User:Dan Gluck

• Merge Luxon and Bradyon into Mass in special relativity if no objections are raised.
• String theory: Rewrite overview, replace first image, add AdS-CFT images.
• Write String theory: a technical review.
• Add general w=p/u into Thermodynamics of the universe, which covers also Cosmic inflation and Big rip cases.
• Supersymmetry breaking.
• Gravitational instanton, instanton, Gravitational singularity (general - add massless fields, conical - blow up of orbifold)
• Angular momentum: commutation relations of J with any vector operator are like those of J with itself.
• Commutator, Commutativity: add a part about significance and use in Quantum mechanics.
• Expand Particle physics in cosmology.
• Expand Lattice QCD some day.
• Lagrange multipliers - add intuition (show 2d case).
• Prove Snell's law using Fermat's principle and Lagrange multipliers (+ add link in the latter to this as an example), and using Maxwell's equations.
• Expand Biblical criticism.
• Add Socrates's debate over whether evil is ignorance in Unsolved problems in philosophy and Problem of evil?
• Mass–energy equivalence: add a section about the difference between E=MC² and E=(1/2)Mv².
• Expand the Meat article and add pictures of the production process.
• Mention [http://www.anonymous.org.il/longshadow.htm this] in Global warming.

(pages I've started or was significantly involved in their writing):

• String theory
• Nuclear magnetic moment
• Shell model
• Woods Saxon potential
• Fermion
• Boson
• Measure (physics)
• Particle physics in cosmology
• E6 (mathematics)
• E7 (mathematics)
• E8 (mathematics)
• Gravitino
• Thermodynamics of the universe
• Proof sketch for Gödel's first incompleteness theorem
• Lattice QCD
• Unitarity (physics)
• Gravitational singularity
• Entropy (arrow of time)
• Arrow of time
• Relationship between string theory and quantum field theory
• Particle statistics
• Picture (string theory)
• Ramond sector
• Neveu-Schwarz sector
• Conformal symmetry
• Friedmann-Lemaître-Robertson-Walker metric
• Euler number (topology)
• Sphaleron
• Beta trefoil fold
• Two Tracts on Government
• Illustrative model of greenhouse effect on climate change

• Deuterium#Nuclear properties
• Quantum number#Quantum numbers with spin-orbit interaction
• SO(10) (physics)#Important subgroups
• Split supersymmetry#Advantages and drawbacks
• Physical cosmology#History of the Universe
• Tachyon#Modern interpretation: Quantum field theory
• Evolution as theory and fact#Predictive power
• Lindemann–Weierstrass theorem#A proof sketch
• Baryogenesis#Baryogenesis within the Standard Model
• Liénard–Wiechert potential#Derivation#Lorenz Gauge, Electric and Magnetic Fields
• Net (mathematics)#Properties (first proof: equivalence of continuity definitions)
• Seafloor spreading#Sea floor global topography: half-space model (may be moved to Mid-ocean ridge in the future).
• Von Neumann bicommutant theorem#Proof (major revision)
• Cochran's theorem#Proof
• Riemann integral#Integrability (rewrote proof which was wrong)
• Conway's Game of Life#Undecidability
• Factor_V#Structure
• Factor_VIII#Structure
• Factor_XIII#Structure
• Endothelial_protein_C_receptor#Structure
• Protein_S#Structure
• Decay-accelerating_factor#Structure
• Arithmetical_hierarchy#Computable_sets
• Post%27s_theorem#Proof_of_Post.27s_theorem
• Primitive_recursive_function#Use_in_first-order_Peano_arithmetic
• Computable_function#Provability
• Machine_that_always_halts#Provability
• Tidal_acceleration#Theory
• Dynamo_theory#Nonlinear_dynamo_theory (revised and added two subsection)
• Gamow_factor#Derivation
• Stellar_nucleosynthesis#Reaction_rate
• Mass–luminosity_relation#Derivation
• Mass–luminosity_relation#Core_and_surface_temperatures
• Radiation zone#Stability against convection
• Radiation zone#Eddington stellar model
• State of the Teutonic Order#Formation of a new nobility
• Separation of powers#Tripartite System
• Hilbert–Bernays provability conditions#Use in proving Gödel's incompleteness theorems
• Deduction theorem#Proof of the deduction theorem
• Spin (physics)#Relation to classical rotation
• Normal force#Physical origin
• Angular momentum#Conservation of angular momentum (except for the "general considerations" part)
• Second law of thermodynamics#Initial conditions at the Big Bang
• Big Bang#Thermalisation
• Chronology of the universe#Electroweak epoch and early thermalization
• Ozone–oxygen cycle#Main reactions in different atmospheric layers

• Dimensional reduction
• Superghost
• Worldsheet
• Secrets of the Baby Whisperer
• Multiplet
• Dilatino
• Adaptin
• Reclinomonas

We first consider the following matrix:

$M\_\{ij\}\; =\; (s\_i\; +\; t\_i\backslash sqrt\{2\})^\{u\_j\}2^\{(s\_i\; +\; t\_i\backslash sqrt\{2\})v\_j\}$

where i runs over all (2S-1)² pairs (s_i, t_i) with -S < s_i, t_i < S, and j runs over all (L₀+1)(L₁+1) pairs (u_j, v_j) with 0 ≤ u_j ≤ L₀, 0 ≤ v_j ≤ L₁.

S is an arbitrarily large integer, L₀ = S [Log(S)], L₁ = [S /Log(S)]. (here [x] denotes the integer value closest to x from below).

M_ij is a (2S-1)² by L matrix, and since (2S-1)² > L for large enough S, we may look at any determinant of an LXL sub-matrix of M, which we denote Δ.

|Δ| can be shown to satisfy an upper bound, |Δ|≤x^-L2/2 for some x>1, as we later discuss.

Now let us assume that $2^\{\backslash sqrt\{2\}\}$ is rational. Then for some integers a, b with b>1, $2^\{\backslash sqrt\{2\}\}\; =\; a/b$. Therefore:

$M\_\{ij\}\; =\; (s\_i\; +\; t\_i\backslash sqrt\{2\})^\{u\_j\}2^\{s\_i\}a^\{t\_i\; v\_j\}b^\{-t\_i\; v\_j\}$,

and hence:

$\backslash Delta\; =\; (A+\backslash sqrt\{2\}B)p\; a^\{t\_i\; v\_j\}b^\{-t\_i\; v\_j\}$, for some integers A, B, p.

Then one uses Liouville theorem on diophantine approximation to show that |Δ| satisfies a lower bound, |Δ| ≥ b^SL₁L.

For every x,b>1 there exists an S large enough such that: b^SL₁L< x^-L2/2. We thus arrive at a contradiction, and therefore $2^\{\backslash sqrt\{2\}\}$ must be irrational.

We turn now to the upper bound of Δ. As S (and hence L) grow larger, the determinant Δ contains multiplication of more factors (which tend to increase its size), but it also contains more lines and columns which become closer and closer to being linearly dependent (which tend to reduce its size), and the second effect is shown to be more prominent .

To show this, we see that every entry in the matrix M satisfies: $M\_\{ij\}\; =\; W^\{u\_j\}\; 2^\{W\; v\_j\}\; f\_j(z\_i)$, with $f\_j\; (x)\; =\; x^\{u\_j\}2^\{W\; v\_j\; (x-1)\}$, $z\_i\; =\; (s\_i\; +\; t\_i\; \backslash sqrt\{2\})/W$ and some $W\; >\; S(1+\backslash sqrt\{2\})$. Note that for all i, j.

Therefore:

$\backslash Delta\; =\; L!\; W^\{L\backslash sum\_j\; u\_j\}\; 2^\{W\; L\; \backslash sum\_j\; v\_j\}\; \backslash Delta\_1\; L!\; W^\{L\backslash sum\_j\; u\_j\}\; 2^\{W\; L\; \backslash sum\_j\; v\_j\}\; \backslash Delta\_1$ where $\backslash Delta\_1$ is the determinant of the LXL sub-matrice f_j(z_i) (instead of M_ij).

Let's try to write a concrete example for the Godel number required here, with Peano arithmetics and the decimal system. We will have to use abbrevations for lengthy expressions.

(under work)

α- alpha privativum, expressing want or absence.

αγείρω (root ΑΓΕΡ-) to bring together, gather, assemble

δωμα a house, a chief room, a hall,

αδρός strong, great. Of persons: large, fine, well-grown.

αγαπάω to treat with affection, love, be fond of

έχω to have or to hold (Ionic imperative: εχεσκον) Iliad: to grip

αυριον dawn, aurora, ουρανός the sky [perhaps source of light?],

ελλος a young deer, fawn

ελλοψ Hesiod = mute (for fish)

ύλη a wood, forest, woodland. Homerus and Herodotus: forest trees.

άνθρωπος man, or woman. (latin: homo, not vir) a human being

οπτάω to cook by means of fire or dry heat.

όφις a serpent, snake

αράχνη a spider, a spider’s web

αρά I. a prayer. Especially a prayer for evil, a curse, imprecation. II. The

effect of the curse, bane.

δόλιχος long

έρα ground

ερώ say, speak

αίθω (1) to light up, kindle. (2) intransitive: to burn or blaze.

αιθάλη soot. Αιθίοψ = Ethiopian = פני אש. αίθος = fire

αστράπτω hurl lightnings (of Zeus) αστραπή = lightning, αστήρ =star

σοφός skilledin any handicraft or art, cunning in his craft. Clever, wise.

βαίνω (ΒΑ-) to walk, to step, to go, to come, to arrive, to depart, etc.

φρέαρ Iliad etc,: a well

βάραθρον a pit, (at Athens a left behing the Acropoliw, into which

criminals were thrown

φαείνω Skt. *bha- to shine, give light בהר, בהק

βύσσος a fine flax and the linen made from it (a later borrowing?)

βωμός any raised platform, or stand, araised place for sacrificing, altar.

πυρός wheat

flee, flight Skt. palay- ברח (Gothic: pliuhan, etc.)

πέσσω I : of the sun: to ripen. II. By the action of fire: to cook, bake.

όχθη גדה

γίγας mostly plural: Γίγαντες = Giants, a savage race destroyed by the Gods

κυλίω to roll, גל (see, γογγύλος – עגול)

γλάφω to scrape up (the ground). γλαφυρος = polished, finished.

γλυπ-, γλυφ- (akin to γλάφω) to carve, cut out with a knife

γοάω, γόος to wail, groan, weep

Αίγυπτος Egypt (αια-γυπ) ארץ גושן

γεφυρόω to bridge over, make passable by a bridge, γέφυρα = a bridge

τιτθός a teat, nipple

γύρος a ring, circle

δύη a woe, misery, anguish, pain.

θολός mud, dirt, the dark juice of the cuttle-fish. θολόω to make turbid

τρέχω to run, move quickly

έρχομαι (fut. ελθω) to come, to go

ολολύζω, αλαλάζω (= crying aloud to the gods in prayer or thanksgiving)

όρος a mountain, a hill (Cf. C.D. Buck, A Dictionary of Selected Synonyms in the Prinicipal Indo- European Languages: “Gr. όρος ..… from IE *er- ‘move, raise, rise’ seen in Skt. ŗ- , G r. όρνυμι , Lat. oriri.”. Heb. רם= high, also connected?

αράω (old verb: to harm)

σφάζω to slay, slaughter, properly by cutting the throat. σφαγή slaughter,

σεύω (έσσευσα) to put in quick motion. σείω to move to and fro. σεισμός = earthquake

σκώληξ a worm.

μέλος (for the σ see μικρ-, σμικρ) a song, tune

[ζέω ( = to boil) זעם (= anger)]

ρέω (ροή) to flow, stream, gush

σπείρω ( Lat. sero) to sow seed Akk. zāru זרע

κόπτω to strike, smite, knock down, cut off chop down

χωμα earth thrown up, a bank, a mound, a dike

Lat. forare , Akk. harāru חרר ( hole, Old Eng.: hol, חור )

άλσος a glade or grove (see ύλη, אלה, etc.)

γάλα (root: ΓΛΑΚ-, ΓΛΑΓ-) milk חלב

connected to γλαύκος, γλυκύς, glow, etc. ? and to λευκός, -- לבן ?

χαλάω Iliad: to slacken, loosen

γάμος, γαμέω) a wedding, wedding-feast, marriage, wedlock.

ξένος In Homer: a guest friend, i.e. any citizen of a foreign state, with whom one

has a treaty of hospitality for self and heirs, a refugee.

σκεπάω to cover, shelter.

σκάπ-τω to dig

σκότος darkness, gloom

χήρα (-ος) a widow, bereaved Akk. Һarābu חרב

and κάρφω to dry, destroy

ορρωδέω to fear, dread, shrink from. (formed so as to express the shuddering

of fear)

χαράττω (ΧΑΡΑΚ-) to cut into, to sharpen, whet, scratch. (χαράσσω)

αρόω to plow

δείδω (epic aor. έδδεισα) to fear, dread ω

εδνόω to betroth, to marry

σφαγ- σφακ- slaughter (see above: טבח (זבח)

δρόσος = dew, υδωρ = water, θάλασσα = sea, τέλμα = standing water, marsh,

pool, pond.

τρέφω (έθρεψα) to rear, feed. τροφή food, nourishment

μογέω, μόγος to toil, to suffer

*δάω (anc. root =learn, perf.: to know) Skt. vid- = to know Akk. idu ידע

οίδα (perf. of to see= know)

οίνος wine

οιωνός = a bird of omen, and also omen. Aesch. οιωνός γόος, but the only

bird that makes a wailing sound – γόος -- is the dove!

Ιάπετος one of the Titans (sons of Uranus and Gaea), father of Atlas,

Prometheus, etc. According to a tradition – rather late—he formed

the body of the first man with earth and water (perhaps his own

tears) into which Athena breathed soul and life.

לא במקרה,הסופר בחר שם זה לאבא של פינוקיו! :Japetto

ύπνος sleep, slumber

ιασπις Akk. (j)ašpu ישפה (but not a basic, primitive word…)

ιθύς straight, direct ιθύνω: make straight, guide in a straight line

καίω to light kindle, Passive: to get burned, καύμα : burning heat.

κικυς (in Homer) strength, vigour.

(h)όλος whole, entire, Akk. kullatu כל

κλείω to shut, close, bar, to confine.

σκύλαξ (OE hwelp) a young dog, puppy, a whelp, generally: a dog -- Κέρβερος

κλωβός a bird cage (El Amarna: kilubi)

κάμνω (root: KAM-) Iliad: to work, of smith’s work.

κύπελλον a big-bellied drinking vessel, a beaker, goblet, cup

κυφός (r.: ΚΥΠ-) bent forward, bent, stooping

κριός a ram

χράω (1) to be eager to do (2) to furnish what is needed. χρη = must, need

κείρω (I) to cut the hair (II) to cut, to hew out (of wood), destroy

γρύψ , Eng. Griffin

κρόκος, IE crocus Akk. kurkanu כרכם

χιτών (κιθών) the garment worn next the skin, in early times: a man’s frock.

Later worn by women as well.

νάσσω, νάττω to press, squeeze, ναστός: a well kneaded cake

λανθάνω (root: ΛΗΘ- ΛΑΘ) to escape notice, be unseen, etc.

λέων a lion Akk. nesu ליש

μανθάνω (r.: ΜΑΘ-) Iliad: to learn, to know, to understand.

λέγω to say, to speak larynx = לע ( whence Arab.

λάρυγξ = לע + ρύζω(=to growl) ?

λωβάομαι to treat despitefully, to outrage, λώβη an outrage, dishonour

λείχω to lick up

γλω̃σσα the tongue, the organ of speech. Homerus: language

μω̃̃̃μος a blame, riducule, disgrace. μωμεύω (Hom.) to find fault.

μίσγω to mix one thing with another, join together, to mingle.

μυελός = marrow, μύχιος = inward, inmost, μυχός = the innermost place.

Connected to μυέω, μυστήρια? סתר – מוסתר?)

Lat. amarus French: amer, = bitter

μετρέω to measure

πίμπλημι (r.:ΠΛΕ- or ΠΛΑ-) to fill full of a thing . Passive: to be filled.

μέγαρον Homer: a large room or chamber, a hall.

βασιλεύς a king, chief

μάσσω to handle, touch

εγγύς = near, near at hand

ναίω, ναιετάω = dwell

νέω to go, νέομαι to go or come

έχις, έχιδνα an adder, viper (Skt. ahi)

πίπτω to fall

δάκνω (root: ΔΑΚ-) to bite

δίδωμι (root: ΔΟ-) to give, to grant

σηκός, σακός a pen for lambs)

σής a moth (which eats woolen stuff)

αγαπάω to treat with affection, to caress, love, be fond of..

γογγύλος round

γερανός a crane

κόραξ a raven, crow

αιξ a goat

αετός an eagle

αχλύς a mist, a mist over the eyes of one dying

άναξ a lord, master, being applied to the gods, esp. Apollo and Zeus.

A title given to all men of rank and note.

άγχω to strangle, throttle, αγχόνη a throttling, strangling, hanging

ενίπ-τω to reprove, upbraid ( connected to όνειδος )

ασκέω to work, to form by art, to fashion, to practice and art.

ίδη in plural: a timber tree, in singular: a wood

ακίς עקצ, עֺקץ

σκορπίος Akk. aqrabu עקרב

Έρεβος Akk. erebu ערב

εγείρω Akk. êru ער (root: ,עור Aram. עיר ) IE *ger- Skt. jagr-, Av. gar-

είς Akk. iśten עשתי- (found only in composites)

[Καφτωρ Akk. Ištar עשתרת Was the island named in honour of the goddess (as Athens for Athena) and later renamed Crete under the influence of Ugarit (as St. Petersburg –Leningrad)?

πεδίον Akk. šadu פדן [a different form of שדה ?]

πω̃; όποι, etc. Lat. qu- פה

πέρδομαι, Skt. pŗd- Akk. balātu פלט (fart, peter, etc.)

πέλας, πελάζω פלש

πατέω פסע (and in the Bible: [פשע

βοάω, βοή, פעה

πόρτις Akk. parru פר, פרה

flight, Skt. palay- ברח ,פרח

οπώρα, fruit Skt. phala- פרי (connected to root פרה = grow)

Lat.flos, IE *bhle-, bhel- Akk.pirhu פרח

πείθω פתה, פֽתה (later borrowing?)

Πύθων Akk. bašmu פתן

σχελίς Akk. şelu צלע

σκοπέω Akk. šafu צפה (and ; שקפ (Latιn: aspicere)

κάπρος = wild boar Lat. caper Akk. şapir צפיר ]

Lat. strictus צרר [ = bound together, whence narrow: Skt : avi-stīrņa- and avistŗa צר (It. stretto, Fr : etroit ; etc )

καλέω to call, to summon, to call by name, to name,

κλαίω to weep, lament, wail, cry.

κράζω, κραυγή, cry out,

καίνω ( = kill, in Iliad) קין (the name) ( Hitt.: kwen-)

εύ-κολος easy

δύσ-κολος difficult

κέλυφος a sheath, case, pod, shell

καλύπτω (r. KΑΛΥΒ-) to cover with a thing

κάννα a reed

κρύος icy cold, chill, frost

κυρέω, κύρω meet with, light upon, fall in with,

κέρας the horn of an animal, horn as a material, anything made of horn

οράω (and λάω) to see, look at, behold

οργή Ι. natural impulse, temperament, ΙΙ. passion, anger, wrath

οργίζω to provoke anger

ορμάω to set in motion, spur on, push on,

ορμή a violent movement onwards, onset, an attack

έρπω to creep, crawl, to move slowly

ρύπος dirt, filth, dirtiness

ορχέομαι to dance in a row, and generally: to dance

εθέλω or θέλω (Doric δήλομαι) to wish, will, purpose

θήρ, φήρ awild beast, a beast of prey

θηράω = to hunt or chase wild beasts θήραμα = the hunted animal

ταυ̃ρος a bull

σκηνή a covered place, a tent, a tented cover

στέλλω I. to set in order, equip, furnish with II. to dispatch, send.

In Medium: to to send for one.

συλάω to strip off, esp. to strip off the arms of a slain enemy, to pillage, plunder,

rob .

λεηλατω̃ to drive away cattle as booty, to make booty, plunder, despoil

λεία booty, plunder. ληστής robber, plundered.

πλήρης full of a thing, complete.

οδούς (gen. oδόντος) a tooth

σινέομαι, σίνομαι to do one harm or mischief,

πνίγω to choke, throttle, strangle

θεάομαι to look on, gaze, behold.

θύω to rush on or along, of a rushing wind. To storm, rage.

θύελλα a furious storm, hurricane.

θύρα a door. In Homer mostly of double doors

πύλη one wing of a pair of double gates. In plural (in Iliad): the gates of a city

έθειρα hair. In Homer in plural: either a horse;s mane, or horsehair crest on

helmets. Εθειράζω = to have long hair.

πηγάζω gush forth with water. πηγή = mostly in plural: running waters, streams

σακίον, σάκκος a sack, bag. Akk. šaqqu שׂק

έρπω to creep, crawl

ρίζα a root (Lesb.: βρίσδα )

πορφύρα the purple-fish, purple dye, purple

ίστημι (r. ΣΤΑ-) to stand. To make to stand. To set up. To raise, rouse, stir up.

τίθημι (r. ΘΕ-) to set up, put, place

πίνω (ρ. ΠΟ-) to drink. πόσις = a drinking, a drink, beverage.

θαυμάζω to wonder, to marvel, be astonished.

θαυ̃μα whatever one regards with wonder, a wonder, a marvel

τρέπω to turn or direct towards a thing.

θώς (Iliad) the jackal