notes

The general features of Emergence

Now that we have sketched the big story of the Universe, let us consider the part played by Emergence in it.  Emergence and Reduction go hand in hand in explanation, but Reduction gets all the glory, and Emergence gets all the blame.

One crucial feature of Physical explanation is the separation, introduced by Newton, of Laws and Initial Conditions.  Laws can be universal and timeless, while initial conditions introduce messiness and contingency.  Another feature of emergence is the role of chance versus determinism.  In classical physics, motion is determined, while in quantum mechanics, probabilities are determined, but outcomes are not.  

In interaction with symmetry breaking, chance also introduces a large history dependence into Physics.  In the standard model, such history dependence is introduced into the deepest features of the Universe, like the masses of the elementary particles, arrived at via the Higgs Mechanism.  The Big Bang is the ultimate initial condition.  The symmetry-broken Laws are considered to be descended from a more perfect and more symmetric initial state.  One book about this idea is even called Perfect Symmetry.

What counts as a Law of Physics anyway?  It was once thought that the spacing of the planets was so regular that it had to be accounted for by a law: the Titus-Bode Law.  Kepler tried to explain it geometrically. It even works for moons!  Now we think it is merely contingent on the initial conditions at the time the solar system formed.  How do we decide what needs explanation and what does not?

Are the Laws of Physics really just expressions of purely mathematical truths?  Are they as inevitable as 2+2=4?  The unreasonable effectiveness of methematics has been commented on.  For example, the mathematics of curved space that Einstein used to formulate general relativity had all been worked out previously by Riemann in the 1850s.  Was it discovered or invented?  This is a perennial question in Philosophy.  How can we understand why there are mathematical laws of physics if we can't even understand where math itself comes form?  Maybe math is just genetic, something we are wired to do.

What does it mean to "explain" something?  What if we can explain a thing "in principle", but not in practice?  What if we want to analyze a thing into parts, but, like a proton and its constituent quarks and gluons, it is actually impossible in principle to take the object apart?  In the case of such "strong interactions", does it even make sense to talk about parts?  Do such things necessarily involve strong emergence?  If so, what do we do when reduction fails?

Here are some links to the sand avalanche segregation experiment I showed at the end of class: [ 1 ][ 2 ][ 3 ][ 4 ]. What would it mean to "explain" this experiment?


Tablet notes: [ Lec 13 ]

The hot big bang

It might seem impossible to know anything about the origin of the universe, but Einstein's 1915 General Theory of Relativity, combined with a lot of astronomical observations have turned what was once speculation into quantitative science: cosmology.

Einstein's theory was first confirmed by Arthur Stanley Eddington's eclipse expedition of 1919.  Today many astronomical effects are understood to be due to bending starlight, such as Einstein rings and crosses. See here for more on light bending.

Some of the players in the history of cosmology are:  Edwin HubbleGeorges LeMaître and Fred Hoyle.  Hubble, who is shown at left, discovered the expansion of the universe and has a famous space telescope named after him.

One of the main tools to understand cosmology is the cosmic microwave background radiation.  This is the radiation left over from the Big Bang, now stretched out into a very cold microwave background.  It has been measure quite carefully by the WMAP satellite among others.

Here is a map made by WMAP of the deviations from uniformity of the background radiation.  These bumps can be used to infer things about the evolution of the universe.  A famous cartoon of this evolution is here.  The surprizing result is that the universe is composed not only of ordinary matter, but also unseen Dark Matter and even weirder Dark Energy.  Here is a pie chart of the composition implied by the observations.  Dark energy is a kind of negative pressure that inflates the universe; the discovery of this acceleration won the 2011 Nobel Prize in Physics.  Here is a nice news story on all this.

The accelerating expansion of the universe can be incorporated into Einstein's general relativity by adding a "cosmological constant".  Einstein originally included this term to fudge his theory into predicting a static universe, a ploy he later called "the greatest blunder of my life".

Working forward from the fluctuations in the density of the early universe, it is possible to simulate the evolution of galaxies, which have an interesting lumpy texture.  Galaxies form from the mutual gravitational instability of the matter and dark matter.  One can even account for the spiral structure of the Mily Way.  

Starting from the standard model and the Big Bang, how do we build a universe? The first stop, just after the symmetry breaking events in the very early universe, is when the quarks assemble themselves into baryons (protons and neutrons).  The universe is then a hot plasma of ionized hydrogen, which eventually cools and becomes transparent.  At this stage the background radiation escapes.  Then this neutral cloud collapses into stars and galaxies and other stuff like early black holes and quasars.  Along the way, all the elements heavier than Hydrogen are synthesized first by a little cooking just after the big bang, and then later in the interior of stars. 

Nuclear fusion joins protons and neutrons into heavier nuclei.  Stellar evolution returns the matter back to the interstellar medium, which can reform into new stars for more cooking.  If they are cold enough, nuclei collect electrons to become atoms.  Even the same element can have different arrangements of protons and neutrons in the nuclei.  The elements can be combined into a famous song. Which is sometimes sung by famous people. Then atoms of the various elements to may be linked by chemical bonds to form molecules, and eventually important biomolecules

Atoms are something we can "see" directly, for example using a scanning probe microscope.  Once can even move individual atoms around using such a microscope. Normally, objects the size and weight of atoms and molecules behave as classical physics would predict, so the chemical bond is approximately the limiting size at which quantum effects are important in everyday Nature.  Of course, there are famous exceptions like superconductors (see video) or superfluids (see video).


Tablet notes: [Lec 11] [no notes for Lec 12 ]

The particle zoo: climbing the chain

The standard model of particle physics forms the lowest level building blocks that we know.  It contains three of the four fundamental forces (electromagnetic, and the strong and weak nuclear forces); only gravity is left out.  These forces are created by the exchange of particles.  All these particles fit on the T shirt.

How did the fundamental particles get these particular properties?  Why do we have the elements that we do?  The explanation for these facts lies in the early universe, and hence involves cosmology and Einstein's general theory of relativity.  The explanation involves the idea of spontaneous symmetry breaking shortly after the Big Bang.

The crucial idea is spontaneous symmetry breaking.  In the beginning, everything is massless and simple and the properties of the elementary particles come from "breaking" this highly symmetric situation as the universe expands.  One obvious case, which is not really understood yet, is the breaking of the matter/antimater symmetry. Another is the Higgs Mechanism -- which involves a new particle that is supposed to explain the origin of mass.  See here for a nice story on how this cocktail party analogy came to be.  The Higgs boson is one of the main things being looked for at the LHC.  The latest info on the search at ATLAS is here.  More on the Higgs mechanism here.

Here is a little cartoon of how things are supposed to have fallen out after the Big Bang.


Tablet notes: [Lec 8] [Lec 8.5] [Lec 9][Lec 10].