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Table of Contents, Index
Lecture Notes
Special Relativity Practice Problems
Special relativity, formulated by Albert Einstein in 1905, has
various practical applications in our daily lives and in
advanced technological systems, some of which might be
surprising given the theory's abstract nature. Here are a few
significant examples:
1. Global Positioning System (GPS)
Time Dilation Correction: The clocks on GPS satellites
experience time differently due to their high speeds
(special relativity) and weaker gravitational fields
(general relativity) compared to clocks on the Earth's
surface. Engineers must account for these relativistic
effects to maintain the accuracy of GPS systems.
You all have GPS receivers
iPhone Apps: Compass.app, GNSS View.app, GPS Location.app
2. Particle Accelerators
Particle Behavior: In particle accelerators like the
Large Hadron Collider, subatomic particles approach
significant fractions of the speed of light. The theory
of special relativity is crucial to predict the
behaviors, mass, and energy of these particles
accurately. At 0.99999999c 𝛾 > 7000
3. Electricity Generation
Nuclear Power Plants: The equivalence of mass and energy
(E=mc^2) is foundational to understanding the energy
release in nuclear reactions in the sun and nuclear power
plants.
4. Electromagnetic Theory
Predicting Electromagnetic Phenomena: Special relativity
helps in accurately describing the behavior of electric
and magnetic fields in different inertial frames, which
is crucial for understanding electromagnetic phenomena in
moving systems.
How Special Relativity Makes Magnets Work (4+ min)
https://www.youtube.com/watch?v=1TKSfAkWWN0
5. Telecommunication
Synchronization of Satellite Systems: Maintaining
synchronized timekeeping among satellites, and between
satellites and ground stations, demands consideration of
relativistic effects.
6. Materials Science
Exploring Properties of Materials: At very high speeds or
energies (such as in certain experimental settings),
relativistic effects can influence the properties of
materials, and understanding this is crucial for
interpreting experimental data accurately.
Einstein's theory of relativity explains fundamental
properties of gold
https://phys.org/news/2015-10-einstein-theory-relativity-fundamental-properties.html
https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry#Color_of_gold_and_caesium
7. Medical Imaging
Positron Emission Tomography (PET): Special relativity is
important for understanding the behavior of particles in
PET scans, as it involves antimatter (positrons) and
their interaction with electrons.
PET scans show that particles have a rest energy, and
special relativity allows to calculate that energy.
Physics and Instrumentation in PET*
http://eknygos.lsmuni.lt/springer/370/13-39.pdf
8. Astrophysics
Cosmic Phenomena: Studying cosmic rays, black holes, and
other high-energy phenomena in the cosmos often requires
employing special relativity to comprehend the behavior
and properties of particles and radiation in these
environments.
Time Dilation:
- Pulsars: The rapid rotation of pulsars can be
understood and accurately modeled only by taking into
account relativistic effects. Time dilation plays a
crucial role in calculating the periods and energies of
pulsar emissions.
- Gamma-Ray Bursts (GRBs): The short timescales of
variability observed in GRBs suggest relativistic motion,
as time dilation allows events that take place over
longer timescales in the source frame to appear much
shorter in the observer's frame.
Length Contraction:
- Jets from Active Galactic Nuclei (AGN): The
relativistic jets emitted by AGN are observed to be
moving at speeds very close to the speed of light.
Special relativity helps in explaining the apparent
superluminal motion (faster than light) and the structure
of these jets.
Relativistic Doppler Shift:
- Redshift and Blueshift: The shift in the wavelength of
light due to the motion of astronomical objects is
calculated using the relativistic Doppler shift formula.
This is crucial for understanding the kinematics of
galaxies, stars, and other celestial bodies.
- Spectral Line Analysis: Analyzing the spectral lines of
stars and galaxies for their velocity components,
especially when they are moving at a significant fraction
of the speed of light.
Energy-Momentum Relation:
- High-Energy Astrophysics: Studying cosmic rays,
high-energy particles, and phenomena like supernova
remnants requires using the relativistic energy-momentum
relation.
- Accretion Disks: In the vicinity of compact objects
like black holes and neutron stars, the material in the
accretion disks moves at relativistic speeds, requiring
special relativity for accurate modeling.
Mass-Energy Equivalence:
- Nuclear Reactions in Stars: The principle of
mass-energy equivalence is crucial for understanding the
energy production mechanisms in stars, where mass is
converted into energy through nuclear fusion.
- Supernovae and Neutron Stars: The processes and
reactions that take place during supernova explosions and
in the dense matter of neutron stars can only be
understood by applying the principles of special
relativity.
Gravitational Lensing:
- While gravitational lensing primarily falls under the
domain of general relativity, the velocities of the
lensing objects and the light can sometimes be high
enough that special relativistic effects need to be
considered.
Cosmology:
- Large-Scale Structure of the Universe: Understanding
the motion of galaxies, the cosmic microwave background
radiation, and other cosmological phenomena involves
relativistic corrections.
Relativistic Beaming:
- The observed brightness of jets and other
relativistically moving objects is affected by
relativistic beaming, which makes objects moving toward
us appear brighter than they would if they were at rest.
9. Electronics
Designing of Electromagnetic Coils: In certain high-speed
applications, special relativity can influence the design
by considering how electric and magnetic fields transform
between different frames of reference.
How Special Relativity Makes Magnets Work (4+ min)
https://www.youtube.com/watch?v=1TKSfAkWWN0)
10. Quantum Mechanics
Relativistic Quantum Mechanics: For particles moving at
speeds that are a significant fraction of the speed of
light, special relativity must be integrated into quantum
mechanics, leading to theories like Quantum
Electrodynamics (QED).
Book Recommendation
QED: The Strange Theory of Light and Matter - published
in 1985 by American physicist and Nobel laureate Richard
Feynman.
Famous the world over for the creative brilliance of his
insights into the physical world, Nobel Prize-winning
physicist Richard Feynman also possessed an extraordinary
talent for explaining difficult concepts to the
nonscientist. QED--the edited version of four lectures on
quantum electrodynamics that Feynman gave to the general
public at UCLA as part of the Alix G. Mautner Memorial
Lecture series--is perhaps the best example of his
ability to communicate both the substance and the spirit
of science to the layperson.
The focus, as the title suggests, is quantum
electrodynamics (QED), the part of the quantum theory of
fields that describes the interactions of the quanta of
the electromagnetic field-light, X rays, gamma rays--with
matter and those of charged particles with one another.
By extending the formalism developed by Dirac in 1933,
which related quantum and classical descriptions of the
motion of particles, Feynman revolutionized the quantum
mechanical understanding of the nature of particles and
waves. And, by incorporating his own readily visualizable
formulation of quantum mechanics, Feynman created a
diagrammatic version of QED that made calculations much
simpler and also provided visual insights into the
mechanisms of quantum electrodynamic processes.
Feynman Diagrams
https://www.youtube.com/watch?v=qe7atm1x6Mg
The applications of special relativity are ingrained in many
advanced technologies and scientific investigations. Even
though its effects are typically negligible at the speeds
encountered in everyday life, they become crucially important
in the high-speed and high-energy regimes encountered in
various technological and astrophysical contexts.
Consequently, special relativity forms a foundational
component of modern physics and technological development.
Finally - How we know that Einstein's General Relativity can't
be quite right (5+ Min)
https://www.youtube.com/watch?v=Ov98y_DCvRY
Interactive Minkowski Diagram
https://sciencesims.com/sims/minkowski/
Lorentz Factor Calculator 𝛾 = 1/√(1-(v^2/c^2))
https://www.azcalculator.com/calc/lorentz-factor-calculator.php
https://en.wikipedia.org/wiki/Lorentz_factor
Five Papers That Shook the World
https://physicsworld.com/a/five-papers-that-shook-the-world/
ON THE ELECTRODYNAMICS OF MOVING BODIES By A. Einstein
http://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf
Beautiful, Simple and Profound (90 min)
https://www.youtube.com/watch?v=R_yk45m4E3M
https://www.youtube.com/watch?v=ASzECGtSpqQ
Spacetime: All the universe's a stage
https://www.symmetrymagazine.org/article/spacetime-all-the-universes-a-stage
sam.wormley@icloud.com