Posts tagged with mass

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)

Why the scientists aren’t combining data from two experiments to get 5-sigma evidence (= “proof”) for the Higgs boson

The Higgs field was postulated nearly 50 years ago, the LHC was proposed about 30 years ago, the experiments have been in design and development for about 20 years, and we’ve been taking data for about 18 months. Rushing to get a result a few weeks early [would be dumb].

The reason we have two experiments at the LHC looking for the Higgs boson is because if one experiment makes a discovery then the other experiment can confirm or refute the discovery. This is why we have both D0 and CDF, both Belle and BaBar, both ATLAS and CMS, both UA2 and UA1

hi-res

## Tachyons

As every sci-fi geek knows, matter may travel faster than the speed of light as long as its mass is imaginary (a multiple of √−1). A so-called tachyon would not overturn special relativity—and it would provide a handy way of resolving any conflicts in a given Star Trek plot.

• 14th Law of How to Write Star Trek: Whenever you’ve written yourself into a hole, instead of re-writing the show so that it’s better, simply make characters issue the word “tachyon” several times toward the end. Everything is magically resolved, returning all aspects of life to the way the show started with no long-term consequences for the characters—which by the way is a great lesson to teach to young adults—and then Spock or Data has an “a-ha!” moment wherein he throws around jargon to further justify the deus ex machina.

The only problem with tachyons, as any sci-fi geek can attest, is that “imaginary” mass is pure fiction! How could anything weigh an imaginary amount?

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Well, I’m not sure that tachyons do exist—although if someone wants to post some arXiv links to relevant papers that would be awesome—but, I will say that “imaginary mass” isn’t that ridiculous of a concept.

As Tristan Needham said in the best book about complex numbers ever, the “imaginary” descriptor only reflects the historical prejudice against √−1.

Do imaginary numbers exist? No. But neither do counting numbers. Numbers are linguistic entities that humans communicate with. Sort of like how trees, flowers, bushes, shrubs, brambles, and vines all exist in nature, but those classifications, concepts, words, groupings are human-language mental constructs. “Five” doesn’t “exist” per se, but mathematical models built with the-thing-that-satisfies-the-properties making five five, do wonderfully at prediction of physics experiments.

Anyway, imaginary numbers exist just as much as other numbers. Just like rational numbers, they’re generated by an operation that comes up as a matter of course in algebra. And algebra seems to have something to do with nature. God knows why. (ohh! which way did I mean it?!)

So I’m not saying imaginary mass exists, but here are some good ways to think about imaginary numbers.

• imaginary numbers are twisted numbers
• imaginary numbers are phase-shifted like a sine wave versus a cosine wave
• an imaginary current heats up a wire but does no useful work

If the mass of a particle is an imaginary number, then … that might help you make sense of tachyons.

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Nerdy side note: E=MC² is not the real equation to describe the conversion of energy into matter or vice-versa.

• E=MC² tells you how to convert stationary matter into energy.
• The real equation is E² = [mc²]² + [pc]².
• (p is momentum.)
• (Notice that the real equation is of the form A²+B²=C². i.e., Energy is the hypotenuse (C) to the triangle sides B=mc² and A=p•c)

You can casually start/interrupt conversations with this knowledge the next time you attend a kegger / black-tie affair. Doing so will win handsome glances from potential sex partners. Also, there is a 0% chance that anyone will think you’re an insufferable know-it-all.