Taboo ‘fundamental’; what distinction are you trying to get at? Change the speed of light holding other parameters constant, and the fine structure constant changes; and vice-versa. Whether you want to consider this a “change in the speed of light” or a “change in alpha” seems to me pretty strictly a matter of taste; and the speed of light (especially its constancy) is much more familiar to most people than is alpha. (Which anyway may not be so constant at high energies, in spite of having ‘constant’ in the name.)
We are pretty far off the original question, but, yeah, there is a distinction. The fine structure constant is indeed more fundamental than the speed of light. How do you change the speed of light and not much else? You have to change at least the fine structure constant (in the IR limit, as you point out) and probably the gravitational coupling strength, and possibly some other free parameters in the standard model, like masses of the electron and quarks (again, in some dimensionless units). Otherwise something will go wrong with the Universe, the common example being carbon not being synthesized by stars. But I agree, these “side effects” of changing the speed of light may not have been important long time ago, or maybe in the galaxy far far away.
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.)
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?
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 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.
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.
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?
Are you assuming (or concluding) that distance and relative motion add the way they do in Newtonian physics? That is observed to not be the case, on the scales and precisions of the GPS system.
In other words, the vector difference between the velocity of object B and C varies depending on the observer, and adding the same constant vector to the velocity of B and C changes the difference between their vectors.
No, I’m saying that you can do or transform all your observations to one frame of reference, and all observers will agree on the results within that frame of reference, no matter what they’re transferring from.
Your assertion is not consistent with current observational evidence. Observers in different frames of reference will not agree on what percentage of a sample of an unstable isotope will decay in the time it takes light to travel the length of an artifact.
Not until they have transformed their observations to a common frame, no. Please re-read what I said. Then let’s see some math. Make an observation of length in one frame of reference, transform it to another, and show that it still disagrees with what observers in that frame of reference measure. Alternatively, make two observations in different frames, transform them to a third, and show that they disagree.
Observer C notices that at time 2, object C is stationary, object L is moving left at 9 Million Kilometers/minute, is 18 Million Kilometers long, and that stick L is 18 Million Kilometers long. C also notices that object R is moving right at 9 Million Kilometers/minute, is 18 Million Kilometers long, and that stick L is 18 Million Kilometers long. C notes a distance of 36 MKm between L and R when they pass the ends of their co-named sticks.
Observers L and R observe that sticks L and R are moving right at 9 Million Kilometers/minute, and that their observed length is 13.5 MKm. They observe that they are 27 MKm apart when they pass the end of their sticks.
Lights at the extreme ends of sticks L and R flashed simultaneously (at the same place and time) with lights located on objects L and R. 45 seconds later, the light from objects L and R has traveled the 13.5 MKm to C; 15 seconds after that, the light from the ends of the sticks arrives (having traveled 18 MKm).
The speed of L to R (and distance between them) is left as an exercise to the reader.
10.1 MKm (13.5MKm *(1-(1/2)^2) for the distance between L and C, but 18MKm for the length of the stick which extends between them. in the reference frame of C. (Distance only diminishes in transformation, while length increases when transformed towards a frame of reference closer to that of the object in question)
Observer L is in the rest frame of object L; consequently he measures its proper length. Observer C is not in the rest frame of object L, and therefore measures a shorter length. Your claim that L measures a shorter length than C indicates that you’re using something other than special relativity, that you’re using special relativity wrong, or that I didn’t understand your description. Please clarify which it is. A diagram may be helpful.
Additionally, this:
Distance only diminishes in transformation
is plain wrong, since you can always do the transformation in the other direction! It doesn’t diminish both ways! And this claim:
length increases when transformed towards a frame of reference closer to that of the object in question
appears to be meaningless; there’s no such thing as a frame of reference “closer to an object”. A frame of reference doesn’t have a location, it has a speed relative to an observer.
Sticks L and R are stationary in the frame of C; objects L and R just happen to be close to the other ends of the sticks at some time, and are stationary in their own reference frames.
At this point I have no idea what is supposed to be happening in your scenario. You’ve got sticks, objects, and observers, and it’s not clear whether any of them are the same or what frames they are in. Please draw a diagram.
Well, speed of light is not a fundamental constant, so they probably mean the fine structure constant or some other dimensionless quantity.
Taboo ‘fundamental’; what distinction are you trying to get at? Change the speed of light holding other parameters constant, and the fine structure constant changes; and vice-versa. Whether you want to consider this a “change in the speed of light” or a “change in alpha” seems to me pretty strictly a matter of taste; and the speed of light (especially its constancy) is much more familiar to most people than is alpha. (Which anyway may not be so constant at high energies, in spite of having ‘constant’ in the name.)
We are pretty far off the original question, but, yeah, there is a distinction. The fine structure constant is indeed more fundamental than the speed of light. How do you change the speed of light and not much else? You have to change at least the fine structure constant (in the IR limit, as you point out) and probably the gravitational coupling strength, and possibly some other free parameters in the standard model, like masses of the electron and quarks (again, in some dimensionless units). Otherwise something will go wrong with the Universe, the common example being carbon not being synthesized by stars. But I agree, these “side effects” of changing the speed of light may not have been important long time ago, or maybe in the galaxy far far away.
But this is just as true if you change alpha! At a minimum, to restore the carbon synthesis rate, you’d have to mess with the proton charge.
The numerical value of a dimensionful constant depends on the system of units you’re measuring it in; that of a dimensionless constant doesn’t.
Well yes, but who cares about the numerical value? Hold the system of units constant and look at the actual physics!
How would you do that? (The metre is now defined in terms of the second and the speed of light.)
I would define the unit of distance in terms of the size of the King’s lower extremities, as God intended. :rolleyes:
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?
Are you assuming (or concluding) that distance and relative motion add the way they do in Newtonian physics? That is observed to not be the case, on the scales and precisions of the GPS system.
In other words, the vector difference between the velocity of object B and C varies depending on the observer, and adding the same constant vector to the velocity of B and C changes the difference between their vectors.
No, I’m saying that you can do or transform all your observations to one frame of reference, and all observers will agree on the results within that frame of reference, no matter what they’re transferring from.
Your assertion is not consistent with current observational evidence. Observers in different frames of reference will not agree on what percentage of a sample of an unstable isotope will decay in the time it takes light to travel the length of an artifact.
Not until they have transformed their observations to a common frame, no. Please re-read what I said. Then let’s see some math. Make an observation of length in one frame of reference, transform it to another, and show that it still disagrees with what observers in that frame of reference measure. Alternatively, make two observations in different frames, transform them to a third, and show that they disagree.
Observer C notices that at time 2, object C is stationary, object L is moving left at 9 Million Kilometers/minute, is 18 Million Kilometers long, and that stick L is 18 Million Kilometers long. C also notices that object R is moving right at 9 Million Kilometers/minute, is 18 Million Kilometers long, and that stick L is 18 Million Kilometers long. C notes a distance of 36 MKm between L and R when they pass the ends of their co-named sticks.
Observers L and R observe that sticks L and R are moving right at 9 Million Kilometers/minute, and that their observed length is 13.5 MKm. They observe that they are 27 MKm apart when they pass the end of their sticks.
Lights at the extreme ends of sticks L and R flashed simultaneously (at the same place and time) with lights located on objects L and R. 45 seconds later, the light from objects L and R has traveled the 13.5 MKm to C; 15 seconds after that, the light from the ends of the sticks arrives (having traveled 18 MKm).
The speed of L to R (and distance between them) is left as an exercise to the reader.
You don’t appear to understand what I mean by “transform”. What does L say the speed (or length, or time) is in the reference frame of C?
10.1 MKm (13.5MKm *(1-(1/2)^2) for the distance between L and C, but 18MKm for the length of the stick which extends between them. in the reference frame of C. (Distance only diminishes in transformation, while length increases when transformed towards a frame of reference closer to that of the object in question)
Observer L is in the rest frame of object L; consequently he measures its proper length. Observer C is not in the rest frame of object L, and therefore measures a shorter length. Your claim that L measures a shorter length than C indicates that you’re using something other than special relativity, that you’re using special relativity wrong, or that I didn’t understand your description. Please clarify which it is. A diagram may be helpful.
Additionally, this:
is plain wrong, since you can always do the transformation in the other direction! It doesn’t diminish both ways! And this claim:
appears to be meaningless; there’s no such thing as a frame of reference “closer to an object”. A frame of reference doesn’t have a location, it has a speed relative to an observer.
Sticks L and R are stationary in the frame of C; objects L and R just happen to be close to the other ends of the sticks at some time, and are stationary in their own reference frames.
At this point I have no idea what is supposed to be happening in your scenario. You’ve got sticks, objects, and observers, and it’s not clear whether any of them are the same or what frames they are in. Please draw a diagram.