Category: the true

Edward Witten : Magic, Mystery, and Matrix

 

“Quantum field theory is a very rich subject for mathematics as well as physics. But its development in the last seventy years has been mainly by physicists, and it is still largely out of reach as a rigorous mathematical theory despite important efforts in constructive field theory. So most of its impact on mathematics has not yet been felt. Yet in many active areas of mathematics, problems are studied that actually have their most natural setting in quantum field theory. Examples include Donaldson theory of four-manifolds, the Jones polynomial of knots and its generalizations, mirror symmetry of complex manifolds, elliptic cohomology, and many aspects of the study of affine Lie algebras.

To a certain extent these problems are studied piecemeal, with difficulty in understanding the relations among them, because their natural home in quantum field theory is not now part of the mathematical theory. To make a rough analogy (Figure1), one has here a vast mountain range, most of which is still covered with fog. Only the loftiest peaks, which reach above the clouds, are seen in the mathematical theories of today, and these splendid peaks are studied in isolation, because above the clouds they are isolated from one another. Still lost in the mist is the body of the range, with its quantum field theory bedrock and the great bulk of the mathematical treasures.”

this is most lovely….

Surreal number tree

[gview file=”http://www.billtoole.net/wordpress/wp-content/uploads/2016/05/Surreal_number_tree.svg”]

By Lukáš Lánský If you want to help me create some nicer or more accurate version of this image, see Python code that generates it. I welcome pull requests. – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=19134117

wikipedia entry

Palden Yonten Thaye Lodro Chokyi Gyaltsen

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Dear Sangha Members and Friends of the Padmasambhava Buddhist Center,

I have the great privilege to share with you one of the most beautiful announcements that I can make: the longtime wishes and prayers of all the PBC members and devoted disciples of Ven. Khenchen Palden Sherab Rinpoche have been answered.

Recently, His Eminence Terton Namkha Drimed Rinpoche discovered the reincarnation of Ven. Khenchen Palden Sherab Rinpoche on the eighth day of this month, just two days ago. He was given the name Palden Yonten Thaye Lodro Chokyi Gyaltsen!

At Padma Samye Ling, the North American Monastery of PBC, we enjoyed a great celebration for the 10th Day of Guru Rinpoche, and all the gathered Sangha rejoiced in this announcement with tremendous joy and excitement.

Now that we have discovered the reincarnation of Ven. Khenchen Palden Sherab Rinpoche, H.E. Terton Namkha Drimed Rinpoche is requesting that everyone recite many Dusum Sangye prayers of Guru Padmasambhava. This is my wish as well. We pray for the continued success of all the Dharma activities of Khenchen Yangsi Rinpoche, that there are no obstacles and everything unfolds very smoothly, for the fulfillment of all of his wishes, and that he will benefit the Teachings and all sentient beings for aeons.

Yours in the Dharma,
Khenpo Tsewang Dongyal

Padma Samye Ling
10th Day of Guru Rinpoche
April 16, 2016

 

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Ramanujan manuscript

Ramanujan

 

Ramanujan’s manuscript. The representations of 1729 as the sum of two cubes appear in the bottom right corner. The equation expressing the near counter examples to Fermat’s last theorem appears further up: α3 + β3 = γ3 + (-1)n. Image courtesy Trinity College library.

see article

vacuum properties of QCD

ActionAPE5LQanimXs30 ChargeAPE5LQanimXs30

The animations above illustrate the typical four-dimensional structure of gluon-field configurations averaged over in describing the vacuum properties of QCD [ Quantum Chromodynamics ]. The volume of the box is 2.4 by 2.4 by 3.6 fm, big enough to hold a couple of protons. Contrary to the concept of an empty vacuum, QCD induces chromo-electric and chromo-magnetic fields throughout space-time in its lowest energy state. After a few sweeps of smoothing the gluon field (50 sweeps of APE smearing), a lumpy structure reminiscent of a lava lamp is revealed. This is the QCD Lava Lamp. The action density (left) and the topological charge density (right) are displayed. The former is similar to an energy density while the latter is a measure of the winding of the gluon field lines in the QCD vacuum.

The animation at left was featured in Prof. Frank Wilczek’s 2004 Nobel Prize Lecture.

Visualizations : Centre for the Subatomic Structure of Matter (CSSM) and Department of Physics, University of Adelaide, 5005 Australia    |    link

dimensionless constants

Parameter Meaning Measured Value
g
θW
gs
Weak coupling constant at mZ
Weinberg angle
Strong coupling constant at mZ
0.6520 ± 0.0001
0.48290 ± 0.00005
1.221 ± 0.022
μ2
λ
Quadratic Higgs coefficient
Quartic Higgs coefficient
~ −10−33
~ 1 ?
Ge
Gμ
Gτ
Electron Yukawa coupling
Muon Yukawa coupling
Tauon Yukawa coupling
2.94 × 10−6
0.000607
0.0102156233
Gu
Gd
Gc
Gs
Gt
Gb
Up quark Yukawa coupling
Down quark Yukawa coupling
Charm quark Yukawa coupling
Strange quark Yukawa coupling
Top quark Yukawa coupling
Bottom quark Yukawa coupling
0.000016 ± 0.000007
0.00003 ± 0.00002
0.0072 ± 0.0006
0.0006 ± 0.0002
1.002 ± 0.029
0.026 ± 0.003
sin θ12
sin θ23
sin θ13
δ13
Quark CKM matrix angle
Quark CKM matrix angle
Quark CKM matrix angle
Quark CKM matrix phase
0.2243 ± 0.0016
0.0413 ± 0.0015
0.0037 ± 0.0005
1.05 ± 0.24
 θqcd CP – violating QCD vacuum phase  < 10−9
Gνe
Gνμ
Gντ
Electron neutrino Yukawa coupling
Muon neutrino Yukawa coupling
Tau neutrino Yukawa coupling
< 1.7 × 10−11
< 1.1 × 10−6
< 0.10
sin θ′12
sin 2θ′23
sin θ′13
δ′13
Neutrino MNS matrix angle
Neutrino MNS matrix angle
Neutrino MNS matrix angle
Neutrino MNS matrix phase
0.55 ± 0.06
≥ 0.94
≤ 0.22
?
ρΛ
ξb
ξc
ξν
Q
ns
Dark energy density
Baryon mass per photon ρb / nγ
Cold dark matter mass per photon ρc / nγ
Neutrino mass per photon ρν / nγ  =  3⁄11 Σ mνi
Scalar fluctuation amplitude δH on horizon
Scalar spectral index
(1.25 ± 0.25) × 10−123
(0.50 ± 0.03) × 10−28
(2.5 ± 0.2) × 10−28
< 0.9 × 10−28
(2.0 ± 0.2) × 10−5
0.98 ± 0.02

 

from Dimensionless constants, cosmology and other dark matters : Max Tegmark, Anthony Aguirre, Martin J. Rees & Frank Wilczek

“Every fundamental property of nature ever measured can be computed from the 32 numbers in this table – at least in principle.” Max Tegmark in Our Mathematical Universe

Now Broadcasting in Planck Definition : Craig J. Hogan

If reality has finite information content, space has finite fidelity. The quantum wave function that encodes spatial relationships maybe limited to information that can be transmitted in a “Planck broadcast”, with a bandwidth given by the inverse of the Planck time, about 2×1043 bits per second. Such a quantum system can resemble classical space-time on large scales, but locality emerges only gradually and imperfectly. Massive bodies are never perfectly at rest, but very slightly and slowly fluctuate in transverse position, with aspectrum of variation given by the Planck time. This distinctive new kind of noise associated with quantum geometry would not have been noticed up to now, but may be detectable in a new kind of experiment.

arXiv:1307.2283v1    |    PDF

holometer_fnal_960

Fermilab Holometer

 

 

 

 

 

 

 

chasing ice

Rather incredible images of glacial calving – this clip was running today at an exhibition at the Louisiana Museum just outside of Copenhagen in Denmark.