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Day 2.2
Measurement-Disturbance and HUP
Watch the Challenge of Quantum Reality from 16:48-19:16 http://www.youtube.com/watch?v=wihrAjFXg3o
1) If we do measurements to determine which slit an electron went through, we find that
a) half of the electron goes through each slit.
b) the whole electron goes through both slits.
c) the whole electron goes through one slit or the other. d) the interference pattern disappears
Whenever you try to detect an electron – whether at the slits or at the screen – you always find a whole
electron or nothing. In addition, if you measure which slit an electron went through, the interference
pattern – which you were trying to explain – disappears.
Instructions: There are two right answers. This is not a good question for a test, but it is a good question
for stirring up discussions and it makes particular sense here because the question is looking at
measurement-disturbance. What you measure changes what your results will be.
2) The Tubingen experiment mentioned in the video was very subtle. Detectors were placed beneath each
slit. Electrons that passed near one of the two detectors generated a tiny current in that detector.
Why is the interference pattern visible at the top but not at the bottom?
At the top the detectors are far enough from the electrons that they can’t tell which slit the electron went
through. As long as the electron could have passed through either slit, there is an interference pattern as if
something went through both slits.
3) If we use light to detect an electron we find that the electron is too small an object to
a) be seen
b) reflect light
c) be unaffected
We can measure a large object and have negligible effect on it if we are careful. This is not the case with
electrons and other small objects.
4) What is measurement-disturbance? Why do we only see it with small objects?
What we choose to measure - affects what we find. This is not the kind of error that we try to minimize in
an experiment. This is a fundamental limit to what it is possible to know.
5) Quantum physics is fundamentally different from classical physics: How does the double-slit
experiment demonstrate each of the 4 key concepts?
 Wave-Particle Duality: Objects can act like waves and like particles.
Individual objects arrive at localized spots (particles) but many form interference patterns (waves).
 Measurement-Disturbance: The act of measuring changes reality.
If you measure which slit the object went through, the interference pattern disappears.
 Intrinsic Randomness: Individual results are fundamentally random
The interference pattern is predictable, but where an individual object will land is not.
 Uncertainty: There are theoretical limits to what can be known.
If we have an interference pattern we cannot know which slit the object went through.
6) Measurement-Disturbance can also be seen very clearly with diffraction.
a) Sketch what will happen if 10 photons go through a slit and 10 photons go through a really narrow slit.
These straight line trajectories are too deterministic. The randomness is suggested by the dashed lines and
somewhat random directions.
b) Making the slit more narrow means that we
A) have a better idea of where the photon was and a better idea where it will go next
B) have a better idea of where the photon was and a worse idea where it will go next
C) have a worse idea of where the photon was and a better idea where it will go next
D) have a worse idea of where the photon was and a worse idea where it will go next
The object must have passed through the slit, so we have a better idea of where it was.
There will be more diffraction, so we have a worse idea of where it will go after the slit.
c) Heisenberg showed that there is a fundamental limit to knowledge of where something is and where it
is going. He wrote this as x p > = h/2. How is this illustrated with diffraction? Veritasium:
Heisenberg’s Uncertainty Principle Explained https://www.youtube.com/watch?v=a8FTr2qMutA
The uncertainty in position x is related to the size of the slits and the uncertainty in momentum p is the
resultant uncertainty in its direction. As position is specified more narrowly, direction gets less defined.
8) How does diffraction demonstrate each of the four key concepts of quantum physics?
 Wave-Particle Duality: Objects can act like waves and like particles.
Individual objects arrive at localized spots (particles) but large numbers of them build up a diffraction
spread or single slit interference patterns (waves).
 Measurement-Disturbance: The act of measuring changes reality.
If you measure where the object is by using a narrower slit, you change where it will be found next.
 Intrinsic Randomness: Individual results are fundamentally random
The spread on the screen is predictable, but where an individual object will land is not.
 Uncertainty: There are theoretical limits to what can be known.
There is a precise mathematical limit to our knowledge of the position and momentum of an object
simultaneously as shown by the width of the slit and the diffraction spread.
9) Physicists have come up with a variety of interpretations, to explain what is happening in the two-slit
experiment. Watch the Challenge of Quantum Reality from 19:18 – 23:10
a) Write a short description of each interpretation.
Collapse – Something vague (a probability wave) goes through both slits and collapses to one spot.
Pilot Wave – The electron is a particle guided by a wave that fills all of space including both slits.
Many Worlds – The electron is a particle. At the slit the universe splits into two – one for each slit that
the electron could go through.
Copenhagen – You can only ask and answer certain questions and they are governed by the math.
Everything else has no meaning.
b) Which interpretation is being used in each of the following?
 Minute Physics: Schrodinger’s Cat https://www.youtube.com/watch?v=IOYyCHGWJq4 , Collapse,
Many World’s
 Minute Physics: What is Wave/Particle Duality? https://www.youtube.com/watch?v=Q_h4IoPJXZw,
https://www.youtube.com/watch?v=_riIY-v2Ym8 Collapse, Pilot Wave,
 PhET https://phet.colorado.edu/en/simulation/quantum-wave-interference Collapse
c) Which one makes the most sense to you? Why?
d) How is an interpretation different from a theory? They all give the same predictions, so they cannot be
proven false. A scientific theory must be able to make predictions that are falsifiable. Interpretations can
serve as a guide to thinking but some physicists think that they are a waste of time and not science..
10) Watch Minute Physics: What is the Uncertainty Principle? https://www.youtube.com/watch?v=7vcUvp3vwg A quantum object is sometimes jokingly referred to as a wavicle or a pave. What is a drawing
that is used in this video that captures wave-particle duality?
Textbook 12.6
10) Heisenberg developed his uncertainty principle by exploring measuring an electron with photons.
a) Why is it better to use a low energy photon?
It will disturb the electron less when they collide, causing less uncertainty in its momentum afterwards.
b) Why is it better to use a high energy photon?
It has a smaller wavelength and so can locate the electron with less uncertainty in its position.
Extra: Diffraction can be used to derive the Heisenberg Uncertainty Principle.
a) The uncertainty of where the photon was, i.e. x, for a slit of width w, will be +/- w/2.
b) The uncertainty of where it was going, i.e. p, is a bit more difficult. The diagram on the left shows
the path of a photon that just lands within the first maximum. The distance from the centre to the first
node is given by L/w. This is called x when we do interference but should be avoided in this
discussion because it will get confused with as uncertainty in position.
The distance from the slits to the screen is L. Label these on the diagram.
p
L/w
P = h/
L
c) The diagram on the right shows the momentum of an undisturbed photon and the momentum of the
diffracted one. The momentum of a photon is given by the de Broglie relation, so p = h/. The
uncertainty in momentum for a photon that lands between the first nodes is the short arrow up. Label
these two on the diagram.
d) The two diagrams form similar triangles because the angles are all the same. Find a formula for p.
p/(h/) = (L/w)/(L)
p = h/w
e) What is the value of x p for a photon that lands within the first maximum? h/2
This is different from Heisenberg’s result by a factor of . Not bad for high school math! We just looked
at photons that made it to the central spot – but the photon could be found further out. The mathematics to
get the proper formula is too difficult.