# Mathematically meaningful meter

1. Oct 14, 2007

### FrankMak

The "size" of the SI meter has its basis in the metric system and it was officially accepted in 1799. We know its size doesn't match its intended 1/10,000,000th division from the equator to the pole, thus it is somewhat arbitrary. Even though the SI meter is defined differently its "size" is the same as that approved in 1799.

Those the created the meter were not aware that its size would be used to establish the velocity of electromagnetic waves.

Had the meter been slightly shorter it could have resulted in a numeric value for the velocity of electromagnetic waves being 314,159,265 meters/sec.

What effect would such a numeric value have had on our "measurement system" and its use in formula dealing with physical law?

2. Oct 14, 2007

### ZapperZ

Staff Emeritus
Is there a reason why you would think that it would make any difference if I measure something in miles, meters, centimeters, etc? Would the natural laws care what measurement scale I use?

Zz.

3. Oct 14, 2007

### ice109

c==1

4. Oct 14, 2007

### cevdet.erturk

I agree with ZapperZ. Meter is just a measurement value that human beings use. That changes nothing in the laws. Maybe the choose of the measurement value can determine the easier way or the harder way for our calculations.

I just wonder, what answer did u expect from the users when u were asking the question?

Last edited: Oct 14, 2007
5. Oct 14, 2007

### ZapperZ

Staff Emeritus
Er.. you may have confused the person who asked the original question versus who made the statement that you agreed to. The OP (FrankMak) was the one who asked the original question and appears to be thinking that a measurement might make a difference in how we measure things and/or how we describe nature.

Zz.

6. Oct 14, 2007

### cevdet.erturk

Done. Sorry.

7. Oct 14, 2007

### FrankMak

It seems that one individual, and I suspect he speaks for others, thinks that the value of a dimensions "size" can make the numeric values associated with it worthless.

Within the last week I had an email interchange with a Professor of Physics that stated it this way, "If Pi were artificially incorporated into definitions so the speed of light had Pi in it, it would be a physically meaningless appearance of pi, and when it canceled or combined with other quantities that had physically meaningful factors of pi, it would be a mess." I expressed the numeric value as 314 159 265, which makes it equal to pi to 9 significant figures.

I thought the whole purpose of "natural units" was to give c, and other values associated with physical law, numeric values that would make them "equation friendly".

If the meter had been slightly shorter and resulted in c = 314,159,265 meters/sec (equaling the current precision of the SI defined numeric for the velocity of electromagnetic waves) one of the unwieldy numeric values would be eliminated. All derived values that use that size meter in their unit descriptor would be defined using it, thus it would be embedded in the system of measurement.

Also, everyone thinks of c in terms of velocity, meters/sec, but the "size" of the meter is that wavelength that occurs c times per second, which in SI gives cf = 299792458 Hz. Too bad that isn't a meaningful value for defining a "unit of energy", and neither is 314,159,265 Hz.

8. Oct 15, 2007

### TVP45

Light would still be exactly the same if we measured its speed as 314159265 meter'/second (where meter' = k meter, where k is some dimensionless multiplier).

pi is the ratio of circumference to diameter for a circle and has no physical significance otherwise.

9. Oct 15, 2007

### rbj

i might suggest to Frank to check out:

http://en.wikipedia.org/wiki/Dimensionless_physical_constant

http://en.wikipedia.org/wiki/Planck_units or
http://en.wikipedia.org/wiki/Natural_units

http://en.wikipedia.org/wiki/Dimensional_analysis
http://en.wikipedia.org/wiki/Fundamental_unit
http://en.wikipedia.org/wiki/Nondimensionalization

ultimately, all of the physical laws can be expressed in such a way that anthropocentric units or physical constants (or any dimensionful units or constants) just go away. then, rather than wonder why the speed of light (whether expressed in meters/second or furlongs/fortnight) is what it is, we would be wondering why the meter (a length approximately as big as people are) is as many Planck lengths as it is or why the second (a period of time closely related to the time it takes biological beings like us to assemble thoughts) is as many Planck times as it is. since the speed of light is always 1 Planck length per Planck time (by definition), when you answer those previous two questions, we have an answer to the question for why the speed of light is 299793458 m/s.

the speed of propagation (whether it's E&M, gravity, whatever "instantaneous" interaction) is finite, not infinite. that's the main physical concept. it doesn't matter what finite speed that is, such differences are not meaningful. whatever finite speed we call it doesn't matter because that finite speed (along with the finite G and $\hbar$) determines the scale of the existence of things. this is why, in my opinion, physicists that propose (and get popular press) theories of variable c or G or whatever are off base. such changes of dimensionful physical constants are meaningless and it's only the dimensionless physical constants (e.g. $\alpha$ or $m_p/m_e$) that have consequence in physical law.

Last edited: Oct 15, 2007
10. Oct 15, 2007

### FrankMak

I know why the speed of light has a particular numeric value. I can go back through science books published in the U.S. some 60 years ago and it was 186,000 miles/sec. The current value then, as it is now, is an artifact of how we define the "size" of a uinit of length and the duration of the second. I am familiar with the various "natural unit" systems. Stoney units were created in 1881 in an attempt to deal with the various unwieldy numeric values attached to physical constants.

I agree with TVP45. It was disconcerting to have a senior professor of physics make the claim that 314159265 meter'/second would make a "mess" in equations. I wonder what type of reply I would have received if I had suggested that the meter' be just under half of the current "size", which could result in a velocity of 628318530 m'/sec for electromagnetic waves. That number has considerable significance in how we interpret electromagnetic phenomena.

It is a physical fact that the velocity of electromagnetic waves vary depending upon the material in which it is allowed to propagate. The purpose of defining a fixed value for the "velocity of light", the SI definition, was to provide a reference value which could be used as a comparison to actual measurements. It is unfortunate that the particular numeric value they chose is not equation friendly.

11. Oct 15, 2007

### ZapperZ

Staff Emeritus
But you are now talking about the GROUP velocity of light in a media. You might want to read our FAQ first before making such statements and using faulty starting points.

I still want to see clear examples, rather than hand-waving arguments here, of what you are claiming. Show me exactly what 'equation' that would have changed had we used a different scale to measure c. Adding a factor or an extra constant term to an equation doesn't make any significant change to a description. Just look at the Uniqueness theorem in E&M. So show me what equation changes dramatically when I use a different units of measurement.

Zz.

12. Oct 15, 2007

### rbj

i wonder what "mess" he was referring to? "c" would still be "c" and the equations would continue to dimensionally homogeneous. any ratio of v/c would continue to be the same dimensionless number.

that number doesn't have any significance, but $2 \pi$ and $4 \pi$ have some reason to naturally appear in equations of physical law.

that's because of interaction with the particles in matter. the speed of E&M in vacuo is the same everywhere and equal to $\sqrt{1/(\epsilon_0 \mu_0)}$

when changing the definition of the meter from the distance between two little scratch marks on a platimun-iridium bar to the distance that light traverses in 1/c seconds (please forgive the dimensional sloppiness), they had to choose c so that the meter so defined had the same quantitative length.

Last edited by a moderator: Oct 15, 2007
13. Oct 16, 2007

### FrankMak

That was the general question in my original post.

I don't know what "mess" the professor was referring to. Perhaps it was due to what rjb is referring...

14. Oct 16, 2007

### ZapperZ

Staff Emeritus
But when you said this:

.. it is no longer a question, but rather something that you've made up your mind on. That was the suspicion that I had when you posted your "question", that you've somehow already decided on something and simply using this question to air out your opinion.

You have made at least a couple of assertion (not questions) to imply that the units of what we measure somehow effect our "equations". Thus, I would like you to specifically point out what these equations are. If you can't, and since everyone else who responded here have categorically mentioned that such a claim isn't valid, then I would say your question has been answered and this thread is done.

Zz.

15. Oct 16, 2007

### FrankMak

Since the professor did not give any examples of how a value that looks like $\pi$, and used to define the velocity of EM waves, would cause a "mess" (apparently effect our equations), I am trying to anticipate what might be his objections before I reply.

I searched through many pages dealing with "units" and could not find any source that discussed what can or cannot be used as a unit of measurement. I am still awaiting response from individuals involved in "Measurement Theory" whether they have definitions that might apply. So far I have been unable to find any articles that even discuss what can be a valid unit of measure in the physical sciences. If anyone can cite some source(s) on this issue it would be appreciated.

I would like to know whether a numeric value that looks like a transcendental number can be used as a unit of measure. In the example I gave it looks like a known transcendental number up to 9 digits of precision. If $\pi$ doesn't cancel with another $\pi$ in an equation, the limiting precision would be some other value with less precision. How much do we care if the numeric value for the velocity of electromagnetic waves is defined as a transcendental number?

16. Oct 16, 2007

### ZapperZ

Staff Emeritus
I'd like to know what instrument that you have where you actually HAVE to care about all those decimal places in the first place!

I notice that you still have not illustrated this with ANY kind of equation. So as far as I'm concerned, this is still something that you've made up and does not exist. We appear to be wasting our time here since this whole discussion is moot.

This line of discussion is over.

Zz.