Special Relativityand the Lives of the Elementary Particles

Caitriana Nicholson

Experimental Particle Physics Group

Overview

• Setting the Scene• Two Simple Postulates• Some Strange Consequences• The World of Particles• Particle Accelerators• Special Relativity & Particle

Accelerators• Summary

Setting the SceneSwiss Patent Office, Bern, 1905

(Picture of Einstein goes here)

1905 - the Annus Mirabilis• March - “On a Heuristic Viewpoint Concerning the Production

and Transformation of Light” (the photoelectric effect)

• April - “On the Motion Required by the Molecular Kinetic Theory of Heat of Small Particles Suspended in a Stationary Liquid” (Brownian Motion)

• June - “On the Electrodynamics of Moving Bodies” (Special Theory of Relativity)

• September - “Does the Inertia of a Body Depend Upon Its Energy Content?” (Equivalence of Mass and Energy)

The Special Theory of Relativity

• Aimed to answer some burning questions:– Could Maxwell’s equations for

electricity and magnetism be reconciled with the laws of mechanics?

– Where was the aether?

2 Simple Postulates

• “The laws of physics are the same in every inertial frame of reference”– The Principle of Relativity

• “The speed of light in vacuum is the same in all inertial frames of reference, and is independent of the motion of the source”– Invariance of the speed of light

What is an inertial frame of reference?

A frame of reference is a system of co-ordinates. An inertial frame is one that’s not accelerating.

Frames of Reference

First Postulate

“The laws of physics are the same in every inertial frame of reference”

Spot the Difference?

Second Postulate“The speed of light in vacuum is the

same in all inertial frames of reference, and is independent of the motion of the source”

(Speed of light c = 3 x 108 metres/second = 670,616,629 mph)

vv

v+u

vc

Here Come The Consequences!

Relativity of Simultaneity

• Events which are simultaneous in one frame may not be in another!

• Each observer is correct in their own frame of reference

A B

A’ B’

Time Dilation

• Observers measure moving clocks to run slow

• The faster the speed, the slower the time

• Observed in caesium clocks flown at high speed

ddl l

x x

The Twins Paradox

• (picture of twins goes here)

Length Contraction

• Observers measure moving objects to be shorter than if they were at rest.

• (Only applies to the direction parallel to the motion!)

l0l

d

E = mc2

Applying relativistic principles to get the kinetic energy of a moving particle gives

Ek = Etotal - mc2

Etotal = Ek + mc2

For a particle at rest, E = mc2

This is the rest mass energy of the particle

Conservation of Mass and Energy

• Total mass + energy is always conserved

• Important consequences:– nuclear fission…

… and nuclear fusion!

© NASA

The Lives of the Elementary Particles

What is particle physics?

• The study of the fundamental structure of the universe!

• The idea of fundamental particles has been around since Ancient Greece (Democritus)…

• …but what we know today as atoms were hypothesised by John Dalton in 1804.

Into the modern era

• Electrons were discovered in 1897 (J.J. Thomson) and nuclei in 1911 (Rutherford).

• Einstein postulated the photon in 1905• And the neutron was discovered in 1930

(Bothe & Becker, Chadwick)• By the mid 1930s, the understanding of

the fundamental structure of matter seemed almost complete.

The Particle Zoo

• The 30s and 40s saw the discovery of a number of particles not found in normal matter - positrons, muons, pions…

• …followed by a whole host of short-lived, unstable particles after 1960.

• These can be classified into leptons (light) and hadrons (heavy) .

• There are now 12 known leptons, but more than 100 hadrons!

• It is clear that these do NOT represent the fundamental structure of matter!

The Standard Model

• In 1964, Murray Gell-Mann proposed the idea of quarks.

• Each hadron is believed to consist of a combination of 2 or 3 quarks.

• These, with the leptons and fundamental forces, form the Standard Model of matter which is generally accepted today.

Beyond the Standard Model

• There are still unanswered questions about the Standard Model!

• Does the Higgs Boson exist?• Do all the fundamental forces unify at

very high energy?• Why are there 3 families of quarks and

leptons?• Does supersymmetry exist?• To answer these questions, we need a

new generation of particle physics experiments!

Particle Accelerators• Used to collide particles at high

energies to probe structure and produce new particles

• Can be linear or ring, fixed-target or colliding beam accelerators

© CERN

Some Colliding-beam Accelerators

• The Stanford Linear Accelerator Center (SLAC) is a linear electron-positron

collider• The TeVatron at FNAL, Illinois is a

proton-antiproton ring collider• HERA, at DESY near Hamburg, is a

proton-electron ring collider• Under construction at CERN is the Large

Hadron Collider (LHC)

CERN, Geneva, Switzerland

© CERN

The LHC• Will collide protons with protons in a 27-

km ring • Protons will reach energies of 7 TeV each

– TeV are particle physicists’ energy units– 1 eV is the energy gained by 1 electron going

through a 1-volt battery

© CERN

LHC detectors• 4 detectors: ALICE, ATLAS, CMS and LHCb• More information from the CERN web page:

http://cern.ch

© CERN

© CERN

How does SR help us?• E = mc2!

– Particles can annihilate with their antiparticles, releasing energy

– Production of new particles

• Accelerator beam energy must be high enough for the mass of particles you want to produce!

• LHC energy is 14 TeV

© LAL-IN2P3

How does SR help us?• Time dilation

– Allowed discovery of the first muons (1937)– Cosmic rays hit upper atmosphere and

create pions– Pions decay to muons– Lifetime in rest frame = 2.2 microseconds!

• If travelling at 0.99c, distance travelled = 653m

– Lifetime in earth frame = 15.6 microseconds• So distance travelled = 4630 m • Far enough to reach earth’s surface and be

detected!

© CERN

• Time dilation (continued)– Allows particles to travel further in

detectors– Easier to detect and identify them!

How does SR help us?

© CERN

© PPARC

How does SR hinder us?

• Harder to accelerate particles up to high enough energy – As their speed approaches c,

acceleration decreases!– Need to have long acceleration times

• SLAC needs a 3-km path length to get speed that Newtonian dynamics would predict for 1.5 cm!

• LHC ring diameter = 27 km!

Summary

• 2 postulates, strange consequences– Relativity of simultaneity– Time dilation– Length contraction– Equivalence of mass and energy

• Consequences for our daily lives• Consequences for particle physics

– Production of new particles– Easier to measure, harder to

accelerate

What about non-inertial frames of reference?

• Einstein waited 10 years to publish his General Theory of Relativity…

… you only have to wait until this afternoon!