EPR+Paradox

=The EPR Paradox= Click on the highlighted topics for further information. The EPR Paradox, or the Einstein-Podolsky-Rosen Paradox, is a thought experiement based of the findings and thoughts of Albert Einstein. It was an attempt to explain quantum mechanics and make it a more complete theory developed by Albert Einstein, Boris Podolsky and Nathan Rosen. EPR pointed out that the current quantum theory had gaps or locality, the idea that two particles separated at a distance can't influence each other without something passing between them, didn't work; put simply, either there were really hidden pieces of information in the universe that quantum theory thought were uncertainties, or locality is untrue. The three scientists were determined that there were gaps on the theory of quantum mechanics. They were also determined to prove that it is possible to predict the momentum and position of a given electron, or photon, with no uncertainty, which to this day, is still impossible. This view of quantum theory implied that the whole "probabilistic view" of the world was wrong. In the paper, the scientists highlighted the two features of the Copenhagen Interpretation that they thought was "absurd"--the "collapse of the wave function," and the idea that every part of a quantum system instantaneously responds to a stimulus affecting any other part.

The essay, officially titled //Can// //Quantum-Mechanical Description of Physical Reality Be Considered Complete?// states:

"In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantityis the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of realitygiven by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete."

The scientists' work, however, was found to be impossible by other scientists' work later on in the century .toc

History
In the early 1900's, Albert Einstein and Max Planckwrote two papers that were essential to the creation and exploration of a new paradigm in physics. This began the area of study that most physicists today know as Quantum Mechanics. As time went on, it occured to the scientific community that the classical mechanics could not accurately describe or explain the world of sub-atomic particles and the atom itself. Soon there were other physicists producing their own theories and experiments that helped develop the Quantum Theory. Of these scientists, Niels Bohrand Werner Heisenbergwere the most adamant in believing that there was no meaningful way to explain the atom's behavior of it's sub-atomic particles. Their case was furthered with the fact that the arithmetic of classical mechanics did not allow and could not produce a way to make predictions on the sub-atomic level. An example of this impossibility to predict with the math or classical mechanics would be that there was no way to precisely predict when or where an electron would emit a photon. Einstein believed however that everything in the universe had a relative cause and effect, meaning that there was some method to this madness. He was famously quoted saying "God does not play dice with the universe.", meaning that everything in nature, whether it be scientific or not, has a cause and effect. In other words, there is always a reason for the actions of the universe. He refused to believe that nature and the universe revolves around an indeterminable and mysterious uncertainty. The disagreement over the ability of quantum theory to adequately describe nature triggered the famous Bohr-Einstein debates. Bohr and Einstein spent many years debating the persona of nature as is it relates to and as it is described by Quantum Mechanics. The debate went on for years and was culminated by Einstein’s final assault which was the Einstein-Podolsky-Rosen paradox.

Explanation
When reading about the paradox for the first time, it's hard to really understand. But the experiment is a thought experiment, not one that you can actually watch and know whats happening. The basis of the EPR Paradox, in short, is shown below: Two electrons, according to the current theory, don't have spin, just as they don't have a position, until it is measured. Take the two electrons and separate them until they are light years apart from each other. Now, measure only one of them. For instance, the electron on the right is measured as having a clockwise spin. Immediately, you know that the other electron has to be a counter-clockwise spin, without ever measuring it. Therefore, the left-hand electron must have had spin all along and current theory is wrong about the electron not being anywhere or having spin before measurement.

This scenario is the foundation of Einstein, Podolsky, and Rosen's paper. One electron that is related to another electron must have some means of "communication" with the other electron. Then we know that we can predict the position, spin, and momentum of one if we know the other's position, momentum, and spin, without ever taking a measurement. And, therefore, the two electrons must have an instantaneous communication between the two. However, the Copenhagen Interpretation said otherwise. It stated that you had to measure the electron before ever knowing anything about it. Even if you could tell what the spin or position was by using the spin and position of the other electron, it doesn't matter. It only matters after you measure the electron.

Copenhagen Interpretation
The Copenhagen Interpretation is the most widely accepted interpretation of quantum mechanics. It was the first attempt to explain the mysteries of quanum mechanics. The Interpretation is comprised of several principal "elements" which are the works of Max Born, Niels Bohr, and Werner Heisenberg. According to this interpretation, the act of measurement causes the calculated set of probabilities of finding an electron to "collapse" to the value defined by the measurement. Put simply, the interpretation states an electron is a wave until a measurement is made, at which point it collapses into a particle. Bohr spearheaded the interpretation. He thought that any single particle—an electron, proton, or photon—never occupies a definite position unless someone measures it. Until you measure a particle, Bohr argued, it makes no sense to ask where it is: It has no concrete position and exists only as a blur of probability. Bohr also described the electron as a wave and as a particle to be "complementary".Bohr felt that the classical and quantum mechanical models were two complementary ways of dealing with physics, which were both necessary. He felt that an experimental observation collapsed the wave function to make its future evolution consistent with what we observe experimentally. He also knew, however, that there was no precise way to find the exact point at which collapse occurred. Any attempt to define the point would yield a different theory of quantum mechanic . This interpretation was accepted very widely because it was an explanation for an anomaly. It was the only way, at the time, of explaining the electron behavior of both a wave and particle. However, many scientists, such as Erwin Schrödinger, and Albert Einstein did not accept the interpretation. Schrödinger used his famous cat example to refute the Interpretation: A cat, along with a flask containing poison, is placed in a sealed box. If a Geiger counter detects radiation, the flask breaks, releasing the poison, killing the cat. According to the Copenhagen Interpretation, Schrödinger stated, the cat would be both dead and alive until the box was opened, which is impossible. He used this thought experiment to prove how ridiculous he tought the Interpretation was. Einstein then went on to say "God does not play dice with the universe." He felt that there had to be an explanation to the wave-particle duality. Quantum mechanics, according to him, was not random. This is what triggered him to develop the EPR Paradox.

Heisenberg Uncertainty Principle
Heisenberg discovered that if the uncertainty in knowing the position of a particle is small, then the uncertainty about the momentum is large and vice versa. His equation describes this.

ΔxΔp ≥ ½h delta - x refers to the space where the particle is confined delta - p refers to the momentum that the particle has h refers to [|Planck's constant] 6.6260693×10E -34 J×sec

The smaller delta-x is, the larger delta-p has to be for the equation to equal half of Planck's constant.

This is exactly what Einstein, Podolsky, and Rosen were trying to prove wrong. They wanted to find a way that they could know both the position and momentum of a particle without being uncertain in either measurement.

Hidden Variables
The Hidden Variables Theory, developed by a minority of physicists, was the beginnings of the EPR Paradox. The most famous proponent of the theory was Einstein, who was convinced of the fact that something was missing in the quantum mechanics theory. He thought that there were additional variables or parameters that would make quantum mechanics a complete theory. These variables were then referred to as hidden variables. Hidden variables would provide more vast knowedge on the probabilities of electrons. Einstein's thoughts became known as the Local Hidden Variables Theory where he looked at the relationship between measurements on two parts of a single system after the parts have been separated. This is the basis the EPR Paradox. The theory was then developed by Einstein with the help of Podolsky and Rosen to create the EPR Paradox.

Bell's Inequality
This inequality, published by John S. Bellin 1964, 29 years ater the EPR Paradox, was proof that Einstein's, Podolsky's, and Rosen's figurings were incorrect. In this year Bell published his proof that contained the theorum stating that if momentum and position were absolute values (existing whether they were measured or not), then his inequality, stated later, would be satisfied. His inequality states: Number(A, not B) + Number(B, not C) ≥ Number(A, not C) One way to understand the inequality is by using regular variables, not by using quantum mechanics. Say the three variables are as follows: Now apply Bell's inequality. The number of people in a group that are male but aren't over 5' 8 added to the number of people over 5' 8 but don't have blue eyes will always be greater than or equal to the number of males that have blue eyes. Thinking of the inequality in terms of quantum mechanics, consider a beam of electrons from an electron gun: Therefore: Number(spin-up zero degrees, not spin-up 45 degrees) + Number(spin-up 45 degrees, not spin-up 90 degrees) ≥ Number(spin-up zero degrees, not spin-up 90 degrees) With this inequality, Bell was trying to disprove the hidden variables theory. Many scientists, including the ones that developed the EPR Paradox figured that there could be aspects of two electrons that could be the same since they were entagled, but they did not depend on eachother. Bell proved that this theory was mathematically impossible with the inequality. The inequaltiy is not violated in quantum mechanics, IF instantanteous communication is present. Instantaneous communication is the theory that when two photons are separated far apart, what happens to one photon will affect the other photon, beacuse they are entangled. An experiment that explains this was carried out by a physicist at the University of Geneva, Switzerland, Nicolas Gisin in 1997. He split a single photon into two "smaller" photons, entagling them, and sent them down fiber optic cable in opposite directions. When the photons where about 10 kilometers apart they ran into a detector. Gisin found that even though a large distance separate the photons, something done to one photon at one end largely affected the photon at the other end instantaneously. If instantaneous communication is ruled out of an experiment, then Bell's inequality is violated.
 * A: Male
 * B: Over 5' 8''
 * C: Blue eyes
 * A: electrons are "spin-up" for an "up" being defined as straight up, which we will call an angle of zero degrees
 * B: electrons are "spin-up" for an orientation of 45 degrees
 * C: electrons are "spin-up" for an orientation of 90 degrees

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This video describes a simplification of the EPR experiment. It uses the example of two gloves, one each in a separate box. The gloves depend upon one another. Once one box is opened the other glove has to be either the right or left glove to make a pair. According to Neils Bohr the gloves remain in a state of being unknown (not left or right, but a mixture) until one box is opened and "measured", the other then becomes the opposite to make the pair. If the right glove is in the open box, then the left glove must be in the closed box and vice versa. Like the gloves, the particles must be a pair so when one particle has been measured having a clockwise spin the other automatically must have a counter-clockwise spin. media type="youtube" key="VW1vJYzN1QE" height="344" width="425" align="center"

Over a 10km distance the EPR paradox was tested. Two photons were passed through 5 km of telephone wires and measured instantaniously. The results show that every time the photons were opposites, however it was completely random which photon ended up at each end. In conclusion scientists decided that the photons remain in a state of unknown until they are measured. Then somehow they become opposites even if they have no chance to communicate.