EPR Paradox in Physics - Definition and Explanation

The EPR paradox (or the Einstein-Podolsky-Rosen Paradox) is a thought experiment intended to demonstrate an inherent paradox in the early formulations of quantum theory. It is among the best-known examples of quantum entanglement. The paradox involves two particles that are entangled with each other according to quantum mechanics. Under the Copenhagen interpretation of quantum mechanics, each particle is individually in an uncertain state until it is measured, at which point the state of that particle becomes certain. At that exact same moment, the other particles state also becomes certain. The reason that this is classified as a paradox is that it seemingly involves communication between the two particles at speeds greater than the speed of light, which is a conflict with Albert Einsteins theory of relativity. The Paradoxs Origin The paradox was the focal point of a heated debate between Einstein and Niels Bohr. Einstein was never comfortable with the quantum mechanics being developed by Bohr and his colleagues (based, ironically, on work started by Einstein). Together with his colleagues Boris Podolsky and Nathan Rosen, Einstein developed the EPR paradox as a way of showing that the theory was inconsistent with other known laws of physics. At the time, there was no real way to carry out the experiment, so it was just a thought experiment or gedankenexperiment. Several years later, the physicist David Bohm modified the EPR paradox example so that things were a bit clearer. (The original way the paradox was presented was somewhat confusing, even to professional physicists.) In the more popular Bohm formulation, an unstable spin 0 particle decays into two different particles, Particle A and Particle B, heading in opposite directions. Because the initial particle had spin 0, the sum of the two new particle spins must equal zero. If Particle A has spin 1/2, then Particle B must have spin -1/2 (and vice versa). Again, according to the Copenhagen interpretation of quantum mechanics, until a measurement is made, neither particle has a definite state. They are both in a superposition of possible states, with an equal probability (in this case) of having a positive or negative spin. The Paradoxs Meaning There are two key points at work here which make this troubling: Quantum physics says that, until the moment of the measurement, the particles do not have a definite quantum spin but are in a superposition of possible states.As soon as we measure the spin of Particle A, we know for sure the value well get from measuring the spin of Particle B. If you measure Particle A, it seems like Particle As quantum spin gets set by the measurement, but somehow Particle B also instantly knows what spin it is supposed to take on. To Einstein, this was a clear violation of the theory of relativity. Hidden-Variables Theory No one ever really questioned the second point; the controversy lay entirely with the first point. Bohm and Einstein supported an alternative approach called the hidden-variables theory, which suggested that quantum mechanics was incomplete. In this viewpoint, there had to be some aspect of quantum mechanics that wasnt immediately obvious but which needed to be added into the theory to explain this sort of non-local effect. As an analogy, consider that you have two envelopes that each contain money. You have been told that one of them contains a $5 bill and the other contains a $10 bill. If you open one envelope and it contains a $5 bill, then you know for sure that the other envelope contains the $10 bill. The problem with this analogy is that quantum mechanics definitely doesnt appear to work this way. In the case of the money, each envelope contains a specific bill, even if I never get around to looking in them. Uncertainty in Quantum Mechanics The uncertainty in quantum mechanics doesnt just represent a lack of our knowledge but a fundamental lack of definite reality. Until the measurement is made, according to the Copenhagen interpretation, the particles are really in a superposition of all possible states (as in the case of the dead/alive cat in the Schroedingers Cat thought experiment). While most physicists would have preferred to have a universe with clearer rules, no one could figure out exactly what these hidden variables were or how they could be incorporated into the theory in a meaningful way. Bohr and others defended the standard Copenhagen interpretation of quantum mechanics, which continued to be supported by the experimental evidence. The explanation is that the wave function, which describes the superposition of possible quantum states, exists at all points simultaneously. The spin of Particle A and spin of Particle B are not independent quantities but are represented by the same term within the quantum physics equations. The instant that the measurement on Particle A is made, the entire wave function collapses into a single state. In this way, theres no distant communication taking place. Bells Theorem The major nail in the coffin of the hidden-variables theory came from the physicist John Stewart Bell, in what is known as Bells Theorem. He developed a series of inequalities (called Bell inequalities), which represent how measurements of the spin of Particle A and Particle B would distribute if they werent entangled. In experiment after experiment, the Bell inequalities are violated, meaning that quantum entanglement does seem to take place. Despite this evidence to the contrary, there are still some proponents of the hidden-variables theory, though this is mostly among amateur physicists rather than professionals. Edited by Anne Marie Helmenstine, Ph.D.

The Making Of The Republic Of Haiti - 3644 Words

EMPIRE STATE COLLEGE THE MAKING OF THE REPUBLIC OF HAITI FROM 1492 TO 1804 THIS PAPER IS PRESENTED IN PARTIAL FULFILLMENT FOR THE REQUIREMENT OF THE COURSE â€Å"OTHER WORLD CIVILIZATIONS† Presented by: Luce-Josie Nicolas June 30th, 2015 Approved by: _______________ The island of Haiti, occupied by The Republic of Haiti and the Dominican Republic is one of several islands discovered by Christopher Columbus during his first voyage to the new world in 1492. At his arrival, Columbus established a settlement on the north coast which he named Navidad . Columbus used three boats to make this voyage possible : the Pinta, The Nina and the Santa Maria. Only Santa Maria reach the rives of America. This boat sank near the site presently known as Cap Haitien. At his arrival on the island of Haiti, Columbus found the Taino Indian They were very hospitable toward Columbus and his men. However, Christophe Colombus and his men brutalized so much the Tainos, they became violent as a direct and implicit response to the intolerance and abuse of the visitors. Columbus left his men in the America and return to Spain with sample of richess of Saint Domingue. For his second, Christopher Colunbus fought bitterly against the Indians natives, destroyed and killed thousands of them in order to settle his troops and invade the entire island. The Spanish were at that time interested in expanding their territories, spread their religious belief, and increase their gold reserve. The island wasShow MoreRelatedDominican Republic vs. Haiti1245 Words   |  5 PagesDominican Republic and Haiti: A Comparison of How One Island Has Two Complete Different Ends Dominican Republic and Haiti: A Comparison of How One Island Has Two Complete Different Ends The Hispaniola is a small island in the Caribbean which is currently composed by the Dominican Republic and the Republic of Haiti. 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They wish everyday they could have even half of what we have. Haiti is a neighbor to the Dominican Republic, the population is about 9.2 million and is widely considered the poorest country in the western hemisphere. 80% of the population live below the poverty line. 54% live on less than $1.25 per day. Life expectancy is only 30 years and that is the lowest in the world. In Haiti there is

Mohandus Karamchand Gandhi Essay Example For Students

Mohandus Karamchand Gandhi Essay Mohandus Karamchand Gandhi was a major figure in Indian history. He was best known for his policy of passive resistance and civil disobedience against unjust laws set by the British government. He inspired other nonviolent movements notably the U.S. civil right movement of the 1950s and 1960s lead by Dr. Martin Luther King, Jr. (Encarta 98). Gandhi was highly influential, some say responsible, for Indias gain of independence and the abolishment of untouchability, the lowest rank under the caste system. Gandhi was born to a middle-class Indian family in 1869 and married at the age of thirteen to Kasturbai Makanji. He began to study law at the University of London in 1888 and as he completed his studies and prepared to return home for India in 1891 he had doubts about his future (Sherrow 34). He lacked the knowledge of Indian law as well as the social connections needed for a successful career. He had never set foot inside an Indian courtroom in his life. He attempted to set up a law practice but had little success. Two years later an Indian firm with assets in South Africa held him as a legal advisor at its office in Durban. While in Durban, Gandhi was treated as a member of an inferior race. He was offended and horrified at the denial of rights and liberties to Indian immigrants. He joined the struggle for elementary rights for Indians. He stood in South Africa for 20 years. He was imprisoned many times. Gandhi began to teach a policy of passive resistance to South African authorities after being attacked and beaten by white South Africans. In 1899 the trouble that had been brewing between the British and the Boers escalated into war (Sherrow 47). Gandhi sided with the Boers in what was known as the Boer war but set up a British ambulance service called the Indian Ambulance Corps. According to Gandhis sense of justice, if you wanted the rights of a British citizen you must perform the duties expected of one. He urged other Indians to serve with him. Because of this act, Gandhi receives two war medals. In 1914 the government of the Union of South Africa made important compromises to Gandhis demands, incl uding recognition of Indian marriages and the abolition of the poll tax for them (Encarta 98). Seeing his work in South Africa complete, he returned to India. Gandhi became a leader in the tough struggle for home rule. After World War I Gandhi started his movement of passive resistance to Great Britain. He was again urging Satyagraha (Sanskrit, truth and firmness). In 1919, Parliament passed the Rowlatt Acts, which banned terrorism and disloyal acts or resistance toward the government. Satyagraha spread through India gaining millions of followers. On April 10th 5,000 gathered to protest the Rowlatt Act. Nearly 400 unarmed Indians are massacred and 1,200 were wounded at Amristar, where this demonstration was held, by British soldiers to punish the Indians (Sherrow 67). Gandhi declares that Britain must leave India. Britain failed to make amends and Gandhi launched and organized a campaign of noncooperation. Government bureaus were boycotted and the streets were blocked by squatting Indians refusing to leave even when beaten (Encarta 98). Gandhi was arrested but was soon released. Gandhi realized that Satyagraha would be necessary and that swaraj, or self-rule, must be their goal. Gandhi asked for massive nonviolent noncooperation throughout India. He urged a boycott of British goods, British schools, universities, jobs, liquor, stores and cloth. He carried a portable spinning wheel in hopes of encouraging others to end Indias dependence of British goods (Sherrow 68). He wore simple homemade clothes. Indians saw him as a saint and began to call him Mahatma, Sanskrit for great soul. His power was great and Indians adored him. .ufdba0a2313007dd4598ca289271fd922 , .ufdba0a2313007dd4598ca289271fd922 .postImageUrl , .ufdba0a2313007dd4598ca289271fd922 .centered-text-area { min-height: 80px; position: relative; } .ufdba0a2313007dd4598ca289271fd922 , .ufdba0a2313007dd4598ca289271fd922:hover , .ufdba0a2313007dd4598ca289271fd922:visited , .ufdba0a2313007dd4598ca289271fd922:active { border:0!important; } .ufdba0a2313007dd4598ca289271fd922 .clearfix:after { content: ""; display: table; clear: both; } .ufdba0a2313007dd4598ca289271fd922 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .ufdba0a2313007dd4598ca289271fd922:active , .ufdba0a2313007dd4598ca289271fd922:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .ufdba0a2313007dd4598ca289271fd922 .centered-text-area { width: 100%; position: relative ; } .ufdba0a2313007dd4598ca289271fd922 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .ufdba0a2313007dd4598ca289271fd922 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .ufdba0a2313007dd4598ca289271fd922 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .ufdba0a2313007dd4598ca289271fd922:hover .ctaButton { background-color: #34495E!important; } .ufdba0a2313007dd4598ca289271fd922 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .ufdba0a2313007dd4598ca289271fd922 .ufdba0a2313007dd4598ca289271fd922-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .ufdba0a2313007dd4598ca289271fd922:after { content: ""; display: block; clear: both; } READ: Law in political science EssayIn 1930 Gandhi proclaimed a new campaign of civil disobedience. It was necessary for the Indian population to refuse to pay the British taxes especially the tax on salt. On March 12, 1930 Gandhi set out at dawn with seventy-nine followers to lead a march to the Indian coast to evaporate the seawater to make salt. This historic march was known as the Salt March. For twenty-four days Gandhi lead the group on the 241-mile march to the sea. People cheered along the way and the group grew. By the time they reached the Dandi on April 5th several thousand people joined them (Sherrow 81). Defying British law the marchers picked up the salt encrusted s and. Many arrests were wade as salt marches took place around the country. About 60,000 people were arrested many people were beaten and injured by police. Less than two weeks later Gandhi was once again arrested but released stopping the campaign after the British made compromises to his demands. In 1932, Gandhi started a new crusade. Once again he was arrested for civil disobedience. While in jail, Gandhi fasted on behalf of the Untouchables. These fasts were effective because great chaos would have broken out if he had died. He was sixty-three now and his body was weak from years of fasting and years of hard work. Friends came to prison and begged him to stop. His wife, Kasturbai, pleaded with him but Gandhi would not end the fast. Doctors warned him that he was near his death. The British government came to an agreement that allowed the Untouchables to be represented in the Assembly. There was an effort to give Untouchables more rights. Due to these changes, Gandhi finally broke his fast on the sixth day. By 1945 it finally seemed possible that Great Britain would give India her independence under the condition that the two nationalist groups, the Muslim League and the Congress Party, resolve their differences. The two groups were unable to live together peacefully. Gandhi stood strongly against the partition of India into Muslim Pakistan and Hindu India but saw that it was essential in order for Great Britain to grant India her independence. He finally agreed to the separation with hopes that peace would be achieved. India and Pakistan became two different states and Great Britain granted India its independence in1947. Riots followed the partition of India and Gandhi fasted until the riots stopped. This fast was successful and brought about peace. Twelve days after this fast, while on the way to a prayer meeting, Gandhi was killed by an assassins bullet. He was cremated according to Hindu tradition the next day in before millions. All countries sent condolences to India and Gandhi be came a historical part of Indias past. Mohandus Karamchand Gandhi was a huge part of Indias past. He contributed many great things to the world such as passive resistance and civil disobedience against unjust laws. He was an enormous figure in the campaign for home rule the attack upon the caste system and the gain of Indias independence. He was an Indian nationalist leader who established his countrys freedom through a nonviolent revolution. He was the Mahatma.