Photon Polarization

A calcite crystal laid upon a paper with some letters showing the double refraction

A recent paper on double-slit trajectories tilted

Watching Photons Interfere: "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer"

is featured at Chad Orzel's highly educational and entertaining weblog, Uncertain Principles, here

It's entertaining as well as informative, but not overly so if one refreshes and bones up or learns for the first time what "photon polarization" is.

The mathematics of Photon Polarization are not difficult, and Photon Polarization is an important field. Its entry in Wikipedia is quite long, so I leave with the introduction and contents of the Wiki article and wish you all great joy exploring on your own:

Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. Individual photons are completely polarized. Their polarization state can be linear or circular, or it can be elliptical, which is anywhere in between of linear and circular polarization.

The description contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well, and forms a fundamental basis for an understanding of more complicated quantum phenomena.

Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description.

The quantum polarization state vector for the photon, for instance, is identical with the Jones vector, usually used to describe the polarization of a classical wave.

Unitary operators emerge from the classical requirement of the conservation of energy of a classical wave propagating through media that alter the polarization state of the wave. Hermitian operators then follow for infinitesimal transformations of a classical polarization state.

Many of the implications of the mathematical machinery are easily verified experimentally. In fact, many of the experiments can be performed with two pairs (or one broken pair) ofpolaroid sunglasses.

The connection with quantum mechanics is made through the identification of a minimum packet size, called a photon, for energy in the electromagnetic field. The identification is based on the theories of Planck and the interpretation of those theories by Einstein. The correspondence principle then allows the identification of momentum and angular momentum (calledspin), as well as energy, with the photon.

Contents  [hide] 1 Polarization of classical electromagnetic waves 1.1 A polarization state vector 1.1.1 Jones vector 1.1.2 Dual of the Jones vector 1.1.3 Normalization of the Jones vector 1.2 Polarization states 1.2.1 Linear polarization 1.2.2 Circular polarization 1.2.3 Elliptical polarization 1.2.4 Physical interpretation of an arbitrary polarization state 2 Energy, momentum, and angular momentum of a classical electromagnetic wave 2.1 Energy density of classical electromagnetic waves 2.1.1 Energy in a plane wave 2.1.2 Fraction of energy in each component 2.2 Momentum density of classical electromagnetic waves 2.3 Angular momentum density of classical electromagnetic waves 3 Optical filters and crystals 3.1 Passage of a classical wave through a polaroid filter 3.2 Example of energy conservation: Passage of a classical wave through a birefringent crystal 3.2.1 Initial and final states 3.2.2 Dual of the final state 3.2.3 Unitary operators and energy conservation 3.2.4 Hermitian operators and energy conservation 4 Photons: The connection to quantum mechanics 4.1 Energy, momentum, and angular momentum of photons 4.1.1 Energy 4.1.2 Momentum 4.1.3 Angular momentum and spin 4.1.3.1 Spin operator 4.1.3.2 Spin states 4.1.3.3 Spin and angular momentum operators in differential form 4.2 The nature of probability in quantum mechanics 4.2.1 Probability for a single photon 4.2.2 Probability amplitudes 4.3 Uncertainty principle 4.3.1 Mathematical preparation 4.3.2 Application to angular momentum 4.4 States, probability amplitudes, unitary and Hermitian operators, and eigenvectors 5 See also 6 References

M51 Gives Birth (again) to New Supernova

The yellow arrow points to new new supernova in my favorite galazy, M51

I know I should probably like my own galaxy best, but it's kind of boring from my perspective. M51 is the coolest.

From this blogpost in Universe Today..

To think that star actually went nova 50,000,000 years ago, and we're just seeing it now. Space is really big.

Have a good weekend all.

Super-determinism

In the context of quantum mechanics, superdeterminism is a term that has been used to describe a hypothetical class of theories which evadeBell's theorem by virtue of being completely deterministic. Bell's theorem depends on the assumption of counterfactual definiteness, which technically does not apply to deterministic theories. It is conceivable, but arguably unlikely, that someone could exploit this loophole to construct alocal hidden variable theory that reproduces the predictions of quantum mechanics.

Bell's theorem assumes that the types of measurements performed at each detector can be chosen independently of each other and of the hidden variable being measured. In order for the argument for Bell's inequality to follow, it is necessary to be able to speak meaningfully of what the result of the experiment would have been, had different choices been made. This assumption is called counterfactual definiteness. But in a deterministic theory, the measurements the experimenters choose at each detector are predetermined by the laws of physics. It can therefore be argued that it is erroneous to speak of what would have happened had different measurements been chosen; no other measurement choices were physically possible. Since the chosen measurements can be determined in advance, the results at one detector can be affected by the type of measurement done at the other without any need for information to travel faster than the speed of light.

John Bell discussed superdeterminism in a BBC interview:^[1]

There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the "decision" by the experimenter to carry out one set of measurements rather than another, the difficulty disappears. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already "knows" what that measurement, and its outcome, will be.

Although he acknowledged the loophole, he also argued that it was implausible. Even if the measurements performed are chosen by deterministic random number generators, the choices can be assumed to be "effectively free for the purpose at hand," because the machine's choice is altered by a large number of very small effects. It is unlikely for the hidden variable to be sensitive to all of the same small influences that the random number generator was.^[2]

See also

• Bell's theorem
• De Broglie–Bohm theory
• Many-worlds

References

1. ^ BBC Radio interview with Paul Davies, 1985
2. ^ J. S. Bell, Free variables and local causality, Epistemological Letters, Feb. 1977. Reprinted as Chapter 12 of J. S. Bell, Speakable and Unspeakable in Quantum Mechanics(Cambridge University Press 1987)

External links

• Reality, locality, and “free will”. Quote: He [Michael J. W. Hall] shows that locality and reality can be retained with a 14% reduction of the experimenters’ “free will”.

Categories: Quantum mechanics

Words to Lose and Their Replacements

1) Philosophy <=== replace with "Logic"

2) Physicist <=== replace with "Realist" , also Physics with "Reality"

3) Doctor <=== replace with "Expert"

Therefore, instead of a PhD in Physics getting a "Doctor of Philosophy in Physics" they would rather earn the exalted and well-earned title of "Expert in Logic of Reality."  Much more descriptive of what they actually are. Well, the good ones, anyway.

4-7) Smart, Stupid, Idiot, Dumb, Dumbarse, Moron, etc. <==== Replace with "Knowledgeable", "Ignorant", "Intelligent", Unintelligent"

Well as far as 4-7 are concerned, I must confess I slip at times and use those words as well. If I do however, you can be sure it's because I'm really, truly pissed ("upset").

Have a nice ("enjoyable") day. 

:-)

Casimir Effect

Casimir forces on parallel plates

In quantum field theory, the Casimir effect and the Casimir-Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, placed a few micrometers apart, without any external electromagnetic field. In aclassical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them.^[1] When this field is instead studied using quantum electrodynamics, it is seen that the plates do affect the virtual photonswhich constitute the field, and generate a net force^[2]—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured, and is a striking example of an effect purely due to second quantization.^[3][4] However, the treatment of boundary conditions in these calculations has led to some controversy. In fact "Casimir's original goal was to compute the van der Waals force betweenpolarizable molecules" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) orvirtual particles of quantum fields.^[5]

Dutch physicists Hendrik B. G. Casimir and Dirk Polder proposed the existence of the force and formulated an experiment to detect it in 1948 while participating in research at Philips Research Labs. The classic form of the experiment, described above, successfully demonstrated the force to within 15% of the value predicted by the theory.^[6]

Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. On a submicrometre scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of 1 atmosphere of pressure (101.325 kPa), the precise value depending on surface geometry and other factors.^[7]

In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; and in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.^[8]

Contents  [hide] 1 Overview 2 Vacuum energy 3 Effects 4 Casimir's calculation 4.1 More recent theory 5 Measurement 6 Regularisation 7 Generalities 8 Wormholes 9 Analogies and the dynamic Casimir effect 10 Repulsive forces 11 Applications 12 See also 13 References 14 Further reading 14.1 Introductory readings 14.2 Papers, books and lectures 14.3 Temperature dependence 15 External links