User:Elauminri/l/TiST0/01

Free style notes, loosely based on introductory musings of Leonard Susskind about string theory. Following material can be found on the index page.

Lecture

Philosophy: The End of Reductionism

Reductionism is a principle or a philosophy that big things are made of little things and little things are made of littler (sic!) things. And nobody in their right mind mistakes a house for bricks or vice versa. Second property of reductionism is a belief that as we go "deeper and deeper" things should get simpler, so called pious hope of reductionism[tm]. But what we've learned so far from modern theories like string theory or quantum gravity and so forth is that they spell the end of reductionism.

But before we go "beyond reductionism" let's first assess how it has worked out up to now. For example counter-intuitively Standard Model of particle physics is not so "simple" after all with:

about 75 different physical entities, about 20 of which are independent i.e. other entities derive properties and behaviors from them,
about 20 distinct numerical parameters i.e. unexplained constants that have to go into theory in order to make it work and produce results in agreement with experimental data.

And yet theory is definitely incomplete. It doesn't encompass gravity or dark matter or any matter (for that matter); it doesn't have particle(s) responsible for inflation! (graviton is unobservable in principle, but we do hope to see gravity waves) and it has a terrible problem of fine tuning. Proposed solution to fine tuning and general philosophical problems it espouses is, in the case of Standard Model, supersymmetry, BUT it:

introduces about (sic!) 100+N new parameters (N is a non-zero, unknown number necessary to understand mechanism of breaking of supersymmetry or spontaneous supersymmetry breaking),
requires doubling the number of all physical entities, in the form of superpartners,
not to mention a bunch of other new, as of yet speculative, bells and whistles needed to make sense of stuff like inflation...

And keep in mind the pious hope[tm] is that things get simpler as we hit the bottom. So it seems that we are going about the explanation in a fundamentally wrong manner. To illustrate the deconstruction of reductionism on its philosophical grounds as loosely defined above let's look at couple of examples from quantum mechanics (QFT to be precise) where the distinction between bricks (littler things) and houses (big things) breaks down irrevocably.

Statistics: Fermion-Boson duality

What happens when you put two fermions together? Well, not exactly identical two (sic!), because then you recover zero. But one right next but not on top of the other? You "get" a boson... LOI[tm]

For example ("biologically" speaking): electrons are fermions, protons are fermions and hydrogen atoms are bosons!

composition (ψ - fermion field - bricks, φ - boson field - house...) and qui pro quo of fund-a-mentality

So, what QFT showed is that we can start from \phi (boson field) as a fundamental concept and describe \psi (fermion field) as "kinks" in the field - continuous (and permanent? aka stable vs "wavy") transitions between energy states...

twisted belt...

It "all" depends on parameters (coupling constants) which picture is a better fit to represent the theory. For small J the fermionic perspective is more appropriate; bosons are complicated systems of point-like fermions held together by complicated sets of interactions. But as J grows fermions become less point-like (kinks spread out) and bosons become more of a singular entities and not force fields like...

So the question of which is fundamental and which is composite doesn't have a unique answer. By varying constants one can morph one thing into the other. Houses "go into" bricks, so to speak...

Keyword: bosonization. Are there similar examples in classical (non-relativistic) particle physics?

Electrodynamics: Electro- or magnetic- monopole?

QED and α manipulation...

Theory: of Strings

String Theory has an answer in the form of basic concepts:

D-branes (after Dirichlet, places where F-strings, Fundamental strings, can end...)
g, coupling constant (probability of string bifurcating... in twoo)

"Actual" particles are formed (in the case of g<<1, when F-strings are lithe and D-branes heavy) by loops of F-strings. As g grows, F-strings turn into black holes (or, in light of next lecture, perhaps we should call them black spheres...) and what's left is D-strings (and gravitons are made up of them!) which by then lose structure and dual into F-strings.

Keyword: S-duality (strength? duality, "I don't know what it's called").

And in mathematically pure string theory g can vary in space, but since we do not see it happening anywhere, even on the cosmological scales, we know that string theory is not even right.

Questions: point-likeness of electron and F- D- by g "convo-evolution"... In one version of the theory there are odd-dimensional D-branes (D-strings, D3-branes, etc) in another version even-. No theory has both D-imensionalities.

Even-dimensional one doesn't have D-strings (only D0-points and D2-planes...).

half-time

A New D-imension of S-pace materializes: now, that's crazy, the silliest thing I ever heard

...as g<<1 gets large... in D0 and S2 (closed F-strings...) theory. It happens in 10D theory (9 space + 1 time) and ends up with 10 space? Keyword: compactification. D0-branes turn into gravitons whole F1-strings (which aren't really F-strings but bounds of D2-branes) turn into elephants? Lot's of hard-core math that only turned out to be true after physicists told mathematicians that it has to "work" like this.

Bizarre, illusive... we don't know which elements are the fundamental... of the duality.

break

Two other interesting things in this bewildering web:

D3-branes are like an ordinary space and an open D1-string ending on it can be viewed as a magnetic monopole, while open F1-string as an electrically charged particle; in this picture e.g. closed F-strings with both ends connected to the D3 can be viewed interacting when they (for a moment) join their ends and split afterwards (scattering),
compactifying 2D (how can I draw that?, this is in the D2-branes version), which - like in the original reproductive version from the title of this section - constitute F-strings in orthogonal? components... no, it's just that smaller "compact" dimension can be viewed as F-string while bigger one as a D0-string?... gulp! Squeezing in one direction while pulling in the other leads to dual role reversal...

Questions: yes, one can view α as ratio of two-dimensions (sic!); "cyclic" infinity of earth (-like proportions;) and if you also go in t-hat direction you get a helix (;LULz all around)

Finish up: idealization of supersymmetry when bosons and fermions are of the same mass. It's like studying perfectly circular orbits (trolololo!): why? because they are easy-ier.

Other: Objects

fluxes, fluxons, flaxes?
orbifolds, orientofolds...
and permutations (actually, it's very easy to get to 10⁵⁰⁰).

Kinda like DNA... It's complicated but not because rules aren't simple, but because there are lots of moving parts. If string theory turns out to be right we may not be able to unravel particle physics completely, because 10⁵⁰⁰ is a major underestimate, heh;) There may be a lot of junk DNA in there.

We have to learn to ask new kind of questions, not What are exact features of the setup? (since anything one can name exactly turns out to be "trivial") but like What are the common/generic features?.

Questions: we can't really distinguish between really infinite dimensions and compact cyclic ones (hmmm[tm]); from theory it looks like changes in g have to happen in discreet jumps... not continuously (since then one could switch directions without noticing...? hmmm...), nothing extraordinary is happening at the Schwarzschild horizon (NEXT).