Ultraviolet catastrophe

The ultraviolet catastrophe results from the equipartition theorem of classical statistical mechanics which states that all modes (degrees of freedom) of a system at equilibrium have an average energy of kT / 2.

An example, from Mason's A History of the Sciences[1], is a piece of string. As a natural vibrator, the string will oscillate with specific modes (the standing waves of a string in harmonic resonance), dependent on the length of the string. In classical physics, a radiator of energy will act as a natural vibrator. And, since each mode will have the same energy, most of the energy in a natural vibrator will be in the smaller wavelengths and higher frequencies, where most of the modes are.

According to classical electromagnetism, the number of electromagnetic nodes in a 3-dimensional cavity, per unit frequency, is proportional to the square of the frequency. This therefore implies that the radiated power per unit frequency should follow the Rayleigh-Jeans law, and be proportional to frequency squared. Thus, both the power at a given frequency and the total radiated power is unlimited as higher and higher frequencies are considered: this is clearly unphysical as the total radiated power of a cavity is not observed to be infinite, a point that was made independently by Einstein and by Lord Rayleigh and Sir James Jeans in the year 1905.

Solution

Einstein pointed out that the difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck. Planck postulated that electromagnetic energy did not follow the classical description, but could only oscillate or be emitted in discrete packets of energy proportional to the frequency, as given by Planck's law. This has the effect of reducing the number of possible modes with a given energy at high frequencies in the cavity described above, and thus the average energy at those frequencies by application of the equipartition theorem. The radiated power eventually goes to zero at infinite frequencies, and the total predicted power is finite. The formula for the radiated power for the idealized system (black body) was in line with known experiments, and came to be called Planck's law of black body radiation. Based on past experiments, Planck was also able to determine the value of its parameter, now called Planck's constant. The packets of energy later came to be called photons, and played a key role in the quantum description of electromagnetism.

Oedipus was the son of King Laius and Queen Jocasta. Before he was born, his parents consulted the Oracle at Delphi, Tiresias. The Oracle prophesied that Oedipus would murder his father and marry his mother. In an attempt to prevent this prophecy's fulfillment, Laius ordered Oedipus's feet to be bound together, and pierced with a stake (which caused him to have permanently swollen feet – hence one meaning of Oedipus which translates to "swollen foot"; it also comes from the Greek root meaning knowledge). Afterwards, the baby was given to a herdsman who was told to kill him. The herdsman, feeling both pity for the child and fear of disobedience, instead gave him to another herdsman. The second herdsman took the infant Oedipus to the king of Corinth, Polybus, who adopted Oedipus as his son because he and his wife, Merope, could not have children. Oedipus was raised as the crown prince of Corinth. Many years later Oedipus was told by a drunk that Polybus was not his real father. Seeking the truth, he looked for the truth from his parents. They denied that he was adopted, but stubborn Oedipus was not sure so instead sought counsel from an Oracle who told him that he was destined to kill his father and mate with his mother. In his attempt to evade the dictates of the Oracle, he decided to flee from Corinth to Thebes. In Thebes, he saved the people from the Sphinx by correctly answering her riddle.

Jocasta bore Oedipus two sons, Polynices and Eteocles (see Seven Against Thebes), and two daughters, Antigone and Ismene.

Many years after the marriage of Oedipus and Jocasta, a plague struck the city of Thebes. Oedipus, in his hubris, asserted that he would end the pestilence. He sent Creon, Jocasta's brother, to the Oracle at Delphi, seeking guidance. When Creon returned, Oedipus was told that the murderer of the former King Laius must be found and either be killed or exiled. In a search for the identity of the killer, Oedipus followed Creon's suggestion and sent for the blind prophet, Tiresias, who warned him not to try to find the killer. In a heated exchange, Tiresias was provoked into exposing Oedipus himself as the killer, and the fact that Oedipus was living in shame because he did not know who his true parents were. Oedipus blamed Creon for Tiresias telling Oedipus that he was the killer. Oedipus and Creon erupted is a heated argument. Jocasta enters and tries to calm down Oedipus. She tries to comfort him by talking to him about where, when, what Laius looked like (she said that Oedipus looked somewhat like him), and how many of the palace people were with Laius. Oedipus became unnevered because his mind started thinking that he might have killed Laius. Suddenly, a messenger arrives from Corinth with the news that King Polybus is dead, who Oedipus still regarded as his true father. The messenger then reveals the fact that Oedipus was adopted. Jocasta , finally realizing Oedipus' true identity, begs him to abandon his search for Laius's murderer. Oedipus mistook her pleas thinking that she was ashamed of him because he might have been a slave. She then went into the palace, where she hung herself. Oedipus seeks verification of the messenger's story from the very same herdsman who was said to have left Oedipus to die as a baby. From that herdsman, Oedipus learned that the infant raised as the adopted son of Polybus and Merope was the son of Laius and Jocasta. Thus, Oedipus finally realizes that earlier at the crossroads, he had killed his own father, King Laius, and as consequence, had married his own mother, Jocasta.

Oedipus goes in search of Jocasta and finds she has killed herself. Taking broches from her gown, Oedipus gouges his eyes. Oedipus asks for a few favors from Creon and leaves the city of Thebes. His daughter Antigone acted as his guide as he wandered blindly through the country, ultimately dying at Colonus, after being placed under the protection of Athens by King Theseus.

His two sons, Eteocles and Polynices, arranged to share the kingdom, each taking an alternating one-year reign. However, Eteocles refused to cede his throne after his year was up. Polynices brought in an army to oust Eteocles from his position, a battle ensued. At the end of the battle, the brothers both killed each other. Jocasta's brother, Creon, took the throne. He made the decision that Polynices was a "traitor," and should not be given burial rites. Defying this edict, Antigone attempted to bury her brother, but Creon ultimately had her killed.

Sail to the Moon


I sucked the moon
I spoke too soon
And how much did it cost?
I was dropped from moonbeams
And sailed on shooting stars

Maybe you'll
Be president
But know right from wrong
Or in the flood
You'll build an Ark
And sail us to the moon
Sail us to the moon
Sail to the moon

I have been on A video shoot for the last month and have had no time to do anything else.
I Am heading to Las vegas on sunday to take photos and video for the Discovery channel on a Parkour (freestyle runners) team. I will post them about a a week after. please check them out then and let me know. much love.

Go to the The Itunes store and look up the podcast for In Rainbows. Radioheads new album. Amazing!!!

Videotape By Radiohead


When I'm at the pearly gates
This will be on my videotape, my videotape
Mephistopheles is just beneath
and he's reaching up to grab me

This is one for the good days
and i have it all here
In red, blue, green
Red, blue, green

You are my center
When i spin away
Out of control on videotape
On videotape
On videotape
On videotape

This is my way of saying goodbye
Because I can't do it face to face
I'm talking to you before

No matter what happens now
You shouldn't be afraid
Because I know today has been the most perfect day I've ever seen.