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Possible Unification of Maxwell’s and Einstein’s Equations 1921, Theodor Kaluza: reworked Einstein’s equations to 5 dimensions. Maxwell’s equations emerged from this process.

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What Is a 5 th Dimension? Dimensions are different directions an object can move (such as x, y, and z coordinates, plus time for our 4). Dimensions are sometimes called degrees of freedom. Oskar Klein and Kaluza reasoned that the 5 th dimension must be very small (even subatomic) because it could not be observed.

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Problems With Kaluza’s Theory Einstein could not find subatomic particles in the Kaluza-Klein theory. It didn’t seem to match reality. Perhaps the equation was just a mathematical happenstance. The theory was rejected, and it was a missed opportunity for physics.

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Chaos of World War II The Nazi party drove Jewish scientists out of Germany. In 1931, the book “One Hundred Authorities Against Einstein” was published. Schrodinger was beaten for trying to stop a storm trooper from beating a Jewish shopkeeper. Max Planck’s son was executed. Neils Bohr was targeted while the Nazis occupied Denmark.

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Start of String Theory In 1968, at CERN, Gabriele Veneziano found that an Euler equation seemed to describe the data he collected on the collision of two atomic particles. Two physicists at UW-Madison expanded Veneziano’s relationship to an S matrix – a hypothesis in which each term described a way in which atomic particles can interact. Could any meaning be derived from this mathematical description?

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Strings In 1970, a group of physicists found that if elementary particles were little vibrating one- dimensional strings, their interactions fit the math that had been developed. The superstring model could only exist if reality had 10 dimensions. The theory was now dictating its own number of dimensions.

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Problems with String Theory There were many anomalies, or situations where math breaks down. There were also mathematical inconsistencies- the theory seemed to contradict itself. It contained too much information, as there were particles that had no relevance to the strong force.

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Possible Theory of Everything? In 1974, Schwarz and Scherk proclaimed that the “extra” particles matched the properties of the hypothesized graviton. String theory was now a particle theory that included gravity.

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More problems The theory required a string one hundred billion times smaller than the string they had proposed earlier. The new string length was roughly the Planck length (10 -33 cm). This was, and still is, far too small to ever be observed or tested.

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Anomalies eliminated In 1984, Schwarz and Michael Green completed a calculation that proved that all of the potential anomalies miraculously cancel out.

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Recap of Standard Model elementary particles Electrons, up-quarks, and down-quarks are the smallest building blocks of matter. There are also three types of neutrinos that permeate space but have little interaction with ordinary matter. The four force particles are also elementary particles. These fundamental particles are treated as points – this creates problems with the equation force=k/r 2

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String Theory Treatment of Elementary Particles String Theory treats elementary particles as tiny, one-dimensional vibrating filaments. Each string can undergo a huge (potentially infinite) number of different vibrational patterns known as resonances, or standing waves. Different vibrational patterns of a fundamental string give rise to different masses and energies. More energy = more mass, like E= mc 2.

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Correlating Particles with Vibrations The lowest fundamental vibration represents massless (or near-massless) elementary particles. Other properties of a particle, such as its charge and spin, are encoded through more subtle features of the string’s vibration. Different elementary particles are actually different “notes” on a fundamental string. The interactions of these particles follow the vibrational laws of string theory.

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The Plank Length solution Relativity called for smooth changes of space, but quantum uncertainty resulted in violent fluctuations of space-time. The fluctuations in force fields at distances less than the Planck length are so great that the mathematics become meaningless. At the Planck length, the quantum mechanical fluctuations are still there; however, they are smooth enough to be handled in a modified relativistic equation.

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More Quantization In string theory, distance also becomes quantized, with the Planck length being the shortest distance possible. Time is quantized from this: the shortest time is the time it takes light to travel the Planck length. This is known as a unit of Planck time. Considering any distance or time less than these is meaningless.

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1984 to 1986 was the first superstring revolution More than one thousand research papers were written in this time. Michael Green said, “the moment you encounter string theory and realize that almost all of the major developments in physics over the last 100 years emerge and emerge with such elegance from such a simple starting point, you realize that string theory is in a class of its own.” String theory requires no input other than a single number that sets the scale for measurements.

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Musical Structure of Nature Each particle is in existence because it represents a possible stable vibration, or note, on the string. The harmonies of the strings are the laws of physics. The melodies are the laws of chemistry. The universe is just a symphony of strings.

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Not the first musical theory of nature In chemistry, Newland’s octave theory of the periodic table hinted at a music like basis of the universe. The ancient Pythagorean “music of the spheres” and “harmonies of nature” guided inquiry throughout the ages.

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Supersymmetry This approach was developed in the 1970s and applied to both string theory and the standard model. It helped solve some math problems in both. Supersymmetry demands more symmetry by pairing fermions to bosons, based on spin. This doubles the number of particles, as none of the new particles have been discovered as of yet.

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Some Problems With String theory There are an infinite number of complicated vibrations, so why aren’t there an infinite number of more massive particles? If they are formed, they must be unstable and break down. All vibrations will be some multiple of the Planck mass (0x, 1x, 2x, 3x, 4x, etc.). A Planck mass is 10 19 times the mass of a proton. All elementary particles are matched with a Planck mass of 0.

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Problems continued Other information, such as spin, is described by more subtle aspects of the vibration. The mathematics of string theory is very complicated, and only approximate solutions have been obtained.

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Five Theories to One In the 1990s, there were actually five different string theories. In 1995, Edward Witten was able to demonstrate that the five theories were actually just five different forms of a single unified theory, which he dubbed M-theory. There had to be ten space dimensions and one time dimension to unify the five theories.

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Membranes Progress in the string theory equation has resulted in predicting membranes (branes). Membranes have much higher energy than strings do. Branes can be one dimensional space (a one- brane), two dimensional space (a two-brain), three dimensional space (a 3-brane) or p- dimensional.

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More about branes Branes can be extremely large- the universe we are experiencing may simply be a three brane. Closed strings are free to migrate within any brane. Open-ended strings can have their ends connected to 1, 2, 3, or p dimensional branes, and so they are not able to travel to other branes.

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Our Universe What evidence is there for M-theory’s 10 space and 1 time dimension? The fact that Newton’s inverse square law works suggests that we live in a 3- brane universe.

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Open and Closed Strings All force particles except the graviton are open strings. The graviton, being a closed string, is free to migrate through any brane or universe. The fact that the inverse square law holds for gravity suggests that there are no other branes for it to migrate into.

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Does this prove M-theory wrong? The inverse square law has only been accurately tested down to 1/10 of a millimeter. If the other seven space dimensions are all coiled up tighter and smaller than 1/10 of a millimeter, M-theory could still hold true.

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Where does string theory go from here? Gravity is the key to detecting other dimensions, since it exists as a closed string. The larger the extra dimension, the more gravity can spill into it, and the weaker gravity’s force will appear in our familiar three space dimensions. String theorists forge ahead and hope these problems will be resolved.

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The Bulk Perhaps M-theory is not just a theory of our universe, but of countless other universes as well. Our universe may be only a tiny slice of the greater universe, called the bulk. Only time will tell!

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String Theory, Quantum Mechanics and Relativity Dr. David Berman Lecturer Department of Physics Queen Mary College University of London.

String Theory, Quantum Mechanics and Relativity Dr. David Berman Lecturer Department of Physics Queen Mary College University of London.

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