Quantum Puzzles and their Applications in Future Information Technologies A Public Lecture by Prof....
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Transcript of Quantum Puzzles and their Applications in Future Information Technologies A Public Lecture by Prof....
Quantum Puzzles and their Applications in Future Information Technologies
A Public Lecture by Prof. Anton Zeilinger
The University of Vienna and The Institute of Quantum Optics and Quantum Information, Austrian Academy of Sciences
7pm Monday, 10th November 2008
Lecture Theatre Boole 4, University College Cork Copyright: Jacqueline Godany
Quantum Fair!Meet the experts in quantum physics from 5.30pm outside Boole 4,
UCC. If you ever had any questions about the weirdness of quantum physics, the experts will be there to answer them and guide you through
the amazing quantum world. Refreshments will be provided.
Work and Conservative Forces (recall: Lecture 12)
Definition: Conservative Force
A force is conservative when it does no net work on moving an object around a closed path (i.e. starting and finishing at same point)
1D:
This is just some function that we need to find to determine the work.
Conservative Systems
In a conservative system, a function G(r) exists, whereas in a non-conservative system it does not exist (and the evaluation of the work integral is more complicated).
Definition: Potential Energy
For a uniform gravitational field (y-direction only):
U(r) depends on objects position in the gravitational field.
Gravity exerts a force mg on the basketball. Work is done by the gravitational force as the ball falls from a height h0 to a height hf.
mgsmghmghW f 0
path travelled doesn’t matter
Conservative Systems
Since:
dt
vda Since:
vdt
sdSince:
Work done in moving a body from A to B in a conservative force is the change
in kinetic energy of the body.
Conservative Systems
For any conservative force field:
The sum of the two terms remains unchanged throughout the force field
where: : total energy, scalar
: kinetic energy KE, scalar
: potential energy PE, scalar
The total mechanical energy (E = KE + PE) of an object remains constant as the object moves, provided that the net work done by external non-conservative
forces is zero.
Principle of Conservation of
Mechanical Energy
Recall nose basher pendulum!
Example
Motorcyclist leaps across cliff. Ignoring air resistance, find speed at which the cycle strikes the ground on the other side. Use conservation of KE + PE expression.
fffinalinitial mghmvmghmvEE 20
20 2
1
2
1
1221
020
ms46m35m70m81.92ms38
2
sv
hhgvv
f
ff
Conservation Laws
Two universal conservation laws:
1. Conservation of angular momentum
(assuming that there are no external torques on the system)
2. Conservation of mechanical energy
(assuming no friction or other non-conservative forces present)
Differentiate the energy (in 1D) with respect to time:
in a conservative systems
since v = dx/dt and a = dv/dt
energy potential theis ),(2
1 2 U(x)xUmvE
constantsin mrvvmrL
The conservation of energy can be used to solve problems in mechanics where Newton's
Laws cannot. The system must be conservative, i.e. no non-conservative forces present.
Conservation of Energy
Example of conservation of energy: free fall
no initial velocity finite initial velocity
v
N
FR
W
Friction – presence of non-conservative force
: kinetic friction coefficient
vo
v
W = mg
N
FR
mgcos
y
x
y component: FR contains no y component:
Note: acceleration of skateboarder purely in x direction
x component:
since FR = RN
since asvv 220
2
Friction – Work and Power
Loss of energy (energy is not conserved, since friction is present):
0
In the absence of friction: and energy conserved.
Define the work done per time interval as
E = KE + PE
using
since y = s sin
This is the power generated:
The average power, P, is the average rate at which work, W, is done, and it is obtained by dividing W by the time, t, required to perform the work. SI Unit: J/s = Watt (W)
Momentum Conservation (p123 M&O’S, p201 C&J)
A B
From Newton’s 3rd law
Consider two objects, A and B moving in opposite directions. Mass of A is mA, mass of B is mB
Velocity of A is vA, velocity of B is vB
acceleration
Rate of change of linear momentum, pA and pB.
Conservation of Momentum
The total linear momentum of an isolated system remains constant (i.e. is conserved). An isolated system is one for which the vector sum of the average external forces acting on the system is zero.
momentum before interaction = momentum after interaction
If there is no external force, than the momenta before and after have to be the same
after
p1
p2
p3
p4
p5
Example: Consider an explosion
before
stationaryobject since 0 vmp
Conservation of Momentum
Example: Consider a two body explosion, e.g. a gun being fired
M + m
Before (b)
m
M
v
VAfter (a)
There are no external forces:
The magnitude of V depends on the energy put into the system:
Summary
Principle of Conservation of
Mechanical Energy
Definition: Conservative Force
A force is conservative when it does no net work on moving an object around a closed path (i.e. starting and finishing at same point)
In words: the total mechanical energy (E = KE + PE) of an object remains constant as the object moves, provided that the net work done by external non-
conservative forces is zero.
Power generated:
The average power, P, is the average rate at which work, W, is done, and it is obtained by dividing W by the time, t, required to perform the work. SI Unit: J/s = Watt (W)
Conservation of momentum: momentum before interaction = momentum after interaction