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The border between Uncertainty and
Undeterminability
Björgvin Hjörvarsson
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Solvay conference 1927
Copenhagen interpretationThe wave-particle duality
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Considerations…..
The quantum-mechanical description cannot simultaneously be complete and consistent. (fullständig och självkonsistent)
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The answer…..
Complementarity - instrumentation.
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To measureIn-between science and
philosophy
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Our body has advanced sensors and analysis...
• Eyes (Photons)
• Ears (Changes in pressure and orientation)
• Smell (Chemicals, gasphase)
• Taste (Chemicals, fluids)
• Skin (Temperature, pressure (touch, vibratons))
Limitations and possibilities!
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The photon detector
NERange ≈ 0.4 -0.7 μm
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Differential pressure sensor
NE
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Sensitivity and principles
Loudness (dB)
Frequency (Hz) NE
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Examples of what we want to measure
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Radiation beyond the range 0.4-0.7 μm must be
”transformed” prior to registration
• Electromagnetic radiation - Transformation in frequency
• Particles - Complete abstraction
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Transformation
Particles
Speed, momentumenergy
Mass, charge,………
1 eV - discuss
E=mc2
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Consequences Event
Equipment -Filter
Theories
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Describe the photo
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Describe...
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What is reality?
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Determine the position and energy of a particle in the
darkest part of our universe!
Thought experiment- ”gedanken experiment”
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Heisenberg (1927)
€
Δx Δpx ≥12h
It is impossible to simultaneously determine the position and the momentum with an arbitrary accuracy.
≈ 5 10-35 Js ≈ 3 10-16 eV s
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Coherence (1)
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Coherence (2)
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Coherence (3)
LASERParallel radiation with well defined energy &Phase coherency!
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Reflectivity
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Reflectivity - film on a substrate
Si
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Reflectivity - Data
MgO
Fe
100
101
102
103
104
105
106
0 0.2 0.4 0.6 0.8 1
Inte
nsity
(cou
nts)
Q (Å-1)
7 103
8 103
9 103
104
0.18 0.19 0.2 0.21 0.22 0.23 0.24
Inte
nsity
(cou
nts)
Q (Å- 1)
Pd
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Neutrons (1)
Neutrons are particles:Mass ≈1.67 10-27 kg (=1.00 u)Extension ≈10-15 m….
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Neutrons (2)
0 0.1
106
107
Inte
nsity
(a.u
.)
Q (Å-1)
Neutron reflektivitet
0 0.1 0.2 0.3 0.4 0.5104
105
106
107
Inte
nsity
(a.u
.)
Q (Å-1)
Neutron reflectivity
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Neutrons !
0 0.1
106
107
Inte
nsity
(a.u
.)
Q (Å-1)
Neutron reflektivitet
0 0.1 0.2 0.3 0.4 0.5104
105
106
107
Inte
nsity
(a.u
.)
Q (Å-1)
Neutron reflectivity
Photons and Neutrons show the SAME properties!
The neutron is extended over at least >>1000 nm !!!
Compare classical radius of ≈10-6 nm !!!
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Think BIG!
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Δv/v ≈ 0.6
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Δv/v ≈ 0.17
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€
Δx Δpx ≥12h
Δv/v ≈ 0.6 Δv/v ≈ 0.17
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Heisenberg (2)
Δx Δpx ≥
12h
ΔE Δt ≥ 1
2h
Undeterminable ->undeterminability
Compare - Los Alamos, -45.
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Conclusions
Undeterminability is determinable
The principle of undeterminability is valid for photons, particles as well as big molecules.
The border between undeterminability and uncertainty is the same as the border between the classical and the quantum world.
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The End
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Heisenberg (2)
€
Δx Δpx ≥12h
€
ΔE Δt ≥ 12h
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• The big quiz / nuclear scattering
0 2 4 6 8 10 12 14 16
100
101
102
103
104
105
Inte
nsity
(co
un
ts /
10
s)
Grazing angle (mrad)