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ASTRO 101: Black Holes Module 7
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Notes for ASTRO 101 based on the official Coursera videos for the class. Covers Module 7.
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Module 7Introduction to Quantum Mechanics:
Quantum Mechanics Origins:
● Emerged in the late 1800s when scientists thought light was fully understood as
electromagnetic waves.
● Maxwell’s equations described light waves, but they failed to explain blackbody
radiation.
● The "Ultraviolet Catastrophe" predicted infinite energy emissions, contradicting
reality.
Planck’s Breakthrough:
● In 1899, Max Planck resolved the Ultraviolet Catastrophe by introducing the
concept of quantized energy packets (quanta).
● Proposed Planck’s constant (h = 6.6 × 10⁻³⁴ Js) to explain energy emissions from
blackbodies.
● Introduced the concept of photons, quantized units of light energy.
Einstein’s Contributions:
● In 1905, Einstein expanded Planck’s work, showing photons have energy
proportional to frequency (E = h × frequency).
● Demonstrated light's particle nature (photons) alongside its wave-like behavior,
leading to the concept of wave-particle duality.
● Earned the 1922 Nobel Prize for explaining the photoelectric effect.
Wave-Particle Duality:
● Light exhibits both wave and particle properties.
● Photons are indivisible energy clumps, like matter particles (e.g., electrons).
● Large numbers of photons mask their clumpy nature, but it’s observable in
experiments with short wavelengths like X-rays.
De Broglie’s Hypothesis (1923):
● Louis de Broglie proposed that matter particles (e.g., electrons) have wave
properties, described by their wavelength (λ = h / mv).
, ● Demonstrated through experiments like the double-slit, where particles show
interference patterns when their de Broglie wavelength is large.
Heisenberg’s Uncertainty Principle:
● Werner Heisenberg showed the position (Δx) and momentum (Δp) of a particle
cannot both be precisely known: Δx × Δp ≥ ħ/2.
● Introduced a limit to certainty in measuring physical quantities.
● Also applies to energy and time (ΔE × Δt ≥ ħ/2).
Applications:
● Wave-particle duality underpins quantum mechanics and modern technologies
like lasers and electron microscopes.
● De Broglie wavelengths explain phenomena at quantum scales, while the
uncertainty principle highlights fundamental limits of measurement.
Summary of Quantum Mechanics Concepts:
● Quantum Mechanics and Intuition:
○ Niels Bohr stated that quantum mechanics is inherently shocking.
○ Richard Feynman remarked that no one fully understands quantum
mechanics due to its counterintuitive nature.
● Quantum Tunneling:
○ Particles can appear on the other side of a barrier without crossing it
traditionally, explained by the Heisenberg Uncertainty Principle.
○ This uncertainty in particle location leads to outcomes like tunneling.
● Heisenberg Uncertainty Principle:
○ It limits the precision with which certain pairs of properties (e.g., position
and momentum) can be known simultaneously.
○ Applies universally, even to vacuums, indicating they are never truly
"empty."
● Quantum Foam:
○ At the quantum scale, spacetime is dynamic and frothing with activity,
producing short-lived "virtual particles."
○ Virtual particles borrow energy briefly and must return it to the universe.
● Hawking Radiation:
○ Near a black hole's event horizon, virtual particles can behave unusually.
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