Workshop Tutorials for Physics
QR4: The Uncertainty Principle
A. Qualitative Questions:
1. The idea of uncertainty is used in many contexts; social, economic and scientific. People often talk
about uncertain times, and when you perform a measurement you should always estimate the uncertainty
(sometimes called the error). In physics the Heisenberg Uncertainty relation has a very specific meaning.
a. Write down the Heisenberg uncertainty relation for position and momentum.
b. Explain its physical significance.
c. Does the Heisenberg uncertainty principle need to be considered when calculating the uncertainties in
a typical first year physics experiment? Why or why not?
d. Discuss the following statement: the uncertainty principle places a limit on the accuracy with which a
measurement can be made. Do you agree or disagree, and why?
2. Brent and Rebecca are discussing quantum mechanics over dinner one evening. Rebecca says that the
thing she really likes about quantum mechanics is that it brings the romance and passion back to physics.
After all, a deterministic or clockwork universe in which everything is predictable is not as exciting as
one in which the uncertainty principle applies. Brent strongly disagrees with her, and explains that “The
uncertainty principle is merely a result of the fact that when you make a measurement of a particle’s
position or momentum, you interact with it, thus changing its state.”
“Ah,” says Rebecca, “but Heisenberg’s original statement of the uncertainty principle translates more
accurately as the indeterminacy principle. You should read his work in the original German. It doesn’t
matter how little the measurement effects the particle, the quantum world is still fundamentally
unpredictable.”
Who do you agree with? Discuss your answer.
B. Activity Questions:
1. Measuring momentum and position I
When the marble is released from the top of the slide it rolls down, gathering momentum as it falls. As it
leaves the end of the slide it has horizontal velocity v. It is accelerated vertically due to gravity, and hits
the floor at a time t  ( 2gh ) after it leaves the end of the slide, where h is the height of the end of the
slide above floor level.
Use the apparatus to find the horizontal momentum of the marble during its flight.
How has your measurement affected the position and momentum of the marble?
Do you know both position and momentum simultaneously? If so, does this contradict the uncertainty
principle?
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2. Measuring momentum and position II
Use the apparatus to measure the time at which the marble passes a given point.
What effect has your measurement had on the marble’s position and momentum?
Do you need to take the uncertainty principle into account in this experiment?
How would it be different if you were measuring the momentum of an electron using this sort of
apparatus?
The Workshop Tutorial Project –QR4: The Uncertainty Principle
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C. Quantitative Questions:
1. Brent is measuring the velocity of a cricket ball as part of a laboratory exercise on uncertainties. In the
meantime his lab partner, Rebecca, has been messing with the structure of space-time and much to her
surprise opened a wormhole into another universe. Brent and the cricket ball are both sucked into the
wormhole and disappear into the other universe where Planck’s constant has a value of 0.6 J.s.
Brent fails to notice this and continues with the experiment. He measures the velocity of the 0.50 kg ball
to be 20.0  1.0 m.s-1.
a. Explain qualitatively how the limits on the uncertainty in the ball’s velocity and position will be
different in the two universes.
b. What would be the uncertainty in the position of the moving cricket ball in the second universe?
Imagine playing cricket in this universe.
c. What would it be like trying to catch a ball?
d. Calculate the de Broglie wavelength for this ball. What sort of effects might you observe?
2. The x, y and z components of the velocity of an electron are measured to be :
vx = (4.00  0.18)  105 m.s-1 ,
vy = (0.34  0.12)  105 m.s-1 and
vz = (1.41  0.08)  105 m.s-1
a. Find the uncertainties in the x, y, z components of the momentum, p.
b. The measurements described above are consistent with the electron being localised in some volume.
What is the smallest volume possible?
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The Workshop Tutorial Project –QR4: The Uncertainty Principle