Mathematically Perfect Triangle

[FrankM]

The small pdf attachment identifies the parameters that define a mathematically perfect triangle. The key to the geometric-mathematical relationship is the use of the wavelength of the precession emission of neutral hydrogen, commonly referred to as the 21 cm value, as the reference. The International System of Units (SI) does not list this value as a "constant" under any category.

 

The angle derived using the SI value for the speed of light is actually a special case, the 45 degree angle being the general case.

 

What branch of physics or mathematics would be interested in the relationship?

 

8/14/03-The MathPerfect04.pdf is a condensed version of what I have been privately distributing to selected individuals. The Universal.pdf attachment covers the characteristics of the triangle in more detail, but I do not use the x100 value for the "21cm" constant. The results are still numerically symmetrical, but differing by x100.

 

http://www.vip.ocsnet.net/~ancient/MathPerfect04.pdf

 

A complete presentation of the characteristics of the mathematically perfect triangle are contained in:

 

http://www.vip.ocsnet.net/~ancient/Universal.pdf

[FrankM]

What I was hoping to do when posting the "Mathematically Perfect Triangle" was to elicit aid in defining the underlying mathematical relationships of the geometric structure that produced the symmetry. The process to produce the symmetry requires one element of the right triangle be "constrained" and I choose the vertical leg for the constrained element in my example, and it will always be equal to one.

 

The use of the linear and angular notation associated with transverse waveforms is "unconventional" but it results in geometric/mathematical relationships that have unusual scope. You can translate (rotate) the angle to 45 degrees and still get symmetry, but you have recognize what is and is not a variable, which is discussed in the Universal.pdf article.

 

I suggest that the process that produced the symmetry is another variant of the geometric/trigonometric forms, which are plane, spherical and hyperbolic geometry, and their associated plane, spherical and hyperbolic trigonometry.

[WebFeet]

There is a theory, the Hooper-Luck Triangle which is an abstract tool using the relationships of energy to determine complex scenarios.

The theory has been developed into an free application which can be downloaded from

http://www.gamert.co.uk

 

Thought you might be interested.

[FrankM]

The Hooper-Luck Triangle (HLT) concept is interesting. The HLT concept is quite a bit more complex than what I found but they share a common factor, one leg of the triangle has to be a constant. I use the term "constrained parameter" for the constant, (see Universal.pdf) and this for a reason. In my application example I use the value of the 21cm line of hydrogen as a "constant", but I find that this value is not listed as a constant on the NIST web site or any other place.

 

I haven't downloaded the application but I intend to. I noted the application uses a "time angle" and I will have to examine what that means. In Universal.pdf, it illustrates that the base value time unit can be a duration other than the earth second. Also, the HLT mentions that the speed of light can be equated to the value of 1, which also is discussed in the Universal.pdf article section titled "Unit of Length, Time and Speed of Light Redefined".

 

I have been distributing the Universal.pdf article to members of the scientific/academic community for several years, and the replies of those that responded range from bizarrre to a one word response (from a Professor of Electrical Engineering), "interesting".

 

From the "gamert" site, Steve Hooper stated, "We have encountered some sceptics, but even they had to admit that the basic principles behind the HLT and the software were 'interesting'."

 

Even more interesting is where I identified the triangle relationships, but that is an issue for another type of forum.

 

FrankM

[Roberto]

Frank, I've read your Universal.pdf document and I thought it interesting too, but I will justify it and I think you will not be very satisfied with the answer.

 

But first, let me say that the critics I will make are only to help you for I see you have a talent and with experience you will do much more interesting things.

 

The reason why the scientific community didn't seem very excited with your manuscript is because systems of unities in physics are really arbitrary. The SI system is just based on useful unities: the meter, the kilogramm, the second, are unities used for a long time and, today, they are indeed defined with reference to more fundamental processes in nature. The meter today is defined with reference to the speed of light and the second with respect to a wavelength related to a transition energy in the cesium atom.

 

But physicists at work do not pay to much attention to units, because they are just conventions. In Quantum Field Theory they do not use the SI system, they use a system named Natural Unities where the speed of light and the Planck constant are set to 1 and every other variable comes in unitites of energy. It has nothing fundamental, it is just convenient to work with that unities, as is convenient to a man in his house to measure the milk in liters or the flour in kilograms.

 

The ultimate goal of physics is to have a theory with only one adjustable parameter: the system of unities. Your work is interesting but has nothing very new or that may be very useful. I'm not trying to be agressive and I hope you take these critics as a kind of help.

[FrankM]

Roberto,

 

I am aware that particle physicists like to work with unity values, as I accessed the following site many years ago when I was examining the concepts of a unity metrology system.

 

http://superstringtheory.com/unitsa.html

 

I also am aware that if you would ever want to translate values from one metrology system to another there must be identifiable relationships. We have no trouble in translating values between what you describe as "useful unities", SI to English, etc. In the unitsa.html page the definition of c=1 was defined. The definition was "extracted" using the second and the meter, neither of which have a "natural relationship" with anything else in the universe, just "useful" defined relationships.

 

The concepts presented in the Universal.pdf article allow one to define a pure mathematical relationship between the speed of light, a unit of time and a unit of distance and you do not have to use the meter or the second. The concept also allows one to translate the value from a unity system to one of convenience, i.e., SI units, which uses the strange circular definition for a second.

 

If particle physicists wish to work with a unity system structured around earth centric values so be it, but I think it defeats their ultimate objective in finding "natural" relationships between truly universal physical values.

[Roberto]

There must be a little mistake when you say that the definition of the speed of light is extracted from the definitions of meter and second. In fact, nowadays, the definition of the second, as I told you in my last post, makes reference to the frequency of the light emitted by the cesium atom in some specified transition, there is not circular about that because you can just detecty the photon emittef in the process and use its frequency to define the second.

 

After that, the meter is defined by means of the distance that light can travel in certain fraction of second. Not a circular definition again. Both definitions are made with reference to basic processes in nature.

 

Physicists do not prefer any system of units, they simply use the one that is more convenient in each case, since hte reference system is not something fundamental. The importance of a unit system comes from padronization of language and measurements and is much more important in engineering and experimental physics, for example, than in theoretical physics.

 

If you propose a new system of units you only need to show applications where it is more convenient than the others at use. COncerning the definition of units, I think people is happy with those they have because they make reference to basic measurable processes.

 

That´s only my opinion.

[FrankM]

One of the original writeups on the right triangle geometric-mathematical relationships was to identify a unity metrology system where the speed of light could be defined independently from the earth centric meter and second. The main weakness was that it didn't directly link between that concept and how it can be directly related to the metrology system of SI units. The unity concept is embodied in the elements which describe the values within Figure 6 of the Universal.pdf article.

 

Universal.pdf now starts out using the SI metrology system and then illustrates how it can transition to a unity type metrology system. It is shown how a unit of time can be mathematically defined in relationship with a mathematically defined speed of light. It is shown how the mathematically defined time unit can be related to any other unit of time, including the SI definition of the second.

 

On the issue of the "second"-

 

I personally knew an engineer that was working on the atomic clock for the Global Positioning System, and this before the first satellite was launched. I knew how they had to "fudge" the time duration trying to get close to the value for the earth second. I also know that the current SI definition of the second was "fudged" to get it close a duration of 1/86,400th of an earth's rotation. I do not believe the current SI second is a "fundamental" physical value, it is simply "a very precise definition of the unit of time". I would rephrase the previous quotation (taken from the following URL) to replace 'the unit of time', to 'a unit of time'.

 

http://physics.nist.gov/cuu/Units/second.html

 

Whether the current SI definition of a second is a fundamental physical unit could be a separate topic for this forum

 

The final quote in Universal.pdf is relevant, as it appears Maxwell was responding to the battle between the metric system and the English system going on at that time.

 

“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.” James Clerk Maxwell, 1873

[Roberto]

These are the definitions of the meter and second in the SI system. The source is the site of the International Bureau of Weights and Measurements at

 

http://www1.bipm.org/en/si/base_units/

 

"The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second."

 

"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."

[FrankM]

The original measured frequency of the cesium transition energy was 9,192,631,830 ± 10 Hz (cps), based upon the duration of the second maintained at Greenwich. When it was decided to use the duration of the second based upon Ephemeris Time, the technicians had to adjust the frequency counter time base (which had been based upon the Greenwich second) to that of the Ephemeris second. The Ephemeris second is slightly shorter than the Greenwich second, thus the frequency counter would count fewer cycles, and this came out to 9,192,631,770 ± 20 Hz. The energy level of the cesium transition did not change, just the way it was counted. See page 6 of the following report:

 

http://www.cl.cam.ac.uk/~mgk25/time/metrologia-leapsecond.pdf

 

All this means is that physical scientists in different locations can compare frequency values with others, it is a "convenient" reference. The report implies that technology will improve upon the precision and at some time a decision eventually will be made to correct the "error", and the world will then have a new value for the duration of the second, as well as all the other values that are dependent upon that definition.

[FrankM]

In the MathPerfect.pdf article, it mentioned that symmetry could be obtained at different angles. MathPerfect04.pdf adds a graphic that illustrates the time angle and a resulting calculation using a 45 degree time angle.

[FrankM]

I had added a figure to the original MathPerfect.pdf article, (MathPerfect04.pdf), to illustrate how the value of the "time duration" (when it is something other than the second) can be represented as a "time angle". When the angle is 25.2640 degrees the time angle value represents how we use the current definition of a second, and the 45 degree angle when the time duration is 0.6255... less than a second. Actually, it is more logical to use the 45 degree time angle as a mathematically defined unit of time, which means the earth second is 1.598... times longer than that reference.

 

There seems little interest in using a mathematically defined "unit of time", even though it would allow a direct mathematical link to other physical constants (Universal.pdf) and could provide a method of developing a "quantum metrology" system of units.

 

The current definition for the "SI" second is basically provincial and has nothing to do with the rest of the universe.

[FrankM]

Originally posted by: Roberto

These are the definitions of the meter and second in the SI system. The source is the site of the International Bureau of Weights and Measurements at

http://www1.bipm.org/en/si/base_units/

 

"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."

 

The only reason they chose the 9,192,631,770 periods is because that just happened to get very close to the theoretically

perfect earth second. If they really wanted to define an ideal "time unit" they should have selected a perfect

integer, 10,000,000,000 periods, but that value would be no more representative of anything "universal" than the

earth second.

 

To keep the original references handy, I have added them here so they can be easily referenced.

 

http://www.vip.ocsnet.net/~ancient/MathPerfect04.pdf

 

http://www.vip.ocsnet.net/~ancient/Universal.pdf