cyanic-selkie/wikianc huggingface dataset:
Uncertainty principle
How did humans learn about uncertainty?
Heisenberg must have been very excited but also very tired when, late at night, he finally made his breakthrough and started proving to himself that it would work. Almost right away he noticed something strange, something that he thought was an annoying little problem that he could make go away somehow. But it turned out that this little nuisance was a big discovery.
Heisenberg had been working toward multiplying amplitudes by amplitudes, and now he had a good way to express amplitude using his new equation. Naturally he was thinking about multiplication, and about how he would multiply things that were given in terms of complicated equations.
Heisenberg realized that besides squaring amplitude he would eventually want to multiply position by momentum, or multiply energy by time, and it looked like it would make a difference if he turned the order around in these new cases. Heisenberg did not think it should matter if one multiplied position by momentum or if one multiplied momentum by position. If they had been just simple numbers there would have been no problem. But they were both complicated equations, and how you got the numbers to plug into the equations turned out to be different depending on which way you got started. In nature you had to measure position and then measure momentum, or else you had to measure momentum and then measure position, and in math the same general situation prevailed. (See the English Wikipedia article Heisenberg's entryway to matrix mechanics if you want to learn the fussy details!) The tiny but pesky differences between results were going to remain, not matter how much Heisenberg wished they would go away.
At the time Heisenberg could not get rid of that one little problem, but he was exhausted, so he handed his work in to his immediate supervisor, Max Born, and went on vacation.
Max Born was a remarkable mathematician who soon saw that the equation that Heisenberg had given him was a sort of recipe for writing a matrix. Dr. Born was one of the few people at that time who was interested in this odd kind of math that most people figured was not good for very much. He knew that matrices could be multiplied, so doing all the calculations for accounting for one physics problem could be handled by multiplying one matrix by another. Just being able to put a complicated procedure into a standard and acceptable form would make it easier to work with. It might also make it easier for other people to accept.
Born was such a good mathematician that he almost immediately realized that switching the order of multiplying the two matrices would produce a different result, and the results would differ by a small amount. That amount would be h/2πi. In everyday life, that difference would be so small that we could not even see it.
On to a formal theory of uncertainty
It took a couple of years, but Heisenberg was able to prove the Uncertainty Principle, which says that Δx × Δp = h/2, which is the number that comes out of the original equations but leaves out the π and the i that have to do with phase changes. Heisenberg explained that he derived his uncertainty principle from this earlier result when he wrote a paper in 1927 introducing this theory.
The constant written h, called the Planck constant, is a mysterious number that often occurs, so we need to understand what this tiny number is. Numerically, it is usually given as 6.62607×10^-34 J s (joule seconds). So it is a quantity that involves energy and time.
It was discovered when Planck realized that the energy of a perfect radiator (called a black-body radiator) is emitted in units of definite size called "quanta" (the singular of this word is "quantum"). Radiated energy is emitted as photons, and the frequency of a photon is proportional to the "punch" it delivers. We experience different frequencies of visible light as different colors. At the violet end of the spectrum, each photon has a relatively large amount of energy; at the red end of the spectrum each photon has a relatively small amount of energy. The way to calculate the amount of energy of a photon is given by the equation E = hν (energy equals the Planck constant times "nu" or frequency).
Another pair of physical quantities goes according to the uncertainty relationship: ΔE × Δt ≥ h, and that pair indicates, among other things, that if we look in interstellar space, some place where we would not expect to find anything at all, and we reduce Δt closer and closer to 0, then to keep the balance shown in the equation ΔE has to get larger and larger—and suddenly something with momentum can pop into existence just for that brief period of time.
How is this indeterminacy (lack of certainty) to be explained? What is going on in the Universe? It is often said that a new theory that is successful can provide new information about the phenomena under investigation. Heisenberg created a math model that predicted the correct intensities for the bright-line spectrum of hydrogen, but without intending to do so he discovered that certain pairs of physical quantities disclose an unexpected uncertainty. Up until that moment nobody had any idea that measurements could not be forever made more and more precise and accurate. The fact that they could not be made more certain, more definite, was a stunning new discovery. Many people were not willing to accept it.
To locate a ship on the sea during the darkest night we could use a searchlight, and that light would not disturb the position or direction of travel of the ship, but locating an electron with light would require hitting it with one or more photons each having enough momentum to disturb the position and trajectory of the electron. Locating the electron with other means would involve holding it in some kind of physical restraint that would also terminate its forward movement.
To locate a photon, the best that can be done without terminating its forward movement is to make it go through a circular hole in a barrier. If one knows the time at which the photon was emitted (by a laser, for instance) and the time that the photon arrives at a detection screen such as a digital camera, then it is possible to compute the time required to travel that distance and the time at which the photon was passing through the hole. However, to permit the photon to pass through it, the circular hole must have a diameter greater than the size of the photon. The smaller the circular hole is made, the closer we come to knowing the exact position of the photon as it goes through it. However, we can never know whether the photon is off-center at that time. If the hole is exactly the same size as the photon it won't pass through. As the diameter of the hole is decreased, the momentum or the direction of the photon as it leaves the hole is more and more greatly changed.
Niels Bohr and his colleagues argued that we get into big trouble if we assume to be true of the things that are too small to be seen even with a microscope anything that we have proof for only on the scale of everyday life. In everyday life, things have a definite position at all times. On the atomic scale, we have no evidence to support that conclusion. In everyday life, things have a definite time at which they occur. On the atomic scale, we have no evidence to support that conclusion. In everyday life, if one observes a factory from the night shift of day one to the day shift of day two and one sees a finished automobile rolled out to the shipping dock it would make no sense to say that it is impossible to tell whether it was delivered during the night shift or during the day shift. But on the atomic scale, we can show instances when we have to count a single photon as having been produced at two times. (If that is not bad enough, we can also show instances where a single photon is produced from two adjacent lasers.)
Part of the difficulty with finding out what is happening on the atomic scale is that we would like to know both where something is and what its trajectory is, and to know both things for the same time, but we cannot measure both position and trajectory at the same time. We either measure the momentum of a photon or electron at one time and then without any more delay than necessary measure its position, or we switch things around and measure position first and momentum second. The problem is that in making the first one take on a pretty definite form (by squeezing down on it in some way) we increase the uncertainty involved in the next measurement. If our initial measurements were so crude that lots of error was introduced in each, then we could improve things by using a lighter touch to do each of them, but we could never get beyond a certain limit of accuracy.
Arguing backwards from the Uncertainty Principle, it looks as though there is in fact no definite position and no definite momentum for any atomic scale thing, and that experimenters can only force things into definiteness within the limit stated by the Uncertainty Principle. Bohr and his colleagues only argued that we could not know anything without making measurements, and when measurements were made we can push things in the direction of more definite position or more definite momentum, but that we can't get the absolute definiteness or certainty that we would like. But others took the possibility seriously, and argued that if the math is right then there cannot be definiteness or certainty in the world of the ultra small. The nature of science is that the math is only a model of reality, and there is no guarantee that it is a correct model.
The math and the practical consequences of the things that the math predicts are so reliable that they are very hard to disagree with, but what the math says about the real world has produced several different ideas. Among the scientists who worked with Niels Bohr in Copenhagen, the uncertainty principle was taken to mean that on an elementary level the physical universe does not exist in a deterministic form. Rather, it is a collection of probabilities or potentials.
Counter to the story woven around the math by the Copenhagen group, there are other stories such as the "multiple universes interpretation" that says that every time there are multiple possible outcomes according to quantum theory, each outcomes occurs in its own new universe. Einstein argued that there are no multiple possible outcomes, so there is only one universe and it is determinate, or, as he put it, "God does not play dice."
Objections against the uncertainty principle
Albert Einstein saw that the new quantum mechanics implied a lack of position and momentum in the time prior to measurements being made, and he objected strongly. He firmly believed that things had definite positions and definite momentums before they were measured, and that the fact that measuring one of a pair of things and disturbing the possibility of accurately measuring the other does not argue for there being a lack of either of them beforehand. He and two of his colleagues wrote what has come to be known as the "EPR paper." That paper argues that there must be characteristics that do determine position and momentum, and that if we could see them, or if we can get information about them, then we can mathematically know and predict position and momentum. For a long time people thought that there was no way to prove or disprove what was for Einstein an article of faith. The argument was very productive because it led to all the modern developments in entanglement.
Mathematically, Einstein has been proven wrong. In 1964 John Stewart Bell developed a math method to distinguish between the behavior of two particles that have determinate states that are merely unknown to the two individuals that investigate them, and two particles that have entangled states that are indeterminate or uncertain until they are measured. His method shows that the probabilities for getting certain results are different under the two different assumptions. His work is called Bell's theorem or Bell's Inequality. Experiments have shown that nature behaves as Bell describes it.
Another route to uncertainty
The initial discussions of Heisenberg's uncertainty principle depended on a model that did not consider that particles of matter such as electrons, protons, etc. have a wavelength. In 1926 Louis de Broglie showed that all things, not just photons, have their own frequency. Things have a wave nature and a particle nature, just as photons do. If we try to make the wave of a thing like a proton narrower and taller, that would make its position clearer, but then the momentum would get less well defined. If we try to make the momentum part of a wave description clearer, i.e., make it stay within a narrower range of values, then the wave peak spreads out and its position becomes less definite.
The wave that is part of the description of a photon is, in quantum mechanics, not the same kind of thing as a wave on the surface of the ocean or the regions of compressed air and rarefied air that make up sound waves. Instead, these wave have peaks or high amplitude regions that have to do with probability of finding something at that point in space and time. More precisely, it is the square of the amplitude that gives the probability of some phenomenon showing up.
The wave that applies to a photon might be a pure sine wave. In that case, the square of the value of every peak would give the probability of observing the photon at that point. Since the amplitudes of the sine waves are everywhere the same, the probability for finding the photon at each of them would be the same. So, practically speaking, knowing the wave for one of these photons would not give a clue about where to look for it. On the other hand, the momentum of a photon is mathematically related to the amplitude of its wave. Since in this case we have a pure sine wave, the amplitude of every cycle of the wave is the same and therefore there is only one momentum value associated with this wave. We would not know where the photon would hit, but we would know exactly how hard it would hit.
In beams of light that focus on some point on a detection screen, the waves associated with the photons are not pure sine waves. Instead, they are waves with high amplitude at one point and much lower amplitudes on either side of that highest peak. Mathematically it is possible to analyze such a wave into a number of different sine waves of different wavelengths. It is a little easier to visualize the reverse of this process by looking at an initial sine wave of one frequency to which is added a second sine wave of a different wavelength, then a third, then a fourth, and so on. The result will be a complex wave showing one high peak and containing a large number of waves of different wavelengths and therefore of different momentums. In that case, the probability that the photon will appear at a certain point is extremely high, but the momentum it delivers can turn out to be related to the wavelength of any one of the component waves. In other words, the value of p = ħ/λ is no longer a single value because all the lengths of the assembled "waves of different wavelength" have to be taken into account.
The simulation shows how to mathematically model the sharpening up of the location of a particle: Superimpose many different wave forms over the original sine wave. The center will form a higher and higher peak, and the rest of the peaks will be increased in number but decreased in height because they will interfere with each other. So in the end there are many different waves in the superposition, each with a different wavelength and (by p = ħ/λ) a different momentum, but only one very high peak, one that grows higher and narrower and gives us something closer and closer to a determinate position.
To make momentum more and more definite, we would have to take away more and more of the superimposed sine waves until we had only a simple sine wave left. In so doing we would progressively diminish the height of the central peak and progressively increase the heights of the competing places where one might find the particle.
So when we start with a wave picture of subatomic particles we typically will always deal with cases with relatively tall central peaks and relatively many component wavelengths. There never will be an exact position or an exact momentum predicted under these circumstances. If the mathematical model is an accurate representation of the real world, then no photon or other subatomic particle has either an exact position or a definite momentum. When we measure such a particle we can choose a method that further squeezes the peak and makes it narrower, or we can choose a method that lowers the peak and evens out the component wavelengths. Depending on what we measure and how we measure it, we can make our location come out more definite or we can make our momentum range narrower. We can take care in designing the experiment to avoid various ways of jiggling the apparatus, but we cannot get rid of the fact that there was nothing completely definite to begin with.
Cultural influences
The Heisenberg Uncertainty Principle has greatly influenced arguments about free will. Under the theories of classical physics it is possible to argue that the laws of cause and effect are inexorable and that once the universe began in a certain way the interactions of all matter and energy to occur in the future could be calculated from that initial state. Since everything is absolutely the result of what came before it, they argued, every decision a human being makes and every situation into which that human being enters was predetermined since the beginning of time. We then have no choice in what we do.
The expressions "quantum leap" and "quantum jump" have become ordinary ways of talking about things. Usually people intend to describe something as involving a huge change that occurs over a short period of time. The term actually applies to the way an electron behaves in an atom either when it absorbs a photon coming in from the outside and so jumps from one orbit around the atom's nucleus to a higher orbit, or when it emits a photon and so falls from a higher orbit to a lower orbit. The idea of Niels Bohr and his colleagues was that the electron does not move between orbits but instead it disappears from one orbit and instantaneously appears in another orbit. So a quantum jump is really not some earth shattering change, but a sudden tiny change.
When humans measure some process on the subatomic scale and the uncertainty principle manifests itself, then human action can be said to have influenced the thing that was being measured. Making a measurement intended to get a definite indication of a particle's location will inevitably influence its momentum and whatever is done to measure that momentum as soon as possible after measuring its position, the probabilities of what momentum will be discovered cannot fail to have been changed. So the uncertainty principle can explain some kinds of interference produced by investigators that influence the results of an experiment or an observation. However, not all observer effects are due to quantum effects or the uncertainty principle. The remainder are "observer effects" but not quantum uncertainty effects.
Observer effects include all kinds of things that operate at our ordinary human scale of events. If an anthropologist tries to get a clear idea of life in a primitive society but his or her presence upsets the community he or she is visiting, then the observations made may be very misleading. However, none of the relevant interactions occur at the level described by quantum mechanics or the uncertainty principle.
Sometimes the word "quantum" will be used for advertising purposes to indicate something new and powerful. For instance, the manufacturer of small gasoline motors, Briggs and Stratton, has one line of four-cylinder low horsepower motors for gasoline mowers and similar garden tools that it calls "Quantum."
Bibliography
Louis de Broglie, Noonday, 1958 Werner Heisenberg Originally published in German, ''Zs. Phys. 33 (1925) 879-893. English translation: Sources of Quantum Mechanics, pp. 261–276. B. L. Van Der Waerden, Dover. Ian J. R. Aitchison, David A. MacManus, Thomas M. Snyder. https://arxiv.org/abs/quant-ph/0404009 http://philsci-archive.pitt.edu/8590/1/Heis1935_EPR_Final_translation.pdf In translation, its title is: "Is a deterministic completion of quantum mechanics possible?" and the translators are Elise Crull and Guido Bacciagaluppi. The translation is dated 02 May 2011.
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The Waffen-SS, an initially small armed section of Heinrich Himmler's Allgemeine SS that grew to nearly a million strong during World War II, was not part of the Wehrmacht, but subject to its Supreme Command.
Origin and use of the terms
Before the rise of the NSDAP, the term Wehrmacht was used in a generic sense to describe armed forces of any nation, being utilized as the "home defence" version of the more general Streitmacht. For example, the term Britische Wehrmacht would identify the British armed forces. Article 47 of the Weimar Constitution of 1919 declared "Der Reichspräsident hat den Oberbefehl über die gesamte Wehrmacht des Reiches" (meaning: "The Reichspräsident holds supreme command of all armed forces of the Reich"). To make a distinction, the term Reichswehr was commonly used to identify the German armed forces.
In 1935, the Reichswehr was renamed Wehrmacht. After World War II and under the Allied occupation of Germany, the Wehrmacht was abolished.
Today the term Wehrmacht refers to Germany's armed forces during the Nazi Germany era and World War II, both in German and English. Note: The Wehrmacht was not only the army (Wehrmacht Heer). Wehrmacht vehicles used by Heer, Luftwaffe or Kriegsmarine had license plates with WH, WL or WM.
History
World War I ended with the armistice (ceasefire) of 11 November 1918. The armed forces were called Friedensheer (peace army) in January 1919. In March 1919, the national assemby passed a law founding a 420,000 strong preliminary army as Vorläufige Reichswehr. The terms of the Treaty of Versailles were announced in May and, in June, Germany was forced to sign the contract. Among other terms, the army was limited to one hundred thousand men with fifteen thousand more in the navy. Tanks and heavy artillery were forbidden and the air force was dissolved. A new post-war military (the Reichswehr) was established on 23 March 1921.
Germany immediately found ways not to keep to these conditions. A secret collaboration with the Soviet Union began after the treaty of Rapallo. Germany helped the Soviet Union with industrialisation and Soviet officers were to be trained in Germany. German tank and air force specialists could exercise in the Soviet Union. German chemical weapons research and manufacture would be done there, plus other projects. Around three hundred German pilots received training at Lipetsk, some tank training took place near Kazan and toxic gas was developed at Saratov for the German army.
After the death of President Paul von Hindenburg on 2 August 1934, Hitler assumed the office of Reichspräsident, and thus became commander in chief. All officers and soldiers of the German armed forces had to swear a personal oath of loyalty to the Führer, as Adolf Hitler now was called. By 1935, Germany was openly breaking the military restrictions of the Versailles Treaty, and conscription was reintroduced on 16 March 1935.
The size of the standing army remained at about the 100,000-man mark decreed by the treaty, but a new group of conscripts equal to this size would receive training each year. The conscription law formalized the name Wehrmacht. The existence of the Wehrmacht was officially announced on 15 October 1935 under Nazi authority. The insignia was a simpler version of the Iron Cross (the straight-armed so-called Balkenkreuz or beamed cross). This had been used as an aircraft and tank marking late in World War I.
Army
The German Army (Wehrmacht) entered the war with a minority of its formations motorized; infantry remained approximately 90% foot-borne throughout the war, and artillery primarily horse-drawn. The motorized formations received much attention in the world press in the opening years of the war, and were cited as the reason for the success of the German invasions of Poland (September 1939), Norway (April 1940), Denmark, Belgium, France and Netherlands (May 1940), Yugoslavia (April 1941) and the early campaigns in the Soviet Union (June 1941).
With the entry of the United States in December 1941, the Wehrmacht found itself engaged in ground campaigns against two major industrial powers. At this critical juncture, Hitler assumed personal control of the Wehrmacht high command, and his personal failings as a military commander arguably contributed to major defeats in the spring of 1943, at Stalingrad and Tunis in North Africa.
Air Force
The German Air Force (Luftwaffe), led by Hermann Göring, contributed many units of ground forces to the war in Russia as well as the Normandy front. In 1940, the Fallschirmjäger paratroops conquered the Belgian Fort Eben-Emael and took part in the airborne invasion of Norway, but after suffering heavy losses in the Battle of Crete, large scale airdrops were discontinued. Operating as ordinary infantry, the 1st Fallschirmjäger Division took part in the Battle of Monte Cassino.
Navy
The German Navy (Kriegsmarine) played a major role in the Second World War as control over the commerce routes in the Atlantic was crucial for Germany, Britain and later the Soviet Union. In the Battle of the Atlantic, the initially successful German U-boat fleet arm was eventually defeated due to Allied technological advances like sonar, radar, and the breaking of the Enigma code. Large surface vessels were few in number due to construction limitations by international treaties prior to 1935. The "pocket battleships" Admiral Graf Spee and Admiral Scheer were important as commerce raiders only in the opening year of the war. No aircraft carrier was operational as German leadership lost interest in the Graf Zeppelin which had been launched in 1938. Following the loss of Bismarck in 1941, with Allied air superiority threatening the remaining battlecruisers in French Atlantic harbours, the ships were ordered to go back to German ports.
Waffen-SS
Although the Waffen-SS was not technically a part of the Wehrmacht, they were under the control of the Wehrmacht High Command during World War 2. They were considered as elite troops, and suffered heavy losses (more than the normal army).
War crimes
The Wehrmacht was used as a tool of state policy in the Second World War, for both military and political aims. There is considerable controversy over the allegations that the Wehrmacht was found to be significantly rather than incidentally involved in the Holocaust, especially because the elements of the SS involved in the Holocaust were not the Waffen-SS and not under the control of the OKW or field commanders. The Wehrmacht ordered and participated in massacres of civilians for reprisals, executions of prisoners of war, summary executions of Soviet political officers and executions of military and civilian hostages as punishment for partisan activities in occupied territories.However, the oft-repeeated claim of breaking the Geneva convention by its treatment of Russian prisoners of war is not correct. Common Clause 2 of the Geneva Convention states that the treatment requirements apply where both parties are signatories of the Conventions. The Germans were signatories, The Russians refused to sign.
Church of God International (United States)
The Church of God, International (CGI) is a denomination of Christianity. It is one of many denominations to come out of the Worldwide Church of God (WCG). The Worldwide Church of God was started by Herbert W. Armstrong.
Beginning
CGI was started in 1978 by four members of the Worldwide Church of God, with minister Garner Ted Armstrong (1930-2003) Garner Ted was excommunicated from the WCG by his father, Herbert W. Armstrong. They argued about beliefs and about how the church should be run.
CGI began in Tyler, Texas. Garner Ted also started the Garner Ted Armstrong Evangelistic Association.
Government
Garner Ted Armstrong led CGI until 1998. Church leaders tried to start a church where the ministers acted as servants to the people. They thought the ministers in the WCG had abused their power over the people. In 1998 Garner Ted Armstrong himself was forced to leave CGI by church leaders. He was accused of sexual assault. Mr. Armstrong left CGI and started the Intercontinental Church of God. Ronald L. Dart, an important leader in CGI also left to start a church called Christian Educational Ministries (CGI). After this, leaders in the CGI tried to move forward and continue "the work". Now, leaders and ministers share power with a "Ministerial Council". The chairman of the Council is elected every three years. Charles Groce served as Chief Executive Officer for the church until 27 June 2015. Then he retired. Vance Stinson is now chairman. The Council also started a program to train new leaders called MAP (Ministerial Apprentice Program). CGI tries to keep a good relationship with many of the other churches that left the Worldwide Church of God. It is a "Ministry Partnership" with a some of them.
Faith and worship
The CGI believes and worships like many other Christian churches, except:
Message and media
CGI has churches in the United States, Canada, Jamaica, Ireland, Australia and the Philippines. CGI has a television program called Armor of God. It also has Prevail Magazine, which discusses Christian living. The church also has a newspaper which comes out every three months called The International News. This newspaper discusses beliefs, worship, prophecy, church news, and world news. The church also supports a program for young people ages 18–30 called Infuse. This includes a quarterly magazine, a website, and service activities for local churches and communities. The program is run by volunteers and includes older people who support the program. It is also open to young people in other churches.
In 2013, the church decided use the internet more to reach people, and is building a new studio to begin broadcasting in high-definition television.