Heres How Schrodingers Cat Works

Heres How Schrodingers Cat Works Erwin Schrodinger was one of the key figures in quantum physics, even before his famous Schrodingers Cat thought experiment. He had created the quantum wave function, which was now the defining equation of motion in the universe, but the problem is that it expressed all motion in the form of a series of probabilities- something which goes in direct violation to how most scientists of the day (and possibly even today) like to believe about how physical reality operates. Schrodinger himself was one such scientist and he came up with the concept of Schrodingers Cat to illustrate the issues with quantum physics. Lets consider the issues, then, and see how Schrodinger sought to illustrate them through analogy. Quantum Indeterminancy The quantum wave function portrays all physical quantities as a series of quantum states along with a probability of a system being in a given state. Consider a single radioactive atom with a half-life of one hour. According to the quantum physics wave function, after one hour the radioactive atom will be in a state where it is both decayed and not-decayed. Once a measurement of the atom is made, the wave function will collapse into one state, but until then, it will remain as a superposition of the two quantum states. This is a key aspect of the Copenhagen interpretation of quantum physics- its not just that the scientist doesnt know which state its in, but its rather that the physical reality is not determined until the act of measurement takes place. In some unknown way, the very act of observation is what solidifies the situation into one state or another. Until that observation takes place, the physical reality is split between all possibilities. On to the Cat Schrodinger extended this by proposing that a hypothetical cat be placed in a hypothetical box. In the box with the cat we would place a vial of poison gas, which would instantly kill the cat. The vial is hooked up to an apparatus which is wired into a Geiger counter, a device used to detect radiation. The aforementioned radioactive atom is placed near the Geiger counter and left there for exactly one hour. If the atom decays, then the Geiger counter will detect the radiation, break the vial, and kill the cat. If the atom does not decay, then the vial will be intact and the cat will be alive. After the one-hour period, the atom is in a state where it is both decayed and not-decayed. However, given how weve constructed the situation, this means that the vial is both broken and not-broken and, ultimately, according to the Copenhagen interpretation of quantum physics the cat is both dead and alive. Interpretations of Schrodingers Cat Stephen Hawking is famously quoted as saying When I hear about Schrodingers cat, I reach for my gun. This represents the thoughts of many physicists, because there are several aspects about the thought experiment that bring up issues. The biggest problem with the analogy is that quantum physics typically only operates on the microscopic scale of atoms and subatomic particles, not on the macroscopic scale of cats and poison vials. The Copenhagen interpretation states that the act of measuring something causes the quantum wave function to collapse. In this analogy, really, the act of measurement takes place by the Geiger counter. There are scores of interactions along the chain of events- it is impossible to isolate the cat or the separate portions of the system so that it is truly quantum mechanical in nature. By the time the cat itself enters the equation, the measurement has already been made ... a thousand times over, measurements have been made- by the atoms of the Geiger counter, the vial-breaking apparatus, the vial, the poison gas, and the cat itself. Even the atoms of the box are making measurements when you consider that if the cat falls over dead, it will come in contact with different atoms than if it paces anxiously around the box. Whether or not the scientist opens the box is irrelevant, the cat is either alive or dead, not a superposition of the two states. Still, in some strict views of the Copenhagen interpretation, it is actually an observation by a conscious entity which is required. This strict form of the interpretation is generally the minority view among physicists today, although there remains some intriguing argument that the collapse of the quantum wavefunctions may be linked to consciousness. (For a more thorough discussion of the role of consciousness in quantum physics, I suggest Quantum Enigma: Physics Encounters Consciousness by Bruce Rosenblum Fred Kuttner.) Still another interpretation is the Many Worlds Interpretation (MWI) of quantum physics, which proposes that the situation actually branches off into many worlds. In some of these worlds the cat will be dead upon opening the box, in others the cat will be alive. While fascinating to the public, and certainly to science fiction authors, the Many Worlds Interpretation is also a minority view among physicists, though there is no specific evidence for or against it. Edited by Anne Marie Helmenstine, Ph.D.

Treaty of Paris 1898

Treaty of Paris 1898 The Treaty of Paris (1898) was the peace treaty signed on December 10, 1898 by Spain and the United States that ended the Spanish-American War. The terms of the treaty also ended the age of Spanish imperialism and established the United States as a world power. Key Takeaways: The Treaty of Paris The Treaty of Paris, signed on December 10, 1898, was a peace agreement between Spain and the United States that ended the Spanish-American War.Under the treaty, Cuba gained independence from Spain, and the United States gained possession of the Philippines, Puerto Rico, and Guam.Marking the end of Spanish imperialism, the treaty established the United States’ position as a world power. The Spanish-American War The 1898 war between the United States and Spain came after three years of fighting by Cuban rebels to win independence from Spain. Happening so close to the coast of Florida, the conflict in Cuba transfixed Americans. Concerns for U.S. economic interests in the region, along with the American public’s outrage over the brutal tactics of the Spanish military spurred public sympathy for the Cuban revolutionaries. With tensions between the U.S. and Spain growing, the explosion of the U.S. battleship Maine in Havana harbor on February 15, 1898 brought the two nations to the brink of war.   On April 20, 1898, the United States Congress passed a joint resolution acknowledging Cuban independence, demanding that Spain abandon its control of the island, and authorizing President William McKinley to use military force. When Spain ignored the U.S. ultimatum, McKinley implemented a naval blockade of Cuba and called for 125,000 U.S. military volunteers. Spain declared war on the United States on April 24, and the U.S. Congress voted to declare war against Spain the next day.   The first battle of the Spanish-American War was fought on May 1, 1898 in Manila Bay, where U.S. naval forces defeated the Spanish armada defending the Philippines. Between June 10 and June 24, U.S. troops invaded Cuba at Guantanamo Bay and Santiago de Cuba. With the Spanish Army in Cuba defeated, the U.S. Navy destroyed the Spanish Caribbean armada on July 3. On July 26, the Spanish government asked the McKinley administration to discuss terms of peace. On August 12, a cease-fire was declared with the understanding that a peace treaty must be negotiated in Paris by October. Negotiations in Paris   Peace negotiations between representatives of the United States and Spain began in Paris on October 1, 1898. The American contingent demanded that Spain acknowledge and guarantee the independence of Cuba and transfer possession of the Philippines to the United States. In addition, the U.S. demanded that Spain pay Cuba’s estimated $400 million national debt. After agreeing to Cuban independence, Spain reluctantly agreed to sell the Philippines to the U.S. for $20 million. Spain also agreed to pay back the $400 million Cuban debt by transferring possession of Puerto Rico and the Mariana island of Guam to the United States. Spain demanded that it be allowed to retain possession of the Philippines capital city of Manila- which had been captured by U.S. forces hours after the August 12 cease-fire had been declared. The United States refused to consider the demand. Representatives of Spain and the U.S. signed the treaty on December 10, 1898, leaving it up to the two nation’s governments to ratify it.   Pages 8 and 9 out of 19 pages comprising the Treaty of Paris, which ended the Spanish-American War. Spain relinquished Cuba, Puerto Rico, Guam, and the Philippines to the United States in exchange of payment of $20,000,000. Spain also agreed to assume the $400,000,000 Cuban debt.   Corbis Historical / Getty Images While Spain signed the agreement days later, ratification was strongly opposed in the U.S. Senate by senators who viewed it as instituting an unconstitutional policy of American â€Å"imperialism† in the Philippines. After weeks of debate, the U.S. Senate ratified the treaty on February 6, 1899 by a single vote. The Treaty of Paris took effect on April 11, 1899, when the U.S. and Spain exchanged documents of ratification.  Ã‚   Significance While the Spanish-American War had been short in duration and relatively inexpensive in terms of dollars and lives, the resulting Treaty of Paris had a lasting impact on both Spain and the United States.   While it suffered initially from the terms of the treaty, Spain eventually benefited from being forced to abandon its imperialistic aspirations in favor of focusing on its many long-ignored internal needs. Indeed the war resulted in a modern Spanish renaissance in both its material and social interests. The post-war period in Spain saw rapid advances in agriculture, industry, and transportation over the following two decades.   As Spanish historian Salvador de Madariaga wrote in his 1958 book Spain: A Modern History, â€Å"Spain felt then that the era of overseas adventures had gone, and that henceforth her future was at home. Her eyes, which for centuries had wandered to the ends of the world, were at last turned on her own home estate.†Ã‚   The United States- whether intentionally or not- emerged from the Paris peace talks as the world’s newest superpower, with strategic territorial possessions stretching from the Caribbean to the Pacific. Economically, the United States profited from the new trade markets it gained in the Pacific, Caribbean, and the Far East. In 1893, the McKinley administration used the terms of the Treaty of Paris as partial justification for annexing the then-independent Hawaiian Islands. Sources and Further Reference â€Å"Treaty of Peace Between the United States and Spain; December 10, 1898.† Yale Law School.â€Å"The Spanish–American War: The United States Becomes a World Power.† Library of Congress.McKinley, William. â€Å"The Acquisition of the Philippines.† U.S. Department of State.de Madariaga, Salvador (1958). â€Å"Spain: A Modern History.† Praeger. ISBN: 0758162367