Download Atomic and Molecular Physics for Physicists Ben-Gurion University of the Negev

Ben-Gurion University of the Negev
Atomic
Atomic and
and Molecular
Molecular Physics
Physics
for
for Physicists
Physicists
Ron Folman
Chapter 3A: The emergence of Quantum Mechanics:
An historical and conceptual overview up to the 21st century.
(Plank, specific heat, atomic spectroscopy, Frank-Hertz, Bohr’s atom)
Main References: Corney A. Atomic and Laser
Spectroscopy, Oxford UP, 1987; QC 688.C67
1987; Chapters in Modern Physics, Open
University
Exercises:
Dudi Moravchik
www.bgu.ac.il/atomchip
www.bgu.ac.il/nanofabrication
www.bgu.ac.il/nanocenter
The emergence of Quantum Mechanics:
An historical and conceptual overview up to the 21st century.
References:
Quantum theory / Asher Peres
Lectures on physics / Richard Feynman
Speakable and unspeakable / John Bell
Interpreting the quantum world / Jeffrey Bub
The undivided universe / David Bohm & Basil Hiley
• Many of the 20th century physicists did not like QM. Some of them were indeed
its fathers e.g. Einstein (photo electric effect) de-Broglie (the wave nature of paticles)
and Schroedinger (the wave formalism).
• The course will present an introduction to the formalism of the theory and its great
success, but for now, let us briefly sample why the theory gave rise to so much dislike
and disbelief.
"It carries in itself the seeds of its own destruction” J.S. Bell (1966).
First example:
The Schroedinger cat
QM predicts that the cat is alive
and dead at the same time!
To explain we need to understand
what is “superposition”
“Quantum cat in Schroedinger’s
thought experiment gets a reprieve
from a rival theory”
Lets say that we have two identical boxes and one ball, and lets say that by some
random process, the ball has the same probability to be in either of the boxes.
The boxes are closed and we have no idea in which of them the ball is.
Classical physics: The ball is here OR there.
QM: The ball is here AND there
(or the poison was released AND not released –
according to some random radioactive decay).
This leads to the cat paradox,
as in reality we have never seen a macroscopic superposition.
What is the justification for the superposition state:
It is the only way we know to explain some experimental observations!
Second example: The wave-particle duality
e.g. the double slit experiment
screen
Niels Bohr
This was always explained as the interference of two waves….
But it happens, even if we send a single photon each time….
Suppressed laser
Real single photon: Atomic cascade
Alain Aspect, Philippe Grangier
The only explanation could be that the photon passes in both slits at the same time!
But, if we put a detector behind each slit, we find that the photon passes
only through one of the slits each time!
source
screen
〰
〰
The conclusion must then be that if “wave” or “particle” are contradicting forms
of reality, then reality is ill defined until we do a measurement!
You don’t have to destroy the photons. Why don’t we measure them, but still let
them pass and see what happens on the screen…
Bohr-Einstein discussion
As Bohr showed Einstein, the above is unachievable due to the uncertainty
principle. Namely, in order to be able to measure the momentum kick of the
photon (to know which slit it went through), the uncertainty in momentum
would have to be small and this means that the uncertainty in position of the
slit would have to be at least of the order of the periodicity of the interference
Pattern, a fact that would totally wash out the pattern.
Actually, its gets even much stranger…
(is complementarity more fundamental than the uncertainty principle…?)
You don’t have to measure them (or kick them)… its enough that you make such
“which path knowledge” available in principle i.e. tag the photons (e.g. polarizers)
(or their environment e.g. emit a photon in a cavity / scully).
No
pattern
Orthogonal
polarizers
But then you can also erase the tagging!
(Raymond Chiao, Paul Kwiat, Aephraim Steinberg)
Polarization
eraser
Pattern
re-appears
How does the photon know at the slit know that in its future there is going to be an eraser?
Trying to get back an indivisible point like particle (our classical perception) with
Bohmian mechanics (David Bohm):
Deterministic particle paths in the double slit experiment. The only uncertainty is
left in the exact initial position of the source.
Third example: The Einstein-Podolsky-Rosen paradox (1935)
formulated with the
Greenberger-Horne-Zeilinger (Mermin) state (1990)
Three spin half particles in the following state
1
2
Ψ = I ↑ >1 | ↑ >2 | ↑ >3 - | ↓ >1 | ↓ >2 | ↓ >3
3
The Pauli matrices
( )
0 1
σx= 1 0
σy=
( )
0 -i
i 0
σz=
( )
1 0
0 -1
( ) and | ↓ > = (01)
1
Defining I ↑ > =
0
Prove that
σz I ↑ > = I ↑ >
σx I ↑ > = I ↓ >
σyI ↑ > = i I ↓ >
σz | ↓ > = - | ↓ >
σx | ↓ > = | ↑ >
σy| ↓ > = -i | ↑ >
Prove that
(1) σ1x σ2yσ3y Ψ= σ1y σ2xσ3y Ψ= σ1y σ2yσ3x Ψ= Ψ
Prove directly (by matrix calculus) that
(σ1x σ2yσ3y)(σ1y σ2xσ3y )(σ1y σ2yσ3x )= -(σ1xσ2xσ3x)
and
(2) σ1xσ2xσ3x Ψ= -Ψ
Note that
1. σ2xσ3y= σ3yσ2x
2. σ2xσ2y= -σ2yσ2x
3. σ2=I
(quantum comutator)
EPR argument:
From (2) it is clear that by measuring the spin x projection of two particles we can
know without a doubt the x spin projection of the third particle. That means all 3 particles
have an “element of reality” i.e. a clear inherent feature defining their independent x spin
projection. Let us call these 3 independent characters who can take the value of +/-1:
m1x, m2x, and m3x.
However, as can be seen from (1) the same values can also be know by measuring the
y projection of the other two particles.
Assuming that all these projections are elements of reality, let us look at their
Values obtained via the two kinds of measurements:
m1x m2y m3y +1
m1y m2x m3y +1
m1y m2y m3x +1
m1x m2x m3x -1 +1
Contradiction!!
Exercise: compare to the original EPR with two particles.
To conclude the source of dislike:
• Lack of determinism (uncertainty principle, probabilistic nature of the wave function)
• Lack of independent reality (Copenhagen Interpretation, wave particle duality)
• Lack of locality (EPR, instant collapse of the wave function)
The theory was found to be extremely successful in describing nature (see rest of the
course), but as two of its fathers put it:
“To try and stop all attempts to pass beyond the present viewpoint of quantum
physics could be very dangerous for the progress of science and would furthermore
be contrary to the lessons we may learn from the history of science. This teaches us,
in effect, that the actual state of our knowledge is always provisional and that there
must be, beyond what is actually known, immense new regions to discover”.
(Louis de-Broglie)
"nobody understands quantum mechanics”
(Richard Feynman)
The official birth photo of QM: