If the Speed of Light changed, would we even notice it.

[WebFeet]

The most fundemental constant that we rely on in the Universe is the Speed of Light.

Many of our measurements are based on its invariant nature, those that aren't depend on a set scale of dimension.
We are well aware that dimensions can vary depending on the strength of the graviational field in which they exist. Time measured by an orbitting satelite will be different to that here on Earth. A metre ruler here on Earth would still measure 1 metre at the event horizon of a BlackHole, but would occupy less space - space being more compressed.

The amount of Mass in a metre rule, using e=mc^2, is inversely proportional to the speed of light.
If we used the metre ruler to determine a fixed length and measured how much time was taken for light to travel from end of it to the other, is this a valid way to measure it ?
After all, are we not essentially measuring the speed of light against itself.

If halfway along the ruler the speed of light decreased by a factor, then the mass would in turn increase and the elapsed time would show that along that metre rule, the speed of light is constant.

Hence my question.

If there were localised variations in the Speed of Light, given that our method of measurement is depedant on the Speed of Light, would we even notice it ?

[Will]

Wouldn't that be dependant on how extreme the difference was in speed?

[WebFeet]

Originally Posted by Will

Wouldn't that be dependant on how extreme the difference was in speed?

A variation could be from zero to whatever number you want to use, + or -.
So in this case size really doesn't matter.

The question is, if our method of measurement is in some way based on the speed of light, albeit through mass or any other association, would that not invalidate the method.

[Will]

it would. i don't know too much about this, but i'm assuming that we measure it based on the most commonly accuring instance. and what i mean by that is that we wouldn't use any speed of light as our constant, but we would use the instances that we see everyday or that are most common.

[Qfwfq]

Tricky matter. Essentially, velocity is a pure (or dimensionless) number and that of light is exactly 1. This is the point of view most appropriate to Special Relativity. A different choice means using different units for spacelike and timelike intervals and this boils down to a choice of space-time coordinates, which certainly has no effect if done globally. Doing it locally is a matter of differential geometry and is what General Relativity is all about. In GR, changing coordinates locally may or may not make a difference physically, the cases in which it does come across as changing the curvature of space, not as changing the velocity of light, unless of course you use a choice of units to this effect.

[WebFeet]

Originally Posted by Qfwfq

Tricky matter. Essentially, velocity is a pure (or dimensionless) number and that of light is exactly 1. This is the point of view most appropriate to Special Relativity. A different choice means using different units for spacelike and timelike intervals and this boils down to a choice of space-time coordinates, which certainly has no effect if done globally. Doing it locally is a matter of differential geometry and is what General Relativity is all about. In GR, changing coordinates locally may or may not make a difference physically, the cases in which it does come across as changing the curvature of space, not as changing the velocity of light, unless of course you use a choice of units to this effect.

Although I made mention of GR in my original post, the problem is not really to do with changing the curvature of space.

I'm sat here trying to think of a way of explaining it a little clearer.... it's not easy.

Essentially the rules of how our Universe works are bound to the constant Speed of Light. All methods of measurement are in some way related to this constant.
If the Speed of Light was not constant, then one of the things that would be effected is the methods we use for measurement.
As the Speed of Light varies, so everything that is derived from it would also be subject to the same variation, including the methods of measurement we use.
These variations would be syncronised between the speed of light and the method, resulting in a constant result.

An analogy would be if there was a constant that everything was blue and when looking for exceptions to this rule you had to look through a blue filter. The result being that everything would conform, there would be no exceptions.

I hope that makes sense, it sort of does to me.

[Will]

Well I'm still of the opinion that the measurement we use is of the most commonly occuring instance of the speed of light. The speed of light may change under certain conditions but for all practical purposes we measure the most frequently observed speed of light.

Now this is a problem because that means that all of our formulas are based on one instance of a variable. I don't know anything about these formulas, but whenever people have told me of formulas involving the speed of light to explain the laws of our universe, i ask them how it could be possible to use something like the speed of light (which is not the same everywhere).

I don't know if any of that made sense. It's late and I may not have phrased that properly, but I guess essentially what I'm saying is that I agree with WebFeet that using something like the speed of light in formulas poses a problem, since it is a value which is not constant. However my thoughts remain that when we apply the speed of light to our formulas we make it a constant by using the most frequently occuring instances of it (the speed of light, that is).

[WebFeet]

Originally Posted by Will

Well I'm still of the opinion that the measurement we use is of the most commonly occuring instance of the speed of light. The speed of light may change under certain conditions but for all practical purposes we measure the most frequently observed speed of light.

It's not the value that we use that I have issue with, but with how we measured it in the first place.

The Speed of Light in a vacuum is a constant. There is no variation as to its measurement, it always come out at exactly the value. Hence why it is known as the Universal Constant.

If every unit of measurement is some way relates back to the Speed of Light, then what we are saying is :-
Measure the Speed of Light with reference to... the Speed of Light. The answer will always be exactly the same.

[Qfwfq]

Originally Posted by WebFeet

the problem is not really to do with changing the curvature of space.

It might not seem obvious to you, but it is. I hadn't misunderstood your point.

To better understand the link between locally changing the velocity of light and curvature, I guess you would need to fully understand differential geometry and GR.

[BlameTheEx]

We would have to propose characteristics of space that don't alter in proportion with C.