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The study between quanta and elementary particles.

Quanta – an indivisible entity of a quantity that has the same value as Planck’s constant which is related to energy and momentum of elementary particles.

Elementary Particle – a particle not known to have substructure or be composed of smaller particles.

It generalizes all classical theories (excluding general relativity), results are typically only observable on the atomic and subatomic scales.

The foundations of quantum mechanics were established during the first half of the twentieth century by Werner Heisenburg, Max Planck, Albert Einstein, Neils Bohr, Erwin Schrodinger, and Wolfgang Pauli

The modern world of physics is notably founded on two tested and demonstrably sound theories of general relativity and quantum mechanics; theories which appear to contradict one another. However, while they do not directly contradict each other theoretically, they are resistant to being incorporated within one model.

Einstein himself is well known for rejecting some of the claims of quantum mechanics. While clearly inventive in this field, he did not accept the more philosophical consequences and interpretations of quantum mechanics

…these consequences are know as Quantum Mechanical Phenomena.

Quantum mechanical phenomena include things such as:

--quantum teleportation

--the EPR paradox

--quantum entanglement

Quantum Teleportation is a quantum protocol where quantum information can be transmitted using an entangled pair of qubits.

Qubit - a two dimensional vector that measures quantum information.

Quantum Teleportation cannot teleport matter, energy, or information at a speed faster than light, but it is useful for quantum communication and calculations.

Assume that A and B share an entangled qubit AB. Let C denote the qubit A wishes to transmit to B.

A applies a unitary operation on the qubits AC and measures the result to obtain two classical bits. In this process, the two qubits are destroyed. B\'s qubit, B now contains information about C however the information is somewhat randomized. More specifically, B\'s qubit is in one of four states uniformly chosen at random and B cannot obtain any information about C from his qubit.

A provides her two measured qubits, which indicate which of the four states B possesses. B applies a unitary transformation which depends on the qubits he obtains from A, transforming his qubit into an identical copy of the qubit C.

The EPR paradox is a dichotomy, which means it yields two results but they’re coincide with each other.

EPR stands for Einstein, Podolsky, and Rosen; who are the people that introduced the thought to show that quantum mechanics isn’t totally physical.

The EPR paradox draws on a phenomenon predicted by quantum mechanics to show that measurements performed on spatially separated parts of a quantum system can apparently have an instantaneous influence on one another. This result is known as “nonlocal behavior” or as Einstein put “a spooky action at a distance”.

The EPR paradox relates to the concept of locality.

Locality states that a physical process at one location should have no immediate effect on something at a different location.

Usually information cannot be transferred faster than the speed of light without contradicting causality, however if you combine quantum mechanics with classical views of physics you can contradict locality without contradicting locality, thus resulting in The EPR Paradox!

Quantum Entanglement is a quantum mechanical phenomena where the quantum states of two or more objects are linked so one object can’t be completely described without mentioning the other(s) even thought they may be spatially separated.

In theory this results in correlations between physical properties of remote systems.

The distance between the two

particles is irrelevant. Some

physicists have theorized that

there are hidden variables that

are determined when the pair of

particles are entangled.

The rules of quantum mechanics curiously appear to prevent an outsider from using these methods to actually transmit information, and therefore do not appear to allow for time travel or Faster Than Light communication.

This misunderstanding seems to be widespread in popular press coverage of quantum teleportation experiments. The ideas are commonly used in science fiction literature without the complicated explanation of course.

The assumption that time travel or superluminal communications is impossible allows one to derive interesting results such as the no cloning theorem, and how the rules of quantum mechanics work to preserve causality is an active area of research.

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