Wheeler–DeWitt equation, 3

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, 2

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

Wheeler–DeWitt equation, 2

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

Backward compatibility, 4

Because the real cost of compatibility is not in the hacks. The hacks are small potatoes. Most hacks are just a few lines of code (sometimes as few as zero), so the impact on performance is fairly low.

No, the real cost of compatibility is in the design.

If you’re going to design a feature that enhances the window manager in some way, you have to think about how existing programs are going to react to your feature. These are programs that predate your feature and naturally know nothing about it. Does your feature alter the message order? Does it introduce a new point of re-entrancy? Does it cause a function to begin dispatching messages that previously did not? You may be forced to design your feature differently in order to accommodate these concerns. These issues aren’t things you can “take out”; they are inherently part of the feature design.

— The Old New Thing

— Raymond Chen

2012.07.28 Saturday ACHK

The Dark Knight Rises, 2

The Dark Knight Rises (2012 movie): At the end, why does Batman give Gordon such a cryptic clue, rather than just revealing his face?

He either wants Gordon to know, or he doesn’t. Why does he take the path where Gordon may or may not work it out?

Siddharth Bhandari, Batman Fanatic

You just killed all the emotion when you considered it a cryptic clue. This scene had such beautiful emotions.

A hero can be as simple as a man putting his coat around a little boy’s shoulders and reassuring him the world hadn’t ended yet.

See the beauty in this quote. He’s not just giving him a clue but implying that Gordon has been a hero for him all these years.

— Quora

2012.07.28 Saturday ACHK

Weinberg–Witten theorem

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

Spontaneous symmetry breaking

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

天使與傻瓜

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If you begin by sacrificing yourself to those you love, you will end by hating those to whom you have sacrificed yourself.

* Self-Sacrifice

– George Bernard Shaw

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天使, 犧牲自己的利益來追求自己的理想.

魔鬼, 犧牲別人的利益來追求自己的理想.

傻瓜, 犧牲自己的理想來追求別人的利益.

智者, 透過實現自己的理想來追求別人的利益.

– Me@2009.09.14, 2010.03.11

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2010.03.11 Thursday (c) All rights reserved by ACHK

Grassmann, 3

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

Semantics

The formal description of a process of assigning a logical value (true or false) to all formulas is called a semantics of the classical propositional logic.

— Cse371, Math371, LOGIC, Fall 2011

— Professor Anita Wasilewska

2012.07.24 Tuesday ACHK

History 3.2

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The further backward you look, the further forward you can see.

— Winston Churchill

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Studying history helps you predict the future by teaching you which things are old enough to be permanent.

– Paul Graham

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2012.07.24 Tuesday ACHK

Anthropic principle, 3

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

Good teacher 2

Bad teacher 2

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The answer to the paradox, I think, is that you have to design for the user, but you have to design what the user needs, not simply what he says he wants. It’s much like being a doctor. You can’t just treat a patient’s symptoms. When a patient tells you his symptoms, you have to figure out what’s actually wrong with him, and treat that.

– Paul Graham

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2010.05.29 Saturday ACHK

The Dark Knight Rises

The great thing about a trilogy is that it feels like you’ve got a beginning, a middle and an end. It’s like an extended version of a regular film. Once you get into a fourth film then it’s just episodic, and I just can’t see him getting excited about making another film where basically you’re just wheeling in different villains.

— Emma Thomas

2012.07.22 Sunday ACHK