what the effect is.
The speed of light is postulated to be the same in both frames of reference; If they 'correct' length to some arbitrary frame of reference, then the amount of time that elapses will be irreconcilable between them- more seconds will elapse for some observers during the average period in which 1/4 to 1/2 of a total mass of an isotope has decayed.
Now you're making the same mistake with the time. Transform your clock into the same frame of reference you're using for length. Duh.
Really now, this is not difficult; why are you going out of your way to assume observers who can't manage to make all their observations in a consistent frame of reference?