1 Introduction
In 300BC, Euclid presented 5 axioms which were said to govern the properties of space[coxeter1989introduction]. For centuries, Euclid's geometry adequately described physical theories. Though Substantiavilists and Relationists were in disagreement as to whether space was causal or not, there was an agreement that Euclid's geometry fitted. However, in 1904, Einstein published his theory of special relativity (hereby referred to as SR). This could not be described by Euclidean geometry: it required a new way of thinking. The leading solution was Minkowski's geometry. I will touch on both geometries in this paper, and the extent to which Minkowski's geometry is a true geometry. I will then consider Poincaré's conventionalist perspective on the true geometry of the world, employing ideas from Einstein, Sklar and Reichenbach to challenge Poincaré's view before concluding that it does not, as Poincaré suggests matter which geometry we use to describe the world.
2 Euclidean Geometry and Relativity
Though not the only geometry, Euclidean geometry had reigned in Physics until Einstein’s theory of SR was published in 1904. It was then that non-Euclidean geometries began to seem necessary for an explanation of these new theories. Before the theory of SR, it was understood that the Newtonian view of space and time was correct[sklar1992philosophy]. Now Euclidean geometry could no longer explain the phenomena that Einstein’s theory described.
Minkowski's solution to the problem of SR was to formulate a new geometry, which he published in 1907. Minkowski's geometry was arguably not a geometry in the same sense as Euclidean or Riemann (spherical)[hartshorne2000geometry] geometry for now four dimensions rather than three were...
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...han the Poincaré's convenience argument.
5 Conclusion
Poincaré, Einstein and Reichenbach each, for his own reasons, took the view that there is no true geometry. Poincaré in 1902, Einstein in 1921 and Reichenbach in 1927. Indeed, Poincaré's arguments for no true geometry were made before Einstein's special relativity was published, and thus before the confusion of Minkowski's geometry had been introduced. But in spite of this, his reasoning held whether or not Minkowski geometry is considered a true geometry: for he viewed geometry as simply a matter of convenience. The author feels that, in spite of Reichenbach reservations on the interpretation of conventionalism, Poincaré's argument holds true. It is not necessary to have a posteriori knowledge in order to formulate a geometry, because we can manipulate laws to fit a geometry- we just might not like the result!
According to Roland Shearer (1992) the release of non-Euclidean geometries at the end of the 19th Century copied the announcement of art movements occurring at that time, which included Cubism, Constructivism, Orphism, De Stijl, Futurism, Suprematism and Kinetic art. Most of the artists who were involved in these beginnings of Modern art were directly working with the new ideas from non-Euclidean geometry or were at least exposed to it – artists such as Picasso, Braque, Malevich, Mondrian and Duchamp. To explain human-created geometries (Euclidean, non-Euclidean), it is a representation of human-made objects and technology (Shearer
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
What was General Relativity? Einstein's earlier theory of time and space, Special Relativity, proposed that distance and time are not absolute. The ticking rate of a clock depends on the motion of the observer of that clock; likewise for the length of a "yard stick." Published in 1915, General Relativity proposed that gravity, as well as motion, can affect the intervals of time and of space.
• The first is the Special Theory of Relativity, which essentially deals with the question of whether rest and motion are relative or absolute, and with the consequences of Einstein’s conjecture that they are
Greene continues with his explanations of the special theory of relativity.Chapter 3: Of Warps and Ripples Green begins the chapter by describing "Newton's View of Gravity" and continues by discussing the incompatibility of Newtonian Gravity and Special Relativity. The author also talks about how Einstein discovered the link between acceleration and the warping of space and time. Greene also discuses the basic aspects of General Relativity. He later points out how the two theories of relativity effect black holes, the big bang, and the expansion of space.Chapter 4: Microscopic Weirdness This chapter describes, in detail, the workings of quantum mechanics.
It is possible that this technology will be explored and improved further with the growing emphasis on energy efficiency. In 1915, he introduced his general theory of relativity, expanding on the special theory of relativity. This theory proved certain relationships between masses, space, and time, significantly influencing the later development of the GPS system, which is now a staple of everyday life.
The theories of relativity were revolutionary. Everybody agrees that Einstein brought about this revolution. Even the people that claim that Einstein just tweaked the theories of Lorentz and Poincaré, admit that Einstein was the first to recognize the physical meaning of the formulations. He understood that the terms and concepts like those of absolute space and absolute time must lose there meaning and other concepts had to replace them, if we were to be able to understand the phenomena of electrodynamics. All this is consistent with a scientific revolution as conceived of by Kuhn. It is then possible to express the revolution in science that Einstein started in terms of Kuhn’s paradigms and paradigm shifts.
Euclidean distance was proposed by Greek mathematician Euclid of Alexandria. In mathematics, the Euclidean distance or Euclidean metric is the distance between two points, which is shown as a length of a line segment and is given by the Pythagorean theorem. The formula of Euclidean distance is a squ...
A hundred years ago, a young married couple sat at a kitchen table talking over the items of the day while their young boy sat listening earnestly. He had heard the debate every night, and while there were no raised voices, their discussion was intense. It was a subject about which his parents were most passionate - the electrodynamics of moving bodies in the universe. The couple were of equal intelligence and fortitude, working together on a theory that few people can comprehend even to this day. Mileva Maric Einstein was considered to be the intellectual equal of her husband Albert, but somehow went unrecognized for her contributions to the 1905 Papers, which included the Special Theory of Relativity. The stronger force of these two bodies would be propelled into the archives of scientific history, while the other would be left to die alone, virtually unknown. Mrs. Einstein was robbed. She deserved to be recognized for at least a collaborative effort, but it was not to be. The role which society had accorded her and plain, bad luck would prove to be responsible for the life of this great mathematician and scientist, gone unnoticed.
In 1905, Einstein’s Theory of Special Relativity was proposed. The reason that it is so "special" is because it was part of the more complex and extensive Theory of General Relativity, which was published in 1915. His theory reshaped the world of physics when it contradicted all previous laws of motion erected by Galileo and Newton. By mathematically manipulating these previous laws of motion, physicists in the nineteenth century were able to explain such phenomena as the flow of the ocean, the orbits of planets around the sun, the fall of rocks, and the random behavior of molecules in gases. At first, Einstein faced great opposition when he came up with his radical new theory because the previous laws of motion proposed by Galileo and expanded upon by Newton had remained valid for over two hundred years. However, it wouldn’t be long before the "cement" in the foundation of Newtonian and Galilean physics would begin to crumble.
"The Foundations of Geometry: From Thales to Euclid." Science and Its Times. Ed. Neil Schlager and Josh Lauer. Vol. 1. Detroit: Gale, 2001. Gale Power Search. Web. 20 Dec. 2013.
Relativity comes in two forms, one known as Special and one known as General. The first postulate of Einstein’s theory states that if two frame that are moving relative to one another at a constant velocity or speed, the laws regarding physics are the same in one as it is in the other. As an example to this we can use a person at the train station. Whe...
Sir Isaac Newton came up with many theories of time and space. Euclid said that there can be a concept of a straight line but Newton said nothing could ever travel in a straight line, see illustration below.
Initially, Albert Einstein was the person to predict the existence of black holes through his General Theory of Relativity, in which he had created several general equations that show the interaction of gravitation as a result of space being curved by matter or energy. In 1915, he published Einstein’s field equations, which specify how the geometry of space and time is influenced by whatever matter and radiation are present, and form the core of Einstein's general theory of relativity (Redd). The general theory relativity was the initial step in the process to finding out more information about black holes. As time went on, there were a few main contributors that solved these equations to help develop better theories on black holes. One of the most important contributors to the development of a better u...
The concept of impossible constructions in mathematics draws in a unique interest by Mathematicians wanting to find answers that none have found before them. For the Greeks, some impossible constructions weren’t actually proven at the time to be impossible, but merely so far unachieved. For them, there was excitement in the idea that they might be the first one to do so, excitement that lay in discovery. There are a few impossible constructions in Greek mathematics that will be examined in this chapter. They all share the same criteria for constructability: that they are to be made using solely a compass and straightedge, and were referred to as the three “classical problems of antiquity”. The requirements of using only a compass and straightedge were believed to have originated from Plato himself. 1