Special Relativity 1

Special Relativity 1 Special Relativity: A Summary Caitlyn Edwards Dr. Gan Modern Physics November 2017

Special Relativity 2 Abstract The physics of Einstein s theory of special relativity differs dramatically from Newtonian physics when dealing with systems that approach the speed of light. The theory of special relativity is based upon two postulates- the principle of relativity and the constancy of the speed of light (Serway, Moses & Moyer, Special Relativity I, p. 10). There are certain consequences within special relativity namely the relativity of simultaneity, length contraction and time dilation (Serway, Moses & Moyer, Special Relativity I, pp. 14-18). The first consequence explores the concept that simultaneity is not an absolute concept but one that depends upon how the observer is moving with respect to another reference frame (Serway, Moses & Moyer, Special Relativity I, p. 14). Length contraction is the concept in which the measurement of length can differ for different observers (Serway, Moses & Moyer, Special Relativity I, p. 18). Lastly, time dilation is the consequence which describes how time for moving objects slows down (Serway, Moses & Moyer, Special Relativity I, p. 16). The last topic discussed in this paper is how the consequences of special relativity is present in processes on Earth.

Special Relativity 3 Newtonian physics and special relativity are different from one another. Newtonian physics, is used to describe systems that travel at speeds much smaller than the speed of light; while the physics within special relativity depicts what happens when the system travels close to the speed of light (Serway, Moses, & Moyer, Special Relativity I, p. 2). According to Serway, Moses and Moyer, in the section Special Relativity I, there are two postulates to special relativity. The first postulate states: The laws of physics have the same form in all inertial frames of reference (Serway, Moses & Moyer, Special Relativity I, p. 2). The second postulate articulates: The speed of light in a vacuum is always measured to be 3.0 x 10 8 m/s 2. The measured value of the speed of light is independent of the motion of the observer or the propagation of the light source (Serway, Moses & Moyer, Special Relativity I, p. 3). So in simpler terms; the speed of light is constant and does not depend on the movement of the observer nor the movement of the source of light and the laws of physics measure to be the same in every inertial reference frame. When discussing inertial reference frames there arises a need to define it: An inertial frame is one in which an object (subjected to no forces) moves in a straight line at a constant speed (Serway, Moses, & Moyer, Special Relativity I, p. 3). This could also be described as a system or frame that moves with a constant velocity in regards to another inertial system (Serway, Moses, & Moyer, Special Relativity I, p. 3). Delving into the theory and physics behind special relativity, it is of importance to have a working understanding of the two postulates. Remember that postulate one, also referred to as The Principle of Relativity (Serway, Moses and Moyer, Special Relativity I, p. 10), conveys that any observer in an inertial reference frame will measure the laws of physics to be the same and the second postulate discusses the constancy of the speed of light (Serway, Moses and Moyer, Special Relativity I, p. 10). Before the time of Einstein, not much was known about

Special Relativity 4 systems traveling with speeds near the speed of light nor the physics that described them. At first it was thought that objects could travel faster than the speed of light and that the speed of light depended on the way it traveled through an ether (Serway, Moses and Moyer, Special Relativity I, p. 7). The Michelson-Morley experiment measured exactly how light interacted with the ether (Serway, Moses and Moyer, Special Relativity I, p. 7). When the experiment was completed, Michelson and Morley came to the conclusion that the speed of light did not depend on the direction of propagation and in turn contradicted the ether hypothesis (Serway, Moses and Moyer, Special Relativity I, p. 8). Einstein took this into consideration when forming the theory of special relativity. He stated that the speed of light is constant no matter the conditions of the observer taking the measurements and intrinsically denies the existence of the ether and proclaims that the speed of light is 3.0x10 8 m/s 2 (c), which is independent of the initial observer (Serway, Moses and Moyer, Special Relativity I, p. 12). Describing systems that move at the speed of light is not an easy task. For example, the idea of absolute time and length do not exist for special relativity (Serway, Moses and Moyer, Special Relativity I, p. 13). This causes different observers to obtain different measurements with respect to their reference frame. As a result, some consequences arise. These consequences are known as the relativity of simultaneity, length contraction, and time dilation. Discussing the topic of simultaneity first, it is stated in Modern Physics: Third Edition, that the measurement of a time interval is dependent upon the reference frame the measurement is made in (Serway, Moses and Moyer, Special Relativity I, p. 14). Thus, it can be derived that events occurring simultaneously in regards to one reference frame, occur at different times in another (Serway, Moses and Moyer, Special Relativity I, p. 13). Performing a thought experiment to gather a better picture of this, imagine a rocket ship traveling to the right at 0.3c

Special Relativity 5 the speed of light and emits a light beam from the front and back ends of the ship simultaneously. An observer on the ship, who is in the inertial reference frame with respect to the ship, concludes that the light beams emitted occur simultaneously. Another observer, free floating in space, witnesses the ship move past him and the emitting of the light beams. However, he does not conclude that the light beams pulsated at the same time. In his perspective he sees the light beam on the front of the ship emit first followed by the one on the back of the ship; concluding the two events occurred at different points in time. The conclusion of this thought experiment is as follows: Two events that are simultaneous in one frame are in general not simultaneous in a second frame moving with respect to the first. That is, simultaneity is not an absolute concept but one that is dependent upon the motion of the observer (Serway, Moses and Moyer, Special Relativity I, p. 14). When examining length contraction, it is natural to assume that in one reference frame or another, the measured length of an object will contract; which is correct. It is important to define the term proper length. Proper length is measured in the reference frame in which the observer taking measurements is at rest with respect to the said object (Serway, Moses and Moyer, Special Relativity I, p. 18). Reflecting back upon the previous thought experiment to explain simultaneity, now think about measuring the ship. It should be apparent that the proper length is the length measured by the observer within the ship since they are at rest with respect to the moving ship and the length measured by the observer floating in space will have contraction. Serway, Moses, & Moyer explain this with a mathematical proof, following with the conclusion: The length of an object measured by someone in a reference frame that is moving relative to the object is always less than the proper length ( Special Relativity I, p. 18). Also stated in the section which discusses length contraction, is the conclusion that length contraction takes place

Special Relativity 6 along the direction of motion as will become clear when looking at the mathematical proof (Serway, Moses and Moyer, Special Relativity I, p. 19). The last consequence being investigated will be time dilation. Time dilation explains the reason that moving clocks tick slower. As was in length contraction, there is the term proper time, which is the time measured by the observer in motion with the said object (Serway, Moses and Moyer, Special Relativity I, p. 16). Referring back to the thought experiment where an observer is in the rocket ship moving to the right at 0.3c and an observer floating in free space, think about the heart rate of the observer within the ship. Which observer would measure the proper heartbeat and which would measure a distorted heartbeat? The observer within the spaceship measures the proper heartbeat. In this reference frame the observer would not measure any differences with respect to themselves so the heartbeat measured will be normal. The observer floating in space is moving with respect to the ship thus, measures a heartbeat slower than the proper heartbeat. It is not just clocks that slow down when moving at speeds near the speed of light, but in fact all physical processes slow down when measured in a reference frame which is moving with respect to said initial reference frame (Serway, Moses and Moyer, Special Relativity I, p. 16). Einstein devised the twin paradox thought experiment as another way of thinking about special relativity. In the twin paradox there is a pair of identical twins. Speedo, one twin, goes on a space trip while Goslo stays on Earth. After a 17.3 Earth year journey traveling at 0.5c Speedo returns finding that Goslo has aged 60 years while Speedo himself has only aged 34.6 years. It might be thought that special relativity only applies to systems traveling in outer space but some consequences can be found in systems on Earth. For example, high-energy particle accelerators that accelerate particles to close the speed of light exhibit the consequence of time

Special Relativity 7 dilation (Weiskopf, Special Relativity). These particles that are radioactive and decay are seen to have a longer lifespan when accelerated to close the speed of light (Weiskopf, Special Relativity). A similar example of this is given in Modern Physics: Third Edition, describing the lifespan of muons in relation to length traveled before the muons decay (Serway, Moses and Moyer, Special Relativity I, p. 16). When taking the lifespan of the muons as the proper time (2.2 microseconds), the muons should only be able to travel 650 meters (Serway, Moses & Moyer, Special Relativity I, p. 17). During this time period the muons should not be able to reach the Earth before decaying (Serway, Moses & Moyer, Special Relativity I, p. 17). But when measuring the lifetime of a muon as observed from Earth, a life span of 16 microseconds with a velocity of 0.99c is observed (Serway, Moses & Moyer, Special Relativity I, p. 17). Using this information, the muon now is able to travel 4700 meters, reaching the Earth (Serway, Moses & Moyer, Special Relativity I, p. 17).

Special Relativity 8 References Serway, R. A., Moses, C. J., Moyer, C. A. (2005). Special Relativity. In Modern Physics (3 rd ed., pp. 2-24). Belmont, CA: Brooks/Cole. Weiskopf, D. Special Relativity. Retrieved November 15, 2017, from http://www.astro.sunysb.edu/rosalba/astro2030/specialrelativity.pdf