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Freethought Freeform

Introduction to Quantum Mechanics

Thursday, March 9, 2023

David Brunco

PFC Board of Directors, Vice President

MIT, B.S., Materials Science and Engineering

Cornell University, Ph.D., Materials Science and Engineering, minor in Physics

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Introductions

Introduce yourself

Name
PFC: Member?, first event?, interests?
Math and Physics background
Why this event?

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Why QM event?

Comes up in past events on Consciousness and Free Will
QM is not well understood, which leads to misunderstanding
Is QM (and thus) physics deterministic or non-deterministic?
Naturalism vs supernaturalism
Structure of event

Mostly video clips (better graphics, etc, than I can do)
Stop for commentary and Q&A
PHET Quantum Simulator
Summary / Conclusion to address Confusion?

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Setting the Bar

In 1965, Nobel prize-winning physicist Richard Feynman famously said, “I think I can safely say that nobody understands quantum mechanics.”

Pay attention to what he says afterwards.

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Schrodinger Eq

Solutions to Schrodinger Equation (1926) describes a QM state

Partial differential equation
Eigenvalue Equation
Observables are “operators”
Complex functions (i)
Wave functions in a Hilbert space
Non-relativistic
(See Dirac Eq for relativistic)

An Introductory QM course has prerequisites of 3 or 4 semesters each of math and physics

Differential Calculus, Integral Calculus, Multivariable Calculus, Differential Equations
Classical (Newtonian) Mechanics, Electromagnetism, Waves and Vibrations

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“Quantum”

Max Planck and black-body radiation (1900)

Classical Mechanics failed to explain the light given off by a black-body vs temperature
Planck proposed light emitted by oscillators of quantized energy

E = nhf

n = 1, 2, 3,….

h = 6.63×10^-34 Joule-sec (Planck constant, small number)

f = frequency of radiation (light)

Einstein and Photoelectric effect (1905)

Photoelectric effect: Electron emission from materials by irradiating with light
Smallest “bundle/packet” of light is called photon, with quantized energy E = hf

Many other examples of quantized (discrete) energy levels,

Emission spectrum from hydrogen atom

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Fermilab – What is QM?

https://www.youtube.com/watch?v=K0VY9_hB_WU

BTW, Feynman diagram at beginning

In interest of time,

Skip 1:50 - 2:48 Quantum (covered earlier)

Wave function 𝛹 is solution to Schrodinger Equation, but what does it mean?

Born interpretation.

Probability density of finding particle at given location = 𝛹*𝛹 = |𝛹|²

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Copenhagen Interpretation

Main principles of the Copenhagen interpretation

System completely described by a wave function 𝛹
𝛹 changes with time by Schrödinger equation.
Description of nature is probabilistic. The probability density for an event given by |𝛹|². (Born rule)
Not possible to know the values of all properties of system at the same time
Matter/energy exhibits a wave-particle duality. An experiment can demonstrate particle-like or wave-like properties; but not both at the same time.
Measuring devices are essentially classical devices and measure classical properties such as position and momentum. Collapse of wave function.
The quantum mechanical description of large systems should closely approximate the classical description.

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Spin

https://toutestquantique.fr/en/spin/ Tout est quantique - spin

Video schematically shows Stern-Gerlach experiment (1922) with a beam of silver atoms, which has one unpaired electron (spin ½).
Solution to the Schrodinger Eq with half-integer angular momentum eigenvalues, e.g. (m = +/- ½)
Spin is an intrinsic “angular momentum” that is a property of the particle (like mass, charge) and is inherently a QM phenomenon.

IT IS NOT SPINNING ABOUT AN AXIS.

SGz followed by SGz.
SGz, followed by SGx, followed by SGz
What about arbitrary angle between first and second measurement?

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Quantum Entanglement

https://www.youtube.com/watch?v=JFozGfxmi8A

Fermilab - Quantum Entanglement and Spooky Action at a Distance

Long video, but covers a lot.
EPR 1935: QM may be an “incomplete” theory with hidden variables accounting for the observed probabilistic results.
John Bell 1964: Developed an inequality equation assuming a hidden variable theory of QM.
For paired production of 2 entangled QM “particles” sent in opposite directions, predictions based on hidden variables and non-hidden variable theories differ for angles not equal to 0, 90, 180, and 270 degrees.
Experiment “violates” Bell’s inequality, thus disproving hidden variable theory.

God rolls dice

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Double Slit Experiment

https://www.youtube.com/watch?v=iVpXrbZ4bnU

Focus on first 9:15 of video
Classical interpretation: Interference pattern for waves not for particles.
QM: Probability distribution of detection pattern consistent with wave theory, even for a single photon or single particle (e.g. electron).
“Particle” goes through both holes simultaneously if we do not “look”, like a wave.
But detection is always at a specific location, like a classical particle.

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PHET QM Simulator

https://phet.colorado.edu/en/simulations/quantum-tunneling

PHET Wave packet and quantum tunneling simulator

"Easy to use" QM simulator, but may need some explanation to interpret results

Energy
Wave function (real and imaginary parts)
Probability Density (Wave function * Wave function complex conjugate)

Free particle

Uncertainty principle
Wave function evolves deterministically per Schrodinger Eq in a superposition of states
Upon measurement/observation, wave function “collapses” probabilistically
After collapse, system continues to evolve per Schrodinger Eq.

QM Tunneling

If barrier is sufficiently “small”, a particle may “appear on the other side (tunnel)” with some probability.
Principle for data write/erase for flash memory (memory sticks, solid source drives, etc.)

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Conclusions

Tegmark: Consciousness and QM https://www.youtube.com/watch?v=R04USRugo90

QM systems are in a superposition of states that are solutions to, and evolve according to the Schrodinger Eq

Tegmark speaks in terms of neuron both firing and not firing in a QM superposition

Observation / measurements results in collapse of wave function

Tegmark speaks in terms of secrets leaking out (corresponding to “measurement”)

Hidden variable theories of QM are inconsistent with experimental data (2022 Nobel Prize)
QM provides quantitatively accurate explanation and predictions of physical phenomena
A satisfactory understanding of its underpinnings and the wave function remains elusive.
Feynman’s “Nobody understands quantum mechanics” is as true today as it was in 1965

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