# Introduction to quantum entanglement

The Leonard Susskind Lectures

http://theoreticalminimum.com/

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*A number of years ago I became aware of the large number of physics enthusiasts out there who have no venue to learn modern physics and cosmology. Fat advanced textbooks are not suitable to people who have no teacher to ask questions of, and the popular literature does not go deeply enough to satisfy these curious people. So I started a series of courses on modern physics at Stanford University where I am a professor of physics. The courses are specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners.
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Why? Why in God’s universe do we need to consider quantum entanglement? Four reasons: 1. As a physical phenomenon, quantum entanglement has solid empirical support. For aficionados of quantum mechanics, it provides the frisson of quantum weirdness. 2. As a philosophical conundrum, quantum entanglement has inspired debate about the interpretation of quantum mechanics. 3. In communications, quantum entanglement leads to potentially game-changing discoveries in the areas of superdense coding, quantum teleportation and quantum cryptography. 4. Quantum entanglement is considered within the neuroscience world and in consciousness science. Investigators include Roger Penrose, Stuart Hameroff, Hiroomi Umezawa, Giuseppe Vitiello, Walter Freeman and Henry Strapp, among others.

Leonard Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University, and Director of the Stanford Institute for Theoretical Physics. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology.

From Wikipedia:

*Quantum entanglement is a physical phenomenon that occurs when particles such as photons, electrons, or molecules the size of buckyballs or small diamonds, interact and then become separated. Before the interaction each particle is described by its own quantum state. After the interaction the pair can still be described with a definite quantum state but each member of the pair must also be described relative to one another. The quantum mechanical description (state) of each member of this pair is indefinite in terms of important factors such as position, momentum, spin, polarization, etc in a manner distinct from the intrinsic uncertainty of a quantum superposition.*

*Quantum entanglement is a product of quantum superposition, i.e., of the fundamental aspect of quantum mechanics where the complete state of a system is expressed as a sum of basis states, or eigenstates of some observable(s). Though it is common to speak of single quantum systems as existing in superpositions of basis states, the same is also valid for the quantum state of a pair or group of quantum systems. If the quantum state of a pair of particles is in a definite superposition, and that superposition cannot be factored out into the product of two states (one for each particle), then that pair is entangled. When a measurement is made on one member of such a pair and the outcome is known (e.g., clockwise spin), the other member of this entangled pair is at any subsequent time always found (when measured) to have taken the appropriately correlated value (e.g., counterclockwise spin). *

*Thus, there is a correlation between the results of measurements performed on entangled pairs, and this correlation is observed even though the entangled pair may be separated by arbitrarily large distances. In the formalism of quantum theory, this effect of measurement happens instantaneously.*

* Repeated experiments have verified that this works even when the measurements are performed more quickly than light could travel between the sites of measurement: there is no slower-than-light influence that can pass between the entangled particles. Recent experiments have shown that this transfer occurs at least 10,000 times faster than the speed of light;[ this merely establishes a lower limit to the speed — it may actually be instantaneous.*

Available on his web site The Theoretical Minimum

http://theoreticalminimum.com/

as well as YouTube

http://www.youtube.com/watch?v=0Eeuqh9QfNI

Dr. Susskind’s lectures on quantum entanglement proceed with Feynmanesque clarity as well as his own special brand of physics humor. As an introduction to quantum mechanics and quantum entanglement, as well as the opportunity to watch a great physicist strut his stuff, these lectures have no equal.