Posts tagged with QCD

Murray Gell-Mann became annoyed with Richard Feynman

• generating anecdotes or stories about himself
• not brushing his teeth
• not washing hands after urinating
• "You’re just a salesman type. You’re just a normal person, not an independent thinker."
• purposefully cultivated outsider image. Feynman, you hipster!

(por Muon Ray)

hi-res

The origins of mass & the feebleness of gravity by Frank Wilczek

tl,dr:

• dark matter & dark energy
• "Even though protons, neutrons, and electrons comprise only 3% of the universe’s mass as a whole, I hope you’ll agree that it’s a particularly significant part of the mass." lol
• "Just because you can say words and they make sense grammatically doesn’t mean they make sense conceptually. What does it mean to talk about ‘the origin of mass’?”
• "Origin of mass" is meaningless in Newtonian mechanics. It was a primitive, primary, irreducible concept.
• Conservation is the zeroth law of classical mechanics.
• `F=MA` relates the dynamical concept of force to a kinematic quantity and a conversion factor (mass).
• rewriting equations and they “say” something different
• the US Army field guide for radio engineers describes “Ohm’s three laws”: `V=IR`, `I=V/R`, and a third one which I’ll leave it as an exercise for you to deduce”
• `m=E/c²`
• Einstein’s original paper Does the inertia of a body depend on its energy content? uses this ^ form
• You could go back and think through Einstein’s problem (knowing the solution) in terms of free variables. In order to unite systems of equations with uncommon terms, you need a conversion factor converting `a ∈ Sys_1` to `b ∈ Sys_2`.
• Min 13:30 “the body and soul of QCD

• Protons and neutrons are built up from quarks that are moving around in circles, continuously being deflected by small amounts. (chaotic initial value problem)
• supercomputer development spurred forward by desire to do QCD computations
• Min 25:30 “The error bounds were quite optimistic, but the pattern was correct”
• A model with two parameters that runs for years on a teraflop machine.
• Min 27:20 The origin of mass is this (`N≡nucleon` in the diagram): QCD predicts that energetic-but-massless quarks & gluons should find stable equilibria around .9 GeV:

Or said alternately, the origin of mass is the balance of quark/gluon dynamics. (and we may have to revise a bit if whatever succeeds QCD makes a different suggestion…but it shouldn’t be too different)
• OK, that was QCD Lite. But the assumptions / simplifications / idealisations make only 5% difference so we’ll still explain 90% of the reason where mass comes from.
• Computer ∋ 10^27 neutrons & protons
• The supercomputer can calculate masses, but not decays or scattering. Fragile.
• Minute 36. quantum Yang-Mills theory, Fourier transform, and an analogy from `{ a stormcloud discharging electrical charge into its surroundings }` to `{ a "single quark" alone in empty space would generate a shower of quark-antiquark virtual pairs in order to keep a balanced strong charge }`
• Minute 37. but just like in QM, it “costs” (∃ a symplectic, conserved quantity that must be traded off against its complement) to localise a particle (against Heisenberg uncertainty of momentum). And here’s where the Fourier transform comes in. FT embeds a frequency=time/space=locality tradeoff at a given energy (“GDP" in economic theory). The “probability waves" or whatever—spread-out waveparticlequarkthings—couldn’t be exactly on top of each other, they’ll settle in some middle range of the Fourier tradeoff.
• "quasi-stable compromises"
• This is similar to how the hydrogen atom gets stable in quantum mechanics. Coulomb field would like to pull the electron on top of the proton, but the quantum keeps them apart.

• "the highest form of musicality"
• Quantum mechanics uses the mathematics of musical notes (vibrating harmonics).
• Quantum chromodynamics uses the mathematics of chords, specifically triads since 3 colour forces act on each other at once.

• Particles are nothing more than stable tradeoffs that can be made between localisation costs (per energy) from QM and colour forces.
• (Aside to quote Wikipedia: “Mathematically, QCD is a non-Abeliangauge theory based on a local (gauge) symmetry group called SU(3).”)

• Minute 40. Because the compromises can’t be evened out exactly due to quanta, there’s some leftover energy. It’s the same for a particular kind of quark-gluon interaction (again, because of the quanta). The .9 GeV overshoot | disbalance | asymmetry in some particular quark-gluon attempts to balance creates the neutrons and protons. And that’s the origin of mass.

Minute 42. Feebleness of gravity.

• (first of all, gravity is weak—notice that a paperclip sticks to a magnet rather than falling to the floor)
• (muscular forces are the result of a lot of ATP conversions and such. That just happens to be even weaker—but if you think of how far removed those biochemical electropulses and cell fibres are from the fundamental foundation, maybe that’s not so surprising.)
• Gravity is 40 orders of magnitude weaker than the electrical force. Not forty times, forty orders of magnitude.
• Planck’s vision; necessary conversion; a theory of the universe with only numbers.
• The Planck distance, even for nuclear physicists, is about 20 orders of magnitude too small.
• The clunkiness of Planck’s constants mocks dimensional analysis. “If you measure natural objects in natural units, you should get something of the order of unity”.
• "If you agree that the proton is a natural object and the Planck scale is a natural unit, you’d be off by 18 orders of magnitude".
• Suppose gravity is a primitive. Then the question becomes: “Why is the proton so light?” Which now we can answer. (see above)

• Simple physics (local interactions, basic = atomic = fundamental = primitive behaviours) should occur at Planck scales. (More complex behaviours then should “emerge” out of this reduction.)
• So that should be, in terms of energy & momentum, 10^18 proton masses, where the fundamental interactions happen.
• The value of the quark-gluon interaction at the Planck scale. “Smart” dimensional analysis says the quantum level that makes protons from the gluon-quark interactions then gets us to ½, “which I hope you’ll agree is a lot closer to unity than 10^−18”.
• Minute 57. “A lot of what we know about the deep structure of the Standard Model is summarised on this slide”
• weak force causes beta decay
• standard model not so great on neutrino masses
• SO(10)’s spinor representation has all the standard model’s symmetries as subgroups
• Minute 67. Trips my regression-analysis circuits. Slopes & intercepts. Affine!
• Supersymmetry would have changed the clouds and made everything line up real nicely. (The talk was in 2004 and this week, in 2012, the BBC reported that SuSy was kneecapped by the latest LHC evidence.)
• "If low-energy supersymmetry turns out to be false, I’ll be very disappointed and we’ll have to think of something else."

(Source: mit.tv)

What is the world made of?There are twelve basic building blocks.

Six of these are quarks—- they go by the interesting names of up, down, charm, strange, bottom and top. (A proton, for instance, is made of two up quarks and one down quark.) The other six are leptons—- these include the electron and its two heavier siblings, the muon and the tauon, as well as three neutrinos.

There are four fundamental forces in the universe: gravity, electromagnetism, and the weak and strong nuclear forces. Each of these is produced by fundamental particles that act as carriers of the force…: …photon…graviton…eight…gluons…three…W+, … W- , … Z.

The behavior of all of these particles and forces is described with impeccable precision by the Standard Model, with one notable exception: gravity.

Video portrayal of the smooth topological charge density of an empty vacuum at Minute 26.

In other words, this is what the empty space between the quarks looks like.

Derek Leinweber discretized QCD theory (that is, put it on a lattice) and did some computations of what that looks like. One conclusion of quantum chromodynamics is that empty space is a wildly dynamical medium due to virtual particles.

The universe is a song, singing itself.

(Source: mit.tv)

## 43 252 003 274 489 856 000

I respect the cube. I cannot fathom it. I do not want to learn how to do it from anybody else. Instead I want to experience the simple moves that hopelessly and mercilessly turn order into disorder.  Whichever way I turn, disorder gives way to more disorder. It seems as hopeless to restore order as it is to get the spilt milk back into the jug.

György Marx

Imagine a solved Rubik’s cube.  Now imagine just one of the corners mis-coloured. You have imagined an impossible state.

It’s impossible to twist just one corner of the cube clockwise or anticlockwise.  It’s impossible to twist just two corners of the cube clockwise or anticlockwise. The minimum change is three corners twisted clockwise, or three corners twisted anticlockwise.

Quarks are like that too. (Solomon Golomb noticed this first.)  The universe never makes just one quark alone, or just two quarks alone.  The universe only makes three quarks together all at once.

There’s more. The universe does put a quark and an antiquark together. (Instead of making a proton or neutron this makes a “meson”).  And likewise, the cube allows a twist and an anti-twist on just two corners.

What does quantum chromodynamics have to do with Ernő Rubik's invention? There is just something similar in their group structure.  Just as a particle's baryon number must be conserved, so a similar SU(3) like property characterizes the cube. Spooky.

And. 43 252 003 274 489 856 000.

There are 43 252 003 274 489 856 000 possible arrangements of the cube, only 1 of which is correct.

43 252 003 274 489 856 000 states of disorder and 1 state of complete order. Need I say the word?  Entropy.