This was a presentation by me for the Young Scientist Award in Physical Sciences Section for the paper which was selected along with two other papers as nominations.

1. AN INSIGHT INTO THE ELEMENTARY
PARTICLES AND THEIR INTRINSIC
PROPERTIES
Suraj Kumar
1

2. About the paper:
• The paper tries to deduce the possible origin
of particles and evolution of their Intrinsic
Properties through Spiral Dynamics.
• The idea to use the approach of Spiral
Dynamics comes from several observations
experienced by scientific communities around
the globe.
2

3. Earlier Observations:
• “The Logarithmic Potential and Exponential
Mass Function for Elementary Particles.” by
Klauss Paasch, PROGRESS IN PHYSICS, Vol. 1,
P39, 2009;
3

4. The Logarithmic Potential and Exponential
Mass Function for Elementary Particles.
• In this paper, they tried an approach of fitting
parts of elementary particle mass involving
logarithmic potential and with a constant
energy pc resulting in points on a logarithmic
spiral lining up under a polar angle Ɵ and
separated by a factor ф .
4

5. Exponential Mass Function
• Our elementary particle mass tends to line up
in a sequence on the logarithmic spiral,
𝑚 𝜑 = 𝑚0ekφ
where 𝑘 =
1
2𝜋
log ф
• One turn of spiral 𝑚 𝜑 corresponds to
multiply 𝑚 𝜑 by ф i.e.
𝑚 𝜑 . ф = 𝑚 𝜑 + 2𝜋
5

6. Plot for Exponential Mass Function
Fig A: The masses of elementary particles placed on the spiral and listed for each resulting sequence starting from the centre. The solid lines
are separated by 45⁰. The red dot in the centre is the electron at 0⁰. The outer limit of the spiral at 135⁰ is about 2 GeV in first figure and at
80⁰ is about 6.5 GeV in second figure. Particles allocated on a sequence, but with masses too large for this scale are marked red in the
attached listings of sequence particles. The top for example is far outside on S6 at 317⁰.
6

7. • This pattern of distribution along a straight line
is achieved with only a specific value of ф as
1.53158 which provides symmetric and
precise result.
• The existence of unique ф is an indication of
possible constituent moving in a logarithmic
potential resulting in the observed exponential
quantization of elementary particle mass.
• The constituent of electron has already been
observed in our next reference paper.
7

8. Earlier Observations (Cont.)
• “Spin-Orbital Separation in the Quasi 1D Mott
Insulator Sr2CuO3.” by Thorsten Schmitt (2012)
• “Not quiet so elementary, my dear electron.” by Zeeya
Merali
• Spinon and Holon were observed in an experiment by
C.L. Kane and Matthew Fisher (1996)
8

9. • Combining the three observations we get that electron
divides at photon’s energy loss of 0.8 eV, 1.5 eV and 3.5 eV.
These quasi particles can move in different directions with
different speed in the material independent of each other.
Fig B: Energy Spectra observed
for the constituent of electron
i.e. Holon, Spinon and Orbiton.
Here Excitation Energy is the
amount of energy required to be
incident through X-Ray for the
particle to get into the state
where it could break into
constituents. Energy Transfer
represents the amount
of energy emitted along with
constituent particles.
9

10. INTRODUCTION TO SPIRAL
STRUCTURE OF ELEMENTARY
PARTICLES.
10

11. Mathematical Approach:
• From the Reaction-Diffusion mathematical model
which explains the local reaction which
transforms the substance and diffusion which
spreads out the substance over a surface in
space, we have
𝒖𝒕 =
𝑫𝜟𝒖 + 𝒇 (𝒖)
where 𝒖 = 𝒖 𝒓 , 𝒕 , 𝜭 describes the
concentration of energy fluxes and 𝑫 is the
diffusion constant of medium.
11

12. • Since fluxes in potential well have associated
direction, in terms of Vector Laplacian we
have Reaction- Diffusion equation as:
𝒖𝒕 = 𝑫[𝑮𝒓𝒂𝒅(𝑫𝒊𝒗 𝒖 ) – 𝑪𝒖𝒓𝒍(𝑪𝒖𝒓𝒍(𝒖))] + 𝒇 (𝒖)
• Considering the Laplacian term at first, we
have 𝑮𝒓𝒂𝒅(𝑫𝒊𝒗 𝒖 ) provides the required
potential to produce the elementary particles,
𝑪𝒖𝒓𝒍(𝑪𝒖𝒓𝒍(𝒖)) is the work performed to produce
the spiral structure for the elementary particle
and 𝑮𝒓𝒂𝒅(𝑫𝒊𝒗 𝒖 ) – 𝑪𝒖𝒓𝒍(𝑪𝒖𝒓𝒍(𝒖)) is the
remaining potential after the formation of
particle’s spiral structure which contributes in
the intrinsic behaviour of elementary particle.
12

13. • Since the spiral emerges in excitable medium as
the result of wave break. Open ends of broken
wave evolve because of dependence of velocity,
𝒗(𝒓) on curvature 𝟏/𝒓, by Eikonal equation:
𝒗(𝒓) = 𝒄𝒐 – 𝑫/𝒓
where 𝒄 𝒐 is velocity of wave in medium and 𝑫
is diffusion constant of excitable medium.
13

14. What is excitable medium for
Elementary Particles?
• For the spiral structure of elementary particles
the excitable medium has the following
properties:
– Has Diffusion constant 𝑫=1 which provides the
free flow to respective fluxes of potential.
– Waves can travel in the medium at the speed of
light i.e. at 𝒄.
This makes our Eikonal equation as:
𝒗(𝒓) = 𝒄 – 𝟏/𝒓
14

15. • Also the Rate of Autocatalysis for such system
is:
𝒚 (𝒓𝒂𝒕𝒆 𝒐𝒇 𝒂𝒖𝒕𝒐𝒄𝒂𝒕𝒂𝒍𝒚𝒔𝒊𝒔) = 𝒄2
• The spiral system of elementary particles are
isolated and no reaction occurs from outside,
but only the diffusion of potential flux takes
place. Thus,
𝒖𝒕 = 𝜟𝒖 = 𝑮𝒓𝒂𝒅(𝑫𝒊𝒗 𝒖 ) – 𝑪𝒖𝒓𝒍(𝑪𝒖𝒓𝒍(𝒖))
15

16. Structure of Spiral:
• A Spiral is described by a periodic function of
phase as
Ф = 𝜴𝒕 + 𝒏𝜭 + Ҩ(𝒓)
where Ҩ 𝒓 = potential function of spiral.
𝜴 = frequency of spiral.
𝒏 = number of arms.
• In spiral structure of elementary particles, we have
Ҩ(𝒓) = 𝑪𝒖𝒓𝒍 𝑪𝒖𝒓𝒍 (𝒖)
Thus, Ф = 𝜴𝒕 + 𝒏𝜭 + 𝑪𝒖𝒓𝒍 𝑪𝒖𝒓𝒍 (𝒖)
16

17. • The distance between two successive arms is the wavelength
of Spiral given as:
𝝀 𝒓 = 𝒓𝒏 – 𝒓𝒏 − 𝟏
𝜭 (𝒓𝟐 ) – 𝜭 (𝒓𝟏 ) = 𝟐𝝅
• We also have a definition for wavelength as:
𝝀 𝒓 = 𝜽(𝒓)
𝜽 𝒓 +𝟐𝝅 𝒅𝒓
𝒅𝜽
𝒅𝜽 = 𝜽(𝒓)
𝜽 𝒓 +𝟐𝝅
[
𝒏
𝒅 𝑪𝒖𝒓𝒍 𝑪𝒖𝒓𝒍 𝒖
𝒅𝒓
] 𝒅𝜽
Since, [
𝒅𝒓
𝒅𝜭
] = −
Ф 𝜭
Ф 𝒓
=
𝒏
Ҩ’(𝒓)
where 𝒏 = number of arms.
• Solving above equation with 𝒏 = 1 gives us the relation:
1
𝒅 𝑪𝒖𝒓𝒍 𝑪𝒖𝒓𝒍 𝒖
𝒅𝒓
≈ 𝜆 (𝑟) =
𝒅 𝑪𝒖𝒓𝒍 𝑪𝒖𝒓𝒍 𝒖
𝒅𝒓
≈
1
𝜆 (𝑟)
17

18. • Deducing the behaviour of particle, with
growth in angle by 𝟐𝝅 or with adding an arm,
the mass and consecutively the frequency
increases by factor ᴓ, minimizing the
wavelength and consecutively the radius of
spiral arms by factor 1 / ᴓ.
Hence, 𝝀 ′ 𝒓 =
𝝀 (𝒓)
√ᴓ
18

19. • Finally, we know that keeping the radius of the
complete spiral constant, if we curl up to
produce an additional arm with angle
preserved, we have a growth in mass by factor
ᴓ .
𝑀𝑎𝑠𝑠 𝑖𝑠 𝑝𝑟𝑜𝑝𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝑡𝑜
1
𝑑𝑟
𝑑𝜃
• The term Ҩ’(𝒓) gives the variation in the
potential required to increase the number of
arms of a spiral.
19

20. • Let us assume to have a wave of constant
wavelength equal to Planck’s length i.e. 𝒍p =
1.616199e-35 meter. Thus we have frequency
also conserved along with wavelength.
• Distributing it along the length of spiral we
have a well stable architecture of the
distribution of particles and anti particles.
• The frequency here is conserved by increase
in angular velocity of rotation of the spiral
since the wavelength is constant.
• It is well reflected through the decrease in
spiral wavelength i.e. 𝝀 ′ 𝒓 . 20

21. Possible Constituent Configuration of
Electron:
Relation between the Spectra
Map and Spiral Structure:
Spin (0.8 eV) : Determined by count of tip
of the Spiral. It provides details of portion of
waves considered in Spiral. Different particle
families of Standard Model as:
• We have integer spin bosons represented along the wavelength of stationary wave
with wavelength𝝀/𝟐 having two tips, unlike fermions which are represented by half
of the boson wavelength i.e. 𝝀/𝟒 having single tip.
21

22. Orbit ( 2 - 3.5 eV) : The orbit of the particle is determined by the mass-energy
quantisation of particle determined in Spiral by
𝒅𝒓
𝒅𝜭
as discussed earlier.
Charge ( 4.3 – 5.6 eV) : The charge of the particle is determined by the direction of
curl provided by the potential i.e.
𝒅 𝑪𝒖𝒓𝒍 𝑪𝒖𝒓𝒍 𝒖
𝒅𝒓
. Its quantisation is done on the
basis of angle of curl.
Charge Angle of Curl (in ⁰)
0 0
1 180
1/3 60
2/3 120
22

23. Character Behaviour Structure
Antiparticle Source Spiral
Particle Sink Antispiral
Fig : Representation of charge deviation of particle. If the particle is
positive charged it takes clockwise rotation and if it’s negatively
charged it takes anti-clockwise direction. The horizontal separation
divides among the Particles and Antiparticles.
Characteristics of particles in different quadrants above:
• Particle annihilates with diagonal quadrant.
• Particle adjacent horizontally attract each other. Since they are both of
same structure i.e. either Particle or Antiparticle with having opposite
direction, they attract each other and can exist closer by.
• Particle adjacent vertically repel each other. Since they are both of
opposite structure with having same direction, they repel each other and
because of this we don’t have annihilation.
23

24. • In the spiral dynamics of particles, the
excitation energy absorbed by the particle
tends to increase the length or thickness of
spiral.
• Conserving the quantity
𝒅𝒓
𝒅𝜭
which represents
the main structure of spiral and also the length
of the spiral, the absorbed energy is emitted
out in the form of photon or transfer energy in
concerned experiment.
24

25. Concluding the Physical Approach:
•
𝒅𝒓(𝒒𝒖𝒂𝒓𝒌)
𝒅𝜭
<
𝒅𝒓(𝒆𝒍𝒆𝒄𝒕𝒓𝒐𝒏)
𝒅𝜭
≪
𝒅𝒓(𝒏𝒆𝒖𝒕𝒓𝒊𝒏𝒐𝒔)
𝒅𝜭
This is because the mass of quark is more
than that of electron and neutrino and mass of
electron is more than that of neutrino, as Mass
is inversely proportional to
𝒅𝒓
𝒅𝜭
.
25

26. Illustration of Acceleration of Particles
in Spiral System:
• Some of the basic facts which we know for
particle accelerators are:
– The mass increases with velocity.
– The velocity in any case can’t reach the speed of
light i.e. particle can never become photon.
In Spiral System, as we increase the velocity of
particle closer to speed of light, the core of the
spiral curls around the axis of acceleration and tip
coincide with the axis of acceleration.
26

27. Fig : Representation of structure of Antispiral when accelerated with velocity closer to speed of light.
• Once the spiral is completely curled up on the axis of acceleration, further increase
in velocity decreases the quantity
𝒅𝒓
𝒅𝜭
. Hence, increases the mass of the particle.
• Also this phenomenon never allows particle to attain a straight waveform free from
curl to behave as photon, since from observations we know that the acceleration also
preserves the curls in the waveform at some extent and can never get free from it.
27

28. Conclusion:
• It is interesting to note that the dynamics of
spirals for galaxy structure can also be used for
elementary particles.
• Further study tries to fit the structure of these
micro spirals of elementary particles into the
macro spirals of cosmos, which can give us the
explanations for the dark potentials.
• This can also be the basic ingredient for the
Unified Theory.
28