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ECURB

The 2,000th person to post in this thread wins!

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That would be me, abusing my mod powers for personal gain. Again.

:rl:

OK, I win :lock:

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C'mon, now...I won at post #128 fair and square.

You, sir, are a liar.

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Time to ratchet this up a notch.

:box:

Rachet away, rachet boy.

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Rachet away, rachet boy.

2000 was a nice round number.

Funny thing is, any number is within ecurb's reach.

..and it's ratchet! Don't you have spell check? :bag:

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2000 was a nice round number.

Funny thing is, any number is within ecurb's reach.

..and it's ratchet! Don't you have spell check? :bag:

I'm stupid. Ask any member of JN.

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How are we ever going to get to 2,000 posts in this thread with ecurb gone?

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2000 is a long way to go, but can be done in a short time with enough people.

:Typotux:

We need PFSIKH to get his butt in here and get to work. damn slacking Patsy fan.

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Natural calf rennet is extracted from the inner mucosa of the fourth stomach chamber (the abomasum) of young calves. These stomachs are a by-product of veal production. If rennet is extracted from older calves (grass-fed or grain-fed) the rennet contains less or no chymosin but a high level of pepsin and can only be used for special types of milk and cheeses. As each ruminant produces a special kind of rennet to digest the milk of its own mother, there are milk-specific rennets available, such as kid-goat rennet especially for goats' milk and lamb-rennet for sheep-milk. Rennet or digestion enzymes from other animals, like swine-pepsin, are not used in cheese production. (Swine-pepsin is, however, used in the analysis of disulfide bonds of proteins.)

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tring theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the standard model of particle physics. The phrase is often used as shorthand for Superstring theory, as well as related theories such as M-theory. By replacing the point-like particles with strings, an apparently consistent quantum theory of gravity emerges. Moreover, it may be possible to "unify" the known natural forces (gravitational, electromagnetic, weak nuclear and strong nuclear) by describing them with the same set of equations. (See Theory of everything.) For a scientific theory to be valid it must be verified experimentally. Few avenues for such contact with experiment have been claimed.[1] With the construction of the Large Hadron Collider in CERN some scientists hope to produce relevant data. It is generally expected though that any theory of quantum gravity would require much higher energies to probe. Moreover, string theory as it is currently understood has a huge number of possible solutions.[2] Thus it has been claimed by some scientists that string theory may not be falsifiable and may have no predictive power.[3][4][5][6]

Studies of string theory have revealed that it predicts higher-dimensional objects called branes. String theory strongly suggests the existence of ten or eleven (in M-theory[7]) spacetime dimensions, as opposed to the usual four (three spatial and one temporal) used in relativity theory; however the theory can describe universes with four effective (observable) spacetime dimensions by a variety of methods.[8]

An important branch of the field is dealing with a conjectured duality between string theory as a theory of gravity and gauge theory. It is hoped that research in this direction will lead to new insights on quantum chromodynamics, the fundamental theory of strong nuclear force.[9][10][11][12]

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Think of a guitar string that has been tuned by stretching the string under tension across the guitar. Depending on how the string is plucked and how much tension is in the string, different musical notes will be created by the string. These musical notes could be said to be excitation modes of that guitar string under tension.

dot.gif In a similar manner, in string theory, the elementary particles we observe in particle accelerators could be thought of as the "musical notes" or excitation modes of elementary strings.

dot.gif In string theory, as in guitar playing, the string must be stretched under tension in order to become excited. However, the strings in string theory are floating in spacetime, they aren't tied down to a guitar. Nonetheless, they have tension. The string tension in string theory is denoted by the quantity 1/(2 p a'), where a' is pronounced "alpha prime"and is equal to the square of the string length scale.

dot.gif If string theory is to be a theory of quantum gravity, then the average size of a string should be somewhere near the length scale of quantum gravity, called the Planck length, which is about 10-33 centimeters, or about a millionth of a billionth of a billionth of a billionth of a centimeter. Unfortunately, this means that strings are way too small to see by current or expected particle physics technology (or financing!!) and so string theorists must devise more clever methods to test the theory than just looking for little strings in particle experiments.

dot.gif String theories are classified according to whether or not the strings are required to be closed loops, and whether or not the particle spectrum includes fermions. In order to include fermions in string theory, there must be a special kind of symmetry called supersymmetry, which means for every boson (particle that transmits a force) there is a corresponding fermion (particle that makes up matter). So supersymmetry relates the particles that transmit forces to the particles that make up matter.

dot.gif Supersymmetric partners to to currently known particles have not been observed in particle experiments, but theorists believe this is because supersymmetric particles are too massive to be detected at current accelerators. Particle accelerators could be on the verge of finding evidence for high energy supersymmetry in the next decade. Evidence for supersymmetry at high energy would be compelling evidence that string theory was a good mathematical model for Nature at the smallest distance scales.

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Pythagoras could be called the first known string theorist. Pythagoras, an excellent lyre player, figured out the first known string physics -- the harmonic relationship. Pythagoras realized that vibrating Lyre strings of equal tensions but different lengths would produce harmonious notes (i.e. middle C and high C) if the ratio of the lengths of the two strings were a whole number.

Pythagoras discovered this by looking and listening. Today that information is more precisely encoded into mathematics, namely the wave equation for a string with a tension T and a mass per unit length m. If the string is described in coordinates as in the drawing below, where x is the distance along the string and y is the height of the string, as the string oscillates in time t,

SinPlot.gif

then the equation of motion is the one-dimensional wave equation

String0.gif

where vw is the wave velocity along the string.

When solving the equations of motion, we need to know the "boundary conditions" of the string. Let's suppose that the string is fixed at each end and has an unstretched length L. The general solution to this equation can be written as a sum of "normal modes", here labeled by the integer n, such that

StringModeSum.gif

The condition for a normal mode is that the wavelength be some integral fraction of twice the string length, or

The frequency of the normal mode is then

The normal modes are what we hear as notes. Notice that the string wave velocity vw increases as the tension of the string is increased, and so the normal frequency of the string increases as well. This is why a guitar string makes a higher note when it is tightened.

But that's for a nonrelativistic string, one with a wave velocity much smaller than the speed of light. How do we write the equation for a relativistic string?

According to Einstein's theory, a relativistic equation has to use coordinates that have the proper Lorentz transformation properties. But then we have a problem, because a string oscillates in space and time, and as it oscillates, it sweeps out a two-dimensional surface in spacetime that we call a world sheet (compared with the world line of a particle).

In the nonrelativistic string, there was a clear difference between the space coordinate along the string, and the time coordinate. But in a relativistic string theory, we wind up having to consider the world sheet of the string as a two-dimensional spacetime of its own, where the division between space and time depends upon the observer.

The classical equation can be written as

String1.gif

where s and t are coordinates on the string world sheet representing space and time along the string, and the parameter c2 is the ratio of the string tension to the string mass per unit length.

These equations of motion can be derived from Euler-Lagrange equations from an action based on the string world sheet

StringActionB.gif

The spacetime coordinates Xm of the string in this picture are also fields Xm in a two-dimension field theory defined on the surface that a string sweeps out as it travels in space. The partial derivatives are with respect to the coordinates s and t on the world sheet and hmn is the two-dimensional metric defined on the string world sheet.

The general solution to the relativistic string equations of motion looks very similar to the classical nonrelativistic case above. The transverse space coordinates can be expanded in normal modes as

BStringModeSum.gif

The string solution above is unlike a guitar string in that it isn't tied down at either end and so travels freely through spacetime as it oscillates. The string above is an open string, with ends that are floppy.

For a closed string, the boundary conditions are periodic, and the resulting oscillating solution looks like two open string oscillations moving in the opposite direction around the string. These two types of closed string modes are called right-movers and left-movers, and this difference will be important later in the supersymmetric heterotic string theory.

This is classical string. When we add quantum mechanics by making the string momentum and position obey quantum commutation relations, the oscillator mode coefficients have the commutation relations

AlphaComms.gif

The quantized string oscillator modes wind up giving representations of the Poincar

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