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Particle physics – interpretation

 

Introduction

 

 

The Standard model does not have a complete interpretation, the current situation as stated by Jim Baggott1 is:

 

 “The theory is not meant to be understood”……. “Today the theory remains a mysterious black top hat from which white rabbits continue to be pulled. Students are advised not to ask how this particular conjuring trick is done”. 

 

A connection between mass and radius has been suggested before as summarized in the introduction of a paper by H.J. Fahr and M. Heyl2. Added to this is the common belief that elementary particles are both wave and particle, and then there should be a mathematical connection between wavelengths, radii and mass. The only missing entity experimentally proven to exist is force and my first step was to produce a force constant.

 

.

 

 

The Linear Force Constant

 

This was found using the known mass and classical electronic radius of the electron

 

Fl = rm..…………………………………. (1) 

 

Linear Force equals the Classical Electron Radius times the electron mass:

 

1.4399648 = 2.817941(fermi) X 0.51099892(MeV)

 

It will be shown that the diameter of each particle is related to the wavelength of the particle vacuum field. The difference between positive and negative charge is not dealt with in this article and the vacuum wave length is considered to be the same for both, where the Fl constant is equal to ‘2r’ (2.8799296).

 

Ec2 = m = Fl/2r………….……………….. (2)

 

Ec2 = Fl/2r………………….…………….. (3)

 

E = energy

c = speed of light

m = mass

Fl = linear force constant (2.8799296)

r = radius

 

 

The Fl constant is used to find the radii of other particles as shown in table 1 col. (e).


 

 

 

Table 1

(PDG data in bold underlined  type)

 

Linear

 

Vacuum field

radius

particle

Force (Fl)

Mass

wavelength

(x 10-15 m)

 

constant

MeV

(fermi)

(fermi)

 

(F=2rm)

(m=F/2r)

(2r = Fl/m)

(2r/2)

(a)

(b)

('c)

(d)

(e)

e

2.8799296

0.51099892

5.6358822

2.817941

µ

2.8799296

105.658369

0.02725699

0.013628

τ

2.8799296

1776.99

0.00162068

0.00081

 

 

 

 

 

u

2.8799296

2.75

1.04724713

0.523624

d

2.8799296

6

0.47998827

0.239994

s

2.8799296

105

0.0274279

0.013714

c

2.8799296

1250

0.00230394

0.001152

b

2.8799296

4250

0.00067763

0.000339

t

2.8799296

174300

0.000016523

0.000008

 

Currently the Standard model does not predict particle radii but, given that all particles have the same charge value; then the formula for finding the Classical Electron Radius produces radii for leptons and quarks proportional to those shown in col. (e) of table 1: Indicating that the Standard model practice of allocating fractional charge values to quarks is open to question.

 

Fractions

 

Fractional charge5 is found in Quantum Hall experiments (TFQHE) and occurs in a number of sequences, The most well known being the so-called ‘fractionally charged electrons’ found by Tsui et al in the sequence 1/3, 2/5, 3/7 etc. The only other instances of this sequence that I have found are cosmological measurements where the fractions refer to the distances between centers.

A cause is needed to explain why particle compaction (or expansion) occurs in a regular sequence and wave structure supplies the cause; at the ‘top’ and ‘bottom’ of each wave cycle the wave force has to switch from ‘increasing’ to ‘decreasing’ (or vice versa) and it is suggested that this provides a natural stop point for compaction and expansion. The next stage was to find the fractional sequence that applies to the diameter of particles (the distance between wave peaks and troughs); by mathematical experiment, I found the sequence 1, 1/2, 1/3, 1/4, 1/5 etc. The manner in which this sequence occurs is illustrated in Fig. 1. Table 4 shows the fractions related to  leptons and quarks as given in the 2004 catalogue issued by the Particle Data Group6.

 

 

 

 

 

 

 

 

Fig.1

Section of table 4 showing five of the particles found by experiment.

(Fractional distances to scale; amplitude not to scale)

 

 

Given that the electron is the 1/5 particle, then the fractions for the other particles are as shown in table 4. The data for leptons and quarks (cols. d, e, and f) are as listed in the Particle Data Group lists for 20046.  

 

 

 

 

 

 

Table 4

(Fl = 2.87992961524744)

 

 

 

theoretical

mass

 

 

 

 

 

Fraction of

remainder

2r

mass

found by

 

 

 

 

 

B1-(A2*B1)=B2

(m=Fl/2r)

experiment

 

c-d

PDG reference

 

 

 

a

b

c

d

 

e

f

 

 

1/1

1

28.17941    (B1)

0.1021998

 

 

 

Graviton?

 

 

1/2

0.5     (A2)

14.089705  (B2)

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 all fractions 1 to 1/1663 and particles

 found by experiment (table 4. Cols. (c) and (d))

 

 

                    

 

Linear force

 

 

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.

 

Some of the unsolved problems of the Standard model involve the relationship between mass, force and radius, I will only make the point that a mathematical relationship is only possible if there is a uniform relationship between particle structures. But, it goes deeper than that; the Inverse Square Law lies at the root of all the force laws and the cause of this common base, is that all particles have the same quantities, only the volume changes. The different forces are simply the different force relationships between particles of different volume.

 

 

References

 

1Beyond Measure, Jim Baggott, OUP, 2003 ISBN 0 19 852536 2

2 http://arxiv.org/PS_cache/astro-ph/pdf/0606/0606448v2.pdf

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

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

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

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