SUPERPOSITION 101
by Oguzhan Ozdemir
with the help of MIT Open Course
FUNDAMENTALS
The photoelectric effect is the emission of electrons or other free carriers when light shines on a material.
Louis-Victor-Pierre-Raymond de Broglie
He was a French physicist.
In his 1924 PhD thesis, he postulated the wave nature of electrons and suggested that all matter has wave properties.
So, what is it?
- Is it a particle?
- Is it a wave?
- Is it a particle moving like a wave?
- Is it a wave made of particles?
It's both things at the same time, yet it's neither!
Are we not smart
enough to understand what it is?
Well, it's not like that.
Because the mathematics works!
ELECTRONS
An empirical fact is that
the only observable colors are individually black and white,
while the only observable hardnesses are individually hard and soft.
Properties of Electrons
In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.
Color and Hardness Boxes
the most unsettling experiments ever done
COLOR
White
Black
HARDNESS
Soft
Hard
$$\textbf{B} = B_0e_z$$
$$\textbf{B} = B_0e_x$$
Repeatability
COLOR
COLOR
Black
0%
0%
100%
100%
White
Correlation
HARDNESS
COLOR
Black
0%
50%
100%
50%
White
Lack of Correlation
Predictions
C
H
C
B
0%
100%
W
50%
50%
Natural Prediction:
100% W, 0% B
Results:
50% W, 50% B
What Does It Tell Us?
There is something unpredictable, non-deterministic, and random about physical processes that we observe in the laboratory.
Uncertainty Principle
The idea that some measurable physical properties of real systems are incompatible with each other.
New Apparatus
H
New Set of Experiments
In: W
H: 50%
I.
In: H
B: 50%
II.
Measure: H
Measure: C
In: W
B: 0%
III.
Measure: C
S: 50%
W: 50%
W: 100%
WTF!?
C
H
C
B
50%
W
50%
Results:
50% W, 50% B
Modification
H
Experimenting Again
In: W
B: 50%
IV.
M: C
W: 50%
Wall: S
Expectation 1:
Output should be down by 50%!
Expectation 2:
All the electrons that come out must be 100% white!
Expectation 1:
Expectation 2:
C
H
C
B
50%
W
50%
Results:
50% W, 50% B
Which Route Did It Take?
H
Logical Possibilities
- It does not take the hard path!
- It does not take the soft path!
- It does not take both!
- It does not take neither!
World We Are Facing
SUPERPOSITION
In the context of our previous experiments,
an initially white electron inside the apparatus with all walls out is
in a superposition of the states of being hard and soft.
World We Are Facing
We have no clue what is going on!
FACTS OF LIFE
1.
2.
3.
4.
5.
6.
Atoms exist.
Randomness exists.
Atomic Spectra: Discrete and Structured.
Photoelectric effect.
Electron diffraction.
Bell's Inequality.
Energy of a Photon
Light comes in chunks with definite energy.
$$E = h\nu$$
$$\lambda\nu = c$$
$$E = c\rho$$
(1)
(2)
(3)
}
$$\rho = \frac{h}{\lambda}$$
(4)
Double Slit Diffraction
Q
Where is the light when it hits the wall?
A
Wave is a distributed object.
It's everywhere.
Not localized.
Interference happens.
Single Electron Experiment
$$E = h\nu$$
$$\lambda\nu = c$$
$$E = c\rho$$
}
$$\rho = \frac{h}{\lambda}$$
Bell's Inequality
$$N(A,\bar{B}) + N(B, \bar{C}) \geq N(A, \bar{C})$$
$$ N(A, \bar{B}) = N(A, \bar{B}, C) + N(A, \bar{B}, \bar{C}) $$
$$ N(B, \bar{C}) = N(A, B, \bar{C}) + N(\bar{A}, B, \bar{C}) $$
$$ N(A, \bar{C}) = N(A, B, \bar{C}) + N(A, \bar{B}, \bar{C}) $$
$$N(\uparrow_0, \downarrow_\theta) + N(\uparrow_\theta, \downarrow_{2\theta}) \geq N(\uparrow_0, \downarrow_{2\theta})$$
$$N(\uparrow_0, \downarrow_\theta) + N(\uparrow_\theta, \downarrow_{2\theta}) < N(\uparrow_0, \downarrow_{2\theta})$$
The Line Between QM and CM
What's Next?
Quantum Mechanics
and this is what it looks like.
{\displaystyle i\hbar {\frac {\partial }{\partial t}}\vert \Psi (\mathbf {r} ,t)\rangle ={\hat {H}}\vert \Psi (\mathbf {r} ,t)\rangle }
So, it's all downhill from here. :)
Further Readings and Resources
MIT OCW, Quantum Physics I Lectures
3Blue1Brown, Light Quantum Mechanics
MinutePhysics, Bell's Theorem: The Quantum Venn Diagram Paradox
Sixty Symbols, Polarization
SUPERPOSITION 101
by Oguzhan Ozdemir
Thank you for listening!
Superposition 101
By Oguzhan Ozdemir