Some of these questions are answered by string/M-theory in its current state; some of these questions were approximately answered even by QFT tools before string theory; some of these questions remain open.

For example, the Wheeler-DeWitt equation (together with its various solutions such as the Hartle-Hawking state) mostly belongs to the third category (the things not yet established). It’s the equation HΨ=0, expressing the idea that the Hamiltonian constraint in GR actually encodes the full evolution in time, something that is possible due to the ambiguous meaning of the word “time” in diffeomorphism-symmetric theories. To solve it, one must first define his own time, by linking it to some coordinate-independent evolving quantity, and so on.

— answered Oct 25 ’11 at 6:50

— Lubos Motl

2012.07.31 Tuesday ACHK

Spinors are objects with a spinor index and in some very particular sense, a spinor index is exactly one-half of a vector index. So the generalized tensors may have either an integral number of indices or they may also have a half-integral number of indices! In a very clever sense, a spinor is a square root of a vector in the same sense as a vector is a square root of a tensor with two indices. How is it possible that we may break letters (indices) into pairs of letters?

— Why are there spinors?

— Lubos Motl

2012.07.30 Monday ACHK

This wave function contains all of the information about the geometry and matter content of the universe.

In fact, the principle of general covariance in general relativity implies that global evolution per se does not exist; the time t is just a label we assign to one of the coordinate axes. Thus, what we think about as time evolution of any physical system is just a gauge transformation, similar to that of QED induced by U(1) local gauge transformation , where plays the role of local time.

— Wikipedia on Wheeler–DeWitt equation

2012.07.29 Sunday ACHK

In theoretical physics, the Weinberg–Witten theorem (WW), proved by Steven Weinberg and Edward Witten, states that massless particles (either composite or elementary) with spin j > 1/2 cannot carry a Lorentz-covariant current, while massless particles with spin j > 1 cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton (j = 2) cannot be a composite particle in a relativistic quantum field theory.

Theories where the theorem is inapplicable

Superstring theory

Superstring theory defined over a background metric (possibly with some fluxes) over a 10D space which is the product of a flat 4D Minkowski space and a compact 6D space has a massless graviton in its spectrum. This is an emergent particle coming from the vibrations of a superstring.

— Wikipedia on Weinberg–Witten theorem

2012.07.27 Friday ACHK

Physicists use the term “spontaneous symmetry breaking” when any one solution of a symmetric problem is not symmetrical, but the whole set of them is. This is precisely what happens with the quintic, or even the quadratic equation.

— January 10, 2004

— This Week’s Finds in Mathematical Physics (Week 201)

— John Baez

2012.07.26 Thursday ACHK

The motivation of Grassmann algebra is

to re-use the boson formulae in fermion calculations

by re-interpretating the symbols as Grassmann variables.

— Me@2012.03.06

2012.07.25 Wednesday (c) All rights reserved by ACHK

The correct version of anthropic principle should be called the anti-anthropic principle, or the law of large numbers:

given a large enough sample size, the probability of a sample fulfilling your requirements is close to 1.

— Me@2012.03.06

2012.07.23 Monday (c) All rights reserved by ACHK