M. Cobal, PIF 2006/7 Units and kinematics. M. Cobal, PIF 2006/7 Units in particle physics.

Slides:



Advertisements
Similar presentations
P Spring 2003 L2Richard Kass Relativistic Kinematics In HEP the particles (e.g. protons, pions, electrons) we are concerned with are usually moving.
Advertisements

H6: Relativistic momentum and energy
Relativistic mechanics
O’ O X’ X Z’ Z 5. Consequences of the Lorentz transformation
Classical Relativity Galilean Transformations
Physics Lecture Resources
Introduction A Euclidean group consists of 2 types of transformations: Uniform translations T(b). Uniform rotations R n (  ). Goals: Introduce techniques.
Special Relativity Lecture 24 F2013 The Postulates Phenomenology The proper frame Time Length Mass energy Measuring events Lorentz transformations 1.
An unstable particle at rest breaks into two fragments of unequal mass
Standard Model Requires Treatment of Particles as Fields Hamiltonian, H=E, is not Lorentz invariant. QM not a relativistic theory. Lagrangian, T-V, used.
Relativistic Invariance (Lorentz invariance) The laws of physics are invariant under a transformation between two coordinate frames moving at constant.
The work-energy theorem revisited The work needed to accelerate a particle is just the change in kinetic energy:
SPECIAL RELATIVITY -Postulates of Special Relativity -Relativity of time –> time dilation -Relativity of length –> length contraction © 2005.
P460 - Relativity1 Special Theory of Relativity In ~1895, used simple Galilean Transformations x’ = x - vt t’ = t But observed that the speed of light,
1 Rene Bellwied, PHY 8800, Winter 2007 Kinematics 1 : Lorentz Transformations all slides are from PDG booklet (by permission)
Homework due Monday. Use Compton scattering formula for Ch5 Q8 An electron volt (eV) is a unit of energy = work done moving an electron down one volt =
P460 - Relativity1 Special Theory of Relativity In ~1895, used simple Galilean Transformations x’ = x - vt t’ = t But observed that the speed of light,
1 Measuring masses and momenta u Measuring charged particle momenta. u Momentum and Special Relativity. u Kinetic energy in a simple accelerator. u Total.
+ } Relativistic quantum mechanics. Special relativity Space time pointnot invariant under translations Space-time vector Invariant under translations.
Problem-solving skills In most problems, you are given information about two points in space-time, and you are asked to find information about the space.
Special Relativity & General Relativity
Chapter 37 Special Relativity. 37.2: The postulates: The Michelson-Morley experiment Validity of Maxwell’s equations.
January 9, 2001Physics 8411 Space and time form a Lorentz four-vector. The spacetime point which describes an event in one inertial reference frame and.
Conservation of momentum is one of the most fundamental and most useful concepts of elementary physis Does it apply in special relativity? Consider the.
IB Physics – Relativity Relativity Lesson 2 1.Time dilation 2.Lorentz Factor 3.Proper time 4.Lorentz contraction 5.Proper length 6.Twin paradox and symmetric.
Special relativity.
Special Relativity Contents: The End of Physics Michelson Morley Postulates of Special Relativity Time Dilation.
Special Relativity: “all motion is relative”
Little drops of water, little grains of sand, make the mighty ocean and the pleasant land. Little minutes, small though they may be, make the mighty ages.
Special Relativity The Failure of Galilean Transformations
Crash Course of Relativistic Astrometry Four Dimensional Spacetime Poincare Transformation Time Dilatation Wavelength Shift Gravitational Deflection of.
PHYS 221 Recitation Kevin Ralphs Week 12. Overview HW Questions Chapter 27: Relativity – History of Special Relativity (SR) – Postulates of SR – Time.
What is Particle Physics The Universe is a remarkable place, full of wonder on scales large, small, and in between. The very large and the very small are.
Consequences of Lorentz Transformation. Bob’s reference frame: The distance measured by the spacecraft is shorter Sally’s reference frame: Sally Bob.
M. Cobal, PIF 2003 Resonances - If cross section for muon pairs is plotted one find the 1/s dependence -In the hadronic final state this trend is broken.
Lecture_06: Outline Special Theory of Relativity  Principles of relativity: length contraction, Lorentz transformations, relativistic velocity  Relativistic.
My Chapter 26 Lecture.
1 Relativity (Option A) A.4 Relativistic momentum and energy.
Consequences of Special Relativity Simultaneity: Newton’s mechanics ”a universal time scale exists that is the same for all observers” Einstein: “No universal.
Physics Society Talk (Sept/20/00): Pg 1 Quantum Mechanical Interference in Charmed Meson Decays TOO BORING.
Chapter 2 Relativity 2.
Minkowski Space Algebra Lets go farther with 4-vector algebra! For example, define the SCALAR PRODUCT of 2 4-vectors. A B ABSuppose A = (A 0,A 1,A 2,A.
Special Relativity /- 5 The End of physics: Black Body Radiation -> Quantum mechanics Velocity of light With Respect to ether Maxwell’s Equations…
Special Relativity Lecture 25 F2013 Lorentz transformations 1.
So what about mass? 1. What happens to time from the frame of reference of a stationary observer on Earth as objects approach c? 2. What notation is given.
Fall 2011 PHYS 172: Modern Mechanics Lecture 9 – The Energy Principle Read 6.1 – 6.7.
Time Dilation and Length Contraction - The Evidence 1.Know how muons are produced in the upper atmosphere 2.Be able to explain the evidence from Rossi’s.
About length contraction Moving bodies are short.
There is no universal, ‘absolute’ time in relativity Einstein postulated that the velocity of light c is the same for all observers. That led to the consequence.
Y x z S y' x' z' S'S' v x  = (x 0, x 1, x 2, x 3 ) (ct, x, y, z) Relativistic (4-vector) Notation compare: x i = (x 1, x 2, x 3 ) = (x, y, z)  =  =
Chapter 2 – kinematics of particles Tuesday, September 8, 2015: Class Lecture 6 Today’s Objective: Polar Coordinates Relative motion – Translating Axes.
MOTION IN ONE DIMENSION
Chapter III Dirac Field Lecture 2 Books Recommended:
Relativity of Mass According to Newtonian mechanics the mass of a body is unaffected with change in velocity. But space and time change…….. Therefore “mass”
Special Theory of Relativity
Special Theory of Relativity
Rigid Body transformation Lecture 1
…understanding momentum in spacetime
Special Relativity Jeffrey Eldred
Units The work done in accelerating an electron across a potential difference of 1V is W = charge x potential W = (1.602x10-19C)(1V) = 1.602x10-19 J W.
PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 25:
Energy and momentum units in particle physics
Chap. 20 in Shankar: The Dirac equation
Kinematics 2: CM energy and Momentum
Relativistic Quantum Mechanics
Concepts of Motion Readings: Chapter 1.
G. A. Krafft Jefferson Lab Old Dominion University Lecture 1
PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 26:
1. Introduction to Statics
Chapter 37 Special Relativity
Presentation transcript:

M. Cobal, PIF 2006/7 Units and kinematics

M. Cobal, PIF 2006/7 Units in particle physics

M. Cobal, PIF 2006/7 Other Units

M. Cobal, PIF 2006/7 QuantityUnits HEUnits SI Lenght1 fm m Energy1 GeV=10 9 eV1.602x J Mass1 GeV/c x Kg h6.59x GeVs1.055x J s c2.998x10 23 fms x10 8 ms -1 hc GeV fm3.162x J m Natural Units = c = 1 Mass 1 GeV Lenght 1 GeV -1 Time 1 GeV -1 1 Volt - + U = 1 eV Units in particle physics

M. Cobal, PIF 2006/7 Co-moving coordinate systems v S S’ x x’’ Example: Muons,    s, in cosmic ray p  =10 GeV  l    v  60 km (not. 600 m) Lorentz contraction: length reduction with motion Time dilatation: Lenght at rest Time at rest Lorentz transformation

M. Cobal, PIF 2006/7 Relativistic kinematics

M. Cobal, PIF 2006/7 4-vector Invariant for rotations : Introducing the metric : Lorentz-invariant  in terms of scalar, 4-vectors Contro-variant 4-vec Co-variant 4-vec Notation

M. Cobal, PIF 2006/7 Four vectors

M. Cobal, PIF 2006/7 Four vectors addition

M. Cobal, PIF 2006/7 Kinematics example

M. Cobal, PIF 2006/7

Observables

M. Cobal, PIF 2006/7

mAmA mBmB mCmC c.m. frame Example EE EeEe 2-Body Decay

M. Cobal, PIF 2006/7

Decay Width

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.