the fundamental unit of c

[michel123456]

After reading this outstanding pdf arxiv first provided on this forum by DH in this thread post #11:

It is stated and commonly accepted that C is a fundamental quantity.

Therefore Nature herself suggests c as a fundamental unit of velocity.

(Trialogue on the number of fundamental constants

Authors: M. J. Duff, L. B. Okun, G. Veneziano, 3.1, page 4)

 

Why then C has no "fundamental unit" (a unit of velocity, call it for example "velocimetre" or "velociconds") and is paradoxically exprimed as a ratio of 2 other units, metres and seconds?

 

How come that the metre or the second is a part of something fundamental?

or

Ultimately, is it possible to have something that is a part of something fundamental ?

 

In the third part of the same paper:

Weinberg [1] defines constants to be fundamental if we cannot calculate their values in

terms of more fundamental constants, not just because the calculation is too hard, but

because we do not know of anything more fundamental. This definition is fine, but does

not resolve the dispute between Gabriele, Lev and me. It is the purpose of this section to

propose one that does. I will conclude that, according to this definition, the dimensionless

parameters, such as the fine structure constant, are fundamental, whereas all dimensionful

constants, including [math]\hbar[/math], c and G, are not.

(Trialogue on the number of fundamental constants

Authors: M. J. Duff, L. B. Okun, G. Veneziano, 4, page 25)

 

And further:

After all, an inhabitant of such a universe (let us identify him with

Feynman’s alien) is perfectly free to choose units in which c = 1, just as we are.

(Trialogue on the number of fundamental constants

Authors: M. J. Duff, L. B. Okun, G. Veneziano, 5, page 26) bolded mine.

 

Wich is a statement that presupposes that there are more than one unit necessary in order to define something fundamental. Isn't that a wrong concept?

Edited December 1, 2012 by michel123456

[Janus]

Seconds, meters etc. are not fundamental, they are arbitrarily defined units (chosen for convenience). The fact that we can define c in terms of meters/sec doesn't make it any less fundamental than the fact that we can define a radian as a number of degrees makes it any less of a natural measure of angle.

[ACG52]

It is stated and commonly accepted that C is a fundamental quantity.

 

Velocity is not a fundamental quantity. It's a derivative of time and distance.

[michel123456]

meters are rods, seconds are clocks.

 

radian and degrees are angles.

 

It can be considered that C is the conversion factor of rods into clocks.

but it should be evident that a number without unit cannot convert rods into clocks (convert meters into seconds). Indeed, C has unit meter/sec, which is a tautology.

 

Once you put a name to something suddenly it exists.

Once you put a name to the unit of velocity (I don't like my 2 first proposals, lets call it "tachys" for the moment ), here we are, tachys exist.

 

Then one can say that a metre is a tachys multiplied by K seconds. (where K is unitless)

 

So, a distance, a metre is something complex (not fundamental) made up of 2 things: velocity and time.

[ACG52]

Then one can say that a metre is a tachys multiplied by K seconds. (where K is unitless)

 

So, a distance, a metre is something complex (not fundamental) made up of 2 things: velocity and time.

 

 

First, K is not unitless, the unit is seconds. You said so right there

 

Second, velocity is already defined as distance/time. That's what your 'tachys' is. So in saying that a meter is tachys * seconds, you're simply taking the derivative factor and reducing it to the fundamental factors, i.e. distance and time

[michel123456]

First, K is not unitless, the unit is seconds. You said so right there

I intended to say that K is a factor, a ratio, an angle.

Put tachys on x axis, put seconds on the Y axis: the result is a surface rectangle representing distance in metres. The angle of the diagonal of the obtained rectangle represents K.

 

 

Second, velocity is already defined as distance/time. That's what your 'tachys' is. So in saying that a meter is tachys * seconds, you're simply taking the derivative factor and reducing it to the fundamental factors, i.e. distance and time

The pizza has just arrived. Coming back in a while.

Back.

yes and no.

Yes to your first 2 sentences.

No to the rest because tachys is supposedly more fundamental than meters. You are dividing meters in order to obtain tachys.

Edited December 1, 2012 by michel123456