Quantum chaos theory studies how the correspondence between quantum mechanics and classical mechanics works in the context of chaotic systems.

— Wikipedia on Chaos theory

2011.11.16 Wednesday ACHK

Does the physicist-turned-comedy icon have any regrets? “What I do is ultimately not similar to physics or computer science,” Cohen admits. “I would like to have lived two lives, to be a scientist in one… So of course I have regrets. Science is more important than what we do, although I do get a lot of satisfaction out of my work.”

— The Futurama of Physics with David X. Cohen

— Alaina G. Levine

2011.11.09 Wednesday ACHK

The story goes that “In 1970, a young physicist named Leonard Susskind got stuck in an elevator with Murray Gell-Mann, one of physics’ top theoreticians, who asked him what he was working on. Susskind said he was working on a theory that represented particles ‘as some kind of elastic string, like a rubber band.’ Gell-Mann responded with loud, derisive laughter.”

— Wikipedia on Leonard Susskind

2011.11.05 Saturday ACHK

Principle of least action, 4.2

To figure out the Lagrangian, note that the kinetic energy of a photon is given as (from Phys 101)

where k is the wave number , and the potential energy of a photon is zero.

— Fermat’s principle and the PoLA

— G.-H. Gweon

2011.11.02 Wednesday ACHK

If the block spacetime model is used, there is no real motion.

For the apparent motion, the infinity representing the infinite steps in the Zeno’s paradox becomes a potential infinity, depending on how many divisions the observer wants to divide the spacetime into.

The calculus explanation of the Zeno’s paradox can be regarded as a potential infinity one, using the epsilon-delta definition of limit.

If spacetime is discrete, the Zeno’s paradox is no paradox. However, with the block spacetime model, whether spacetime is infinitely divisible is irrelevant.

— Me@2011.10.28

2011.10.31 Monday (c) All rights reserved by ACHK

knucklebumpler had this to say: “This is solved by the “block time” view of time that’s forced on us by special relativity and the relativity of simultaneity. So there’s no need for one event to have “happened” before some ‘future’ event. We can just regard the whole thing as one big four dimensional block of space-time.” – David Zaslavsky Jun 25 at 20:58

2011.10.30 Sunday ACHK

Farnsworth: These are the dark matter engines I invented. They allow my starship to travel between galaxies in mere hours.

Cubert: That’s impossible. You can’t go faster than the speed of light.

Farnsworth: Of course not. That’s why scientists increased the speed of light in 2208.

Cubert: Also impossible.

— A Clone of My Own

— Futurama

2011.10.26 Wednesday ACHK

Principle of least action, 4

Indeed Fermat’s principle does not hold standing alone, we now know it can be derived from earlier principles such as Huygens’ principle. Historically, Fermat’s principle has served as a guiding principle in the formulation of physical laws with the use of variational calculus (see Principle of least action).

— Wikipedia on Fermat’s principle

Fermat’s principle is very similar to the principle of least action but the derivation of Fermat’s principle from the principle of least action is less straightforward than you might think.

— Lubos Motl

2011.10.26 Wednesday ACHK

String theory 7.2

Although the physics of string theory can in principle be background-independent, perturbative formulations of this theory do not make this independence manifest because they require starting with a particular solution and performing a perturbative expansion about this background. Non-perturbative formulations such as matrix theory and AdS/CFT resolve that issue and are fully background independent.

— This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2010)

— Wikipedia on Background independence

2011.10.24 Monday ACHK

Coherent states 6.2 | Quantum coherence, 6.2

Every-day electromagnetic radiation, such as radio and TV waves, is also an example of near coherent states (macroscopic quantum coherence). That should “give one pause” regarding the conventional demarcation between quantum and classical.

— Wikipedia on Coherent states

A laser is a device that emits light (electromagnetic radiation) through a process of optical amplification based on the stimulated emission of photons. The emitted laser light is notable for its high degree of spatial and temporal coherence, unattainable using other technologies.

Temporal (or longitudinal) coherence implies a polarized wave at a single frequency whose phase is correlated over a relatively large distance (the coherence length) along the beam. A beam produced by a thermal or other incoherent light source has an instantaneous amplitude and phase which vary randomly with respect to time and position, and thus a very short coherence length.

— Wikipedia on Laser

The amplitude of the EM wave does not have an a-priori well-defined value. The photon number must follow a Poisson distribution. The coherent states provide the most well-defined magnitude and phase. They come closest to the classical notion of a wave.

— Dr. Michael A. Parker

The amount of quantum noise in the electric field is completely independent of the phase. As the field strength, i.e. the oscillation amplitude α of the coherent state is increased, the quantum noise or uncertainty is constant at 1/2, and so becomes less and less significant. In the limit of large field the state becomes a good approximation of a noiseless stable classical wave.

— Wikipedia on Coherent states

Classical electromagnetic wave can be regarded as coherent states of photons, not because the photons are coherent with each other, which is not well-defined, but because each photon is in a coherent state, which evolves around the classical trajectory, providing a near definite classical electromagnetic wave amplitude.

— Me@2011.10.12

2011.10.13 Thursday (c) All rights reserved by ACHK