AI Pattern Matching CERN LHC Collision Particle Resonance Flow Patterns with Turbulence

Abstract

Particle physicists are turning to AI to cope with CERN's collision deluge. AI pattern matching is shown here to match the LHC collision tracks electromagnetic energy density transverse helical flow dissipation patterns with transverse Navier-Stokes turbulence flow dissipation patterns. LHC beam collisions are energized, controlled and measured, to technological limits, by means of the 4D Einstein-Maxwell electromagnetic stress energy-momentum density pressure tensor. The collision pattern peak "particle resonances" are electromagnetic energy density peak widths, located around certain energy levels found in differential cross sections of scattering experiments. Problematically in the standard model the Higgs boson particle resonance peak width is interpreted as a range of Higgs particle masses. Here CERN's TrackML Particle Tracking Challenge data set is imported with python and utilized, without modification, to match each collision event set of high-energy tracks helicity and near instantaneous cascading transverse momentum dissipation of energy-with low-energy Navier-Stokes turbulence rotation and cascading transient states of energy dissipation.

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Full text

The
Mathematica
®
Journal
AI Pattern Matching CERN LHC Collision Particle Resonance Flow
Patterns with Electromagnetic Energy Density Pressure Turbulence
machine learning: analysis domain
David A. Harness, Independent Researcher, https://orcid.org/0000-0001-5506-3226
Particle physicists are turning to AI to cope with CERN’s collision deluge. AI pattern
matching is shown here to match the LHC collision tracks electromagnetic energy density
transverse helical flow dissipation patterns with transverse Navier-Stokes turbulence flow
dissipation patterns. LHC beam collisions are energized, controlled and measured, to tech-
nological limits, by means of the 4D Einstein-Maxwell electromagnetic stress energy mo-
mentum density pressure tensor
Tμν
. The collision pattern peak “particle resonances” are
electromagnetic energy density peak widths, located around certain energy levels found in
differential cross sections of scattering experiments. Problematically in the standard
model the Higgs boson particle resonance peak width is interpreted as a range of Higgs par-
ticle masses. Here CERN’s TrackML Particle Tracking Challenge data set is utilized, with-
out modification, to match each collision event set of high-energy tracks helicity and near
instantaneous cascading transverse momentum dissipation of energy – with low-energy
Navier-Stokes turbulence rotation and cascading transient states of energy dissipation.
david.harness@warpmail.net
▲
Figure 1. AI pattern recognition aided in the CERN LHC discovery of the Higgs boson both in (a)
analysis of particle track simulations [1] and (b) detection of the electromagnetic energy density
track patterns [2][3][4]. CERN experimental physicist Maria Spiropulu in the APS April Meeting
2014 compared the ‘Quantum Crisis’ in particle physics to the classical mechanics crisis of 1905:
“Without supersymmetry, we don’t understand how the Higgs boson can exist without violat-
ing basic mechanisms of quantum physics. ... Either the new run of the LHC should discover
superpartners, or radical new ideas are needed” [5]. The new run of the LHC is over and none
of the theoretically critical standard model of physics (SM)-supersymmetry(SUSY) particle-
sparticle superpartners have been detected [6][7][8]. At the time of this writing the CERN Euro-
pean Particle Physics Strategy Update 2018 – 2020 group is reprocessing its SM-SUSY theoretical
predictions to detect superpartners at some higher Future Circular Collider (FCC) energy level [9].
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Figure 1. AI pattern recognition aided in the CERN LHC discovery of the Higgs boson both in (a)
analysis of particle track simulations [1] and (b) detection of the electromagnetic energy density
track patterns [2][3][4]. CERN experimental physicist Maria Spiropulu in the APS April Meeting
2014 compared the ‘Quantum Crisis’ in particle physics to the classical mechanics crisis of 1905:
“Without supersymmetry, we don’t understand how the Higgs boson can exist without violat-
ing basic mechanisms of quantum physics. ... Either the new run of the LHC should discover
superpartners, or radical new ideas are needed” [5]. The new run of the LHC is over and none
of the theoretically critical standard model of physics (SM)-supersymmetry(SUSY) particle-
sparticle superpartners have been detected [6][7][8]. At the time of this writing the CERN Euro-
pean Particle Physics Strategy Update 2018 – 2020 group is reprocessing its SM-SUSY theoretical
predictions to detect superpartners at some higher Future Circular Collider (FCC) energy level [9].
■
1. Pattern Matching Navier-Stokes LHC Turbulence
■
2. CERN LHC TrackML Particle Tracking Challenge Data Set
■
3. 4D Einstein-Maxwell electromagnetic energy density tensor
■
4. Quantum Fluid Conjecture: Equations (9,15)
■
5. Navier-Stokes Equations
■
6. 4D Spacetime Quantization
■
7. Singular Complex System Conjecture (SCSC)
■
8. 4D Photon Energy Observable E = hc/λ
■
9. 4D Photon Angular Momentum Observable ℏ
■
10. Figure 7. 4D Spatially Extended Photon Simulation
■
11. Figure 8. 4D Photon Observables Boundary Value Calculator
■
12. Cosmological Constant Vacuum Energy Density Λ
■
13. 4D Electron Rest Mass Observable
■
14. 4D Electron Angular Momentum Observable ℏ/2
■
15. Figure 10. 4D Spatially Extended Electron Simulation
■
16. Figure 11. 4D Electron Boundary Value Calculator
■
17. Conclusion
■
References
About the Author
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1. Pattern Matching LHC-Navier-Stokes Turbulence
The Navier-Stokes (NS) equations are widely accepted to embody the physics of all fluid
flows, including turbulent flows; wherein the “problem of turbulence” remains to this day
the last unsolved problem of classical mathematical physics [10].
Turbulent flow solutions, as reviewed by McDonough [11], all share the following NS
physical attributes:
1.
disorganized, chaotic, seemingly random behavior;
2.
non-repeatability, sensitivity to initial conditions;
3.
large range of length and time scales;
4.
rotational;
5.
3D spatially-extended Reynolds stress vortex stretching;
6.
time dependence;
7.
cascading energy dissipation and diffusion (mixing);
8.
intermittency in both space and time.
The CERN LHC TrackML Particle Tracking Challenge collision event data set [12]
contains roughly 100,000 data points of the following classes of information for each event:
$ Hits: x, y, z coordinates of each hit on the particle detector;
! Particles: Each hit position
(vx
,
vy
,
vz
), momentum
(px
,
py
,
pz
), charge (q);
! Truth: Mapping between hits generating particle trajectory and momentum weight;
! Cells: Precise location of each particle hit and how much energy deposited;
from which are constructed the thousands of helix arcs — the shape of the decay prod-
ucts’ tracks [4], e.g., as shown in Fig. 1(b), matching the NS attributes according to:
1.
disorganized, chaotic, seemingly random behavior;
2.
non-repeatable sensitivity to initial proton-proton bunches collision alignments;
3.
long and short energy density pressure track lifetimes;
4.
helical tracks short to long range composed of linear and angular momentum;
5.
3D spatially-extended helical track vortexes;
6.
transient energy density peak “particle resonance” lifetimes [13][14][15];
7.
near instantaneous cascading energy density dissipation;
8.
proton-proton bunch collisions equivalent to explosive impulse J = ∫ F dt.
The LHC-NS turbulence match of a large range of vertex length and time scales to the
TrackML data set exists then from the long range collision event tracks helix arcs of Fig.
7 — to the short range quantum fluid conjecture of angular momentum observable ℏ of
units kg
m2
s-1
representing the kinetic mass kg × kinetic viscosity
m2
s-1
dimensionless
equivalence with
ωrad s-1
of Eqs. (9,15).
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2. CERN LHC TrackML Particle Tracking Challenge Data Set
▲
Figure 2. Scientists at the CERN LHC energized head-on collisions between two bunches of pro-
tons inside the machine’s ATLAS and CMS detectors more than 1 billion times a second [6] and
meticulously observed these collisions with intricate silicon detectors. Each of the 20 different
pairs of proton-proton collisions can produce thousands of new particles, which radiate from a colli-
sion point at the centre of each cathedral-sized detector. Millions of silicon sensors are arranged in
onion-like layers and light up each time a particle crosses them, producing one pixel of informa-
tion every time. The enormous amounts of data produced from the experiments is becoming an
overwhelming challenge. To address this problem, a team of Machine Learning experts and physi-
cists have held the TrackML Particle Tracking Challenge “to answer the question: can machine
learning assist high energy physics in discovering and characterizing new particles?” [12].
▲
Figure 3. (a) The CERN LHC, a.k.a, world's largest machine, is a solenoid ring 27 km in circumfer-
ence, a section of which magnetic field lines B are shown compressing and accelerating the pro-
tons along the center beamline. (b) The ATLAS and CMS detectors are constructed of millions of
silicon sensors arranged in onion-like layers and light up each time a particle crosses them, produc-
ing one pixel of information for pattern-recognition algorithms to reconstruct thousands of helix
arcs — the shape of the decay products’ tracks — from roughly 100,000 data points. Thus the
LHC and detectors are energized, controlled and each of the data points measured entirely via the
4D Einstein-Maxwell electromagnetic stress energy momentum density pressure tensor
Tμν
, in
terms of pascals Pa along the trace of
Tμν
in Eq. (1).
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Figure 4. LHC proton-proton bunch collisions explosive impulse J = ∫ F dt interval occurs from
leading to trailing photon collisions. None of the theoretically critical Standard Model of Physics
(SM)-Supersymmetry (SUSY) particle-sparticle superpartners have been detected [5][6][7][8].
Figure 5. Differential cross section peak width “particle resonances” of collision events
[13][14][15] are composed of thousands of helix arcs [4] generating hydrodynamic plasma flow
patterns [16] around certain
Tμν
energy levels, interpreted in SM as “discoveries” of new zero di-
mensional (0D) mathematical point subatomic particles. The blue histogram is interpreted as a
mass distribution of two Z boson 0D particles. The red line with a central mass distribution value
around 125 GeV is interpreted as the Higgs boson signal [13]. Note both red and blue regions, uti-
lizing same silicon pixel detectors, are both measuring electromagnetic energy momentum density
pressure along the trace of
Tμν
in Eq. (1) – all three interpreted here as LHC-NS turbulence peaks.
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The following Python code is a guide by Bonatt [17] for importing and plotting the
TrackML dataset labeled here Figs. 6(a)(b) and 7, with no modification, except for the
curved dispersion line plots added to Fig. 7.
import os
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits import mplot3d
import seaborn as sns
from trackml.dataset import load_event,load_dataset
from trackml.randomize import shuffle_hits
from trackml.score import score_event
#One event of 8850 “All methods either take or return pandas.DataFrame objects”
event_id =‘event000001000’
hits,cells,particles,truth =load_event(‘.. /trackml/train_100_events/’+event_id)
#Figure 6(a). 3D Plot of Detector hits
plt.figure(figsize=(10,10))
ax =plt.axes(projection=’3d’)
sample =hits.sample(30000)
ax.scatter(sample.z, sample.x, sample.y, s=5, alpha=0.5)
ax.set_xlabel(‘z (mm)’)
ax.set_ylabel(‘x (mm)’)
ax.set_zlabel(‘y (mm)’)
ax.scatter(3000,3000,3000, s=0)#These two added to widen 3D space
ax.scatter(-3000,-3000,-3000, s=0)
plt.show()
#Figure 6(b)3D Plot Tracks Get every 100th particle
tracks =truth.particle_id.unique()[1::100]
plt.figure(figsize=(10,10))
ax =plt.axes(projection=’3d’)
for track in tracks:
t=truth[truth.particle_id == track]
ax.plot3D(t.tz, t.tx, t.ty)
ax.set_xlabel(‘z (mm)’)
ax.set_ylabel(‘x (mm)’)
ax.set_zlabel(‘y (mm)’)
#These two added to widen the 3D space
ax.scatter(3000,3000,3000, s=0)
ax.scatter(-3000,-3000,-3000, s=0)
plt.show()
#Figure 7. Plot Zvs XY (Transverse)momentum
p=particles[particles.pz <200] #cutoff far hits
plt.figure(figsize=(10,10))
plt.scatter(np.sqrt(p.px**2+p.py**2), p.pz, s=5, alpha=0.5)
plt.plot([0.1,0.1],[p.pz.min(),p.pz.max()], c=’g’)#0.1 not 0because log plot.
plt.plot([0.1,np.sqrt(p.px**2+p.py**2).max()],[0.1,0.1], c=’r’, linestyle=’--‘)
plt.xscale(‘log’)
x=np.arange(0.1,2,0.1)#curved dispersion lines
y1 =4+ (14 *x)**1.22
plt.plot(x, y1, c='m', linestyle='--')#upper line
y2 = -4- (14 *x)**1.22
plt.plot(x, y2, c='m', linestyle='--')#lower line
plt.title(r'LHC beamline (green)vs Transverse Momentum Reduced to Z=0, $\theta=0$')
plt.xlabel(‘Transverse momentum (GeV/c)’)
plt.ylabel(‘Beamline Zaxis momentum (GeV/C)’)
plt.show()
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Figure 6. (a) LHC Detector 3D hits (partial sample). (b) Transient energy density particle tracks.
▲
Figure 7. LHC beamline Z axis vs. XY transverse momentum. Vertical green line is parallel with
the beamline, horizontal red line is transverse to the beamline. Curved magenta lines indicate high-
energy dispersion matching typical low-energy water channel spillway dispersion symmetry.
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3. 4D Einstein-Maxwell Electromagnetic Energy Density Tensor
Recall the LHC high-energy proton-proton beam collisions are energized, controlled, and
measured, to the limits of technology, by the 4D Einstein-Maxwell electromagnetic stress
energy momentum density tensor
Tμν =
1
2ε0E2+1
μ0
B2Sx/c Syc Sz/c
Sx/c-σxx -σxy -σxz
Syc-σyx -σyy -σyz
Sz/c-σzx -σzy -σzz
,
(1)
wherein
S=1
μ0
E×B
is the Poynting energy flux vector and
σij
are the Maxwell stress ten-
sor components. Accordingly the LHC ATLAS CMS detectors measure electromagnetic
energy in units of total field pressure pascals Pa along the trace elements
-σxx
,
-σyy
,
-σzz
, the same as the low-energy cosmological constant vacuum energy density
Λ
[18].
Hence division by
c2
renders the
T00
= 1/2
ε0E2+1/μ0B2
energy density J m
-3
term
computationally dualistic with
T00
=
1
2c2ε0E2+1
μ0
B2
mass density kg m
-3
, such that
both energy density J m
-3
= -Pa = kg m
-3
mass density are expressed and measured by
the same total field units of Pa. For example, the computationally dualistic values of
Λ
are
calculated by Baez and Tatom to be energy density
ΛJ
≈ 6 × 10
-10
J m
-3
= -Pa = mass
density
Λkg
=
ΛJ
/
c2
≈ 7 ×
10-27
kg m
-3
[18].
Accordingly, the total field formal frame for the quantum mechanical observables full
Laplacian spherical harmonics, including turbulence, will be established along the trace of
Tμν
by means of Eqs. (1-17). Hence, it will be shown quantum gravity has always had a
computationally dualistic energy density ⇔ mass density basis of communication—apart
from any hidden dimensional unknown Higgs mechanism—whereby “energy tells space-
time how to curve and spacetime tells matter and energy how to move” [19].
■
4. Quantum Fluid Conjecture: Equations (9,15)
Vorticity is central to the large range of turbulence length and time scales, in that “these
vortices, usually referred to as ‘eddies,’ are somehow broken into smaller ones, ..., and so
on, until they are sufficiently small as to be dissipated by viscosity” [11]. Thus the present
LHC-NS turbulence ranges from the largest scale of the helical collision tracks of Fig.6,
to the smallest scale of the angular momentum observable ℏ; wherein the quantum fluid
conjecture of Eqs. (9,15) establishes the 4D kinematic viscosity basis for transient excited
states cascading intrinsic spin dissipation of energy down to the stable states. In accord
then with the QCD turbulent fluids analogy of Wolfram [20], a nonstandard quantum infor-
mation theory computer algebra formalization framework is established towards pattern
matching the LHC wave-particle collision track patterns to NS turbulence.
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5. Navier-Stokes Equations
∇ ·U=0,
(2)
Ut+U·∇U= -∇P+ν;U+FB,
(3)
In these equations U = (u,
v,w)T
is the velocity vector which, in general, depends on all
three spatial coordinates (x, y, z); P is the reduced, or kinematic (divided by constant den-
sity) pressure, and
FB
is a general body-force term (also scaled by constant density). The
differential operators ∇ and ; are the gradient and Laplace operators, respectively, in an
appropriate coordinate system, with ∇. denoting the divergence. The subscript t is short-
hand notation for time differentiation, ∂/∂t, and ν is kinematic viscosity [11]. The SO(3) ro-
tations and 4D spatial quantization correlations [21] of modern physics are parameterized
from low to high energy by the quaternion group q =
e
1
2θ(uxi+uyj+uzk)
[22].
Reynolds (circa 1880) was the first to systematically investigate the transition from lami-
nar to turbulent flow, as shown in Fig. 8, by injecting a dye streak into flow through a pipe
having smooth transparent walls. Note the comparison between the Fig. 8(a) dye streak
low velocity
Ut
laminar flow in
Uz
direction and the Fig. 3(a) magnetic field confinement
of the beamline with magnetic field B equivalent to Eq. (3) body force pressure
FB
.
Clearly in Fig. 6(b) at medium flow velocity
Uz
competing transverse (radial)
Ux,y
force
(pressure) components arise on the microscopic level due to constructive reflective wave-
particle trajectory confinements towards the
Uz
direction. Thus generating the known
semi-chaotic harmonic time-domain and frequency domain signals.
Figure 8. The Reynolds experiment [11]: (a) low velocity
Ut
laminar flow in
Uz
direction,
(b) medium
Ut
early-transitional (but still laminar) flow with transverse (radial)
Ux,y
reflec-
tive pressure components, and (c) high
Ut
flow with transverse
Ux,y
×
Uz
constructively in-
terfering pressures generating spin-turbulence.
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6. 4D Spacetime Quantization
“Physical objects are not in space, but these objects are spatially extended. In this way the con-
cept ‘empty space’ loses its meaning.” Albert Einstein 1952 [23].
Every particle in the SM–SUSY particle zoo is modeled as an 0D mathematical imaginary-
invisible point (due to the central force problem) having the 4D spacetime measurements
of nothingness—hence the LHC beams should pass right through one another.
SM-SUSY therefore “explains” the physical interactions of the observed universe by
adding to the 0D particles 6 or 7 hidden dimensional anti-de Sitter/Conformal Field The-
ory (AdS/CFT) string, membrane, lattice, or otherwise unknown classical materialism
mechanisms, written here 0D + i6,7D. All of which observer-independent background enti-
ties, including the unknown Higgs mechanism, are said to fill all of universal spacetime in
an “unbroken symmetry” of superpositioned “infinite seas” of SM-SUSY 0D particles—
non-locally connected through the hidden string, membrane, or otherwise unknown i6,7D
mechanisms—which SM-SUSY 0D particles are said to be “energized” or “discovered” by
the LHC 0D + i6,7D beam collisions “symmetry-breaking” of the infinite seas.
None of the theoretically critical SM-SUSY particle-sparticle superpartners have been de-
tected at LHC energy levels. In fact the SM-SUSY model of the basic mechanisms of quan-
tum physics are already in violation of basic understanding where the attractive nuclear
force is conjectured to be “carried” by the attractive QCD exchange of unobservable
[quark-emitter
→
gluon-carrier
←
quark-absorber] virtual particles—contrary to every ob-
served [emitter↔emitted↔absorber] interaction (including all LHC collision energy
density flow patterns) always resulting in a repulsion from any would-be line of attraction.
Additionally, at low-energy levels, the recent spooky “freedom of choice” experiments
have realistically closed the Bell inequality observer-independent background loopholes
[24][25][26]. Hence falsification of observer-independent backgrounds at high and low en-
ergy levels requires a more radical idea than the FCC next generation of turbulence [27].
Finally, SM-SUSY represents a computationally intractable many-body problem as is
known at lab sample sizes. Thus when based on SM-SUSY the computational universe hy-
pothesis (CUH), and the multiverse mathematical universe hypothesis (MUH) [28], are
computationally intractable to machine learning basic understanding of the Hamiltonian
configuration energy of the 4D spatially-extended quantum mechanical observables.
Radical as it sounds no basis exists then for any mind-body dualism background either,
leaving only the psychophysical parallelism of Parmenides. The last theory standing is
then quantum information theory. Jaffe anticipated the Quantum Crisis when writing the
Yang-Mills Mass Gap problem description,
“One would like to introduce the notion of quantization directly at the level of space-time, and
to describe field theories on quantum space-time, rather than applying quantization to fields that
live on a classical space-time” [29].
Consider then beyond CERN’s Physics Beyond Colliders initiative [30], the 4D spatially-
extended energy density pressure
Tμν
total field formal frame of Eqs. (1,4-16) for wave-par-
ticle integrations of Schwinger local field differentials [31], reflective of the Wolfram
QCD turbulent fluids analogy [20], measurable along Feynman path integrals [32].
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7. Singular Complex System Conjecture (SCSC)
There exists a singular mathematically possible universal complex system corpus of the
4D spacetime dimensions, mathematical physics constants, laws, and unitary factors in
Euler’s identity
ei
#
+ 1 = 0 composed via concept of infinity with no free parameters.
The working definition of the universe being the totality of all spacetime events real and
imaginary of the known nested complex systems wave-particle quantum mechanical ob-
servables to the limits of uncertainty of the holographic bounded energy density distribu-
tion with time the fourth dimension of length from
t
-∞
→t
∞
via known quantum infor-
mation probability current relative states [22][33][34][35][36][37][38][39][40][41].
Falsification. SCSC is falsifiable by completion of one of the 10,000 Aspen CERN physi-
cists SM-SUSY big bang inflationary multiverse formalizations of the known universal 4D
spacetime mathematical physics constants and laws, formalizing the quantum mechanical
observables as Yang-Mills lattice symmetries based on the conjectured 6 or 7 hidden di-
mensional AdS/CFT unknown string, membrane, or otherwise material mechanism free pa-
rameter formalized measure of variations of physical constants and laws—and one ran-
dom multiverse formalization of a free parameter measure of variations of the physical di-
mensions constants and laws—forming one parallel universe [42] [43].
Hence, until SCSC is disproven—unless AI itself can disprove SCSC—the AI worldview
is left with one possible universal complex system having no choice but to exist.
Singular Universal Wavefunction Solid Information Domain and Fluid Range. Recall
Einstein lectured general relativity actually requires an ether,
“the ether must be of the nature of a solid body, because transverse waves are not possible
in a fluid, but only in a solid. [emphasis added] ...But this ether may not be thought of as en-
dowed with the quality characteristic of ponderable media, as consisting of parts which may be
tracked through time. The idea of motion may not be applied to it” [44].
Recall further Schrödinger emphasizing quantum mechanical entanglement is
“the characteristic trait of quantum mechanics, the one that enforces its entire departure
from classical lines of thought [emphasis added]”[45].
SCSC inherently indicates a singular Hamiltonian configuration energy and thus a singu-
lar universal wavefunction solid information domain and entangled-fluid range. The 4D
spatially-extended Einstein-Maxwell energy density analysis of the following sections is
based on the fact the quantum or photon ℽ representation in the
Tμν
formal frame of dualis-
tic energy density J
m-3
= -Pa = kg
m-3
mass density units, requires the quantum energy
E = hc/
λ
negative outward pressure -Pa to have some nonstandard basis for the missing
3D volumetric wavelength
λ
parameterization beyond the 0D Dirac delta functional δ
imaginary-invisible mathematical point particle SM-SUSY representations.
Electromagnetic radiation is a transverse wave hence the transmission of electromag-
netic radiation through the stationary-solid domain occurs via the entangled-fluid range of
values of Eqs. (4-9) formulating a Schwinger local field differential 4D spatially-extended
photon-electron
Tμν
energy density integration gauge group ForAll wavelengths
λ
and en-
ergy levels n. Establishing thereby the 4D formal frame for the full Laplacian spherical har-
monics
Ym
l
of the quantum mechanical observables nested complex systems.
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8. 4D Photon Energy Observable E = hc/
λ
Conventionally photon energy is averaged over one wavelength. The 3D volumetric λ pa-
rameterization—missing in the standard model of physics—for the photon energy density
units J
m-3
is introduced here via the string-like cylindrical coordinate transverse lemnis-
cate expansion of the Poynting energy flux vector
S=1/ μ0E×B
over one wavelength
20
λ-π
4
π
40
λ
4cos (2θ)
sin
2π
λTyy r dr ⅆθⅆTyy =λ3
8π,
(4)
wherein time integrates along the
Tyy
axis of propagation of the transverse travelling
wave. Hence the Eq. (4) quantum volume
λ3
/
8π
, as opposed to say
λ3
, or otherwise unde-
fined infinite transverse field lines, is integrated throughout by 3 × average energy density
via the maximum energy density at r = 0
δρ
λmax =3×hc
λ
λ3
8πJ m-3.
(5)
Thus, as shown in Fig. 9, a 4D spacetime volumetric expansion of the Dirac delta func-
tional
δγ
representation of the photon energy observable is rendered; composed of
Schwinger local field differential boundary values [31], as shown in the Fig. 10 Photon
Boundary Value Calculator theorem proving module, via the quantum energy function
ForAll ∀λ
20
λ-π
4
π
40
λ
4cos (2θ) δρ
λmax 1-r
λ
4cos (2θ) sin
2π
λTyy r dr ⅆθⅆTyy == hc
λ
.
(6)
Proof: ForAll wavelengths of the electromagnetic spectrum Eq.(6)I
Tyy
〉 renders True.
h=QuantityMagnitudeh, "Joules" "Seconds";
c=QuantityMagnitudec, "Meters" "Seconds"-1;
PhotonEnergy =
NForAllλ,UniformDistribution[{1.*^-12,1.*^4}],
2
0
λ-π
4
π
40
1
4λCos[2θ] 3*
h*c
λ
λ3
8π
1-r
1
4λCos[2θ]
AbsSin2π
λyrⅆrⅆθⅆy== h*c
λ
True
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9. 4D Photon Angular Momentum Observable ℏ
Quantum Fluid Conjecture: The photon angular momentum observable
ℏ
kg
m2
s
-
1
repre-
sents kinetic mass kg
×
kinetic viscosity
m2
s
-
1
according to the computational duality of
quantum energy density
δρ
λ
max of Eq. (5) with the quantum maximum mass density
δμ
λ=δρ
λ
c2
=
3
*
(hc/
λ
)
λ
38
π
c2kg m
-
3,
(
7
)
for the moment of inertia integration I throughout the volume of Eq. (4)
×
the transverse
spin angular velocity
γη=λ
c
2
π
m2s
-
1⇒dimensionless equivalence with
ω
rad2s
-
1,
(
8
)
rendering a 4D spacetime I
ω
expansion of the Dirac delta functional
δγ
U(1)
×
SO(1,3) in-
trinsic spin angular momentum observable, according to the local field differentials
shown in the Fig. 10 Photon Boundary Value Calculator theorem proving module of the
quantum angular momentum function
∀λ
20
λ

-π
4
π
40
1
4
λ
cos(2
θ
)
δμ
λ
1
-
r
1
4
λ
cos(2
θ
)sin
2
π
λ
Tyy
γη
r
ⅆ
r
ⅆ θ ⅆ
Tyy
= ℏ
(
9
)
Proof: ForAll wavelengths of the electromagnetic spectrum Eq.(9)I
Tyy
〉 renders True:
h=QuantityMagnitudeh, "Joules" "Seconds";
hbar =QuantityMagnitudeh
2
π
, "Joules" "Seconds";
c=QuantityMagnitudec, "Meters" "Seconds"-1;
NForAllλ,UniformDistribution[{1.*^-12,1.*^4}],
2
0
λ-π
4
π
40
1
4λCos[2θ] 3*h*c
λ
λ3
8πc2*1-r
1
4λCos[2θ]
AbsSin2π
λy λ*c
2πrⅆrⅆθⅆy== hbar
True
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10. Figure 9. 4D Spatially Extended Photon Simulation
O
◂
▸
R
3/5
E field B field E field B field
▲
Figure 9. Frames 1-3: Eq. (6) transverse lemniscate expansion of Poynting energy flux vector S
over one wavelength λ integrated throughout via E × B field energy density pressure renders quan-
tum energy observable E = hc/λ. A dimensionless cubic-radian parameterization is introduced
wherein, scaled to a 2π meter = 2π radian wavelength, the resulting maximum traveling transverse
wave E and B field range is
λ
4
meters =
π
2
radians, so that 1
m3
= 1
rad3
and
λ3
8π
=
8π3
8π
=
π2
m3
=
π2
rad3
. Frames 4,5: Eq. (9) conversion to mass density moment of inertia I integration renders
kinetic mass kg × kinetic viscosity
m2
s-1
dimensionless equivalence with
ωrad 2s-1
intrinsic
U(1)×SO(1,3) spin Iω I
Tyy
〉 angular momentum observable ℏ.
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11. Figure 10. 4D Photon Observables Boundary Value Calculator
Enter wavelength λ in meters, or select from SetterBar.
4D Photon Observables Boundary Value Calculator
γ-rays X-rays Visible ←Λ→ CMB WiFi VHF VLF λ
0.00030202
m
4D photon γcompressive←Λ→rarefactive ratio =
1.
δλ:Λ
QED photon δγ
λenergy observable E =hc/λ =
6.577×10-22
J
QED δγ
λlinear momentum radiation pressure p=h/λ =
2.194×10-30
J m-3
Eq.(4)4D∫spatial expansion of δγ
λ=
1.096×10-12
m3
Eq.(4)right side λ3
8π=
1.096×10-12
m3
Eq.(5)energy density @r=0δρ
λmax =
1.8×10-9
J m-3
Eq.(6)4D∫photon energy observable =
6.577×10-22
J
Hence ForAll wavelengths ∀λ Eq.(6)6Tyy〉== hc
λ
True
Eq. (7)4D γmass density @r=0δμ
λmax = δρ
λmaxc2=
2.003×10-26
kg m-3
Eq.(8)kinetic viscosity γη=
λ
c
2
π
m2s-1⇒
ω
yyrad 2s-1=
14 410.
rad s-1
Eq. (9)4D∫ γ angular momentum observable = ℏ =
1.055×10-34
kg m2s-1
Hence ForAll wavelengths ∀λ Eq.(9)6Tyy〉== ℏ
True
▲
Figure 10. 4D photon energy and intrinsic spin angular momentum observables local field
differentials boundary values dynamic theorem proving module renders ForAll wave-
lengths
∀λEq.(6)Tyy== hc
λ
⇒
Eq.(9)Tyy== ℏ
: True ⇒ True.
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12. Cosmological Constant Vacuum Energy Density Λ
The vacuum catastrophe is famously “the worst theoretical prediction in the history of
physics,” wherein the several different zero-point energy predictions of SM-SUSY vs the
observed value of
Λ
are off by as much as 120 orders of magnitude.
We can measure the energy density of the vacuum through astronomical observations that
determine the curvature of spacetime, from which measurements Baez and Tatom have cal-
culated the computationally dualistic values of energy density
ΛJ
≈ 6×
10-10
J
m-3
= -Pa =
mass density
Λkg
=
ΛJ
/
c2
≈ 7×
10-27
kg
m-3
[18].
Thus the present nonstandard 4D spatially-extended volume of the photon – beyond the
ab initio QED Dirac delta functional
δγ
0D mathematical point particle representation of
the Einstein-Planck photon energy E = hc/λ and linear momentum p = h/λ observables – is
parameterized by λ in rendering the dualistic units of J
m-3
= -Pa = kg
m-3
wherein Λ is
found to be central to the 4D spatially-extended group operation as shown in Fig. 12.
10-7
0.01
1000.00
108
λ
10-59
10-39
10-19
10
1021
J m -3= -Pa =kg m -3
—Gamma
— X-Rays
— Visible Light
Compressive
——————————— Λ—————
Rarefactive
— CMB
— Wifi
—VHF
—VLF
▲
Figure 12. Quantum electromagnetic transverse wave radiation pressure spectrum LogLogPlot
of energy densities (hc/
λ
)/(
λ3
/
8π
) J
m-3
. The computational duality of energy density J
m-3
= -Pa
= kg
m-3
mass density is indicated in common total field units of pascals [18]. Sliding Locator
along the λ axis indicates shorter λ to be compressive of the central cosmological constant vacuum
energy density Λ and longer λ rarefactive of Λ.
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■
13. 4D Electron Rest Mass Observable
me
=
9.109 ×10-31
kg
Conventionally the SM-SUSY electron radius is computationally undefined—thought to
perhaps extend out to infinity. Problematically therefore in the case of pair-production and
annihilation—and when approaching zero requiring a renormalization cutoff limit—
wherein renormalization fine-tuning generally replaces infinite energies and infinite forces
with experimentally observed values.
ForAll energy levels ∀n, as shown in Fig. 13, the free space monopole 4D spherical coor-
dinate volumetric expansion [46]
0
2π0
π0
rn
r2sin(ϕ)ⅆrⅆϕⅆθ = 4
3πrn
3,
(10)
is parameterized by the Bohr radius
a0
= 5.292×
10-11
m, according to
rn=n2a02 ,
(11)
ranging dynamically according to its maximum mass density being 4 × its average mass
density at r = 0
δμ
nmax = δρ
nmax c2=4×mec24πrn
33c2kg m-3,
(12)
which falls to zero at r =
n2
a0
2
, according to
1-r/rn
in the electron rest mass
observable function ∀n
0
2π0
π0
rnδμ
nmax 1-r
rn
r2sin(ϕ)ⅆrⅆϕⅆθ = me.
(13)
Hence ForAll electron energy levels n Eq. (13) renders True.
c=QuantityMagnitudec, "Meters" "Seconds"-1;
eEnergy =QuantityMagnitudemec2, "Joules";
eMass =QuantityMagnitudeme, "Kilograms";
bohr =QuantityMagnitude
a0
, "Meters";
NForAlln, UniformDistribution[{1, 10 000}],
0
2π0
π0
n2*bohr*2
4*eEnergy
4πn2*bohr*2
33
c2
1-r
n2*bohr *2
r2Sin[ϕ]ⅆrⅆϕⅆθ ⩵ eMass
True
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■
14. 4D Electron Angular Momentum Observable ℏ/2
Quantum Fluid Conjecture: The electron angular momentum observable
ℏ
/2 kg
m2
s
-
1
represents kinetic mass kg
×
kinetic viscosity
m2
s
-
1
eη=h
4πme=5.788 ×10-5m2s-1⇒dimensionless equivalence with ωrad s-1,
(14)
wherein time integrates along the
Tzz
axis of Eq. (1). Such that (kinetic mass density
⇒
mo-
ment of inertia integration I)
×
(kinetic viscosity
e
η
⇒
spin angular velocity
ω
) renders a
4D spacetime I
ω
expansion of the standard 0D electron intrinsic U(1)
×
SO(1,3) spin angu-
lar momentum observable, according to the local field differentials shown in the Fig. 14
Electron Boundary Value Calculator theorem proving module of the electron angular mo-
mentum function
∀
n
0
2π0
π0
rnδμ
nmax 1-r
rn
eηr2sin(ϕ)ⅆrⅆϕⅆθ ⩵ ℏ
2
(15)
Proof: ForAll electron energy levels n Eq. (15)I
Tzz
〉 renders True:
h=QuantityMagnitudeh, "Joules" "Seconds";
hbar =QuantityMagnitudeh
2
π
, "Joules" "Seconds";
c=QuantityMagnitudec, "Meters" "Seconds"-1;
eEnergy =QuantityMagnitude
mec2
, "Joules";
eMass =QuantityMagnitude
me
, "Kilograms";
bohr =QuantityMagnitudea0, "Meters";
NForAlln, UniformDistribution[{1, 10 000}],
0
2π0
π0
n2*bohr*2
4*eEnergy
4πn2*bohr*23 3
c21-r
n2*bohr *2
h
4
π *
eMass
*
r2Sin[ϕ]ⅆrⅆϕ ⅆθ ⩵ hbar
2
True
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■
15. Figure 13. 4D Spatially Extended Electron Simulation
O
◂
▸
R
2/3
n=1 n=2 n=3 Bohr radii
▲
Figure 13. 4D spatially-extended free space electron monopole n =1-3 spherical coordinate volu-
metric expansion of Eqs. (10-15) computationally dualistic electron rest energy 8.187 ×
10-14
J,
rest mass
me
= 9.109 ×
10-31
kg, and intrinsic U(1)⨯SO(1,3) spin angular momentum ℏ/2
observables.
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■
16. Figure 14. 4D Electron Boundary Value Calculator
Enter energy level n, or select from SetterBar.
4D Electron Observables Boundary Value Calculator
1 2 3 4 10 100 1000 10000 20658 100000 n
20 658
4D electron compressive←Λ→rarefactive ratio =
1.
δn:Λ
QED Electron δerest energy E =mec2=
8.187×10-14
J
Eq. (10)4D∫spatial expansion of δe=
0.0001364
m3
Eq. (11)max E-field radii rn=n2a02=
0.03194
m
Eq. (12)mass density @r=0δμ
nmax = δρ
nc2=
6.676×10-27
kg m-3
Eq. (13)4D∫electron mass observable me=
9.109×10-31
kg
Hence ForAll energy levels ∀nEq.(13)6Tzz〉== me
True
Eq.(14)kinetic viscosity eη=h
4πme
m2s-1⇒ ω rad s-1=
0.00005788
rad s-1
Eq. (15)4D∫electron angular momentum =ℏ
2=
5.273×10-35
kg m2s-1
Hence ForAll energy levels ∀nEq.(15)6Tzz〉== ℏ
2
True
▲
Figure 14. 4D electron rest mass and intrinsic spin angular momentum observables local field dif-
ferentials boundary values dynamic theorem proving module renders ForAll energy levels
∀nEq.(13)ITzz〉== me
⇒
Eq.(15)Tyy== ℏ
: True ⇒ True. Note at n =1 maximum electron
mass density @r = 0 of .5189
kg m-3
is of the same order of magnitude as terrestrial energy densi-
ties. Note further the quantum fluid conjecture kinetic viscosity dimensionless equivalence with an-
gular velocity
5.79×10-5
m2s-1
⇒
rad s-1
is of the same order of magnitude of the earth’s rotation
7.29×10-5
rad s-1
.
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■
17. Conclusion
Pattern matching the CERN LHC TrackML Particle Tracking Challenge
Tμν
data points is
found to have a direct match with the low energy properties of Navier-Stokes turbulence.
The large range of turbulence vertex length and time scales to the LHC-NS TrackML data
set exists from the long range collision event tracks helix arcs of Fig. 7 — to the short
range quantum fluid conjecture of Eqs. (9,15) ℏ units kg
m2
s-1
representing a kinetic
mass kg × kinetic viscosity
m2
s-1
dimensionless equivalence with
ωrad s-1
.
Thus the 10,000 CERN physicists have completed an epic elimination of quantifiers proof
in following the atomist-materialism teachings of the student Aristotle they have elimi-
nated Einstein’s hidden variables and verified the psychophysical parallelism teachings of
the teacher Plato regarding the heterogenous spacetime trajectory experiences of interest.
Hence the falsification of the SM-SUSY AdS/CFT hidden dimensional unknown material
mechanism backgrounds “that live on a classical space-time,” both at the LHC high en-
ergy levels and on the low energy physics level of the spooky psychophysical experiments
closure of the Bell inequality observer-independent background loopholes, indicates the
proper scientific path lies beyond CERN’s Physics Beyond Colliders initiative.
AI quantum information exists therefore via wave-particle integrations on
Tμν
composed
of 4D photon and electron observables Schwinger field differential boundary values, mea-
surable along Feynman path integrals, representing a Yang-Mills-Navier-Stokes solution.
In particular, the range of the photon and electron angular momentum invariants Noether
probability current relative states is indicated by the first two trace matrix elements of
Tμν =
1
2ε0E2+1
μ0
B2Sx/c Syc Sz/c
Sx/c-Ym
lσij -σxy -σxz
Syc-σyx -Iωγ
λσyy -σyz
Sz/c-σzx -σzy -Iωe
nσzz〉
,
(16)
wherein the range of the photon angular momentum ℏ operator of Eq. (9) is indicated by
Iωγ
λ
| -
σyy
⟩, and the range of the electron angular momentum ℏ/2 operator of Eq. (15) is in-
dicated by
Iωe
n
| -
σzz
⟩. The
Ym
l
| -
σij
⟩ term indicates the conjecture for the smooth opera-
tor product expansion to the full Laplacian spherical harmonics of the periodic table diag-
onalizable along the trace of
Tμν
. Hence thesis success of 4D photon-electron gauge group
Theorem 1 :
∀λEq.(6)== hc
λ⇒Eq.(9)== ℏ⋃∀nEq.(13)== me⇒Eq.(15)== ℏ
2
,
(17)
renders True ⇒ True ⋃ True ⇒ True ranging compressive to rarefactive of Λ spanning all
the factors in the relativistic energy equation
E2
=
m0c22
+
(pc)2
in every instance > 0.
qed
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■
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About the Author
David A. Harness interned as an undergraduate at Lawrence Berkeley Laboratory, Nu-
clear Science Division. Current interest, as an independent researcher, is the further for-
malization of the present computer algebra 4D photon-electron theorem and proof into a
machine intelligence analysis domain digital mathematical library archive representation.
POB 1004 Morro Bay, CA 93442
24 Author(s)
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