The border between Uncertainty and

Undeterminability

Björgvin Hjörvarsson

Solvay conference 1927

Copenhagen interpretationThe wave-particle duality

Considerations…..

The quantum-mechanical description cannot simultaneously be complete and consistent. (fullständig och självkonsistent)

The answer…..

Complementarity - instrumentation.

To measureIn-between science and

philosophy

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!

The photon detector

NERange ≈ 0.4 -0.7 μm

Differential pressure sensor

NE

Sensitivity and principles

Loudness (dB)

Frequency (Hz) NE

Examples of what we want to measure

Radiation beyond the range 0.4-0.7 μm must be

”transformed” prior to registration

• Electromagnetic radiation - Transformation in frequency

• Particles - Complete abstraction

Transformation

Particles

Speed, momentumenergy

Mass, charge,………

1 eV - discuss

E=mc2

Consequences Event

Equipment -Filter

Theories

Describe the photo

Describe...

What is reality?

Determine the position and energy of a particle in the

darkest part of our universe!

Thought experiment- ”gedanken experiment”

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

Coherence (1)

Coherence (2)

Coherence (3)

LASERParallel radiation with well defined energy &Phase coherency!

Reflectivity

Reflectivity - film on a substrate

Si

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

Neutrons (1)

Neutrons are particles:Mass ≈1.67 10-27 kg (=1.00 u)Extension ≈10-15 m….

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

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 !!!

Think BIG!

Δv/v ≈ 0.6

Δv/v ≈ 0.17

€

Δx Δpx ≥12h

Δv/v ≈ 0.6 Δv/v ≈ 0.17

Heisenberg (2)

Δx Δpx ≥

12h

ΔE Δt ≥ 1

2h

Undeterminable ->undeterminability

Compare - Los Alamos, -45.

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.

The End

Heisenberg (2)

€

Δx Δpx ≥12h

€

ΔE Δt ≥ 12h

• 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)