Modern Physics Chapter 2

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Constant Speed of Light c = 3 x 108 m/s Why did it take so long to figure this out?

Constant Speed of Light Think about everyday speeds Helios Galileo

Albert Einstein (3/14/1879 – 4/18/1955) 1894 (Age 15) The Investigation of the State of Aether in Magnetic Fields Failed entrance exam to ETH (Swiss Fed. Inst. Tech.) 1895 Chasing light idea, Special Relativity 1900 Finished ETH (physics and math) Swiss patent office clerk (EM devices) 1905 (Annus Mirabelis) 4 papers Photoelectric Effect Brownian Motion Special Relativity Matter and Energy Equivalence

c Constancy 1884 – J. C. Maxwell formulated four equations to describe light, which depend on c being constant Electric charges cause electric fields No magnetic monopoles to cause magnetic fields Changing magnetic fields cause electric fields Electron currents and changing electric fields cause magnetic fields

Michelson-Morley 1887-1907: Find the velocity of the Aether

Michelson-Morley 1887-1907: Find the velocity of the Aether v mirror u c Light source Beam splitter mirror screen

Michelson-Morley 1887-1907: Find the velocity of the Aether mirror Light source Beam splitter mirror screen

Einstein’s Postulates Physics is the same regardless of inertial frame Light moves with constant speed in the eyes of all observers

Postulate 1 Suppose you are sitting in a soundproof, windowless room aboard a hovercraft moving over flat terrain. Which of the following can you detect from inside the room? May have multiple answers. 1. rotation 2. deviation from the horizontal orientation 3. motion at a steady speed 4. acceleration 5. state of rest with respect to ground Answer: 1, 2, and 4. There are no experiments that can detect uniform motion (or rest); we can sense any motion that causes acceleration.

Postulate 1 Suppose you are sitting in a soundproof, windowless room aboard a hovercraft moving over flat terrain. Which of the following can you detect from inside the room? May have multiple answers. 1. rotation 2. deviation from the horizontal orientation 3. motion at a steady speed 4. acceleration 5. state of rest with respect to ground Answer: 1, 2, and 4. There are no experiments that can detect uniform motion (or rest); we can sense any motion that causes acceleration. Answer: 1, 2, and 4. There are no experiments that can detect uniform motion (or rest); we can sense any motion that causes acceleration.

Postulate 1 As far as we can tell, we don’t know which frame is actually doing the moving as long as no acceleration is involved. Answer: 1, 2, and 4. There are no experiments that can detect uniform motion (or rest); we can sense any motion that causes acceleration.

Postulate 2 Sound is longitudinal and has no polarization Speed of Light : Speed of Sound as Aether : Air c is constant with respect to source or medium? Sound depends on both vs = vsource + vair Aether? Can it move radially wrt all sources?

Postulate 2 The speed of light is constant as found empirically (Michelson-Morely) and theoretically (Maxwell)

Consequences How do we rectify our conceptual notion of additive velocities? We have to change our idea of space-time Space-time is not the same for all inertial frames

Consequences How do we rectify our conceptual notion of additive velocities? Simultaneous events in one frame that are at different locations will not be simultaneous in a different inertial frame (relative simultaneity) Two events occuring at the same location in one frame will have different temporal separation in another inertial frame (time dilation) The length of an object in one inertial frame will be different in a different inertial frame (length contraction)

Relative Simultaneity The train and platform experiment from the reference frame of an observer onboard the train. The train and platform experiment from the reference frame of an observer on the platform.

Space-Time Diagram Stationary frame (on train) Moving frame (platform) ct’ ct’ ct ct ct ct’ t = 0 t = 1 t = 2 x’ x’ x x’ x x

Relative Simultaneity

Time Dilation Events occur in the same location are denoted with the prime frame, S’.

Time Dilation Events occur in the same location to someone riding along with the timer. Therefore, on the timer it is the prime frame (t’). Someone off of the timer observes Events at two different locations. Therefore, a stationary frame is unprimed. ct’ h ct h x x v

Time Dilation From previous slide Bring c into square root by squaring it Replace h with ct’ Square both sides to get rid of square root Cancel c in first term on right Solve for t by bringing it to left hand side by itself. Simplify by pulling t out of both terms on the right hand side by. Square root both sides

Time Dilation

The Relativistic Correction, g

Plot of gn

An Example of Time Dilation 1971 U. S. Naval Observatory flew jets around the world Some East, with Earth’s rotation Some West, against Earth’s rotation

The Twin Paradox Events occur in the same location to the spaceship. Therefore, it is the prime frame. Earth Planet X t = 0 s t = ? 20 ly t’ = 0 s t’ = ? v = 0.80 c

The Twin Paradox How do we reconcile that the relative motion between Earth and spaceship should make it impossible to determine which one sees time dilation?

The Relativistic Correction, g Time for those moving at high speed appears to go slower than when stationary.

Length Contraction An object in motion will appear shorter than an object at rest. t1 t2 v t=t2-t1

Muon Decay Evidence of Special Relativity Muons (μ-) decay to mu neutrino (vμ), electron anti-neutrino (ve), and an electron (e-) in 2.2 μs (2.2 x 10-6 s) in the muon’s rest frame Feynman diagram

Muon Relativity Muon speed v = 0.994 c At the top of a 2 km high mountain we detect 560 muons/hr. How many should reach sea level (2 km below)? 2 km

Muon Relativity

Classical Galilean Relativity

Lorentzian Relativity

Lorentzian Relativity S S’ Light flash occurs on a moving train x x’ vt x’ x

Lorentzian Relativity S S’ Light flash occurs on a moving train x x’ vt x’ x

Lorentzian Relativity

Velocity Transformation

Velocity Transformation

Velocity Transformation

Velocity Transformation S frame v = 0 S’ frame meteor v = 0.8c u = - 0.6c

Velocity Transformation S frame v = 0 S’ frame v = 0.8c u = -c

Mechanics Requirements Expectations Valid in all inertial frames Physics does not change with relative velocity Reduce to classical expectations at low speed Agreement with experiment/observation Expectations

Lorentzian Momentum y y’ 2 2 2 2 2 2 1 1 1 1 1 x x’ S S’ v

Momentum

Momentum

Momentum

Mechanics Requirements Expectations Valid in all inertial frames Physics does not change with relative velocity Reduce to classical expectations at low speed Agreement with experiment/observation Expectations

Energy

Energy

Energy

Energy

Higgs Boson - LHC Circumference is 27 km

Higgs Boson - LHC mp = 1.6726217 x 10-27 kg c = 2.99792458 x 108 m/s Each Beam 450 GeV  vp = 0.999998 c 3.5 TeV  vp = 0.999999991 c proton proton

The Neutrino – Neutron Decay p e Wolfgang Pauli (1930) Neutron decays don’t conserve energy or momentum Hypothesized the neutrino SuperKamiokande 1998-present Measure the mass of the neutrino MINOS – Main Injector Neutrino Oscillation Search 2005-present No neutrino mass (v = 1.000051 c) v

The Neutrino – Neutron Decay p e v

Energy Accelerator vs. Collider

Energy Massless Particles

Length Contraction

Muon Relativity Muon speed v = 0.98 c 3 km ? km t = ? μs t’ = 2.2 μs