HEP – Lesson 4 (High Energy Particle Physics)

HEP – Lesson 4 (High Energy Particle Physics) “Louis Pasteur’s theory of germs is ridiculous fiction.” -- Pierre Pachet, Professor of Physiology at Toulouse, 1872. Disclaimer: Included so not to appear bias towards physics

Lesson 4 – Time Dilation & Length Contraction

Overview • Recap on Lorentz Transformations? • Time Dilation. • Length Contraction. • Energy-mass equivalence. • Summary? Matthew M Reid

Lorentz Trans • Lets recap on the Lorentz Transformations seen in lesson 1. Matthew M Reid

Lorentz Trans • Lets recap on the Lorentz Transformations seen in lesson 1. • For a boost (motion) in the x-axis. Matthew M Reid

Lorentz Trans • Lets recap on the Lorentz Transformations seen in lesson 1. • For a boost (motion) in the x-axis. inverse transformations Matthew M Reid

Lorentz Trans • Lets recap on the Lorentz Transformations seen in lesson 1. • For a boost (motion) in the x-axis. inverse transformations • Remember the primed variables describe the moving reference frame. Matthew M Reid

Time Dilation • What happens to time observed between two references frames where one is in motion? Matthew M Reid

Time Dilation • What happens to time observed between two references frames where one is in motion? • Lets say we measure the time the stationary man observes, as seen from the shuttle. Matthew M Reid

Time Dilation • What happens to time observed between two references frames where one is in motion? • Lets say we measure the time the stationary man observes, as seen from the shuttle. • Assume the measurement is made at the same place, but at two different times. Matthew M Reid

Time Dilation • What happens to time observed between two references frames where one is in motion? • Lets say we measure the time the stationary man observes, as seen from the shuttle. • Assume the measurement is made at the same place, but at two different times. BUT Matthew M Reid

Time Dilation • What happens to time observed between two references frames where one is in motion? • Lets say we measure the time the stationary man observes, as seen from the shuttle. • Assume the measurement is made at the same place, but at two different times. • From a space ship you would see that time ticks take longer, by a factor . OR Matthew M Reid

Time Dilation • Example 1! What time will the space shuttle observe on earth if it is travelling and 1 second passes on earth. Matthew M Reid

Time Dilation • Example 1! What time will the space shuttle observe on earth if it is travelling and 1 second passes on earth. • and , where . Matthew M Reid

Time Dilation • Example 1! What time will the space shuttle observe on earth if it is travelling and 1 second passes on earth. • and , where . • More time has elapsed on earth according to the space shuttle Matthew M Reid

Time Dilation • Proof of Special Relativity? Some of you may need it, many e.gs Matthew M Reid

Time Dilation • Proof of Special Relativity? Some of you may need it, many e.gs • It plays a key role in a multi-billion dollar industry, the Global Positioning System (GPS). TomTom! Matthew M Reid

Time Dilation • Proof of Special Relativity? Some of you may need it, many e.gs • It plays a key role in a multi-billion dollar industry, the Global Positioning System (GPS). TomTom! • The satellite clocks are moving at in orbits that circle the Earth twice a day. Special relativity says that rapidly moving clocks tick more slowly. Approx 7 microseconds per day. Matthew M Reid

Time Dilation • Proof of Special Relativity? Some of you may need it, many e.gs • It plays a key role in a multi-billion dollar industry, the Global Positioning System (GPS). TomTom! • The satellite clocks are moving at in orbits that circle the Earth twice a day. Special relativity says that rapidly moving clocks tick more slowly. Approx 7 microseconds per day. • The relativistic time offset of asatellite clock is so large that, if left uncompensated, it would cause navigational errors of the km order, which increase day by day!! Matthew M Reid

Length Contraction • Similar concept to the derivation of time dilation, except now we assert that the time is constant and we measure two distinct points. Matthew M Reid

Length Contraction • Similar concept to the derivation of time dilation, except now we assert that the time is constant and we measure two distinct points. • What does a stationary observer measure for the length of a stick, OR Matthew M Reid

Length Contraction • Similar concept to the derivation of time dilation, except now we assert that the time is constant and we measure two distinct points. • What does a stationary observer measure for the length of a stick, OR • If the stick at rest is measured to be, L then, when it is in motion its length contracts by a factor . Matthew M Reid

This property leads to the infamous where in this equation m is the rest mass (I like for convention). Matthew M Reid

This property leads to the infamous where in this equation m is the rest mass (I like for convention). • The full relationship is usually given as:- Matthew M Reid

This property leads to the infamous where in this equation m is the rest mass (I like for convention). • The full relationship is usually given as:- • This tells us that mass and energy are equivalent and can be interchanged given some “work”. Matthew M Reid

This property leads to the infamous where in this equation m is the rest mass (I like for convention). • The full relationship is usually given as:- • This tells us that mass and energy are equivalent and can be interchanged given some “work”. • This relation is a truly beautiful example of theoretical physics. It is tried and test many times a second at CERN. Matthew M Reid

Einstein's paper in 1905 lead to many innovations and realisations about the world in which we live • Gave rise to GPS Matthew M Reid

Einstein's paper in 1905 lead to many innovations and realisations about the world in which we live • Gave rise to GPS • Gave rise to accelerator physics (hadron therapy, cancer treatment) Matthew M Reid

Einstein's paper in 1905 lead to many innovations and realisations about the world in which we live • Gave rise to GPS • Gave rise to accelerator physics (hadron therapy, cancer treatment) • Also provided tools for mans darkest hour. • “Tsar” 50 mega tonne bomb detonated over Artic Circle by Soviet Union (Russia) in 1961 darkest hour. Matthew M Reid

Einstein's paper in 1905 lead to many innovations and realisations about the world in which we live • Gave rise to GPS • Gave rise to accelerator physics (hadron therapy, cancer treatment) • Also provided tools for mans darkest hour. Wipe out 6 Birmingham Cities • “Tsar” 50 mega tonne bomb detonated over Artic Circle by Soviet Union (Russia) in 1961 darkest hour. Matthew M Reid

Summary • Recap on Lorentz transformations and used them to derive two main results; time dilations and Lorentz contraction. • Seen the mass energy equivalence relation. • Now we can start implementing some of these in our code. • Next time we begin looking at Lorentz Invariance. We touched upon rotational invariance where the distance of a vector was the same after a rotation… We will do something similar for Lorentz vectors. May also just code?... Matthew M Reid

HEP – Lesson 4 (High Energy Particle Physics)