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The Constant Linear Force (CLF) model

 

 

 

My aim is to show that data found by particle experiments can be interpreted in way that unites the basic quantities (Energy, Force, Mass, Charge, Radius and wavelength) of elementary particles in a single equation and that all elementary charged particles are compaction states of a single elementary particle.

 

Since 1918 various cosmologists1 have suggested that there is a relationship between mass and radius such that Ru and Mu equals 1. In an expanding universe we would expect particles to change in unison with universal expansion leading to the question, is there a relationship between mass and radii of particles? If the answer is yes then there should be an arbitrary constant or a constant value, to which all the other values relate. It is proposed that linear force is constant for all elementary particles giving the formula:

 

 

Fl = 2rm..…………………………………. (1) 

 

As Relativity and CLF are both classical theories there should be a link between them. Mass is common to both Einstein’s formula and the Constant Linear Force (CLF) formula, giving:

 

Ec2 = m = Fl/2r………………………….. (2)

 

E = energy

c = speed of light

m = mass

Fl = linear force

r = radius

 

The choice of 2r (where r would also produce a constant) is to allow for the inclusion of wavelength. We intend to show that 2r = λ allowing the substitution:

 

Ec2 = m = Fl/λ………………………….. (3)

 

Linear force is found using the classical electron radius, electron mass and equation (1). Given that linear force is a constant, it can be used together with mass numbers2 and equation (1); to find the radii of other particles as shown in table 1.

 

Table 2 shows that providing all particles have a charge value of 1, the formula for the classical radius produces the same radii values as that shown in table 1 indicating that the arbitrary allocation of fractional charge to quarks is incorrect.

 

It is proposed that although particles can change their form, the number of particles in infinity, remains constant. The two remaining particles with radii that can be found by experiment justify this claim.

 

Table 3 uses the sum of the linear force of the particles to calculate the radii of proton and neutron and compare the result with the radii found by experiment3; columns A and D give the best match. Indicating that, in particle interactions, it is the number of particles that is conserved.

 

Fractional waves are found in Fractional Quantum Hall Experiments4. It is proposed that particles are compacted by the fractional wave pattern; it follows that particle diameters should be determined by the fractional wave sequence 1, 1/2, 1/3, 1/4,  1/5 etc. Table 4 compares the mass calculated using wavelength, linear force constant and equation 1, with the mass values found by experiment as listed in the Particle Data Group lists for 2004. Fig. 1 shows table 4 in graph form and includes those wave fractions for which no experimental particle is listed in the 2004 PDG list.

 

 

 

 

Linear force

 

 

radius

force

force

 

 1

1

4.5

 

 2

2

9

 

 3

3

13.5

 

 4

4

18

 

 5

5

11.52

 

 6

6

8

 

 7

7

5.877551

 

 8

8

4.5

 

 9

9

3.555556

 

 10

7.29

2.88

 

 11

6.024793

2.380165

 

 12

5.0625

2

 

 13

4.313609

1.704142

 

 14

3.719388

1.469388

 

 15

3.24

1.113198

 

 16

2.847656

 

 

 17

2.522491

 

 

 18

2.25

 

 

 19

2.019391

 

 

 20

1.8225

 

 

 21

1.653061

 

 

 22

1.506198

 

 

 23

0.728412

 

TOTALS

 

 

field (linear force)

90

90

nucleus or shell

45

45

 

 

 

 

 

Fig.1

The table and graph shows how the same total linear force is distributed in two different vacuum fields.

Force is distributed in equal quantities either side of the point of maximum force.

 

 

 

Table 1

(PDG data in bold type)

 

 

 

 

CLF model

 

Force (F)

Mass2(m)

 

radius

particle

constant

MeV

 

 x 10-15 m

 

(F=rm)

(m=F/r)

(r = Fl/m)

r

(a)

(b)

('c)

(d)

(e)

e

2.8799296

0.51099892

5.6358822

2.82E+00

΅

2.8799296

105.658369

0.02725699

1.36E-02

τ

2.8799296

1776.99

0.00162068

8.10E-04

 

 

 

 

 

u

2.8799296

2.75

1.04724713

5.24E-01

d

2.8799296

6

0.47998827

2.40E-01

s

2.8799296

105

0.0274279

1.37E-02

c

2.8799296

1250

0.00230394

1.15E-03

b

2.8799296

4250

0.00067763

3.39E-04

t

2.8799296

174300

0.000016523

8.26E-06

 

 

 

 

Table 2

(current data in bold type)

 

 

 

 

 

 

 

 

classical

 

 

 

 

 

 

 

 

r

particle

e

(e2)

εo

me

c2

(cdef)

b/g=ro (cm)

 

a

b

c

d

e

f

g

h

e

       

0.51099892

 

5.11E+06

2.817900E-13

΅

       

105.658369

 

1.06E+09

1.362830E-15

τ

       

1776.99

 

1.78E+10

8.103275E-17

 

0.0012

1.44E-06

12.56637061

8.85E-12

 

8.99E+16

 

 

u

       

2.75

 

2.75E+07

5.236159E-14

d

       

6

 

6.00E+07

2.399906E-14

s

       

105

 

1.05E+09

1.371375E-15

c

       

1250

 

1.25E+10

1.151955E-16

b

       

4250

 

4.25E+10

3.388103E-17

t

       

174300

 

1.74E+12

8.261296E-19

Given that all particles have the same charge as the electron, then the formula for finding the Classical electronic radius

produces the same value for radii (col h) as that given in col d of table 1.

 

 

 

 

 

      

       

 

Table 3

(data from experiments in bold type)

 

Proton

Possible Neutron structures

 

 (SM and CLF)

(SM)

 

(CLF)

 

A

B

C

D

sub-particles (a)

uud

ddu

dduep

uudep

mass   (b)

11.5

14.75

15.772

12.522

r = Fl/m (c)

0.375643

0.292874

0.456494

0.574974

2r  (d)

0.751286

0.585748

0.912988

1.149948

r (fermi)  (e)

0.805

1.1

1.1

1.1

 

 

 

 

 

(e) - (d)     (f) 

+0.053714

+0.514252

+0.187012

-0.049948

 

 

 

Table 4

Fl = 2.87992961524744

 

 

 

theoretical

mass

 

 

 

 

 

 

fraction of

λ

mass

found by

 

 

 

 

 

 

remainder

B1-(A2*B1)

(m=Fl/λ)

experiment

 

c-d

PDG reference

 

 

 

a

b

c

d

 

e

 

 

 

1/1

1

28.17941

0.1021998

 

 

 

Graviton?

 

 

1/2

0.5

14.089705

0.2043996

0.26

±48 

-0.06

56 CHETYRKIN 98 THEO MS scheme

1/3

0.3333333

9.3931367

0.3065994

0.3

±10 

0.01

57 CUCCHIERI 98 LATT MS scheme

1/4

0.25

7.0448525

0.4087991

0.43

± 8

-0.02

52 MALTMAN 99 THEO MS scheme

1/5

0.2

5.635882

0.5109989

0.510998918

electron

 

 

 

 

1/6

0.1666667

4.6965684

0.6131987

0.553

±12 

0.06

55 BECIREVIC 98 LATT MS scheme

1/7

0.1428571

4.02563

0.7153985

0.66

±19 

0.06

58 DOMINGUEZ 98 THEO MS scheme

1/13

0.0769231

2.1676469

1.3285972

1.3

±0.3

0.03

ASTIER 00D NOMD 

 

1/17

0.0588235

1.6576124

1.7373963

1.7

±0.3

0.04

1 AUBIN 04A LATT MS scheme 

 

1/18

0.0555556

1.5655228

1.8395961

1.79

±0.38

0.05

VILAIN 99 THEO MS scheme 

1/23

0.0434783

1.2251917

2.350595

2.3

±0.4

0.05

3 NARISON 99 THEO MS scheme 

1/27

0.037037

1.0436819

2.7593942

2.7

 ±0.06 4.72

0.06

3 AUBERT 04X THEO

 

1/28

0.0357143

1.0064075

2.8615939

2.9

±0.6

-0.04

2 JAMIN 02 THEO MS scheme 

 

1/30

0.0333333

0.9393137

3.0659935

3

±0.7

0.07

5 NARISON 95C THEO MS scheme 

1/33

0.030303

0.8539215

3.3725929

3.4

±0.11

-0.03

5 HOANG 04 THEO 

 

1/35

0.0285714

0.805126

3.5769924

3.6

±0.03 4.68

-0.02

4 BAUER 04 THEO 

 

1/37

0.027027

0.7616057

3.781392

3.8

±0.2 

-0.02

27 EICKER 97 LATT MS scheme 

1/38

0.0263158

0.7415634

3.8835918

3.9

±0.5

-0.02

6 AUBIN 04A LATT MS scheme 

 

1/39

0.025641

0.722549

3.9857916

3.95

±0.3 

0.04

17 CHIU 02 LATT MS scheme 

40

0.025

0.7044853

4.0879913

4.05

±0.6 

0.04

19 MALTMAN 01 THEO MS scheme 

1/41

0.0243902

0.6873027

4.1901911

4.19

±0.9

0.00

7 JAMIN 02 THEO MS scheme 

1/42

0.0238095

0.6709383

4.2923909

4.25

±0.7

0.04

5 NARISON 95C THEO MS scheme 

1/43

0.0232558

0.6553351

4.3945907

4.4

±0.1 ±0.4

-0.01

14 BECIREVIC 03 LATT MS scheme 

1/44

0.0227273

0.6404411

4.4967905

4.5

±0.11

0.00

6 MCNEILE 04 LATT 

 

1/45

0.0222222

0.6262091

4.5989903

4.57

 

0.03

20 AOKI 00 LATT MS scheme 

46

0.0217391

0.6125959

4.70119

4.7

±2 

0.00

21 GOECKELER 00 LATT MS scheme 

1/51

0.0196078

0.5525375

5.212189

5.2

±0.9

0.01

7 JAMIN 02 THEO MS scheme 

 

1/63

0.015873

0.4472922

6.4385864

6.4

±1.1 8

0.04

NARISON 99 THEO MS scheme 

 

1/69

0.0144928

0.4083972

7.0517851

7

±1.1

0.05

9 JAMIN 95 THEO MS scheme 

 

1/72

0.0138889

0.3913807

7.3583844

7.4

±0.7

-0.04

10 NARISON 95C THEO MS scheme 

223

0.0044843

0.1263651

22.790552

22.7

±20 

0.09

61 EICKER 97 LATT MS scheme 

1/224

0.0044643

0.1258009

22.892752

22.8

±14.1 

0.09

59 CHETYRKIN 97 THEO MS scheme

1/744

0.0013441

0.0378756

76.036639

76

±0.09 

0.04

9 CORCELLA 03 THEO

 

1/793

0.001261

0.0355352

81.044428

81

±0.09

0.04

7 BAUER 03 THEO

 

1/827

0.0012092

0.0340743

84.519221

84.5

±0.10

0.02

11 EIDEMULLER 03 THEO

 

1/861

0.0011614

0.0327287

87.994014

88

±0.05

-0.01

16 KUHN 01 THEO

 

1/900

0.0011111

0.0313105

91.979805

92

±0.06

-0.02

13 MAHMOOD 03 THEO

 

1/910

0.0010989

0.0309664

93.001803

93

±0.05

0.00

8 BORDES 03 THEO 

 

1/930

0.0010753

0.0303004

95.045799

95

± 4 

0.05

49 GOECKELER 00 LATT MS scheme

1/969

0.001032

0.0290809

99.03159

99

±0.090 ±0.025

0.03

18 PINEDA 01 THEO

 

1/978

0.0010225

0.0288133

99.951388

100

±0.82

-0.05

19 BARATE 00V ALEP

 

1/979

0.0010215

0.0287839

100.05359

100

±14 

0.05

50 AOKI 99 LATT MS scheme 

1/1008

0.0009921

0.0279558

103.01738

103

±0.57 

0.02

15 ABBIENDI 01S OPAL

 

1/1027

0.0009737

0.0274386

104.95918

105

±17 

-0.04

40 GAMIZ 03 THEO MS scheme

1/1037

0.0009643

0.027174

105.98118

106

±0.031

-0.02

12 ERLER 03 THEO

 

1/1086

0.0009208

0.0259479

110.98896

111

±12 

-0.01

55 BECIREVIC 98 LATT MS scheme

1/1115

0.0008969

0.025273

113.95276

114

±12 

-0.05

45 MALTMAN 02 THEO MS scheme

1/1125

0.0008889

0.0250484

114.97476

115

±0.06

-0.03

17 NARISON 01B THEO 

 

1/1135

0.0008811

0.0248277

115.99675

116

±0.10

0.00

10 DEDIVITIIS 03 LATT 

 

1/1145

0.0008734

0.0246108

117.01875

117

±0.070

0.02

14 PENIN 02 THEO

 

1/1155

0.0008658

0.0243978

118.04075

118

±17 

0.04

41 GAMIZ 03 THEO MS scheme

1/1223

0.0008177

0.0230412

124.99034

125

± 2 ± 8 38 

-0.01

BECIREVIC 03 LATT MS scheme

1/1262

0.0007924

0.0223292

128.97613

129

±16

-0.02

44 JAMIN 02 THEO MS scheme

1/1272

0.0007862

0.0221536

129.99812

130

± 9 ±16 

0.00

39 CHIU 03 LATT MS scheme

1/1370

0.0007299

0.0205689

140.0137

140

±15 

0.01

48 AOKI 00 LATT MS scheme

1/1448

0.0006906

0.0194609

147.98529

148

±48 

-0.01

56 CHETYRKIN 98 THEO MS scheme

1/1487

0.0006725

0.0189505

151.97108

152

±27 

-0.03

47 KOERNER 01 THEO MS scheme

1/1663

0.0006013

0.0169449

169.95824

170

-3

-0.04

42 ALIKHAN 02 LATT MS scheme 

 

Fig.2

Graph of table 4.

                                                  -------------------------------------------------

 

Ec2 = m = Fl

 

 Einstein's equation uses the energy generated by movement and given that movement cannot be instantaneous, allows Einstein to include time in his work on relativity; but the maximum energy is only present on one radial. By ignoring movement and time the Constant linear force (CLF) equation gives the structure of static particles and allows an explanation of compaction to show that all particles are compactions of a single elementary particle. Both Einstein and CLF give the same mass value for the same radius, even when movement causes the same radius value to apply to different particles. The potential energy and rest mass of Einstein's equation are equal to the linear force and mass of the CLF equation.

 

Fig 3

                            

 

References

 

1 arXiv:astro-ph/0606448 v1      19 June 2006

2 S. Eidelman et al., Phys. Lett. B 592, 1 (2004) (bibtex)

3 http://www.terra.es/personal/gsardin/news13.htm

4 http://nobelprize.org/nobel_prizes/physics/laureates/1998/press.html