Introduction, measurement of uncertainty, Heisenberg microscope, challenges to Heisenberg principle, examples of Heisenberg uncertainty principle, applications of uncertainty principle

1. Heisenberg Uncertainty
Principle

2. Werner Karl Heisenberg
(1901-1976)
◦ The germen physicist
◦ Nobel price in physics in 1932 for his work in
nuclear physics and quantum theory
◦ The paper of uncertainty relation is his most
important contribution to physics
◦ He was very talented and intelligent student .he
impressed his teachers with his ambition and
brilliance
◦ He never produce other grades than straight A’s
◦ Once professor Wien of the university of
Munich gave him an F in experimental physics
,because he handle the laboratory instruments
clumsily

3. introduction
◦ Uncertainty principle is stated by Werner
Karl Heisenberg in 1927
◦ This principle gives a very vital relation of
momentum and position of an object
◦ This principle sated that:
◦ The position and
momentum of a particle
cannot be simultaneously
with arbitrary high
precision”

4. ◦ Historically, the uncertainty principle has been confused with a related
effect in physics, called the observer effect, which notes that:
◦ “ Measurements of certain systems cannot be made without
affecting the system, that is, without changing something in a
system. “
◦ Heisenberg utilized such an observer effect at the quantum level as a
physical "explanation" of quantum uncertainty
◦ it has since become clearer, however, that the uncertainty principle is
inherent in the properties of all wave-like systems and that it arises in
quantum mechanics simply due to the matter wave nature of all
quantum objects

5. Heisenberg realised that:
◦ In the world of vary small particles ,one can not measure any
property of particles without interacting with it in some way
◦ This introduce unavoidable uncertainty in result
◦ One can never measure all the properties exactly
Complementary variable :
◦ Energy and time
◦ Position and momentum
◦ Spin on different axis
◦ Entanglement and coherence

6. Measuring of position and
momentum of an electron
◦ Shine light on electron and detect reflected light using a microscope
◦ Minimum uncertainty in position is given by the wave length of light
◦ So to determine the position accurately, it is necessary to use light with short
wavelength

7. ◦ By plank’s law E=hc/
◦ A photon with a short wavelength has a large energy
◦ Thus it would impart a larger kick to electron
◦ But to determine accurate momentum electron must only be
given a small kick
◦ Use light with short wavelength :
Accurate measurement of position but not momentum
◦ Use light with long wavelength:
Accurate measurement of momentum but not position

8. Heisenberg's microscope:
◦ Heisenberg's gamma-ray microscope
for locating an electron .
◦ The incoming gamma ray is
scattered by the electron up into the
microscope's aperture angle θ.
◦ The scattered gamma-ray is shown in
red. Classical optics shows that the
electron position can be resolved only
up to an uncertainty Δx that depends
on θ and the wavelength λ of the
incoming light.

9. Experiment
◦ He imagines an experimenter trying to measure the position and momentum of an
electron by shooting a photon at it
Problem 1 –
◦ if the photon has a short wavelength, and therefore, a large momentum, the
position can be measured accurately.
◦ But the photon scatters in a random direction, transferring a large and uncertain
amount of momentum to the electron.
◦ If the photon has a long wavelength and low momentum, the collision does not
disturb the electron's momentum very much, but the scattering will reveal its
position only vaguely.
Problem 2 –
◦ If a large aperture is used for the microscope, the electron's location can be well
resolved but by the principle of conservation of momentum, the transverse
momentum of the incoming photon affects the electron's beamline momentum
and hence, the new momentum of the electron resolves poorly. If a small aperture
is used, the accuracy of both resolutions is the other way around.

10. Einstein challenge
◦ Einstein argued that:
◦ "Heisenberg's uncertainty equation implied that the
uncertainty in time was related to the uncertainty in
energy, the product of the two being related to Planck's
constant."
◦ he said, an ideal box, lined with mirrors so that it can
contain light indefinitely. The box could be weighed before a
clockwork mechanism opened an ideal shutter at a chosen
instant to allow one single photon to escape. "We now know,
explained Einstein, precisely the time at which the photon
left the box."
◦ "Now, weigh the box again. The change of mass tells the
energy of the emitted light. In this manner, said Einstein, one
could measure the energy emitted and the time it was
released with any desired precision, in contradiction to the
uncertainty principle."

11. Boher's answer
◦ "since the box must move vertically with a change in its weight, there will
be uncertainty in its vertical velocity and therefore an uncertainty in its
height above the table. ... Furthermore, the uncertainty about the
elevation above the earth's surface will result in an uncertainty in the
rate of the clock,
◦ Through this chain of uncertainties, Bohr showed that Einstein's light
box experiment could not simultaneously measure exactly both the
energy of the photon and the time of its escape."

12. Example of baseball
◦ A boy throw a 0.1 kg baseball at 40 m/s
◦ So momentum is = mv=(0.1)(40)
=4 kg m/s
Suppose momentum is measured with accuracy of 1
percent
i.E
p= 4/100
p= 4.10-2 kg m/s
The uncertainty in position is :
 h = 1.3 x 10-33m
4

13. Example for electron
◦ Electron has mass = 9.11x10-31 kg
◦ So momentum = mv = 9.11x10-31 x 6x106
◦ = 3.6 x10-29 m/s
◦ Uncertainty in position is
 h = 1.4 x 10-4 m
4

14. Heisenbeg uncertanity
principle involving energy and
time
◦ The more accurate we know the energy of a body ,less accurately we
know how long it possessed that energy
◦ The energy can be known with perfect precision (=0) only if the
measurement is made over an infinite period of time (t=)

15. Applications:
◦ Applications dependent on the uncertainty principle for their
operation include extremely low-noise technology such as that
required in gravitational wave interferometers.
◦ Limitations
It is impossible to know path position and momentum exactly