PHPH--105 : Modern Physics105 : Modern Physics

ContentsContents

Special theory of relativitySpecial theory of relativity

Basics of Quantum MechanicsBasics of Quantum Mechanics

Reference BooksReference Books

Relativity PartRelativity Part

1.1. Introduction to Special Relativity:Introduction to Special Relativity:

R. Resnik; Wiley Eastern (New Delhi) 1968R. Resnik; Wiley Eastern (New Delhi) 1968

2.2. An Introduction to MechanicsAn Introduction to Mechanics: :

D. Kleppner and R.J. Kolenkow (Tata Mc D. Kleppner and R.J. Kolenkow (Tata Mc Graw Hill) 1973 Graw Hill) 1973

3.3. Special Relativity:Special Relativity:

A. P. French (ELBS and Nelson) 1972A. P. French (ELBS and Nelson) 1972

Evaluation SchemeEvaluation Scheme

InIn--semester (50%)semester (50%)Quizes (20% total)Quizes (20% total)

One MidOne Mid--semester (30%)semester (30%)One MidOne Mid--semester (30%)semester (30%)

All tests and midAll tests and mid--sem are compulsory and no sem are compulsory and no rere--exam or compensation in any form will be exam or compensation in any form will be given on any ground whatsoever.given on any ground whatsoever.

EndEnd--semestersemester (50%)(50%)

Modern Physics Modern Physics (How Modern?)(How Modern?)

Not really so modern.Not really so modern.

Seeds were grown more than a century Seeds were grown more than a century

ago.ago.

Michelson in 1899Michelson in 1899 The more important fundamental laws and facts The more important fundamental laws and facts of physical science have all been discovered, and of physical science have all been discovered, and they are so firmly established that the possibility of they are so firmly established that the possibility of their ever being supplanted in consequence of the their ever being supplanted in consequence of the new discoveries is exceedingly remote.Our new discoveries is exceedingly remote.Our future discoveries must be looked for in sixth future discoveries must be looked for in sixth future discoveries must be looked for in sixth future discoveries must be looked for in sixth place of decimalplace of decimal

Ref: Introduction to Modern Physics : F.K. Richtmyer, E. H. Kennard, John N. Cooper ( Tata Mc. Graw Hill) 1976, 6th Edition

Some accepted concepts of Some accepted concepts of

Newtonian mechanicsNewtonian mechanics

Mass, length and time are frame independent. Mass, length and time are frame independent.

There is NO ultimate speed.There is NO ultimate speed.

Clouds on Classical PhysicsClouds on Classical Physics

The beauty and clearness of the dynamical The beauty and clearness of the dynamical

theory, which asserts light and heat to be theory, which asserts light and heat to be

modes of motion is at present obscured by modes of motion is at present obscured by

two cloudstwo clouds--Lord Kelvin in 1900Lord Kelvin in 1900two cloudstwo clouds--Lord Kelvin in 1900Lord Kelvin in 1900

Cloud1: The motion of Earth in EtherCloud1: The motion of Earth in Ether

Cloud2: Failure of MaxwellCloud2: Failure of Maxwell--Boltzmann Boltzmann doctrine regarding doctrine regarding EquipartitionEquipartition of Energyof Energy

Need of new ideasNeed of new ideas

Classical approach did not lead to Classical approach did not lead to

solution.solution.

Electromagnetic theoryElectromagnetic theory

Newtonian MechanicsNewtonian Mechanics

Classical StatisticsClassical Statistics

Newer ideas required.Newer ideas required.

CloudsClouds

The first cloud started disappearing The first cloud started disappearing

quickly in 1905.quickly in 1905.

The second needed much more time and The second needed much more time and The second needed much more time and The second needed much more time and

took almost 25 more years to show sign took almost 25 more years to show sign

of dissolution.of dissolution.

This courseThis course

Is meant to give an idea of the failures of Is meant to give an idea of the failures of

the then wellthe then well--established Classical established Classical

Physics.Physics.

Also gives a flavor of the new Physics Also gives a flavor of the new Physics

that developed after these failures.that developed after these failures.

ApproachApproach

We shall start with the first cloud and We shall start with the first cloud and discuss the Special Theory of Relativity discuss the Special Theory of Relativity that was developed as a result of it.that was developed as a result of it.

We shall then move to the second cloud We shall then move to the second cloud and discuss Quantum Theory and then and discuss Quantum Theory and then possibly Quantum Statistics.possibly Quantum Statistics.

Relativity of what?Relativity of what?

There are really three theories of relativity:

Relativity pre-Einstein (Galileo)

Special Theory of Relativity (1905) Special Theory of Relativity (1905)

General Theory of Relativity (1915)

Relativity is concerned with the question:

What is the nature of space and time?

Inertial Frame of ReferenceInertial Frame of Reference

Isolated objects move with constant Isolated objects move with constant

VelocityVelocity

We shall assume , unless specifically mentioned, that observations are being made only in an inertial frame of reference.

In Special Theory of RelativityIn Special Theory of Relativity

in an inertial frame of reference.

It may be noted that, though earth undergoes a rotational and orbital

motion, for all practical purposes, any set of axes fixed on the earth is

treated as inertial frames of reference.

Absolute space and absolute time:

Suppose that you are on a plane. At 12:00, you leave your seat to talk to a friend seated a few rows in front of you. At 12:15, you return to your seat. You might say that: at 12:15, you were at the same point in space where you were at 12:00. However, what would a ground-based person claim?

If the plane were going 600 mi/hr, that person might say: at 12:15, you were at a point in space 150 miles away from where you were at 12:00.at 12:00.

Who is right? According to Aristotle, space and time areuniversal and you have moved.

But the Earth is moving around the Sun, and the Sun around the Galaxy and the Galaxy is whizzing through space?.

Newtons lawNewtons law

Velocity is a frame dependent quantity.Velocity is a frame dependent quantity.

Acceleration is same in all inertial Acceleration is same in all inertial

frames.frames.frames.frames.

Newtons law depends on acceleration Newtons law depends on acceleration

and Forceand Force..=

r rF ma

Two Inertial FramesTwo Inertial Frames

y yS S

r( )r t

r( )r t

OO

z

x,x

z

r( )R t

)(')()( trtRtrrrr

+=

= +rr r

r r r

r R r

Velocity and AccelerationVelocity and Acceleration

= +

=

r r r

r r

ov v v

a a

Newtons Law in Different FramesNewtons Law in Different Frames

Force is normally expected to be frame Force is normally expected to be frame independent independent

Newtons law is valid in all inertial Newtons law is valid in all inertial

=r rF ma

Newtons law is valid in all inertial Newtons law is valid in all inertial framesframes

From this law, velocity can be evaluated in any From this law, velocity can be evaluated in any frame, if needed. frame, if needed.

We must specify the frame to know the We must specify the frame to know the velocity.velocity.

Galilean Galilean Newtonian relativityNewtonian relativityball dropped by the passenger

For both the passenger (the moving observer) and the ground observer, Newtons law is found to be valid, though the paths are different. By doing this experiment, the passenger cannot say definitely that I am moving or I am at rest.

Conservation laws tooConservation laws too

Since laws of conservation of linear momentum, Since laws of conservation of linear momentum, angular momentum and kinetic energy follow angular momentum and kinetic energy follow Newtons laws, these conservation laws too hold Newtons laws, these conservation laws too hold good in all inertial frames, though the numerical good in all inertial frames, though the numerical good in all inertial frames, though the numerical good in all inertial frames, though the numerical values of these dynamical quantities are different values of these dynamical quantities are different in different (inertial) frames.in different (inertial) frames.

Problem No. 1Problem No. 1

Lorentz force is velocity dependent.Lorentz force is velocity dependent.

( )F q E v B= + r r rr

ConsequenceConsequence

S is an observer on the groundS is an observer on the train moving with a constant velocity v

e???coincidenc aJust

loop. in the emfan is there

though0,F frame), (moving frame S' toaccording But,

l.dFemf induced theTherefore, zero.non is

on F force, Lorentz theframe, S toAccording

mag

mag

=

= rv

mag

e???coincidenc aJust

Is this due to an accidental symmetry ?

But the classical Doppler effect of sound is not symmetrical !

Problem No. 2Problem No. 2

Speed of light in vacuum is a fundamental constant, given by

1

00

=

=

c

m/s 103c that so

)N/m10(4 umspace/vacu free ofty permeabili magnetic

)/NmC10(8.85 umspace/vacu free ofty permittivi electric

8

2 7-

0

2212-

0

=

=

=

pi

Is Speed of light frame Is Speed of light frame

dependent?dependent?

cur

c ur

Classically, the relative speed should be different in the above two cases, contradicting the notion that c is a fundamental constant.

If yesIf yes

Are fundamental constants Are fundamental constants o o and and o o frame dependent?frame dependent?

That means basic electric and magnetic That means basic electric and magnetic

forces are also frame dependent.forces are also frame dependent.

Or is it that?Or is it that?

The following expression valid only in The following expression valid only in

some specific frame?some specific frame?

1

o o

c

=

The Second Option impliesThe Second Option implies

All the inertial frames, though equivalent All the inertial frames, though equivalent

from mechanical point of view are not from mechanical point of view are not

equivalent from electromagnetic point of equivalent from electromagnetic point of

view.view.view.view.

A A special inertial framespecial inertial frame may then exist, may then exist,

which can be identified as which can be identified as absolute restabsolute rest..

What is your pick?What is your pick?

Do you allow fundamental constants to Do you allow fundamental constants to

become frame dependent?become frame dependent?

OrOrOrOr

You allow a special inertial frame?You allow a special inertial frame?

Ideally None?Ideally None?

But if there is no other choice given, one But if there is no other choice given, one

is likely to prefer lesser evil, which is the is likely to prefer lesser evil, which is the

second choicesecond choice..

EtherEther

Earlier ideas favored the concept of a Earlier ideas favored the concept of a

special frame.special frame.

It also favored the usual notion that a It also favored the usual notion that a

medium is necessarily required for wave medium is necessarily required for wave medium is necessarily required for wave medium is necessarily required for wave

propagation.propagation.

It was imagined that the universe is filled It was imagined that the universe is filled

with ocean of ether. It was assumed to with ocean of ether. It was assumed to

be at absolute rest and the earth moves be at absolute rest and the earth moves

relative to that.relative to that.

ImplicationsImplications

All planets, stars, galaxies float in ether.All planets, stars, galaxies float in ether.

The speed of light is c only in this The speed of light is c only in this

medium as given by the expression medium as given by the expression

involving fundamental constants.involving fundamental constants.involving fundamental constants.involving fundamental constants.

In other frames (such as the earth), the In other frames (such as the earth), the

speed of light could be different from c. speed of light could be different from c.

One can determine the speed of the One can determine the speed of the

frame by measuring the speed of light in frame by measuring the speed of light in

that frame, by the relative velocity eqn.that frame, by the relative velocity eqn.

ImplicationsImplications

Going by the speed of sound (330 m/s in air) in Going by the speed of sound (330 m/s in air) in various media, the ether should be extremely rigid various media, the ether should be extremely rigid to support such a large value for c, yet allowing the to support such a large value for c, yet allowing the earth and other objects to move freelyearth and other objects to move freely

Broader ImplicationBroader Implication

Though all the inertial frames are Though all the inertial frames are

equivalent from mechanical point of equivalent from mechanical point of

view, they need not be from the view, they need not be from the

electromagnetic point of view.electromagnetic point of view.electromagnetic point of view.electromagnetic point of view.

But is there any process, which is purely But is there any process, which is purely

mechanical?mechanical?

Is it Chance?Is it Chance?

Is it only by chance that nature has made Is it only by chance that nature has made

mechanical processes equivalent in mechanical processes equivalent in

inertial frames but not the inertial frames but not the

electromagnetic processes?electromagnetic processes?electromagnetic processes?electromagnetic processes?

Are you Happy with the situation?Are you Happy with the situation?

Look at ExperimentsLook at Experiments

Michelson Morley ExperimentMichelson Morley Experiment

Can we experimentally measure different Can we experimentally measure different

speeds of light in different frames?speeds of light in different frames?

Attempt was unsuccessful.Attempt was unsuccessful.

Idea behind the experiment

A B

VLet AB=l

The apparatus, fixed to the earth moves in ether.Relative to the apparatus, the velocity of light along AB is c-v andvelocity of light along AB is c-v andalong BA it is c+v.

Total time taken for the round trip ist=l/(c-v) + l/(c+v)

Let t0 be the time when there is no movement in ether. i.e., t0=2l/c

Then, t-t0 2(l/c)(v2/c2), which is too

small to be observed because the orbital speed of earth (v) is only 30 km/s

Michelson Michelson -- MorelyMorely experimentexperiment

Interferometric technique

l

v

M2

M, M1 and M2 are mirrors. The apparatus moves with a speed v (earths speed) in ether.

l1

l2

M

M1

is taken time thent,dispalceme horizontal a have

M2 and M mirrors thesince MM2M,path For the

.)/1(

12 t time theslide,

earlier in theshown as MM1M,path For the

22

11

=

cvc

l

shift. fringe a give shoulddifferent are t' andt fact that The

t' is differenc timenew theapparatus, theRotating

ll ifeven 0, )t-(t t ,clear that isIt

./1

12t

is taken time thent,dispalceme horizontal a have

2112

22

22

==

=

cvc

l

Result of MM experimentResult of MM experiment

The fringe shift was zero.The fringe shift was zero.

This implies either (This implies either (ii) there is no ether drift ) there is no ether drift (v=0) or (ii) there is no ether at all.(v=0) or (ii) there is no ether at all.

It was shown by experiments that the first It was shown by experiments that the first It was shown by experiments that the first It was shown by experiments that the first option is not possible.option is not possible.

Ruling out the existence of ether actually rules Ruling out the existence of ether actually rules out the concept of a frame that is at absolute out the concept of a frame that is at absolute rest. That is, there is no special inertial frame. rest. That is, there is no special inertial frame.

Clue from electromagnetismClue from electromagnetism

According to Einstein, the result of the coil-magnet experiment was not a coincidence. He noted The observable phenomena here depend only on the relative motion between the coil and the magnet, against the customary view that draws a sharp distinction between the two cases. Examples like this suggest, distinction between the two cases. Examples like this suggest, electrodynamics, like mechanics, possesses no properties corresponding to the idea of absolute rest.

Postulates of Special Theory of RelativityPostulates of Special Theory of Relativity

Laws of Laws of PhysicsPhysics are same in all inertial are same in all inertial

frames of references. No preferred frames of references. No preferred

inertial frame exists.inertial frame exists.

The speed of light c is same in all The speed of light c is same in all

inertial frames.inertial frames.

First Postulate ImpliesFirst Postulate Implies

No absolute rest. No absolute rest.

No absolute velocities.No absolute velocities.

No ether. No ether. No ether. No ether.

Space is filled with nothing.Space is filled with nothing.

We require something real to which we We require something real to which we

can attach our frame of reference and can attach our frame of reference and

only with respect to that frame we can only with respect to that frame we can

talk of velocities.talk of velocities.

Second Postulate impliesSecond Postulate implies

cur

c ur

Both the observers will tell the same value for c, against the usualvelocity addition law.

cv

correct

c-v

v

c

v

WRONG

CORRECT

Quote from Prof. Herman Quote from Prof. Herman BondiBondi::

The special theory of relativity is a necessary The special theory of relativity is a necessary consequence of any assertion that the consequence of any assertion that the unity unity of Physicsof Physics is essential, for it would be is essential, for it would be intolerable for all inertial systems to be intolerable for all inertial systems to be intolerable for all inertial systems to be intolerable for all inertial systems to be equivalent from dynamical point of view yet equivalent from dynamical point of view yet distinguishable by optical measurements...distinguishable by optical measurements...

New Approach NeededNew Approach Needed

Relative velocity formula requires Relative velocity formula requires

modification.modification.

A new formulation is needed which can A new formulation is needed which can A new formulation is needed which can A new formulation is needed which can

ensure that the speed of light is same in ensure that the speed of light is same in

all the inertial frames.all the inertial frames.

The new formulation must be consistent The new formulation must be consistent

with the first postulatewith the first postulate

SummarySummary

Absolute rest and absolute speed are wrong Absolute rest and absolute speed are wrong notions.notions.

Speed of light in vacuum, which is the highest Speed of light in vacuum, which is the highest for any wave, does not obey the usual rules of for any wave, does not obey the usual rules of for any wave, does not obey the usual rules of for any wave, does not obey the usual rules of relative velocity.relative velocity.

There is There is anan ultimate speed, against what we ultimate speed, against what we thought in the beginning (classical).thought in the beginning (classical).