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J. Modern Physics, 2010, 1, 147-149 doi:10.4236/jmp.2010.12021 Published Online June 2010 (http://www.SciRP.org/journal/jmp) Copyright © 2010 SciRes. JMP Empirical Relations about the Number of Dimensions in Theoretical Physics with the Concept of Common and Unshared Dimensions Tomofumi Miyashita Miyashita Clinic Mitsuya-Kita, Osaka, Japan Email: tom_miya@plala.or.jp Received April 21st, 2010; revised May 16th, accepted May 21st, 2010. Abstract How many dimensions are there in the universe? Currently, there is confusion about the number of dimensions in the universe. Empirical rela tions about the numb er of dimensions in th eoretical physics with the con cept of common sp ace- time 4 dimensions and unshared dimensions are described in this report. Keywords: Kaluza-Klein, Superstring, Super gravity, N a m b u St ri n g, Unshared Dimensions 1. Introduction Einstein discovered space-time 4 dimensions. In order to complete the theory of everything (TOE), the numbers of dimensions have been increased. Currently, there is con- fusion about the number of dimensions in the universe. There is a simple question, “How many dimensions are there in the universe?” The concept of “unshared dimensions” is very suitable solution. Unshared dimensions belong to each particle and the numbers of unshared dimensions are different between the diffe rent ki n ds o f part i cl es. This paper presents empirical relations about the number of dimensions in theoretical physics with the concept of common space-time 4 dimensions and un- shared dimensions. 2. Empirical Relations about the Number of Dimensions in Theoretical Physics 2.1 The Concept of Unshared Dimension There are two kinds of dimensions. One is common space- time 4 dimensions and the other is unshared dimensions which belong to each particle. The common space-time 4 dimensions are entirely same dimensions which Einstein discovered. Unshared dimensions are something internal dimen- sions in each particle. The concept of unshared dimen- sions is discovered empirically. So, the mathematical explanation of “unshared dimensions” is the next stage argument. It is important that even the space has one unshared dimension. So, the definition of the space is different from the common space-time 4 dimensions. 2.2 Empirical Relations about the Number of Dimensions in Theoretical Physics The number of unshared dimensions can be expressed empirically as: Unshared dimension = 4 × (4 – N + 1)/N (1) N is the number related with the symmetry. Calculated unshared dimensions are shown in Table 1. Empirical relations about the number of dimensions in theoretical physics are shown in Table 2. When N = 3, then unshared dimensions are 8/3. In this case, explaining for quarks is difficult. 8 and 1/3 is re- lated with a quark, because the number of gluon is 8 and a quark must exist with three particles. Simple evidences supported unshared dimensions can be shown in the next section. 3. The Evidence of Unshared Dimensions 3.1 Empirical Relations between the Masses of Leptons If leptons have 6 unshared dimensions, the mass of lep- tons are expected like this. 76 7x k dxxkM (2) Here, M, k and x are the mass of lepton, constant co- efficient and the value of unshared dimensions. Empirical Relations about the Number of Dimensions in Theoretical Physics with the Concept of Common and Unshared Dimensions Copyright © 2010 SciRes. JMP 148 7 1 m M y (3) Here, m and y are the mass of electron and the seventh power root of ratio with electron. The calculation results are shown in Table 3.The square of correlation coeffi- cient between the generation and the seventh power root of mass ratio is 0.9996 shown in Figure 1. It is impossi- ble that this result is only coincidence. The expected mass of the forth lepton and the fifth lep ton are 14.3 GeV and 70.5 GeV respectively. The peak of 14.3 eV was reported [1] and th ere remains the possibility of the forth lepton. The expected leptons which have larger generation number should be very unstable, since they cannot be discovered still yet. But there are many experimental reports about the reactions around the expected energy. The reports published in the internet are much more than those around the unexpected energy. 3.2 The Mass of Weak Boson Weak boson is related with electrons and neutrino. Then, the number of unshared dimension is 26 (= 10 + 20 – 4). The 27th power root of ratio between Weak boson and electron are shown in Table 4. The result is near the generation number 2. If the generation number is 3, the mass of Weak boson is 4 × 106 TeV and it is impossible to observe. Figure 1. Empirical Relation about the mass of lepton Table 1. Calculated unshared dimensions N 4 3 2 1 (0) particle The space quark lepton neutrino consciousness Unshared dim ension 1 8/3 6 16 infinite Table 2. Empirical relations about the number of dimensions in theoretical physics Theory common The space quark lepton neutrino total Kaluza-Klein 4 1 - - - 5 Superstring (~1980s) 4 - - 6 - 10 Super gravity 4 1 - 6 - 11 Nambu string 4 - - 6 16 26 Superstring (~2000s ) 4 1 - 6 16 27 Table 3. The seventh power root Generation mass (MeV) Mass ratio The seventh power root of mass ratio electron 1 0.51099906 1 1 Muon 2 105.6 206.6540005 2.141653053 Tauon 3 1776.99 3477.481935 3.20549411 4th 4 14371.76031 28124.82729 4.321 5th 5 70548.8140 138060.5555 5.424 6th 6 257713 504331 6.526 7th 7 768658 1504226 7.629 8th 8 1977637 3870138 8.732 Empirical Relations about the Number of Dimensions in Theoretical Physics with the Concept of Common and Unshared Dimensions Copyright © 2010 SciRes. JMP 149 Table 4. The 27th power root Generation mass (MeV) Mass ratio The 27th power root of mass ratio electron 1 0.51099906 1 1 W-boson 2 80398 157334.9274 2.021601712 Z-boson 2 91187.6 178449.6433 2.036632582 4. Summary The concept of common space-time 4 dimensions and unshared dimensions are discovered empirically. Simple evidences supported unshared dimensions can be shown from the mass of particles. It is very useful concept to answer for the question, “How many dimensions are there in the universe?” REFERENCES [1] C. Friberg, E. Norrbin, T. Sjöstrand, “QCD Aspects of Leptoquark Production at HERA,” Physics Letter B, Vol. 403, No. 3-4, June 1997, pp. 329-334. |