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HEP – Lesson 4 (High Energy Particle Physics)

Dive into concepts of time dilation, length contraction, and energy-mass equivalence in Lesson 4 of High-Energy Particle Physics. Understand Lorentz transformations, prove special relativity, and learn about their applications like in GPS systems. Unravel the mysteries of time and space!

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HEP – Lesson 4 (High Energy Particle Physics)

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  1. 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

  2. Lesson 4 – Time Dilation & Length Contraction

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

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

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

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

  7. 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

  8. 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

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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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

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