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Proposal For A Universal Particle Equation"
Ian Beardsley"
March 8, 2026"
Abstract"
A Normal force where , which we suggest is invariant, is
introduced that determines a master equation for the proton, neutron, and electron, a kind of
Universal Particle Equation. It is suggested that when we push on a particle we rotate some of
its temporal velocity into spacial velocity and resistance to this rotation is experienced as the
normal force pushing back creating inertia that we experience as mass."
The Proposal"
We can form two equations where the proton radius to its mass produces about 1-second [3,
4]:"
1. "
2. "
(Proton Mass)"
(Proton Radius)"
(Planck Constant)"
(Light Speed)"
(Gravitational Constant)"
1/137 (Fine Structure Constant)"
Using equation 6, equations 1 and 2 directly yield [3, 4]:"
3. "
4. "
5. "
F
n
= h /(ct
2
1
)
t
1
= 1#second
ϕ ⋅
πr
p
α
4
Gm
3
p
1
3
⋅
h
c
= 1second
1
6α
2
⋅
r
p
m
p
4πh
Gc
= 1second
m
p
: 1.67262E − 27kg
r
p
: 0.833E − 15m
h:6.62607E − 34J ⋅ s
G: 6.674E − 11N
m
2
kg
2
α :
m
p
= κ
p
πr
2
p
F
n
G
F
n
=
h
ct
2
1
t
1
= 1second
! of 2 4
where . Here we see in equation 3, the cross-sectional area of the proton
is exposed to the normal force, , mediated by the ‘stiffness of space’ as measured
by G, producing the proton mass, ."
We suggest equations 1 and 2 are correct because they yield the proton radius closely. They
give it as (by equating them) [3, 4]:"
6. "
"
The CODATA value from the PRad experiment in 2019 gives"
"
With lower bound , which is almost exactly what we got."
We can see equation 6 may be the case because we get it from Planck Energy ,
Einsteinian energy, , and the Compton wavelength when we
introduce the factor of , which is the golden ratio conjugate, where the golden ratio,
[3, 4]."
I explain this factor by invoking Kristin Tynski, her paper titled: One Equation, ~200 Mysteries:
A Structural Constraint That May Explain (Almost) Everything [2]."
Tynski shows that for any system requiring consistency across multiple scales of observation
has the recurrence relation:"
7. "
Which she says leads to"
8. "
Whose solution is ."
For the proton radius in our computations we will use"
"A measurement of the atomic hydrogen Lamb shift and the proton charge radius"%
by Bezginov, N., Valdez, T., Horbatsch, M. et al. (York University/Toronto)%
Published in Science, Vol. 365, Issue 6457, pp. 1007-1012 (2019)."
It has a value of "
κ
p
= 1/(3α
2
)
A
p
= πr
2
p
F
n
m
p
r
p
= ϕ ⋅
h
cm
p
r
p
= (0.618)
6.62607E − 34J
(299,792, 458m /s)(1.67262E − 27kg)
= 0.8166E − 15m
r
p
= 0.831
±
0.014f m
r
p
= 0.817E − 15m
E
p
= hν
p
E
p
= m
p
c
2
λ
p
= h /(m
p
c) = r
p
ϕ
Φ = 1/ϕ = ( 5 + 1)/2 ≈ 1.618
scale(n + 2) = scale(n + 1) + scale(n)
λ
2
= λ + 1
Φ
r
p
= 0.833
±
0.012f m
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The 1-second verification follows from the resulting Universal Particle Equation [3]:"
9. "
Proton: , = fine-structure constant=1/137:"
"
Neutron: :"
"
Electron: :"
"
We suggest for the electron may be because it is the fundamental quanta (does not
consist of further more elementary particles)."
(neutron radius)"
(classical electron radius)"
Equation 9 is a Natural Law. In general we can write the universal law as [4]:"
10. "
"
"
"
t
1
=
r
i
m
i
⋅
πh
Gc
⋅ κ
i
κ
p
=
1
3α
2
α
t
1
=
0.833 × 10
−15
1.67262 × 10
−27
⋅
π ⋅ 6.62607 × 10
−34
(6.674 × 10
−11
)(299,792, 458)
⋅ 6256.33 = 1.00500seconds
κ
n
=
1
3α
2
t
1
=
0.834 × 10
−15
1.675 × 10
−27
⋅
π ⋅ 6.62607 × 10
−34
(6.674 × 10
−11
)(299,792, 458)
⋅ 6256.33 = 1.00478seconds
κ
e
= 1
t
1
=
2.81794 × 10
−15
9.10938 × 10
−31
⋅
π ⋅ 6.62607 × 10
−34
(6.67430 × 10
−11
)(299,792, 458)
⋅ 1 = 0.99773seconds
κ
e
= 1
r
n
= 0.834E − 15m
r
e
= 2.81794E − 15m
m
i
= κ
i
πr
2
i
F
n
G
F
n
=
h
ct
2
1
F
n
=
6.62607015 × 10
−34
#J·s
(299,792,458#m/s)(1#s)
2
= 2.21022 × 10
−42
#N
t
1
= 1second
! of 4 4
References"
1. Bezginov, N., Valdez, T., Horbatsch, M. et al. (York University/Toronto)%
Published in Science, Vol. 365, Issue 6457, pp. 1007-1012 (2019) “A measurement of the
atomic hydrogen Lamb shift and the proton charge radius”"
2. Tynski, K. (2024). One Equation, ~200 Mysteries: A Structural Constraint That May Explain
(Almost) Everything."
3. Beardsley, I. (2026) How Physics and Archaeology Point to a Natural Constant of 1-Second"
4. Beardsley, I. (2026) The Sublime and Mysterious Place of Humans in the Cosmos; A Work
in Exoarchaeology