Maxwell had it correct

[FrankM]

In 1873, James Clerk Maxwell stated:

["Maxwell quote"]"The most universal standard of length which we could assume would be the wavelength of a particular kind of light... Such a standard would be independent of any changes in the dimensions of the earth, and should be adopted by those who expect their writings to be more permanent than that body."

 

This statement was made during the debate on whether the British should adopt the metric system. Maxwell thought that a "natural" length should be selected as a standard of length. The total metric package was intended to make commercial transactions easier, and the scientific community was encouraged to go along with this purpose by adopting the "values" for scientific inquiry.

 

Had Maxwell been aware of an unseen "light" that illuminates our galaxy, he would have found its wavelength suited scientific inquiry better than the "meter". If one chooses a natural wavelength as a standard of length it results in a interesting numeric result, the numeric value of the frequency of the wavelength becomes the same value as the numeric value of the velocity of the wavelength.

 

If the wavelength of the neutral hydrogen (H1) emission (approx 21 cm) had been chosen as the "universal standard of length (USL)", the frequency would be 1420.4057517667 (10^6) cycles per second, and the scientific value for the speed of light would be 1420.4057517667 (10^6) USLs per second.

 

The wavelength of the H1 emission goes into the meter about 4.737... times. Divide 1420.405.... by that number and you get 299792458 m/sec.

[swansont]

The utility of a standard is related to how easy and how well it can be measured. The 21 cm transition has a lifetime of around 10 million years, so while that makes the linewidth narrow it also makes measurements of an unperturbed atom difficult.

 

An atomic wavelength was used starting in 1960: the wavelength of a transition in Kr-86. Secondary transitions were also used, like Hg-198 and Cd-114.

[FrankM]

The utility of a standard is related to how easy and how well it can be measured.

It would be better if a "standard" had relevance to what one is trying to accomplish. When the meter was first proposed over 200 years ago, its earthly origins were prompted by commerce and politics of that time. Slightly thereafter, Thomas Young demonstrated that "light" had the property of waves and these waves had specific lengths. It did not occur to scientists of that time that a "unit of measure" akin to a "wavelength" might be more useful in their research into the "nature of the universe". James Maxwell was aware of this in 1873, and I am sure he was not alone.

 

Some 25 years later Max Planck identified that "energy quanta" could be related to the "wavelength" of an emission.

 

Just think how much simpler it would be if a known natural "wavelength" was selected as the scientific "unit of measure", all scientific inquiry would be related to a known universal length. Max Planck and James Maxwell didn't know about the H1 emission and its wavelength, but the scientific establishment today does know this.

 

The group involved with developing "standards" know that the current defintions for the base units are not based upon true physical constants.

 

http://www.iupap.org/commissions/interunion/iu1/u1-2005.pdf

 

the consensus that now exists on the desirability of finding ways of defining all of the

base units of the SI in terms of fundamental physical constants so that they are

universal, permanent and invariant in time;

 

Unfortunately, they see nothing wrong with the "meter", which certainly is not based upon a "fundamental physical constant", neither is the SI second.

[CPL.Luke]

however it is a unit that most people are familiar with at this point, and forms a nice and easy system with which to measure just about anything you would want to measure.

 

who cares if its actually based on something fundamental?

[swansont]

Unfortunately, they see nothing wrong with the "meter", which certainly is not based upon a "fundamental physical constant", neither is the SI second.

 

How are the meter and second not based on fundamental constants? And how would the 21 cm line be based on those constants?

[FrankM]

who cares if its actually based on something fundamental?

Physicists apparently care or they wouldn't have expended considerable effort to find "natural units" that they hope would provide a better "fit" between the mathematics of science and what they know about the physical universe.

 

How are the meter and second not based on fundamental constants?

 

There is a difference between fundamental constants and "defined constants".

 

The real duration of the SI second is based upon the average ephemeris second (in 1953) and this was then tied to so many transitions of a particular Cesium isotope to give it a stable reference. The duration of the SI second does not have a real relationship to any mathematical or physical science constant except by definition, it is still based upon an astronomical duration.

 

The original meter was supposed to be defined as 1/10,000,000 of the distance between the equator and either pole, but the survey was inaccurate. It still has no scientific basis (just vaguely geographic) and it is the same length, but it is now defined in relationship to the SI second. The folks at NIST do not note just how peculiar it is to define a "unit of length" by a time duration. The Swiss Office of Metrology metrology website is quite direct.

 

http://www.metas.ch/en/scales/meter.html

 

From this can be concluded that the unit of length is dependent on the unit of time, the second."

 

Related to the "defined value for the speed of light" is this statement by a Professor at the Univ. of Colorado.

 

http://www.colorado.edu/philosophy/vstenger/Briefs/c.pdf

 

Now, perhaps someday it will turn out that defining distance this way was a bad move and some clock- independent operational definition of distance should be re-introduced. But, until then, without a redefinition of distance, any claim that c is variable is simply false.

 

The ~21 cm wavelength is a real universal physical length, the result of a unique atomic level process. If anything, the meter should be related to that "wave length" rather than viceversa.

 

As noted earlier, there are approx. 4.737963... H1 wavelengths in a meter, and if you multiply that number times the SI speed of light (299792458) you get 1420.4057.... (10^6) H1 wave lengths per second. This puts it right back to the Maxwell suggestion, and it results in the speed of light being defined by using the H1 wavelength as the "standard of length". This results in the "frequency" having the same numeric value as the speed of light, which is very convenient.

 

There remains one problem, the time duration is still the SI second, but it can be defined in relationship to the H1 wavelength and mathematical constants.

[swansont]

Why does it matter if a unit length is one wavelength, or ten? Or twenty, or 2159.325? Those are just constants. Or if the time unit is one oscillation or 9192631770 oscillations? Your choice limits how well you can actually realize the standard — what good would it do to have one standard that is a "natural" length but can only be measured to, say 1%, if you had a different standard and you can measure the same distance to 0.001%? (for sake of argument; actual standards measurements are much better than this)

[FrankM]

Why does it matter if a unit length is one wavelength, or ten? Or twenty, or 2159.325? Those are just constants.

The same reason why SI units use "one meter" or "one second" as the starting point.

 

The utility of a standard is related to how easy and how well it can be measured.

I still have a problem with a standard that is based upon how easy and well it can be measured as compared to whether it is relevant to its intended use.

 

The IUPAP CCU group is well aware that many of their "constants" have no relationship to the physical universe that they are trying to "measure".

 

At the moment we have electronic counter technology that goes several digits beyond our defined reference value for the duration of the second, and the CCU group knows that they are approaching a time when the "second" has to be redefined in relationship to another transition frequency that has a higher cyclic rate. Whether they will try to improve the accuracy of the base "duration" remains a question, but that really accomplishes nothing as it has no relationship to anything they are measuring.

 

Astronomers have already defined a measurement unit that is more suitable for what they are measuring, the AU, so why can't the scientific community define their base units such that they are related to what they are attempting to measure? I do not understand why they hang onto the meter, which is pretty close to a medieval value, and the second, which is purely an astronomical value.

 

It is possible to define a "standard" set of base units, which will include a mutually defined "time duration," that is based upon the H1 wavelength and mathematical constants, and they will have numeric values that are absolutely precise beyond 100+ significant figures. Our current measurement technology cannot reach anywhere near this precision, but it would provide a reference wherein those that develop instruments to use the "standard" units would know exactly how close they were to their numerical values.

[FrankM]

It is easier to present the concept mentioned in the previous post graphically by showing the relationships in a geometric form.

 

The graphic in TrianglePair-SI.pdf illustrates the relationships when in SI units.

 

http://www.vip.ocsnet.net/~ancient/TrianglePair-SI.pdf

 

The constant of proportionality between the triangle pair is the hypotenuse of one multiplied by the vertical leg of the other. When the results of both sets are equal the triangles are mutual, one is the inverse of the other.

 

With the vertical leg of each being kept constant, thus when the angle is changed, one element of the constant of proportionality becomes a function of the angle. SI units are valid for just the one angle illustrated.

[swansont]

The same reason why SI units use "one meter" or "one second" as the starting point.

 

That doesn't answer the question.

 

I still have a problem with a standard that is based upon how easy and well it can be measured as compared to whether it is relevant to its intended use.

 

The IUPAP CCU group is well aware that many of their "constants" have no relationship to the physical universe that they are trying to "measure".

 

They name three in your earlier link, none of which are the meter or the second. They list the kilogram, the Kelvin and the Ampere.

 

At the moment we have electronic counter technology that goes several digits beyond our defined reference value for the duration of the second, and the CCU group knows that they are approaching a time when the "second" has to be redefined in relationship to another transition frequency that has a higher cyclic rate. Whether they will try to improve the accuracy of the base "duration" remains a question, but that really accomplishes nothing as it has no relationship to anything they are measuring.

 

I don't think we do have counter technology that good; we do phase measurements at the transition frequency. And that you'd go to an optical standard because you can realize it more precisely, i.e. it's easier to do a good measurement. The enabling technology for that is the femtosecond comb, which allows you to tie RF all the way up to optical transitions in a phase-stable manner. It's not because you have direct counters that good.

 

Astronomers have already defined a measurement unit that is more suitable for what they are measuring, the AU, so why can't the scientific community define their base units such that they are related to what they are attempting to measure? I do not understand why they hang onto the meter, which is pretty close to a medieval value, and the second, which is purely an astronomical value.

 

It is possible to define a "standard" set of base units, which will include a mutually defined "time duration," that is based upon the H1 wavelength and mathematical constants, and they will have numeric values that are absolutely precise beyond 100+ significant figures. Our current measurement technology cannot reach anywhere near this precision, but it would provide a reference wherein those that develop instruments to use the "standard" units would know exactly how close they were to their numerical values.

 

Astronomers use AU, light-years and parsecs because they are convenient to the scale of their measurements.

 

The precision of a defined value is infinite - it's a defined value. The trick is how well you can measure it to be able to apply it. If you can't measure it, it isn't very useful. You have to define some values and derive the rest. Currently the second and speed of light are defined, and the meter is derived. Defining the meter would mean deriving the second. You're just buying a different problem without solving anything.

[swansont]

It is easier to present the concept mentioned in the previous post graphically by showing the relationships in a geometric form.

 

The graphic in TrianglePair-SI.pdf illustrates the relationships when in SI units.

 

http://www.vip.ocsnet.net/~ancient/TrianglePair-SI.pdf

 

The constant of proportionality between the triangle pair is the hypotenuse of one multiplied by the vertical leg of the other. When the results of both sets are equal the triangles are mutual, one is the inverse of the other.

 

With the vertical leg of each being kept constant, thus when the angle is changed, one element of the constant of proportionality becomes a function of the angle. SI units are valid for just the one angle illustrated.

 

I have no idea what you are doing with this. 21 cm and 1420 MHz are going to be related because their product is the speed of light. What are the other numbers?

[swansont]

From what I could find, the best measurement of the 21 cm line is a few parts in 10^13. The realization of the second is done to one or two parts in 10^15.

[FrankM]

Inadvertent post.

[FrankM]

I have no idea what you are doing with this. 21 cm and 1420 MHz are going to be related because their product is the speed of light. What are the other numbers?

I think it is a matter of perspective, physicists do not think of EM waves in terms of angular notation and some in other disciplines do. My shortest response to the concept was from a professor of electrical engineering, who responded with one word, "interesting!"

 

The triangle pair is representing the relationship between wavelength and frequency in an angular form, which I think makes it easy to visualize. I know this is not taught but the concept is not new. It also allows the relationships to be expressed using a trigonometric function, the cosecant function, when the vertical leg is held as a constant.

 

When the vertical legs are held as a constant, changing the angle of both equally results in a different value for the hypotenuse of both triangles. The constant of proportionality is calculated the same way, but it will not add up to a value for the "speed of light" that we are familiar with. The mathematical relationships are perfectly valid, one of the parameters of the constant of proportionality has changed with the angle, the duration of the unit of time. If you wanted to have a different "time base" for calculating the speed of light this provides a seamless transition.

 

When rotated to 45 degrees you now have a numeric value for the speed of light that can be calculated to nearly unlimited precision if you do not use centimeters. Just as a meter is a physical length that is given a value of "one" as a base unit of measure, the length of the wavelength of the H1 emission can be given a value of "one" as a scientific base unit of measure. The end result is a set of base units that are mathematically derived using a natural physical length and a natural mathematical constant expressed as an angular frequency value.

 

The Backwards.pdf article illustrates the progression from the 26.2540 degree to 45 degree angle. As I stated, it is backwards from the way it should be developed, but I have found contemporary scientists understand the process easier if I start with SI units.

 

http://vip.ocsnet.net/~ancient/Backwards.pdf