Special Relativity I by Robert Nemiroff Michigan Tech

Physics X: About This Course a. Pronounced "Fiziks Ecks" b. Reviews the coolest concepts in physics c. Being taught for credit at Michigan Tech a. b. c. d. Michigan Tech course PH 4999 Aimed at upper level physics majors Light on math, heavy on concepts Anyone anywhere is welcome a. Wikipedia, web links, and lectures only d. No textbook required

Special Relativity a. Key postulates and formulas • Time dilation and the Feynman light clock • Length contraction • E=mc 2 and mass-energy equivalence

Speed of Light Paradox You move away from a flashlight. How fast do you see the photons from the flashlight move? 1. Slower than when you were not moving – The same speed as when you were not moving – Faster than when you were not moving

Speed of Light Paradox You move away from a flashlight. How fast do you see the photons from the flashlight move? 2. The same speed as when you were not moving That all observers always measure the same speed of light is possibly the most fundamental and profound experiment in all of physics.

Speed of Light Paradox A person passes you moving at 0. 9 c. They report launching a person further moving 0. 9 c relative to them in the same direction. Roughly how fast do you see this person move? 1. 0. 9 c – 1. 8 c – Just below c

Speed of Light Paradox Answer: 3. Just below c Information cannot move faster than c. No physical object you see can move faster than c. This is extremely strange and understanding this is one of the greatest achievements of humanity, in my opinion.

Special Relativity: Variables and Units a. c = speed of light in meters/sec b. v = speed in meters/sec (of the moving frame) c. L = Length in meters ("proper length": in its rest frame) d. L'= Length in meters (measured by a moving frame) e. t = time in seconds ("proper time": in its rest frame) f. t' = time in seconds (measured by a moving frame) g. mo = mass in kilograms ("proper mass": in its rest frame)

Special Relativity: Key postulates a. Developed by Albert Einstein • The Principle of Relativity o You can't tell if you are on a smooth train moving at constant speed • The Principle of Invariant Light Speed o Everyone measures light to move at speed c locally o Information cannot move faster than c.

Special Relativity: Key practices One must identify specific observers. One must identify specific frames of motion. One must identify specific experiments. One must identify specific single observations.

Special Relativity: Simultaneity A train passes you. You touch a person standing in the middle of a train car, causing a spark. Do you see light from the spark hit each car end simultaneously? 1. Yes. – No. – Only if the train person does. – Doesn't anybody care if the train catches fire?

Special Relativity: Simultaneity Answer: 2. No. You see light hit the end that moves closest to you first. Strangely, the train person sees the light hit both ends at the same time. This shows that different observers can disagree on whether two events occur simultaneously.

Special Relativity: Simultaneity Observers in different locations may not agree on which of two events occurred first.

Special Relativity: Time Dilation a. A clock moving relative to you will appear to run slow a. How much? : b. Feynman light clock: At rest Moving at speed v

Special Relativity: Time dilation You have a particle at rest that takes 2. 22 microseconds to decay. Another identical particle, just born, now zips by at near light speed. How long do you measure for this particle to decay? 1. Less than 2. 22 microseconds • The same: 2. 22 microseconds • More than 2. 22 microseconds • I'm just happy it's not 6. 66 microseconds

Special Relativity: Time dilation 3. More than 2. 22 microseconds Non-relativistic muons are seen to decay in the laboratory in 2. 22 microseconds. Cosmic ray muons, traveling near light speed, take up to five times longer to decay, in agreement with SR time dilation.

Special Relativity: Length Contraction a. Moving objects contract in their direction of motion a. Relativity: The movers think YOU are contracted • Is either object "really" contracted? o The basis for numerous "paradoxes".

Special Relativity: Mass-Energy Equivalence a. E=m c 2 o Most famous formula in physics • In terms of rest mass E=mo c 2 / (1 - v 2/c 2)1/2 • So that m = mo / (1 - v 2/c 2)1/2 • Mass, energy, momentum diverge as v -> c.

Special Relativity: Mass-Energy Equivalence a. Kinetic Energy Ek = E - mo c 2 o Expand for small v gives o Ek=mo c 2 (1 + (1/2) v 2/c 2 + (3/8) v 4/c 4 -. . . ) - mo c 2 o Ek = (1/2) mo v 2 +(3/8) mo v 4 / c 2 +. . .