special relativity

Einstein 1905

• laws of electromagnetism should be consistent with the principle of relativity
• spacetime interval (ds)^2 = (dt)^2 - (dx)^2

Minkowski diagram 1908

• https://dudarion.github.io/Interactive-Minkowski-diagram/

train and track frame of reference

• fire two beams from the center of the train to the ends
• observer on the train, both beam reach the ends at the same time
• observer on the track, the beam reaches the back of the train first

Sagnac effect

• due to rotation
• sync two clocks on earth, take one east/west around the earth
• two clocks will be out of sync

Explains electromagnetism

• a positive charge moving in the same direction as the electons
  • in its frame, the positive charges are moving and due to length contraction
  • the denser positive charge leads to repulsion
• when moving in opposite direction, attraction occurs due to the denser electrons
• magnetic field in our frame becomes electic field

spacetime interval of two events

• two events separated by distance D and time T where (cT)^2 = D^2
  • then it also satisfies this equation in all frames since c = D/T
• more generally if two events have (cT)^2 - D^2 = s^2, this value s^2 is invariant
• in all frames
  • s^2 > 0 are timelike separated, there is a frame they occur at the same place
    • s is the time interval in that frame!
  • s^2 < 0 are spacelike separated, there is a frame they occur at the same time
  • s^2 = 0 are lightlight separated, a single photo may be present at both events
• all observers agree about which pairs of events are causal!

time dilation explained with light clock

• light travels further in the moving clock
• muons have a 1.5 microsecond halflife but detected on earth’s surface
  • time dilation from our perspective
  • length contraction from the muon’s perspective

https://en.wikipedia.org/wiki/Spacetime_diagram

• time dilation
• length contraction
• speed of causality

relativity of simultaneity

• Does the past still exist?
• Did the future already happen?

Block universe

• Rietdijk–Putnam argument for eternalism

references It’s About Time: Understanding Einstein’s Relativity by N. David Mermin WSU: Special Relativity with Brian Greene https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/index.html https://theoreticalminimum.com/courses/special-relativity-and-electrodynamics/2012/spring Intro to Special Relativity Course