Introduction to Astro-Atomic Unitless

Transcription

1 Introduction to Astro-Atomic Unitless CLAUDE ZIAD BAYEH 1, 2 1 Faculty of Engineering II, Lebanese University 2 EGRDI transaction on Physics (2004) LEBANON claude_bayeh_cbegrdi@hotmail.com NIKOS E.MASTORAKIS WSEAS (Research and Development Department) Agiou Ioannou Theologou , Zografou, Athens,GREECE mastor@wseas.org Abstract: - The Astro-Atomic Unitless is a numerical constant (or scalar) without unit; it is equal to the speed of the light ( in m/s) in a vacuum and it is dimensionless. It is used to eliminate and to avoid many prefixes units as in the SI units, non SI units and in many others units of measurement, it can be used also with numerical constants, vectors and matrices. It has many exponents values that gave a wide range of unitless that can describe elements with extremely small dimensions such as particles and extremely large dimensions such as universe. It can be considered as an accompaniment of a unit and it can be written behind or above the unit by using some bars and points in a way to give each value a specific symbol. Key-words:- non-si units, metric system, unitless, SI units, SI prefixes, Astronomy, Atomic, Dimension. 1 Introduction The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units. The SI was established in 1960, based on the metrekilogram-second system, rather than the centimetregram-second system, which, in turn, had a few variants. The SI is declared as an evolving system, thus prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses, and as the precision of measurements improve. SI is the world's most widely used system of measurement, which is used both in everyday commerce and in science [1-4]. The basic seven units of measurement are: meter m, Kilogram Kg, Second s, Ampere A, Kelvin K, Candela Cd and Mole mol. Derived units are formed from multiplication and division of the seven base units and other derived units and are unlimited in number; for example, the SI derived unit of speed is meter per second, m/s. Some derived units have special names; for example, the unit of resistance, the ohm, symbol Ω, is uniquely defined by the relation Ω = m 2 kg s 3 A 2, which follows from the definition of the quantity electrical resistance [5-8]. In this paper, The Astro-Atomic unitless is an original study introduced by the author, it is also introduced into the scientific domain to replace many prefixes units and to facilitate the manipulation of units whatever are SI or non SI units, constant values, exponents, and many others. The basic value is equal to the speed of the light in a vacuum ( cc = ββ = ) and it is unitless and dimensionless. By using exponent numbers like cc ii (with ii Z and ii [ 6,6] {0}) one can obtain an important range of the unitless that can describe elements with extremely small dimensions (e.g. photon, gluon, quarks, very small particles ) or extremely large dimensions (e.g. universe, black hole, very intensive energy ). In the other hand, many expressions can be simplified and constant values to be simpler to memorize, to use or to manipulate. The importance of this unitless is that one can obtain the desired goal by using only some points or some bars above a specific unit (e.g. MMMMMMMM oooooooooooo = kkkk = 1.23 kkkk ; SSSSSSSSSS llllllhtt = mm/ss = 1 (mmmm/ss) = 1 (mm /ss); etc ). ISBN:

2 2 Why the Astro-Atomic unitless is introduced? Many units were introduced in the past with their prefixes, including metric systems, non metric systems, SI prefixes, Non-SI prefixes and many others systems. All these units are limited in the use and in conversion for example the unit Inch can t be used to measure the distance between countries other units are used for example Km (Kilometer). The unit g (gram) can t be used to measure the weight of the earth or planets, other units can be used with prefixes as Kg (kilogram). The unit Yard can t be used to measure the distance between galaxies and so on. One can conclude that each unit is used to a specific object, there is no a single unit that can be used to measure all sizes and dimensions. For this reason and many others, the author introduced a new system that can solve the gap of units and its limitation, e.g. the units mentioned in the above examples can be used for a general purpose by introducing the Astro-Atomic unitless (ββ) in the corresponding unit. E.g. the Yard unit after introducing the Astro-Atomic unitless ββ can be used to measure the dimension of a photon and at the same time it can used to measure the distance between two galaxies. The same concept is used for other units. It is developed in the following Sections. In the following figures (Figure 1) and (Figure 2), a simple example appears in order to give an idea about the importance of the Astro-Atomic unitless ββ used with other existing units in order to generate a wide range of dimensions for one unit. Fig. 1: distance between the Sun and the star TET 1 ORI A written respectively in Astro-Atomic Unitless (Kmβ or Km ), Light years and in Kilometers. Figure 2: distance between Galaxies M 31 and M 33 written respectively in Astro-Atomic Unitless (Kmβ or Km ), and Kilo-parsec. In the previous figures 1 and 2, the main units used are LY (light year) and kpc (KiloPerSec) which are specific units to measure the distance between stars and galaxies respectively. But we can use the Km unit to measure them by introducing the Astro-Atomic Unitless. So, as we see that the Astro-Atomic unit less is an accompaniment of the used unit Km in order to measure extremely large distance such as galaxies and extremely small distance such as atoms and particles with a simple method. This is not the case of any other unit till now. 3 The concept of Astro-Atomic unitless The speed of the light in vacuum is given as cc = mm/ss and this speed is constant for all references (till now) according to Einstein s second postulate [8]. So the idea of the Astro-Atomic unitless is to put all values, expressions and constants in relation with the speed of the light in vacuum for many reasons, and of course it has many advantages. 3.1 Definition of the Astro-Atomic unitless The author define the symbol ββ as Astro-Atomic unitless; it is equal to the constant cc (Speed of Light) and it has many exponents values (cc ii with ISBN:

3 Recent Advances in Systems Science and Mathematical Modelling ii Z and ii [ 6,6] {0}) that gives a wide range of numerical constants. It can be considered as an accompaniment of any unit and any scalar. One can write it in two forms using ββ in the right side of a unit (e.g. uuuuuuuuββ ) or by putting a bar or points on the unit (e.g. uuuuuuuu ). Whatever the form of the Astro- Atomic unitless is, the result must be the same. 3.2 Definition of ββ with different values The general symbol of the Astro-Atomic unitless is given as xx ββii with xx a symbol that has many forms and shapes. It can take the following shapes above ββ ( ββ; ββ ; ββ ; ββ ; ββ aaaaaa ββ ), and ii is a numerical value defined as ii = ±1. One take ii = 1 to describe an extremely big element or dimension and ii = 1 to describe an extremely small element or dimension. So the different values can be written as the following forms: 1 ββ = cc uuuuuuuuuuuuuuuu 1 ββ 1 = cc uuuuuuuuuuuuuuuu 1 ββ = cc uuuuuuuuuuuuuuuu 1 ββ 1 = cc uuuuuuuuuuuuuuuu 1 ββ = cc uuuuuuuuuuuuuuuu 1 ββ 1 = cc uuuuuuuuuuuuuuuu 1 ββ = cc uuuuuuuuuuuuuuuu 1 ββ 1 = cc uuuuuuuuuuuuuuuu 1 ββ = cc uuuuuuuuuuuuuuuu 1 ββ 1 = cc uuuuuuuuuuuuuuuu 1 ββ = cc uuuuuuuuuuuuuuuu 1 ββ 1 = cc uuuuuuuuuuuuuuuu 3.3 Two forms of the Astro-Atomic unitless can be used We can write the Astro-Atomic unitless in two forms whether using xx ββii in the right side of a unit (e.g. uuuuuuuuββ ) or by using the unit with the following form yy with yy a symbol that has many forms and uuuuuuuu shapes in coherence with xx ββii. It can take the following forms above the unit: 1 uuuuuuuuββ 1 uuuuuuuu = 1 cc uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 1 uuuuuuuu = 1 cc 1 uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 uuuuuuuu = 1 cc 2 uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 1 uuuuuuuu = 1 cc 2 uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 uuuuuuuu = 1 cc 3 uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 1 uuuuuuuu = 1 cc 3 uuuuuutt uuuuuuuu 1 uuuuuuuuββ 1 uuuuuuuu = 1 cc 4 uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 1 uuuuuuuu = 1 cc 4 uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 uuuuuuuu = 1 cc 5 uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 1uuuuuuuu = 1 cc 5 uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 uuuuuuuu = 1 cc 6 uuuuuuuu uuuuuuuu 1 uuuuuuuuββ 1 1 uuuuuuuu = 1 cc 6 uuuuuuuu uuuuuuuu Astro-Atomic unitless can be used with numerical constants e.g.: 1 ββ 1 = 1 cc ββ 1 1 = 1 cc ISBN:

4 Recent Advances in Systems Science and Mathematical Modelling 1 ββ 1 = 1 cc ββ 1 1 = 1 cc ββ 1 = 1 cc ββ 1 1 = 1 cc ββ 1 = 1 cc ββ 1 1 = 1 cc ββ 1 = 1 cc ββ 1 1 = 1 cc ββ 1 = 1 cc ββ 1 1 = 1 cc Examples using the Astro-Atomic unitless with units: Kilometer unit 1 KKKKKK = 1 KKKK KKKK 1 KKKKββ 1 = 1 KKKK KKKK Joule unit 1 JJββ = 1 JJ JJ ; 1 JJββ 1 = 1 JJ JJ Kilogram unit 1 KKKKββ = 1 KKKK KKKK ; 1 KKKKββ 1 = 1 KKKK KKKK Second unit 1 ssββ = 1 ss ss ; 1 ssββ 1 = 1 ss ss Speed of light: CC 0 = mm ss 1(mm/ss ) = 1 mmmm = 1 (mm /ss) = ss Mass of the Sun: MM ssssss = KKKK = gg ggββ = gg Mass of the earth: MM eeeeeeee h = KKKK KKKKββ = KKKK = gg Crab Nebula located about 6500 light years from the earth: DD = 6500 llll KKKK KKKKββ = KKKK Mass of the proton in rest: MM pppppppppppp = KKKK KKKKββ 1 = KKKK Mass of the electron in rest: MM electon = KKKK mmmmββ 1 = mmmm The age of the universe 15 billiards years aaaaaa = ss ssββ = ss The Plank Constant h: h = JJ. ss JJ. ssββ 1 = JJ. ss Electro Volt 1 eeeeββ = 1 eeee eeee ; 1 eeeeββ 1 = 1eeee eeee The Energy according to Einstein: EE = mmcc 2 ; KKKK. mm ss 2 EE = mm; ss)2ββ EE=mm; KKgg.(mm/ss)2 KKKK. (mm/ And so on 4 Practical examples In this section, some practical examples are introduced in order to give an idea about how to use the Astro-Atomic unitless 5 SI prefixes and their equivalent in the Astro-Atomic Unitless ISBN:

5 Power of ten Prefix Abbreviation Equivalent in Astro-Atomic Unitless yocto- y ββ zepto- z KKββ 1 (kilo- ββ 1 ) atto- a mmββ 1 (milli- ββ 1 ) femto- f ββ pico- p KKββ nano- n mmββ micro- u ββ Mega- M mmmm 10 9 Giga- G ββ Tetra- T KKKK Peta- P mmββ Exa- E ββ Zetta- Z KKββ Yotta- Y mmββ Table 1: presents the equivalence between the Prefixes of SI and Astro-Atomic Unitless One can use prefixes as: K (Kilo-) and m (milli-) with the Astro-Atomic Unitless and forget the others prefixes if they can t give any meaning to a value or an expression. In the same way, one can make equivalence between all types of units and numerical constants with the Astro-Atomic Unitless to simplify expressions and to eliminate the unused units. expressions (e.g.: billions of years, billiards of tones, millions of light years ). -It is used to eliminate the exponent part of a value or a constant (e.g: kkkk kkkk ). -It is simple to do the conversion from the Astro- Atomic Unitless to another type of units and vice versa. -It relates all measure to the speed of light which is very important especially in the relativity. 6 Advantages of the Astro-Atomic Unitless The Astro-Atomic Unitless has many advantages: -It can be used with all units systems including SI units and Non-SI units. -It can replace numerical constants (or scalars) that have very large or very small values (e.g.: 10 34, 10 33, ) -It can represent an extremely big element (e.g. universe, galaxies ) or an extremely small element (e.g. gluon, quarks, photon, anti-particle ). -It can be considered as an accompaniment of a unit and it can be written behind or above the unit. -It is used to eliminate and replace many prefixes for powers of ten (10) from a result or from an equation (refer to section 4). -It is used to avoid writing many alphabetical expressions or words describing a value or numerical 7 Conclusion Usually, the scientists and engineers create many units systems to describe elements in the nature and they introduce a big number of prefixes and metric systems in a way to reduce as possible the complexity of expressions and values, but in the other hand, they create a complexity by using these prefixes and metric systems. For example: to measure the distance between two points one usually uses the following units: (light year, parsec, Hubble, astronomical unit, light second, nautical mile, mile, furlong, yard, foot, inch, mil, kilometer, twip, Plank length, Bohr radius, Angstrom, Fermi ), as seeing this huge number of units can be complicated to use and it is difficult to convert from a unit to another without having a software converter. These disadvantages give the Astro-Atomic Unitless a huge advantages ahead other unitless, dimensionless and ISBN:

6 units of measurement. By using the Astro-Atomic Unitless, one can choose one metric system or unit (e.g. km) and eliminate the other units that became useless. The same thing is applied to any metric system or any unit of measurement. This Astro- Atomic Unitless isn t introduced to disrespect scientists and inventors or anybody who gave a value to the science, but the main goal of this unitless is to facilitate the measurement without using many complex systems). References: [1] International Bureau of Weights and Measures, The International System of Units (SI) (8th ed.), ISBN , (2006). [2] Ian Mills (29 September 2010). Draft Chapter 2 for SI Brochure, following redefinitions of the base units". CCU, Retrieved 1 (January 2011). [3] Barry N. Taylor & Ambler Thompson Ed., The International System of Units (SI), Gaithersburg, MD: National Institute of Standards and Technology, Retrieved 18 (June 2008), pp. 23. [4] Ambler Thompson and Barry N. Taylor, Guide for the Use of the International System of Units (SI), (Special publication 811), Gaithersburg, MD: National Institute of Standards and Technology, (2008), p. 3. [5] The International System of Units (SI) (8 ed.). International Bureau of Weights and Measures (BIPM), (2006), pp [6] Thompson, A.; Taylor, B. N. (July 2008). "NIST Guide to SI Units Rules and Style Conventions". National Institute of Standards and Technology, Retrieved 29 December [7] University physics with modern physics, tenth edition, 2000, H.D. young & R.A. Freedman, Addison-Wesley publishing company, ISBN x. [8] ALBERT EINSTEIN la theorie de la relativite restreinte et generale, traduit par Maurice Solovine, Gauthier-villars, BORDAS, paris, 1976, ISBN ISBN: