Originally proposed in 1899 by German physicist Max Planck, these units are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are only one system of natural units among other systems, but are considered unique in that these units are not based on properties of any prototype object, or particle (that would be arbitrarily chosen) but are based only on properties of free space.

— Wikipedia on Planck units

2012.09.01 Saturday ACHK

Thus, the holographic correspondence is not just a wild new possibility for a quantum theory of gravity. Rather, in a fundamental way, it connects string theory, the most studied approach to quantum gravity, with theories of quarks and gluons, which are the cornerstone of particle physics.

— The Illusion of Gravity

— Juan Maldacena

2012.08.31 Friday ACHK

The accuracy of the measured value of G has increased only modestly since the original Cavendish experiment. G is quite difficult to measure, as gravity is much weaker than other fundamental forces, and an experimental apparatus cannot be separated from the gravitational influence of other bodies. Furthermore, gravity has no established relation to other fundamental forces, so it does not appear possible to calculate it indirectly from other constants that can be measured more accurately, as is done in some other areas of physics.

— Wikipedia on Gravitational constant

2012.08.30 Thursday ACHK

Charge (physics), the susceptibility of a body to one of the fundamental forces

— Wikipedia on Charge

2012.08.29 Wednesday ACHK

An important technical difference between decoherence and the collapse of the wave function is that decoherence actually doesn’t decide which result will be measured. It just diagonalizes the density matrix to diag(p1,p2,…,pN) where p_i then play the role of the probabilities that the individual preferred basis vectors will be detected. Because the information about the relative phases is getting quickly lost, the off-diagonal elements rapidly converge to zero. But decoherence never transforms the density matrix with the many p’s to something like (0,0,1,0,…,0). Never, ever. Quantum mechanics remains the only player here and its predictions remain and will always stay probabilistic. One can never and one will never restore determinism and decoherence doesn’t try to do anything of the sort.

— Lubos Motl

2012.08.28 Tuesday ACHK

Such QFTs arise naturally in generalizations of QCD from three colors to a larger number of colors, N.

— Solving quantum field theories via curved spacetimes

— Igor R. Klebanov and Juan M. Maldacena

2012.08.27 Monday ACHK

Compactification quantizes momentum.

— String Theory Demystified, p.218

— David McMahon

2012.08.24 Friday ACHK 

Like most individuals, and probably, most mathematicians outside his field, I do not deeply understand much of Thurston’s work. But he did have a rather large impact on my life insofar as a paragraph of his has stayed with me several years (not many do, I’m afraid), and has been my reminder to slow down whenever I find myself saying “psh, that was easy, all I had to do was browse through the documentation”:

I prided myself in reading quickly. I was really amazed by my first encounters with serious mathematics textbooks. I was very interested and impressed by the quality of the reasoning, but it was quite hard to stay alert and focused. After a few experiences of reading a few pages only to discover that I really had no idea what I’d just read, I learned to drink lots of coffee, slow way down, and accept that I needed to read these books at 1/10th or 1/50th standard reading speed, pay attention to every single word and backtrack to look up all the obscure numbers of equations and theorems in order to follow the arguments.

If a Fields medalist needed to slow down to read some maths, I can slow down to really understand whatever it is that I’m doing. And when I tell myself “I’ve learned that already!” I stop and ask whether I learned it at a “1/50th pace.”

— kevinalexbrown 1 day ago

— Hacker News

2012.08.24 Friday ACHK

One must distinguish gauge symmetries and global symmetries. A gauge symmetry is a redundancy of a description, not a property of a physical system.

— Lubos Motl

2012.08.23 Thursday ACHK

The correct version of anthropic principle should be called the anti-anthropic principle.

— Me@2011.11.10

The reasonable version of anthropic principle should not be called as “anthropic principle” at all, but “multi-verse natural selection”.

— Me@2011.10.23

2012.08.13 Monday (c) All rights reserved by ACHK

John Wheeler is also a co-father of the Wheeler-DeWitt equation, the vanishing Hamiltonian constraint applied to the “wave function of the Universe” in quantum gravity that is expected to replace the equations of motion as soon as it is properly formulated. The Hartle-Hawking wave function remains the most famous solution of the WDW equation.

— John Wheeler: 1911-2008

— Lubos Motl

2012.08.11 Saturday ACHK

Sir William Timothy Gowers, FRS (born 20 November 1963, Wiltshire) is a British mathematician. In 1998 he received the Fields Medal for his research connecting the fields of functional analysis and combinatorics.

Tricki

Tricki.org is a Wikipedia-style project collecting methods of mathematical problem solving conceived in 2008 and launched by Gowers, Olof Sisask and Alex Frolkin in March 2009. Terence Tao and Ben Green are among those to have contributed articles.

The Cost of Knowledge

In January 2012 Gowers made a post on his personal blog which initiated a project called The Cost of Knowledge. The blog post called for a boycott of Elsevier. The Cost of Knowledge is a petition for change in which researchers commit to discontinue support for Elsevier journals. As a result, Gowers has been credited with starting the Academic Spring.

— Wikipedia on Timothy Gowers

2012.08.09 Thursday ACHK

The ring circuit came about because Britain had to embark on a massive rebuilding programme following World War II. There was an acute shortage of copper, and it was necessary to devise a scheme that used less copper than would normally be the case.

— Wikipedia on Ring circuit

2012.08.08 Wednesday ACHK

In the new paper, this concept is taken very seriously. “The wave function” is interpreted as nothing else than the Hawking-Hartle wave function of the Universe. You know, the Hawking-Hartle wave function is something like a wave functional of quantum gravity that solves the Wheeler-deWitt equation (a sophisticated definition of the quantum equation

    H.psi = 0

that is appropriate in general relativity but whose exact meaning requires a working quantum theory gravity, i.e. it requires string theory). The Hawking-Hartle wave function is a functional of the fields of quantum gravity on S^3, if you allow me to deal with the “most realistic” example, and this functional may be calculated as the path integral of quantum gravity defined in the ball B^4 inside this S^3, with the right boundary conditions at the sphere S^3. The Hawking-Hartle state is then the functional of these boundary conditions.

— Lubos Motl

2012.08.06 Monday ACHK

Lumo ‧ 7 years ago

Dear Anonymous,

I agree that loop quantum gravity may also be viewed as an attempt to make sense out of the WDW equation. Unfortunately it is not a consistent or successful attempt – simply because the Hamiltonian constraint can’t be defined. (In fact, even the physical Hilbert space is not well-defined.) See an older article “A very meaningful paper on loop quantum gravity”.

All the best
Lubos

Anonymous ‧ 7 years ago

But even the Wheeler-deWitt equation needs to be regularized!

Lumo ‧ 7 years ago

That’s right. This is why you need string theory to transmute the WDW equation from a heuristic speculation to a meaningful law of physics.

— Lubos Motl

2012.08.02 Thursday ACHK

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