I found something incredible regarding the connection between
microscales (the atom’s proton) and macro scales (the solar
system) if you want to get very close to modern measurements of
the proton and to exactly a characteristic time of one second.
The radius of a proton is not constant, but depends of the nature
of the experiment, because protons are thought to be a fuzzy
cloud of subatomic particles. Therefore, not using in our
equations for protons and the characteristic time of one second,
but the right ratio of terms in the fibonacci sequence, we find that
ratio is 5/8:!
!
!
=0.6303866!
If!
0, 1, 1, 2, 3, 5, 8, 13,…!
is the fibonacci sequence whose successive terms converge on
, the golden ratio, then the two terms that come closest to this
are 5/8=0.625.!
This is a characteristic time from!
!
ϕ
r
p
= ϕ
h
cm
p
ϕ =
r
p
m
p
c
h
=
(0.833E − 15)(1.67262E − 27)(299,792,458)
6.62607E − 34
ϕ
ϕ ⋅
πr
p
α
4
Gm
3
p
1
3
⋅
h
c
= 1.0335seconds
that has a value of!
!
1.0007seconds!
Combining!
!
with!
!
Gives the radius of a proton to be!
!
!
With this, while we get very close to one second (1.0007
seconds) with the fibonacci ratio of 5/8 we also get something
5
8
⋅
(352275361)π(0.833E − 15m)
(6.674E − 11)(1.67262E − 27)
3
1
3
⋅
(6.62607E − 34)
299,792,458
=
5
8
⋅
πr
p
α
4
Gm
3
p
1
3
⋅
h
c
= 1.0007seconds
(
1
6α
2
4πh
Gc
)
⋅
r
p
m
p
= 1second
r
p
=
5
8
h
cm
p
r
p
=
5
8
(6.62607E − 34)
(299,792,458)(1.67262E − 27)
= 0.8258821E − 15m
very much in line with the most recent measurement for the
radius of a proton.!
Thus for the solar system we truly have!
!
ℏ
⊙
= (1.00seconds)KE
e
