Everything comes unglued Blackbody Radiation Photoelectric …mjburns.net/SPH Blackbody ppt.pdf · 2 Atomic scale effects Small Dx means large Dv since 4 h v mx D D Example: an electron

1

Blackbody Radiation

Photoelectric Effect

Wave-Particle Duality

SPH4U

Everything comes unglued

The predictions of ―classical physics‖ (Newton‘s

laws and Maxwell‘s equations) are sometimes

completely, utterly WRONG. classical physics says that an atom‘s electrons should fall

into the nucleus and STAY THERE. No chemistry, no

biology can happen.

classical physics says that toaster coils radiate an infinite

amount of energy: radio waves, visible light, X-rays,

gamma rays,…

The source of the problem

It‘s not possible, even ―in theory‖ to know

everything about a physical system. knowing the approximate position of a particle corrupts

our ability to know its precise velocity (―Heisenberg

uncertainty principle‖)

Particles exhibit wave-like properties. interference effects!

The scale of the problem

Let‘s say we know an object‘s position to an accuracy Dx.

How much does this mess up our ability to know its speed?

Here‘s the connection between Dx and Dv (Dp = mDv):

That‘s the ―Heisenberg uncertainty principle.‖ h 6.610-34 J·s

4

hp x

D D

―It is physically impossible to predict simultaneously the exact

position and exact momentum of a particle.‖

2

Atomic scale effects

Small Dx means large Dv since4

hv

m xD

D

Example: an electron (m = 9.110-31 kg) in an atom is confined to a region of size x ~ 510-11 m.

How is the minimum uncertainty in its velocity?

Plug in, using h = 6.610-34 to find v > 1.1106 m/sec

Example

The speed of an electron (m = 9.110-31 kg) is measured to

have a value of 5 x 103 m/s to an accuracy of 0.003 percent.

Determine the uncertainty in determining its position.

31 3

27

9.11 10 5.00 10

4.56 10

mkg

s

kg m

s

p mv

27

31

0.00003 4.56

0.

10

1.37 10

00003

kg m

s

kg

p

m

p

s

D

34

31

4

6.63 10

44 1.37 1

0.38

0

3 8 10

5

4

. 5

J shx

kg mp

s

m

m

hx p

m

D

D

D D

Example

The speed of an bullet (m = 0.020 kg) is measured to have a

value of 300 m/s to an accuracy of 0.003 percent. Determine

the uncertainty in determining its position.

0.020 300

6

m

p

kgs

m

k

v

g m

s

4

0.00003 6

1.8 1

0.

0

00003

k

p

m

s

k

p

g

g m

s

D

3

34

4

1

6.63 10

44 1.8

2.93 1

10

0

4

m

J shx

h

m

x p

kgp

s

D

D

D D

Example

A proton has a mass of 1.67 x 10-27 kg and is close to

motionless as possible. What minimum uncertainty in its

momentum and in its kinetic energy must it have if it is

confined to a region :

(a) 1.0 mm

(b) An atom length 5.0 x 10-10m

(c) About the nucleus of length 5.0 x 10-15m

3

ExampleA proton has a mass of 1.67 x 10-27 kg and is close to




(a) 1.0 mm

3

34

3

2

6.63 10

4 4 1.0 10

4

5.28 10

J

h

shp

x

x p

m

kg m

s

D

D

D

D

34

5

27 3

6.63 10

4 4 1.67 10 1.0 10

3.16 10

p m

J sh

m

s

v

vm x kg m

D

D

D

D

2

2

2

3

7 5

7

11.67 10 3.16

8.33 1

1

0

02

2

1m

kgs

J

KE mv





(b) An atom length 5.0 x 10-10m

3

25

4

10

6.63 10

4 4 5.0 10

1.0 0

4

6 1

J shp

kg

x

s

x

m

m

hp

D

D D

D

34

27 10

6.63 10

4 4 1.67 10 5.0 1

2

0

63.

J shv

m

p m

x m

v

m

s

kg

D

D

D

D

2

2

27

24

11.67 10 63

3.33 1

22

1

2

0

.m

kgs

m

J

KE v





(c) About the nucleus of length 5.0 x 10-15m

3

20

4

15

6.63 10

4 4 5.0 10

1.0 0

4

6 1

J shp

kg

x

s

x

m

m

hp

D

D D

D

34

6

27 20

6.63 10

4 4 1.

6.32 10

67 10 1.06 10

J shv

m x kg m

p

m

s

m v

D

D

D D

2

2

2

1

7 6

4

11.67 10 6.32

3.33 10

0

2

2

1

1m

kgs

K

J

mv

m

E

Notice that when we consider a particle

(say a proton), that is confined to a small

region, the Quantum Mechanics requires

that such a particle cannot have a precise

momentum (or even momentum of zero).

This means that even at absolute zero, this

proton must have kinetic energy. This

energy is called the ―zero point energy‖,

and there is no way to avoid this.

Quantum Mechanics!

At very small sizes the world is VERY

different!

Energy can come in discrete packets

Everything is probability; very little is absolutely

certain.

Particles can seem to be in two places at same

time.

Looking at something changes how it behaves.

4

Another Consequence of

Heisenberg‘s Uncertainty

Principle

A quantum particle can never be in a state of rest,

as this would mean we know both its position and

momentum precisely

Thus, the carriage will

be jiggling around the

bottom of the valley

forever

Blackbody Motivation

• The black body is importance in thermal radiation theory and practice.

• The ideal black body notion is importance in studying thermal radiation and electromagnetic radiation transfer in all wavelength bands.

• The black body is used as a standard with which the absorption of real bodies is compared.

Hot objects glow (toaster coils, light bulbs, the sun).

As the temperature increases the color shifts from Red to

Blue.

The classical physics prediction was completely wrong! (It

said that an infinite amount of energy should be radiated by

an object at finite temperature.)

Blackbody RadiationDefinition of a black body

A black body is an ideal body which allows

the whole of the incident radiation to pass

into itself ( without reflecting the energy ) and

absorbs within itself this whole incident

radiation. This propety is valid for radiation

corresponding to all wavelengths and to all

angels of incidence. Therefore, the black

body is an ideal absorber and emitter of

radaition. The blackbody will then radiate at

a wavelength that is related to its absolute

temperature. One should picture a hot oven

with an open door emitting radiation into its

cooler surroundings or, if the surroundings

are hotter, one pictures a cool oven with an

open door taking in radiation from its

surroundings. It is the open oven door, which

is meant to look black—and hence absorbs

all colours or frequencies—that gives rise to

the term black body.

5

Maxwell‘s Classical Theory

Rayleigh-Jeans Law

The Ultraviolet Catastrophe

4

2),(

ckTTI

This formula also had a

problem. The problem was

the term in the denominator.

For large wavelengths it fitted

the experimental data but it

had major problems at

shorter wavelengths.

Planck Law

Higher temperature: peak intensity at shorter

22 1( , )

5

1

hcI T

hc

kTe

Blackbody Radiation:

First evidence for Q.M.

Max Planck found he could explain these curves if he

assumed that electromagnetic energy was radiated in discrete

chunks, rather than continuously.

The ―quanta‖ of electromagnetic energy is called the photon.

Energy carried by a single photon is

E = hf = hc/

Planck‘s constant: h = 6.626 X 10-34 Joule sec

E = nhf, n=1, 2, 3, 4

6

Blackbody Radiation:

First evidence for Q.M.

It was more difficult for atoms to absorb very high energy

photons (short wave lengths thus high frequency).

E = nhf, n=1, 2, 3, 4

Planck himself matched mathematics to the data. He

used mathematics as a device to obtain the correct

answer which he initially believed was still in classical

Newtonian physics.

QuestionsA series of light bulbs are glowing red, yellow, and blue.

Which bulb emits photons with the most energy?

The least energy?

Which is hotter?

(1) stove burner glowing red

(2) stove burner glowing orange

Blue! Lowest wavelength is highest energy.

E = hf = hc/

Red! Highest wavelength is lowest energy.

Hotter stove emits higher-energy photons

(shorter wavelength = orange)

Colored Light

Which coloured bulb‘s filament is hottest?

1) Red

2) Green

3) Blue

4) Same

Coloured bulbs are identical on the inside – the glass is tinted

to absorb all of the light, except the color you see.

max

Visible Light

Photon

A red and green laser are each rated at

2.5mW. Which one produces more

photons/second?

1) Red 2) Green 3) Same

Red light has less energy/photon so if they both have

the same total energy, red has to have more photons!

# photons Energy/second

second Energy/photon

Power

Energy/photon

Power

hf

7

Wein‗s Law

Wein Displacement Law

- It tells us as we heat an object up, its

color changes from red to orange to

white hot.

- You can use this to calculate the

temperature of stars.

The surface temperature of the Sun is

5778 K, this temperature

corresponds to a peak emission =

502 nm = about 5000 Å.

T

bmax

Wien‘s Displacement Law

(nice to know)

To calculate the peak wavelength

produced at any particular temperature,

use Wien‘s Displacement Law:

T · peak = 0.2898*10-2 m·K

temperature in Kelvin!

The Wave – Particle Duality

OR

Light Waves

Until about 1900, the classical wave theory of light described

most observed phenomenon.

Light waves:

Characterized by:

Amplitude (A)

Frequency (n)

Wavelength ()

Energy of wave is a A2

8

Waves or Particles ?

Ball, Car, cow, or point like objects called particles.

They can be located at a location at a given time.

They can be at rest, moving or accelerating.

Falling Ball

Ground level

Physical Objects:

Waves or Particles ?

Ripples, surf, ocean waves, sound waves, radio waves.

Need to see crests and troughs to define them.

Waves are oscillations in space and time.

Direction of travel, velocity

Up-down

oscillations

Wavelength ,frequency, velocity and amplitude defines waves

Common types of waves:

Particles and Waves: Basic difference in behaviour

When particles collide they cannot pass through each other !

They can bounce or they can shatter

Waves and Particles Basic difference:

Waves can pass through each other !

As they pass through each other they can enhance or cancel

each other

Later they regain their original form !

9

And then there was a

problem…

In the early 20th century, several effects were observed

which could not be understood using the wave theory of

light.

Two of the more influential observations were:

1) The Photo-Electric Effect

2) The Compton Effect


Electrons are attracted to the (positively charged) nucleus by the

electrical force

In metals, the outermost electrons are not tightly bound, and can

be easily ―liberated‖ from the shackles of its atom.

It just takes sufficient energy…

Classically, we increase the energy

of an EM wave by increasing the

intensity (e.g. brightness)

Energy a A2

But this doesn‘t work ??

PhotoElectric Effect

An alternate view is that light is acting like a particle

The light particle must have sufficient energy to ―free‖ the

electron from the atom.

Increasing the Intensity is simply increasing the number

of light particles, but its NOT increasing the energy of each

one!

Increasing the Intensity does diddly-squat!

However, if the energy of these ―light particle‖ is related to their

frequency, this would explain why higher frequency light can

knock the electrons out of their atoms, but low frequency light

cannot…

Nobel Trivia

For which work did Einstein receive the Nobel Prize?

1) Special Relativity E = mc2

2) General Relativity Gravity bends Light

3) Photoelectric Effect Photons

4) Einstein didn‘t receive a Nobel prize.

10


Light shining on a metal can ―knock‖

electrons out of atoms.

Light must provide energy to overcome

Coulomb attraction of electron to nucleus

The Apparatus

When the emission of photoelectrons from the cathode occurs, they travel across the vacuum tube toward the anode, due to the applied potential. Even when the variable potential is dropped to zero, the current does not drop to zero, because the kinetic energy of the electrons is still adequate enough to allow some to cross the gas (thus creating a current).

If we make the variable source of electrical potential negative then this has the effect of reducing the electron flow. If the anode is made more negative, relative to the cathode, a potential difference, the cutoff potential, V0, is reached when the electrons are all turned back.

The cutoff potential corresponds to the maximum kinetic energy of the photoelectrons. They do not have the KE to make it across the gap.

Classical physics prediction

Electrons can be emitted regardless of the incident frequency, though it

will take longer time for smaller incident wave amplitude.

There should be a time delay between the wave illumination and the

emission of electrons.

The higher the wave intensity, the higher electron energy, and thus the

higher the stopping voltage.

1

f

Modern physics explanation

The electromagnetic wave consists of many lumped energy particles

called photons.

The energy of each individual photon is given by the Joule

hfE

040_PhotoelectEff.MOV

11


If N is the total number of photons incident

during time interval T, then the total incident

optical energy in Joules is:

The incident energy per second (power) is given

by:

n=N/T is the number of incident photons per

second.

E Nhf

NP hf

T Watt = J/Sec.


Interaction (absorption / emission) between the

electromagnetic wave and matter occurs through

annihilation/creation of a quantized energy (photon).

In the photoelectric effect, each single absorbed photon

gives its total energy (hf) to one single electron.

This energy is used by the electron to:

Overcome the attraction force of the material.

Gain kinetic energy when freed from the material.

Modern physics explanation Work function (): It is the minimum required energy

required by an electron to be free from the attraction force

of the metal ions.

Some of the electrons may need more energy than the

work function to be freed.

Total Energy

Zero

-ve

+ve

The most

energetic

electrons in the

material


Total Energy

Zero

-ve

+ve

The most

energetic

electrons in the

material

hf

hf

12


Total Energy

Zero

-ve

+ve

The most energetic electron

outside the material

2

maxmv2

1hf

hf


The electrons that need only the work function to

be freed, will have the greatest kinetic energy

outside the metal.

The electrons requiring higher energy to be

freed, will have lower kinetic energy.

2

max

1

2hf mv


Thus, there is a minimum required photon

energy (hfo) to overcome the work function of the

material (note f0 is called the cutoff frequency).

If the incident photon energy is less than the

work function, the electron will not be freed from

the surface, and no photoelectric effect will be

observed.

ohf

=No photoelectric

current

If hf<

If f< fo


The most energetic electrons are stopped by the reverse

biased stopping potential Vo.

o

2

max eVmv2

1

maxK hf

13


The stopping potential doesn’t depend on the incident

light intensity.

The stopping potential depends on the incident

frequency.

oo ffheV

oo hfeVhf

2

maxmv2

1hf

o o

hV f f

e

Slope = h/e

Photoelectric Equation

Since the cutoff potential is related to the maximum

kinetic energy with which the photoelectrons are

emitted: for a photoelectron of charge e and kinetic

energy Ek, and retarding potential V0. Then we have

(loss is KE = gain in PE) : Ek=eV0.

Ephoton(hf)=Φ+Ek (Φ, the work function, is energy

with which the electron is bound to the surface, Ek is

the kinetic energy of the ejected photoelectron)

Ek=hf-Φ : This tells us that if f is small such that

hf=Φ, no electrons will be ejected.

Threshold Frequency

Photoelectrons are emitted from the

photoelectric surface when the incident light

is above a certain frequency f0, called the

threshold frequency. Above the threshold

frequency, the more intense the light, the

greater the current of photoelectrons

Threshold frequency The intensity (brightness) of the light

has no effect on the threshold

frequency. No matter how intense the

incident light, if it is below the threshold

frequency, not a single photoelectron is

emitted.

14

Photoelectric Effect Summary

Each metal has ―Work Function‖ (Φ) which is the minimum energy needed to free electron from atom.

Light comes in packets called Photons

E = h f h=6.626 X 10-34 Joule sec

Maximum kinetic energy of released electrons

K.E. = hf – Φ

Photoelectrons are emitted from the photoelectric surface when the incident light is above a certain frequency f0, called the threshold frequency.

Vary wavelength, fixed amplitude

electrons

emitted ?

What if we try this ?

Photoelectric Effect (Summary)

No electrons were emitted until the frequency of the light exceeded

a critical frequency, at which point electrons were emitted from

the surface! (Recall: small large n)

No

Yes, with

low KE

Yes, with

high KE

Increase energy by

increasing amplitude

“Classical” Method

electrons

emitted ?

No

No

No

No

Another

symbol for

frequency

Photo-Electric Effect (Summary)

―Light particle‖

Before Collision After Collision

In this ―quantum-mechanical‖ picture, the energy of the light particle

(photon) must overcome the binding energy (work function, Φ) of the

electron to the nucleus.

If the energy of the photon does exceed the binding energy, the

electron is emitted with a KE = Ephoton – Ebinding.

The energy of the photon is given by E=hn, where the constant h =

6.6x10-34 [J s] is Planck‘s constant.

SummaryIf light is under your control: You can set the frequency (wavelength, colour)

and intensity. Your apparatus can count any ejected electrons. You create a

higher potential relative to the metal plate, then the ejected electrons will be

pulled into the collector and forced into the ammeter circuit. If you are

interested in the energy of the ejected electrons, you would make the

potential of the collector for and more negative with respect to the surface

and eventually you will reach a voltage level where the ejected electrons

can no longer reach the collector. This potential is called the Stopping

potential, Vo.

The maximum kinetic energy of the ejected electrons will then be:

0electronKE qV

By the definition of the eV, the Stopping Potential expressed in volts will

have the same numerical value as the electron energy expressed in eV.

That is a Stopping Potential of 2.7 V implies a maximum electron energy of

2.7 eV

15

SummaryHow does this explain the photoelectric effect? For our metal with 2.7 eV

work function, then a single photon would need an energy of 2.7 eV to eject

an electron. If you used red light (650 nm), then the photons in the beam

would have energy

34 8

19

9

6.63 10 3 103.06 10 1.91

650 10photon

hcE hf eV

These photons will be absorbed, but they do not have enough energy to

eject electrons.

1eV=1.60x10-19JCurve for material 2

Curve for material 1

Slope= Planck‘s constant, h

fo (material 2)

fo (material 1)

Φ (material 1)

Φ (material 2)

Frequency (Hz)

Energy (eV)

Often the photoelectric equation is illustrated on a graph of KE vs frequency. On this graph, the

slope ALWAYS equals Planck's constant, 6.63 x 10-34 J sec. It NEVER changes. All lines on this

type of graph will be parallel, only differing in their y-axis intercept (-f) and their x-axis intercept

(the threshold frequency).

The threshold frequency is the lowest frequency, or longest wavelength, that permits

photoelectrons to be ejected from the surface. At this frequency the photoelectrons have no

extra KE (KE = 0) resulting in

0 = hf – Φ

hf =Φ

Ephoton =Φ

Note that red light has such a low frequency (energy) that it will never eject photoelectrons -

that is, the energy of a red photon is less than the work function of the metal.

If suitable light is allowed to fall on plate 'P', it will give out photo electrons as shown

in the figure. The photo electrons are attracted by the collector 'C' connected to the

+ve terminal of a battery. The glass tube is evacuated. When the collector 'C' is kept

at +ve potential, the photo electrons are attracted by it and a current flows in the

circuit which is indicated by the galvanometer.

Threshold frequency is defined as the minimum frequency of incident light which can

cause photo electric emission i.e. this frequency is just able to eject electrons with

out giving them additional energy. It is denoted by f0.

The Minimum amount of energy which is necessary to start photo electric emission

is called Work Function. If the amount of energy of incident radiation is less than the

work function of metal, no photo electrons are emitted.

It is denoted by Φ. Work function of a material is given by Φ=hf0.

It is a property of material. Different materials have different values of work function.

The negative potential of the plate 'C' at which the photo electric current becomes

zero is called Stopping Potential or cut-off potential. Stopping potential is that value

of retarding potential difference between two plates which is just sufficient to halt the

most energetic photo electrons emitted.

It is denoted by "Vo"

Review

What happens to the rate electrons are emitted

when increase the brightness?

more photons/sec so more electrons are emitted.

Rate goes up.

What happens to max kinetic energy when

increase brightness?

no change: each photon carries the same energy as

long as we don‘t change the color of the light

Question

16

Photoelectric Effect: Light Frequency

What happens to rate electrons are emitted

when increase the frequency of the light?

as long the number of photons/sec doesn‘t change,

the rate won‘t change.

What happens to max kinetic energy when

increase the frequency of the light?

each photon carries more energy, so each electron

receives more energy.

Question

Which drawing of the atom is more correct?

This is a drawing of an electron‘s p-orbital probability

distribution. At which location is the electron most likely to

exist?

32

1

QuestionYou observe that for a certain metal surface illuminated with

decreasing wavelengths of light, electrons are first ejected

when the light has a wavelength of 550 nm.

a) Determine the work function for the material.

b) Determine the Threshold Potential when light of

wavelength 400 nm is incident on the surface




a) Determine the work function for the material.

hc

34 8

9

19

6.63 10 3 10

550 10

3.62 10

2.25

mJ s

s

m

J

eV

It is quicker is we

use hc=1240eV nm

1240

550

2.25

hc

eV nm

nm

eV

17




b) Determine the Threshold Potential when light of

wavelength 400 nm is incident on the surface

12402.25

400

0.85

photons

hc

eV nme

K

Vnm

e

E E

V

QuestionSuppose you find that the electric potential needed to shut

down a photoelectric current is 3 volts. What is the maximum

kinetic energy of the photoelectrons.

The given potential is the stopping potential V0

19

19

1.6 10 3

4.8 10

3

o

C V

eV

q

J

U V

This is the maximum kinetic energy of the photoelectron

QuestionIf the work function of the material is known to be 2eV, what is

the cut-off frequency of the photons for this material.

The cutt-off frequency is the frequency above which electrons

can be freed from the material. That is, the frequency of

radiation whose energy is equal to the work function

15

14

2

4.14 10

4.83 10

c

cE hf

fh

eV

eV s

Hz

19

34

14

2 1.6 10

6.63 10

4.83 10

c

c

E hf

fh

J

J s

Hz

or

So is light a

wave or a

particle ?

On macroscopic scales, we can treat a large number of photons

as a wave.

When dealing with subatomic phenomenon, we are often dealing

with a single photon, or a few. In this case, you cannot use

the wave description of light. It doesn‘t work !

18

Is Light a Wave or a Particle? Wave

Electric and Magnetic fields act like waves

Superposition, Interference and Diffraction

Particle

Photons

Collision with electrons in photo-electric effect

Both Particle and Wave !

Are Electrons Particles or Waves?

Particles, definitely particles.

You can ―see them‖.

You can ―bounce‖ things off them.

You can put them on an electroscope.

How would know if electron was a wave?

Look for interference!

Young‘s Double Slit w/ electron

Screen a distance

L from slits

Source of

monoenergetic

electrons

d

2 slits-

separated

by d

L

Electrons are Waves?

Electrons produce interference pattern just

like light waves.

Need electrons to go through both slits.

What if we send 1 electron at a time?

Does a single electron go through both slits?

Hitachi Double Slit.wmv

19

Electrons are Particles

If we shine a bright light, we can ‗see‘

which hole the electron goes through.

(1) Both Slits (2) Only 1 Slit

But now the interference is gone!

Electrons are Particles and Waves!

Depending on the experiment electron can

behave like

wave (interference)

particle (localized mass and charge)

If we don‘t look, electron goes through both

slits. If we do look it chooses 1.

Electrons are Particles and Waves!

Depending on the experiment electron can

behave like

wave (interference)

particle (localized mass and charge)

If we don‘t look, electron goes through both

slits. If we do look it chooses 1.

I‘m not kidding it‘s true!

Schroedinger‘s Cat

Place cat in box with some poison. If we

don‘t look at the cat it will be both dead

and alive!

Poison

Here

Kitty, Kitty!

20

Momentum of a Photon

Compton found that the

conservation of

momentum did hold for

X-ray scattering collisions

at an angle (Compton

effect)

2

p mv

Ep v

c

E

c

hf

c

hf

f

h

The Compton Effect

In 1924, A. H. Compton performed an experiment

where X-rays impinged on matter, and he measured

the scattered radiation.

Problem: According to the wave picture of light, the incident X-ray gives up

energy to the electron, and emerges with a lower energy (ie., the amplitude

is lower), but must have 21.

M

A

T

T

E

R

Incident X-ray

wavelength

12 > 1

Scattered X-ray

wavelength

2

e

Electron comes flying out

Louis de Broglie

Quantum Picture to the RescueIf we treat the X-ray as a particle with zero mass, and momentum p = E / c,

everything works !

Incident X-ray

p1 = h / 1

e

Electron

initially at

rest

2 > 1

Scattered X-ray

p2 = h / 2

e

pe

e

Compton found that if the photon was treated like a particle with

mometum p=E/c, he could fully account for the energy & momentum

(direction also) of the scattered electron and photon! Just as if 2 billiard

balls colliding!

Compton Scattering (nice to know)

Compton assumed the

photons acted like other

particles in collisions

Energy and momentum were

conserved

The shift in wavelength is

(1 cos )o

e

h

m c D

Compton wavelength

21

DeBroglie‘s Relation

The smaller the wavelength the larger the photon‘s momentum!

The energy of a photon is simply related to the momentum by:

E = pc (or, p = E / c )

The wavelength is related to the momentum by: = h/p

The photon has momentum, and its momentum is given by simply p = h /

.

p = h /

Quantum Summary

Particles act as waves and waves act as

particles

Physics is NOT deterministic

Observations affect the experiment

Four QuantumParadoxes

Paradox 1 (non-locality):Einstein’s Bubble

Situation: A photon is emitted from an isotropic source.

22



Its spherical wave function Y expands like an inflating

bubble.


Question (Albert Einstein):

If a photon is detected at Detector A, how does the

photon’s wave function Y at the location of Detectors

B & C know that it should vanish?


Its spherical wave function Y expands like an inflating

bubble.

It is as if one throws a beer bottle into

Lake Ontario. It disappears, and its

quantum ripples spread all over the

Atlantic.

Then in Copenhagen, the beer bottle

suddenly jumps onto the dock, and the

ripples disappear everywhere else.

That’s what quantum mechanics says

happens to electrons and photons when

they move from place to place.


Experiment: A cat is placed in a sealed box containing a device that has a 50%

chance of killing the cat.

Question 1: What is the wave function of the cat just before the box is opened?

When does the wave function collapse?

Paradox 2 (Y collapse):Schrödinger’s Cat

1 1

2 2( dead + alive ?)Y

Question 2: If we observe Schrödinger, what is his wave function during the

experiment? When does it collapse?The question is, when

and how does the

wave function

collapse.

•What event collapses

it?

•How does the

collapse spread to

remote locations?

23

Paradox 3 (wave vs. particle):Wheeler’s Delayed Choice

A source emits one photon.

Its wave function passes

through slits 1 and 2, making

interference beyond the slits.

The observer can choose to either:

(a) measure the interference pattern at

plane s1, requiring that the photon travels

through both slits.

or

(b) measure at plane s2 which slit image it

appears in, indicating that

it has passed only through slit 2.

The observer waits until

after the photon has

passed the slits to decide

which measurement to

do.

*

**

Thus, the photon does not

decide if it is a particle or a

wave until after it passes

the slits, even though a particle

must pass through only one slit and a wave must pass

through both slits.

Apparently the measurement choice determines

whether the photon is a particle or a wave retroactively!

Paradox 3 (wave vs. particle):Wheeler’s Delayed Choice

Paradox 4 (non-locality):EPR ExperimentsMalus and Furry

An EPR (einstein Poldalsky Rosen)

Experiment measures the correlated

polarizations of a pair

of entangled photons, obeying

Malus’ Law [P(rel) = Cos2rel]


An EPR Experiment measures the

correlated polarizations of a pair



The measurement gives the same result

as if both filters were in the same arm.

24


An EPR Experiment measures the

correlated polarizations of a pair



The measurement gives the same result

as if both filters were in the same arm.

Furry proposed to place both photons in

the same random polarization state.

This gives a different and weaker

correlation.


Apparently, the measurement on the right side of the apparatus causes (in some sense of the word cause) the photon on the left side to be in the same quantum mechanical state, and this does not happen until well after they have left the source.

This EPR “influence across space time” works even if the measurements are light years apart.

Could that be used for FTL signaling? Sorry, SF fans, the answer is No!

FourInterpretations

of Quantum Mechanics

Scientists who subscribe to the Collapse interpretation make a

choice. They believe that when you accept the electron‘s wave

nature, you must give up on the electron‘s particle nature.

In this interpretation, the electron leaves the source as a particle that

is governed by one set of laws, but then ―expands‖ into a spread-out

wave as it passes through the slits. The electron is now governed by

new laws. However, before we can measure this wavy, spread-out

quantum electron it ―collapses‖ back into a particle and arrives at

only one of the many possible places on the screen.

The consequence of choosing the Collapse interpretation line of

thinking is that you must accept that an electron physically changes

from particle to wave and back again. These two realities, including

the laws that describe them, alternate uncontrollably

The Collapse Interpretation

25

The Pilot Wave interpretation avoids this unexplained collapse altogether. Scientists

who subscribe to this interpretation choose to believe that the electron always exists

as a classical particle and is only ever governed by one kind of physical law, for both

the familiar classical as well as quantum phenomena. However, to account for the

electron‘s wave behaviour this description requires the introduction of an invisible

guiding wave.

In this interpretation, wave-particle duality is explained by assuming that electrons

are real particles all of the time, and are guided by an invisible wave. The electron‘s

wave nature is attributed to this abstract wave, called a Pilot Wave, which tells the

electron how to move. To obtain the interference pattern in the double-slit experiment,

this wave must be everywhere and know about everything in the universe, including

what conditions will exist in the future. For example, it knows if one or two slits are

open, or if a detector is hiding behind the slits.

The Pilot Wave interpretation embodies all of the quantum behaviour, including all the

interactions between classical objects like the electron, the two-slit barrier, and the

measuring devices. In contrast to the Collapse interpretation where the collapsing

electron wave was considered real, in the Pilot Wave interpretation the wave is an

abstract mathematical tool. This interpretation has a consequence. The Pilot Wave

interpretation, which was invented to deal with an electron as a real physical object,

suffers the fate of being permanently beyond detection

The Pilot Wave InterpretationThe Many-Worlds Interpretation

Supporters of the Many Worlds interpretation, similar to the Pilot Wave idea,

choose to accept that electrons are classical particles. Then they go even further,

demanding that all elements of the theory must correspond to real objects—unlike

the collapsing electron or the Pilot Wave. Supporters insist on only measurable,

physical objects within the world. This world is constantly splitting into many

copies of itself.

When electrons demonstrate wave behaviour they exist in a superposition of many

different states. To Many Worlds supporters, who maintain the idea of an electron

as a classical particle, a parallel universe must exist for each of the electron‘s

possible states. When the electron reaches the slits, it has to choose which slit to

go through. At that moment, the entire universe splits into two. In one universe, the

electron passes through the left slit as a real particle. In the other universe it

passes through the right slit as a real particle. The consequence of accepting the

Many Worlds interpretation, with many quantum particles constantly facing similar

choices, is the requirement that our universe must be constantly splitting into an

almost infinite number of parallel universes, each having its own copy of every one

of us

The Copenhagen InterpretationAdvocates of the Copenhagen interpretation choose to limit their discussion directly to the

experiment and to the measurements on physical objects. Questions are restricted to what

can be seen and to what we actually do. They try to think about experiments in a very

honest way, without invoking extra theoretical ideas like the on-off switching of the Collapse

idea, or the guidance supplied by the invisible Pilot Wave, or the proposed splitting into

Many Worlds.

It is tempting to come up with mental pictures about what is happening that go beyond the

results of an experiment, and to try to interpret what is happening by means of those hidden

theoretical mechanisms. The previous interpretations attributed the mysterious wave–

particle duality to imaginative mathematics. In the Copenhagen interpretation much of this

mystery is attributed to what happens when an experimenter enters the lab and interacts

with the quantum mechanical system. With the Copenhagen perspective, the mathematics

only deals with the experimenter‘s information about measurement interactions with the

quantum mechanical system.

The consequence of accepting the Copenhagen interpretation is a fundamental restriction

on how much you can read into experimental results. We know that electrons are particles

when they are fired from the source, and we know that they are particles when they hit the

screen. What happens to electrons in the middle, what they are ―doing‖, or what they really

―are‖ is not possible to know. In the Copenhagen interpretation these are unfounded

questions. We may call an electron a wave or a particle, but ultimately those names are no

more than suitable models.

Let’s Compare

Documents

Everything comes unglued Blackbody Radiation Photoelectric …mjburns.net/SPH Blackbody ppt.pdf · 2 Atomic scale effects Small Dx means large Dv since 4 h v mx D D Example: an electron