By: Victor Jeung 1. 2. All laws of physics are valid in all inertial frame of references. Light travels through space at a speed of c = 3.00 × 108 m/s, relative to all inertial frames of reference. Simultaneity is not an absolute concept Two events that are simultaneous in one frame of reference are not simultaneous in another frame of reference; that is in motion with respect to the first Definition: Slowing down of time in a system as seen by an observer in motion relative to the system ∆𝑡𝑠 Equation: ∆𝑡𝑚 = 2 𝑣 1− 2 𝑐 ∆𝑡𝑠 (proper time) is the time interval that separates two events measured by an observer to whom the events occur at the same position ∆𝑡𝑚 is the time interval measured by an observer external to the system Objects cannot have a speed equal to or greater than the speed of light Definition: Shortening of distances in a system as seen by an observer in motion relative to the system 𝑣2 − 2 𝑐 Equation: 𝐿𝑚 = 𝐿𝑠 1 𝐿𝑚 (proper length) is the length of the object measured by an observer at rest relative to the object 𝐿𝑠 is the length of the object measured by an observer moving relative to the beginning and end points of the length being measured 𝑚𝑣 Equation: 𝑝 = 𝑚 (rest mass) is the mass of an object when the object is at rest 𝑣2 1− 2 𝑐 Conservation of mass-energy: rest mass and energy are equal Equations: 𝐸𝑡𝑜𝑡𝑎𝑙 = 𝑚𝑐 2 𝑣2 1− 2 𝑐 𝐸𝑟𝑒𝑠𝑡 = 𝑚𝑐 2 1. a) b) c) d) The Star Wars spacecraft Tie Fighter flies at a speed of 0.8c with respect to the Earth. Luke Skywalker determines the time interval between the two events on Earth is 20h. What is the time interval for Tie Fighter? 16.7h 20h 30h 33.3h 1. a) b) c) d) The Star Wars spacecraft Tie Fighter flies at a speed of 0.8c with respect to the Earth. Luke Skywalker determines the time interval between the two events on Earth is 20h. What is the time interval for Tie Fighter? 16.7h 20h 30h 33.3h In this question, we are determining ∆𝑡𝑚 . Using the time dilation equation, substitute the given information for: ∆𝑡𝑠 = 20ℎ 𝑣 = 0.8𝑐 and solve for ∆𝑡𝑚 . ∆𝑡𝑚 = ∆𝑡𝑚 = ∆𝑡𝑠 𝑣2 1− 2 𝑐 20ℎ (0.8𝑐)2 1− 𝑐2 ∆𝑡𝑚 = 33.3ℎ 2. a) b) c) d) It is the year 3000. A rocket passes by at a speed of 0.3c. The length of the rocket is 100m. What is the length at rest? 108.4m 104.8m 108m 104m 2. a) b) c) d) It is the year 3000. A rocket passes by at a speed of 0.3c. The length of the rocket is 100m. What is the length at rest? 108.4m 104.8m 108m 104m In this question, we are determining 𝐿𝑠 . Using the length contraction equation, rearrange to solve for 𝐿𝑠 instead of 𝐿𝑚 by substituting the given information for: 𝐿𝑚 = 100𝑚 𝑣 = 0.3𝑐 and solve for 𝐿𝑠 . 𝑣2 𝐿𝑚 = 𝐿𝑠 1 − 2 𝑐 𝐿𝑚 𝐿𝑠 = 𝑣2 1− 2 𝑐 100𝑚 𝐿𝑠 = (0.3𝑐)2 1− 𝑐2 𝐿𝑠 = 104.8𝑚 At what speed will the length of a 1.5m hockey stick look 2/3 shorter? a) 0.75c b) 2.25𝑥108 m/s c) a and b d) 3𝑥108 m/s 3. At what speed will the length of a 1.5m hockey stick look 2/3 shorter? a) 0.75c b) 2.25𝑥108 m/s c) a and b d) 3𝑥108 m/s 3. In this question, we are determining 𝑣. Using the length contraction equation, rearrange to solve for 𝑣 instead of 𝐿𝑚 by substituting the given information for: 𝐿𝑚 = 1𝑚 𝐿𝑠 = 1.5𝑚 and solve for 𝑣. 𝐿𝑚 = 𝐿𝑠 𝑣2 1− 2 𝑐 𝐿𝑚 2 𝑣 =𝑐 1− 𝐿𝑠 1𝑚 2 𝑣 =𝑐 1− 1.5𝑚 𝑣 = 0.75𝑐 𝑜𝑟 2.25𝑥108 m/s What is the relativistic momentum of a proton travelling at 0.95c through a particle accelerator? 𝑘𝑔∙𝑚 a) 5 2 4. 𝑠 −27 𝑘𝑔∙𝑚 b) 5𝑥10 𝑠2 −27 𝑘𝑔∙𝑚 c) 5.1𝑥10 𝑠2 d) None of the above What is the relativistic momentum of a proton travelling at 0.95c through a particle accelerator? 𝑘𝑔∙𝑚 a) 5 2 4. 𝑠 −27 𝑘𝑔∙𝑚 b) 5𝑥10 𝑠2 −27 𝑘𝑔∙𝑚 c) 5.1𝑥10 𝑠2 d) None of the above In this question, we are determining 𝑝. Using the relativistic momentum equation, substitute the given information for: 𝑚 = 1.67𝑥10−27 𝑘𝑔 𝑣 = 0.95𝑐 and solve for 𝑝. 𝑝= 𝑝= 𝑚𝑣 𝑣2 1− 2 𝑐 (1.67𝑥10−27 𝑘𝑔)(0.95𝑐) (0.95𝑐)2 1− 𝑐2 𝑘𝑔 ∙ 𝑚 −27 𝑝 = 5.1𝑥10 𝑠2 Superstring theory is the favoured version of string theory Fundamental entities in the universe are microscopic, multidimensional strings Strings are made of 10 or more dimensions, but only 3 are seen Einstein’s general relativity theory incorporated in Kaluza’s geometrical representation of electromagnetic field results in a five-dimensional universe Strings are assumed to obey Einstein’s equations in spacetime resulting in a possibility to combine quantum mechanics with general relativity Gravity remains as the only force that can be associated with space-time Einstein’s theory of special relativity revises conceptions of time, length and energy allowing us to analyze the effects of motion at high speeds Einstein’s equation of total relativistic energy makes it possible to predict the amount of energy available from processes resulting in a decrease of mass e.g. Energy available from the complete conversion of coal For further reading please refer to the pages found on the HowStuffWorks website titled: How Special Relativity Works (http://science.howstuffworks.com/science-vs- myth/everyday-myths/relativity.htm) What is string theory? (http://science.howstuffworks.com/science-vsmyth/everyday-myths/string-theory.htm) EinsteinFest - Perimeter Institute for Theoretical Physics. (n.d.). Perimeter Institute for Theoretical Physics. Retrieved January 4, 2012, from http://www.perimeterinstitute.ca/en/Outreach/Online_Viewers/EinsteinFest/ Giancoli, D. C. (2005). Physics principles with applications (6th ed.). Upper Saddle River, N.J.: Pearson/Prentice Hall. Hirsch, A. J. (2003). Nelson physics 12. Toronto: Nelson Thomson Learning. McFarland, E. L. (1991). Special relativity (2 ed.). Guelph: Department of Physics, University of Guelph. Wolfe, J. (n.d.). Relativity: Einstein's theory of relativity in animations and film clips. Einstein Light. School of Physics at UNSW, Sydney, Australia. Retrieved January 4, 2012, from http://www.phys.unsw.edu.au/einsteinlight/