Chapter 29Chapter 29

Physics of the Physics of the AtomAtom

A Brief Overview of Modern A Brief Overview of Modern PhysicsPhysics

2020thth Century revolution Century revolution• 1900 Max Planck1900 Max Planck

Basic ideas leading to Quantum theoryBasic ideas leading to Quantum theory

• 1905 Einstein1905 Einstein Special Theory of RelativitySpecial Theory of Relativity

2121stst Century Century• Story is still incompleteStory is still incomplete

Basic ProblemsBasic Problems The speed of every particle in the The speed of every particle in the

universe always remains universe always remains less thanless than the the speed of lightspeed of light

Newtonian Mechanics is a limited Newtonian Mechanics is a limited theorytheory• It places no upper limit on speedIt places no upper limit on speed• It is contrary to modern experimental resultsIt is contrary to modern experimental results• Newtonian Mechanics becomes a specialized Newtonian Mechanics becomes a specialized

case of Einstein’s Theory of Special Relativitycase of Einstein’s Theory of Special Relativity When speeds are much less than the speed of lightWhen speeds are much less than the speed of light

Galilean RelativityGalilean Relativity

Choose a Choose a frame of referenceframe of reference• Necessary to describe a physical eventNecessary to describe a physical event

According to Galilean Relativity, the According to Galilean Relativity, the laws of mechanics are the same in all laws of mechanics are the same in all inertial frames of referenceinertial frames of reference• An inertial frame of reference is one in An inertial frame of reference is one in

which Newton’s Laws are validwhich Newton’s Laws are valid• Objects subjected to no forces will move Objects subjected to no forces will move

in straight linesin straight lines

Galilean Relativity – ExampleGalilean Relativity – Example

A passenger in an A passenger in an airplane throws a airplane throws a ball straight upball straight up• It appears to move It appears to move

in a vertical pathin a vertical path• The law of gravity The law of gravity

and equations of and equations of motion under motion under uniform uniform acceleration are acceleration are obeyedobeyed

Galilean Relativity – Example, Galilean Relativity – Example, contcont

There is a There is a stationary observer stationary observer on the groundon the ground• Views the path of Views the path of

the ball thrown to the ball thrown to be a parabolabe a parabola

• The ball has a The ball has a velocity to the right velocity to the right equal to the equal to the velocity of the velocity of the planeplane

Galilean Relativity – Example, Galilean Relativity – Example, conclusionconclusion

The two observers disagree on the shape The two observers disagree on the shape of the ball’s pathof the ball’s path

Both agree that the motion obeys the law Both agree that the motion obeys the law of gravity and Newton’s laws of motionof gravity and Newton’s laws of motion

Both agree on how long the ball was in the Both agree on how long the ball was in the airair

Conclusion:Conclusion: There is no preferred frame of There is no preferred frame of reference for describing the laws of reference for describing the laws of mechanicsmechanics

Galilean Relativity – LimitationsGalilean Relativity – Limitations Galilean Relativity does Galilean Relativity does notnot apply to experiments apply to experiments

in electricity, magnetism, optics, and other areasin electricity, magnetism, optics, and other areas Results do not agree with experimentsResults do not agree with experiments

• The observer should measure the speed of the pulse as The observer should measure the speed of the pulse as v+cv+c

• Actually measures the speed as cActually measures the speed as c

Newtonian Mechanics

1. In the absence of forces, a body moves with uniform speed in a straight line.

2. In the presence of force, the body changes its state of motionin such a way that

ptF

t

vmF

)(

Based on the premise of Absolute Space and Absolute Time.

Newton wrote “Absolute space in its own nature, without relation to any external, remains always similar and immovable.”

However, Newton himself recognized that there is an ambiguity in his argument.

“But because the parts of space cannot be seen, or distinguishedfrom one another by our senses, therefore in their stead we usesensible measures of them. For from the positions and distances of things from any body considered as immovable, we define all places; and then with respect to such places, we estimate all motions,considering bodies are transferred from some of those places into others. And so, instead of absolute places and motions, we use relative ones; and without any inconvenience in common affairs.

- Isaac Newton -

Newton’s law of mechanics holds true in any inertial frames.

platforms moving with a uniform speedRelative to a platform

z

x

y

r = (x,y,z)z’

x’

y’ vt

r = (x’,y’,z’) x’ = x – vt y’ = y

z’ = z

vx’ = vx – vvy’ = vy

vz’ = vz

Luminiferous EtherLuminiferous Ether

1919thth Century physicists compared Century physicists compared electromagnetic waves to mechanical electromagnetic waves to mechanical waveswaves• Mechanical waves need a medium to support Mechanical waves need a medium to support

the disturbancethe disturbance The The luminiferous etherluminiferous ether was proposed as the was proposed as the

medium required (and present) for light medium required (and present) for light waves to propagatewaves to propagate• Present everywhere, even in spacePresent everywhere, even in space• Massless, but rigid mediumMassless, but rigid medium• Could have no effect on the motion of planets or Could have no effect on the motion of planets or

other objectsother objects

Verifying theVerifying theLuminiferous EtherLuminiferous Ether

Associated with an ether was Associated with an ether was an an absolute frameabsolute frame where the where the laws of e & m take on their laws of e & m take on their simplest formsimplest form

Since the earth moves Since the earth moves through the ether, there through the ether, there should be an “ether wind” should be an “ether wind” blowingblowing

If v is the speed of the ether If v is the speed of the ether relative to the earth, the relative to the earth, the speed of light should have speed of light should have minimum or maximum values minimum or maximum values depending on its orientation to depending on its orientation to the “wind”the “wind”

Michelson-Morley ExperimentMichelson-Morley Experiment

First performed in 1881 by Michelson First performed in 1881 by Michelson Repeated under various conditions Repeated under various conditions

by Michelson and Morleyby Michelson and Morley Designed to detect small changes in Designed to detect small changes in

the speed of lightthe speed of light• By determining the velocity of the earth By determining the velocity of the earth

relative to the etherrelative to the ether

Michelson-Morley EquipmentMichelson-Morley Equipment Used the Michelson Used the Michelson

InterferometerInterferometer Arm 2 is aligned along Arm 2 is aligned along

the direction of the the direction of the earth’s motion through earth’s motion through spacespace

The interference pattern The interference pattern was observed while the was observed while the interferometer was interferometer was rotated through 90°rotated through 90°

The effect should have The effect should have been to show small, but been to show small, but measurable, shifts in the measurable, shifts in the fringe patternfringe pattern

Michelson-Morley ResultsMichelson-Morley Results

Measurements failed to show any change Measurements failed to show any change in the fringe patternin the fringe pattern• No fringe shift of the magnitude required was No fringe shift of the magnitude required was

ever observedever observed Light is now understood to be an Light is now understood to be an

electromagnetic wave, which requires no electromagnetic wave, which requires no medium for its propagationmedium for its propagation• The idea of an ether was discardedThe idea of an ether was discarded

The laws of electricity and magnetism are The laws of electricity and magnetism are the same in all inertial framesthe same in all inertial frames

Einstein’s Principle of RelativityEinstein’s Principle of Relativity

Resolves the contradiction between Resolves the contradiction between Galilean relativity and the fact that the Galilean relativity and the fact that the speed of light is the same for all observersspeed of light is the same for all observers

PostulatesPostulates• The The Principle of RelativityPrinciple of Relativity: All the laws of : All the laws of

physics are the same in all inertial framesphysics are the same in all inertial frames• The The constancy of the speed of lightconstancy of the speed of light: the speed : the speed

of light in a vacuum has the same value in all of light in a vacuum has the same value in all inertial reference frames, regardless of the inertial reference frames, regardless of the velocity of the observer or the velocity of the velocity of the observer or the velocity of the source emitting the lightsource emitting the light

The Principle of RelativityThe Principle of Relativity

This is a sweeping generalization of the This is a sweeping generalization of the principle of Galilean relativity, which refers principle of Galilean relativity, which refers only to the laws of mechanicsonly to the laws of mechanics

The results of The results of any kindany kind of experiment of experiment performed in a laboratory at rest must be performed in a laboratory at rest must be the same as when performed in a the same as when performed in a laboratory moving at a constant speed laboratory moving at a constant speed past the first one.past the first one.

No preferred inertial reference frame No preferred inertial reference frame existsexists

It is impossible to detect absolute motionIt is impossible to detect absolute motion

The Constancy of the Speed of The Constancy of the Speed of LightLight

Been confirmed experimentally in many waysBeen confirmed experimentally in many ways• A direct demonstration involves measuring the A direct demonstration involves measuring the

speed of photons emitted by particles traveling speed of photons emitted by particles traveling near the speed of lightnear the speed of light

• Confirms the speed of light to five significant Confirms the speed of light to five significant figuresfigures

Explains the null result of the Michelson-Explains the null result of the Michelson-Morley experimentMorley experiment

Relative motion is unimportant when Relative motion is unimportant when measuring the speed of lightmeasuring the speed of light• We must alter our common-sense notions of space We must alter our common-sense notions of space

and timeand time

Consequences of Special Consequences of Special RelativityRelativity

Restricting the discussion to concepts of Restricting the discussion to concepts of length, time, and simultaneitylength, time, and simultaneity

In relativistic mechanicsIn relativistic mechanics• There is no such thing as absolute lengthThere is no such thing as absolute length• There is no such thing as absolute timeThere is no such thing as absolute time• Events at different locations that are observed Events at different locations that are observed

to occur simultaneously in one frame are not to occur simultaneously in one frame are not observed to be simultaneous in another frame observed to be simultaneous in another frame moving uniformly past the firstmoving uniformly past the first

L

cLt

cLtt

total

inout

/2

/

In 19th century, physicists believed in luminiferous ether and that

Light travels with the speed of light,c relative to this light medium.

Now, let’s consider the effect that we are making this measurement on the surface of earth which is moving through the ether with a speed v, close to 18 miles/s

LMoving with v

)/( vcLt

vtLct

out

outout

L

)/( vcLt

vtLct

in

inin

)/1(

1222 cvc

L

vc

L

vc

Lttt inouttotal

However, Michelson-Morley’s experiment showed with a high precision ttotal = 2L/c

Accurate measurements of speed of light give the valuec = 2.998 x 108 m/s no matter how the light source or/and the measurer are moving!!

Serious conflict with then current understanding based on Newtonian world.

Albert Einstein (1879 – 1955)

In 1905, He provided a new view on space-time,and proposed a new theory of mechanics which is consistent with Newtonian mechanics in the limit of low speed.

1921 Nobel Prize in Physics“for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect"

In his 1905 paper, Einstein proposes:

… the same law of electrodynamics and optics will be valid for all frames of reference for which the equation of mechanics holdgood. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate….

+ the experimental observation that the speed of light is c regardless Of the reference frame where the light source or the observer resides.

a fundamental physical constant

1. Neither an object nor any form of energy can be accelerated to a speed as fast as or faster than c.

2. The mass of an object increases when its speed increases.3. Mass is a form of energy in the sense that mass and energy can be

interchanged. 4. An observer observes that the clock moving with a speed relative to

the observer is clicking slower than his.5. When a long object is moving fast in its length direction passing by an

observer, the observer will measure the length of the object is shorter than that at rest relative to the observer.

Time Dilation

Einstein Clock

L1 round trip time = 2L/c

is longer than

Time interval from the point of view of the stationary observer

Time interval from the point of view of the observer moving with The clock

=22 /1

1

cv

Time Dilation, SummaryTime Dilation, Summary

The time interval The time interval Δt between two events Δt between two events measured by an observer moving with measured by an observer moving with respect to a clock is longer than the time respect to a clock is longer than the time interval Δtinterval Δtpp between the same two events between the same two events measured by an observer at rest with measured by an observer at rest with respect to the clockrespect to the clock

A clock moving past an observer at speed A clock moving past an observer at speed v runs more slowly than an identical clock v runs more slowly than an identical clock at rest with respect to the observer by a at rest with respect to the observer by a factor of factor of 22 /1 cv