(Source: https://en.wikipedia.org/wiki/Higgs_mechanism)

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

(Source: http://www.quantumdiaries.org/2012/06/28/why-we-shouldnt-combine-higgs-searches-across-experiments/)

Are you a physicist and want to learn intermediate microeconomics as quickly as possible? Here you go.

Minute 18

• Goods = vector space
• Price = covector
• Expenditure = their inner product
• Foliate the vector space by hypersurfaces convex to the origin with codimension 1. Indifference surfaces / isoutility surfaces.
• (no local minima/maxima, ever-increasing)
• Look at the inverse images, given a particular choice of price = budget constraint. Affine hyperplanes of codimension 1, translated from the origin, which are all based on the kernel of the pricing vector.
• The central dogma: agents spend up to their budget constraint reaching the highest level surface intersecting with the convex hull.
• People buy the unique basket whose tangent space at the basket to the indiffference space is equivalent to the kernel of the pricing vector in force.
• The space of all such baskets, given any income level but the same pricing system, is called the Engel curve.
• Minute 34: income vs substitution effects

Minute 31. For the economists in the audience. This is a really good point. We measure the inflation from period to period by some formula like

What’s up with multiplying prices from timepoint 2 against quantities from timepoint 1? That doesn’t really make sense does it. If prices changed in the next period then that induced a response in purchasing behaviour.

Not to mention that e.g., hats have fallen out of fashion for men since a century ago—so the price of hats no longer merits a high weight in the basket of what price increases are killing the budgets.

What we really want to do is use a connection. That gives us parallel transport across timepoints.

(Source: http://pirsa.org/)

(Source: http://pirsa.org/06050010/)

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.

Alberto Güijosa

Lawrence Krauss, author of A Universe from Nothing lecturing on cosmology.

• Don’t really agree with or like his monolithic straw-man representation of “religion” versus “science” at minute 6. “Religion pretends to know all the answers” .

  Sub-i, sub-j, larry. There are many religions and many sciences.

• Minute 14. Edwin Hubble’s original data! straight-line plot through a bunch of dispersed points. “That’s why we know he was a great scientist” — nobody laughed in the tape, but I did — “he knew that he should draw a straight line through a cloud of points”. I also love it when people take the time to go through an old paper, pull things out, and present them anew.
• I have never understood the business of standard candles. To me it seems like you have two degrees of freedom (distance and brightness), only one of which can be knocked out by the measurement of apparent brightness.

  So say we figure out a “standard candle” — a star with a particular colour signature that tells us “The star is at X phase of its life, is made up of Z, and such stars always shine at a constant brightness of 1 for Q million years.”

  But still — how do we know that our theory is right? How do we know, know, know that  it’s really brightness of 1? It’s not like we can triangulate. And it’s certainly not like we’ve been there and seen it first-hand.

• I had the same problem in a discussion with a geologist a few months ago. I sometimes get the sense that working scientists are so immersed in the practical fact that, yes, for all intents and purposes we know X to be true, that they’re not willing to step back to an abstract, philosophical level and say: “Well, if you really keep pulling on the threads, there are assumptions at the bottom of everything, so yes, we really don’t absolutely know X to be the case. However, Philosophical Prig, we don’t really know we’re not living in The Matrix either! So hush up and get back to doing something relevant.” But that’s the kind of answer I really want to hear: no, we don’t know know know, but for all practical purposes, yes we know.
• Minute 15. How old is the universe? So Hubble got the answer wrong in 1929, and it was obviously wrong. “Scientists don’t know what they’re doing”

  But I had the same reaction to people talking about dark matter in the 90’s. “What is this stuff we call dark matter? Or dark energy?” As I understood it at the time, “dark matter” just represented a 90% fudge factor in astronomical measurements. It could be that gravity or quarks or anything else about the laws of physics is simply different in other parts of the universe. And how would we rule out that hypothesis? We just rule it out by assuming that the laws of Nature are the same everywhere, because that’s what we’ve assumed for the last few hundred years and it’s always worked out. Straight-line extrapolation to “That assumption must be true now and everywhere” despite that we’re now talking about multiple galaxies so unimaginably far away.

• Minute 18:30 “This is a Hubble plot, much better than Hubble’s plot. It was made after the discovery that on a log-log plot, everything is a straight line.” Again, no laughs, but I thought that was hilarious.
• Calculations that estimate the total energy in all vacuums add up to 10^28 times the observed mass of the universe. Whoops.
• Dark matter here on Earth? Let’s go down into the mines and measure it. (By the way, where would the physicists be if those evil resource-extraction companies in Lead, South Dakota hadn’t negotiated with the legal entities that be and drilled into the Earth’s crust? Way to play it as it lies, Sandia Labs. #scruples)
• Flat, closed, or open universe? (also why are these the only three options?) Well, we only observe 30% of the mass thta would be required to make the universe flat.
• A gigantic, gigantic, um, really gigantic triangle — to measure the curvature of the universe.
• That’s what those microwave-background radiation detecting balloons in Antarctica have been doing.
• There’s always something there, even when there’s nothing. (see this video of the quantum fields flickering about in empty space)
• 90% of the mass of a proton is due to the vacuum. (not delta spikes, more like 1/x or exp(−x) integrals.) Therefore your mass is 90% due to quantum fluctuations around the zero point energy.
• The universe also has a net total energy of 0. Hence the possibility of “a universe from nothing” (our universe needn’t have a Creator since there is enough mass/energy in the physical vacuum that those virtual fluctuations could have acted as a Prime Mover).
• 70% + 30% = 100%
• Making our place in the Universe even less special. “Regular” matter—the stuff we observe—is only a 1% pollution in the uniform dark-energy / dark-matter background of the universe.
• Deep-future scientists (like in a few billion years) won’t be able to observe other galaxies. Measuring the universe, they will observe (correctly) that their galaxy is the only one around, and that there is nothing but empty, eternal space around them.
• So they will be “Lonely and ignorant, but dominant. Of course those of us who live in the United States are already used to that.”

(Source: http://www.youtube.com/)

birdflight as map from space→time

Galileo and multiplication of objects

Lawvere decomposition

Categorial decomposition of Galilean spacetime.

Sean Carroll tells us that it was Galileo who first si rese conto che motion can be separated into:

• motion in the x direction — ẋ or x′[t]
• motion in the y direction — ẏ or y′[t]
• motion in the z direction — ż or z′[t]

and, importantly, that physical laws should be the same for all the 360° × 360° orthonormal choices of (x,y,z). It was Galileo’s idea that you can draw axes, that forces can be decomposed onto those axes, and that forces along one axis behave independently of each other.

For example if you kick a football, it goes forward x′[t], chips up y′[t], and bends left z′[t]. If you kicked it off a cliff, it would retain its exact same forward x'[t] speed even after it dropped y<0 below the plane of the cliff at an ever increasing speed. (NB: That’s not actually true, which is why we say “in a vacuum”.)

The traditional way to talk about a path γ is talking in tuples:

• First, you have some points
• Then, you have a 3-basis.
• Then, you have an interval.
• If you want to talk about kicking the ball, you would probably call the ball a point, say “there is” a vector space tangent to the ball, and your single kick of the ball constitutes a single force-vector applied (instantaneously) to the point, I mean ball. “Then” — by which I mean “at higher values of t∈interval” — the ball “is” chipped up in the air, “then” back on the ground.
• The path γ is any member of the product (pairing) of 3-basis with interval.

path γ ∈ time × space*

* space in the geographer’s sense; the casual, not mathematical, sense of the word space. Lawvere calls mathematical space a “universe” … like the theoretical universe that the theory lives in

All of this “you have” — it’s a violation of E′. The “false subject” in English sentences that start with “There are” is repeated over, and over, and over again in mathematics (hence the invention of the symbol ∃).

Now cometh F William Lawvere, 3 centuries later, with a conceptual breakthrough.

path γ : time → space

The categoryists use labelled dots and labelled arrows to sketch concepts. So in pictures 2 and 3 you can see projection arrows splitting 3-space into a 2-plane (ground) and a 1-line (air). (Arrows sometimes seem backwards in category theory. Galileo projects 3D onto 1D + 2D, so something like “coprojection” would be the natural piecing together of independent sub-motions to get the full picture.)

And the Galileo example is just meant to be a shared thing we can all discuss. But this same thought-pattern — categorial decomposition — I can use on non-chalkboard things from my life as well. Gottman-style 2-eqn relationship dynamics; speculating about some economics in the news; love triangles; the deeper you plant this seed, the more places you see it.

Without science, explaining why there is something rather than nothing requires explaining every leaf, rock, beetle and star.

Cosmology and evolutionary theory pare the explanation requirement down … we might have to explain only a physical law or three, and everything else … can follow naturally. … [I]t might be that we don’t have to explain why there is matter and energy, perhaps not even why there is three-dimensional space and time or why physical constants have the values they have.

It is also possible, although harder to conceive, that we could explain everything down to nothing: no physical laws, only logic. Putting that another way, it might be that naive mental pictures of nothing are logically impossible.

Aaron C. Brown, reviewing Why There is Something Rather than Nothing by Lawrence Krauss

The Newtonian view of a smooth background space which acts as a container in which the events in the universe take place is giving way to the view of Leibnitz (sic) in which the contents of the universe themselves give rise to space.

Burra G. Sidharth