Maintenance Laws in Margin Doxy and Relationship Between Adequacy - Assignment Example

Running Header: Discussing the Relationship between Symmetry and Conservation Laws in Field Theory Name: Course: University: Lecturer Outline Introduction ………………………………………………………………………………..,3 Relationship …………………………………………………………………………………5 Significance of Noether’s theory……………………………………………………………6 Conclusion ………………………………………………………………………………….7 Works Cited…………………………………………………………………………………8 Discuss the Relationship between Symmetry and Conservation Laws in Field Theory Introduction Conservation laws were better understood after Noether advanced her Theorem which served to show how symmetry and conservation laws were linked. According to Noether, there is an appropriate conservation law for any symmetry which results from the action of a physical system. Previously, general theory was used for field equations but according to Byers (1996) many people including Albert Einstein were concerned with the fact that the theory did not include how energy was conserved. Thus, the variation principle had a weakness which had to be solved and this was adequately done by Noether. This theory did not just solve the general theory weakness but also laid a foundation for other discoveries such as the gauge field symmetries (Byers, 76). For any physical theory, the time space and rotation transformations are said to remain valid. Thompson (1994) has an easy way to understand description of Noether’s theorem which he says that “the continuous symmetry property of a system has corresponding conserved quantities” (p.5). With such a relationship, it is easy to establish conserved quantities of physical systems using their symmetries. This relationship is established from things that have continuous symmetry. According to Fujita (2007), Noether’s theorem holds that there is a conserved current for a continuous symmetry of a Lagrangian density. Thus, systems that are known to have varying energy over time such as waves are not applicable. The assumption is that the object is not dependent on its position in space and it need not be symmetric physically. Thus, even asymmetrical objects conserve quantities or laws of motion as provided by Noether’s theorem. The symmetry used here refers to the properties exhibited by the physical object and not its appearance. The fact that laws such as the Newton law remain unchanged makes it possible to find some variable quantities concerning physical objects. The laws of physics are therefore symmetrical as time does not make them change and are hence described as being invariant. This means that it does not matter how much time elapses between the applications of any of the conservation laws since they remain the same. This also applies to space variations as going to a different location does not bring any changes to the physical laws. Hanc, Tuleja and Hancova (2003) explain this by saying that the results of an experiment performed at a different location will be the same if the experiment were done in another location. This is because all researches will apply the same constants during the experiment with regard to laws of motion. The only variants are things such as velocity since when an object is in motion; it will depend on how fast it is moving. Hanc, Tuleja and Hancova (2003) also assert that the principle of least action is required for a deep connection between symmetry and conservation laws. This is because the principle is important in physical systems that are acted upon since someone would find it easy to establish the relevant equations. The principle is useful in solving many physics and mathematical problems including those associated with architectural designs. The principle of least action is also used in explaining the path taken by light which is believed to take the shortest path between one point and another. Relationship Physical objects have certain special properties which are better referred to as symmetries in physics or mathematics. McMahon (35) describes symmetry as change that leaves invariant the equation of motion. He also introduces the difference between internal and external symmetries where field changes that happen without regard to space-time are referred to as the internal symmetries and vice versa. Conservation law is based on the premise that for a physical system that is in motion, its quantity remains unchanged. This applies to time and space in that changing the time or space of an object will not alter the physical laws. Cecire (2002) shows the six conservation laws that are used in Physics: Conservation of momentum, Conservation of charge, and Conservation of energy, Conservation of baryons, Conservation of angular momentum, and Conservation of leptons. The baryons and leptons are similar to the electric charges and they too have quantities that are conserved. In a space translation, there is a linear momentum as a conserved quantity while in a time translation; there is energy as conserved quantity. Similarly, objects in rotation have an angular momentum and all these show how symmetry and conservation laws are related. In each of the symmetries, there is no interference with the conserved quantities of energy or momentums. Hence, physical laws hold when time and space are shifted or when the system is rotated. Change is only seen during the application in that when an object changes motion or the way of movement, the application of the laws of nature will be different. The electric charge is also part of the conserved quantities and is used for particles. When charge is moved from one particle to another, it happens in such a way that the total quantity of charges remain the same. Thus, it is also applicable in Noether’s theorem since no charge is lost during transfer. There is also color charge identified which just like the electric charge is conserved. During transfer, the particles including those with color charges are acted upon by electric and magnetic forces In physics, the conserved quantities have certain characteristics that describe their nature. First is that for any object, its conserved quantity cannot be created and hence this is something that is part of the object. Thus, you cannot simply alter it such as adding to its quantity in any way. The second is that the conserved quantity cannot be destroyed hence no matter what happens to the physical object, the conserved quantity remains the same unless it is a dissipative system. The other characteristic is that you can transfer the quantity exactly as it is between objects. Linear momentum which is associated with space means that when a physical object moves, it goes in a straight line. With this, the momentum can only be transferred and to stop the movement, the momentum has to be transferred to another that can take all the quantity of the momentum, otherwise only a part of it may be transferred. Similarly, a rotating object can only stop if the angular momentum it has can be transferred to another similar object. During the rotation, there is no difference in the appearance of the object expect for the fact that it is in motion but something such as its size does not reduce or add. Significance of Noether’s theory The aspect of conserved quantities in objects can be used in mathematics to solve equations. However, Hanc, Tuleja and Hancova (2003) are of the opinion that it is much easier to understand symmetry arguments when used in physical ideas rather than mathematics. This is because their application in mathematical derivations is at a much higher level. Nevertheless, it makes it possible for people to find properties of an object with regard to motion and this is simply through the use of how the symmetry of an object is associated with a corresponding physical law. This is more applicable in calculus of variations in mathematics where you can derive integrals that have been given as unknown functions. Theories identify several symmetries which also determine the number of conserved quantities that are present in physical objects. It is found that much symmetry present in an object make it a lot easier in solving problems and are thus preferred. The Noether’s theorem help in relating charge, energy and momentum as conserved quantities to symmetries (MacMahon, p.35). Noether’s theorem is an opportunity for students to understand the importance of symmetry in physical objects in the world. This relationship also helps people in predicting future conditions since it makes known come conditions such as the constants. Conclusion The connection between symmetry and conservation laws indicates how important it is to have some constants. This is what helps experts in both physics and mathematics to come up with similar results, for instance, regarding studies when the same set of conditions remain the same so each of them knows the quantity to be used. This also helps to show when something has been influenced externally since the results will show a difference unless the calculations have not been done correctly. The understanding of the application of symmetry in physics makes it possible for anyone to solve equations. For instance, rotating an object does not interfere with the quantity in it since the angular momentum of a physical system which can be described as the vector direction and momentum cross product should be conserved according to Noether’s theorem. Works Cited 1. Byers, Nina. E. “Noether's discovery of the deep connection between symmetries and conservation laws.” Presented at the symposium on the heritage of Emmy Noether in algebra, geometry, and physics. Israel Mathematical Conference Proceedings Vol. 12, 1999 . Retrieved from 2. Byers, Nina. History of original ideas and basics discoveries in particle physics. H. B. Newman and T. Ypsilantis ed., New York: Plenum Press (1996).p74-6 3. Cecire, Ken. “Conservation Laws.” 2002 Retrieved from 4. McMahon, David. Quantum field theory demystified. New York. McGraw-Hill Professional. 2008. 5. Fujita, T. Symmetry and its breaking in quantum field theory. New York. AMACOM. 2007. 6. Hanc, Jozef., Tuleja, Slavomir., & Hancova, Martina. “Symmetries and conservation laws: Consequences of Noether's theorem.” American Journal of Physics, Vol. 72, No. 4, pp. 428–435, April 2004. 7. Thompson, W. J. Angular Momentum: an illustrated guide to rotational symmetries for physical systems John Wiley & Sons, Inc., 1994. p.5 doi: 10.1002/9783527617821 Read More