Theory of Relativity

• Time Traveling


  Associated and revolutionized by Albert Einstein, though he did not coin the term
• Frame of Reference


  Any frame of reference is either at rest or moving at a constant motion relative to an observer
• Inertial Frame of Reference

  • A frame of reference that is at a constant motion with respect to other frames of reference
  • Completely follows or obeys the Newtonian laws of motion
  • The body at rest needs to be at rest forever, for an infinite amount of time, or for as long as an object can
  • Any body that is at a constant motion (constant velocity or speed) needs to be at a constant motion
• Non-Inertial Frame of Reference

  • A frame of reference that is at a constant acceleration with respect to other frames of reference
  • The object moves at a constant speeding up at a certain path
• Newtonian Mechanics


  • All motions are relative to a particular frame of reference
  • 2 Factors to consider in detecting motion: The presence of the observer, The presence of the frame of reference
• Concrete Example of Newtonian Mechanics

  • Ball
  • POV #1: Person standing inside the train, the ball is moving to the right at 3 m/s
  • POV #2: Bystander who observes the motion of the train, the other person, and the ball, the ball is moving at 8 m/s because the train is also moving at 5 m/s while the ball is moving 3 m/s
• Galilean Invariance (Principle of Relativity)


  The laws of motion are the same in all inertial frames of reference
• Classical Relativity


  • Things move relative to each other
  • Anyone is connected with everyone else and things are connected with each other
  • There is no such thing as absolute rest or absolute motion
• Examples of Classical Relativity

  • Picture frames hung on a wall, in a house that is situated on Earth, are not perfectly at rest since the Earth and these picture frames are also at rest
  • Riding in a bullet train wouldn't make you feel like you are moving, but you are actually moving since you are connected to the bullet train
• Maxwell's Equation


  • Light is propagated in space as electromagnetic waves
  • James Maxwell calculated the speed of electromagnetic radiation, from radio waves to gamma waves, which is 3x10^8 m/s
  • Maxwell believed in luminiferous ether, the postulated medium for the propagation of light, so the speed of light would only be constant in an absolute frame of reference
  • Maxwell's equations do not retain their original expressions from one inertial frame of reference to another
• Special Relativity


  States that the motions of an object are relative to the inertial frame of reference, hence things move relative to each other - no absolute rest and motion
• Einstein's 2 Postulates of Special Relativity

  1. The Relativity Principle: The laws of motion are the same in every inertial frame of reference

  2. The Constancy of the Speed of Light: The speed of light in a vacuum must be the same in all inertial reference frames
• 5 Consequences of Special Theory of Relativity

  • Relativity of Simultaneity: Relativity of simultaneity is not an absolute concept, but depends on the observer's frame of reference

  2. Time Dilation: The slowing down of a clock as determined by an observer who is in relative motion with respect to that clock
• Light does not require any medium to travel on. It can travel in an empty space.
• The faster you go through space, the slower you move in time. The slower you move through space, the faster you move in time.
• Simultaneous events


  One observer notices the events as simultaneous, and the other observer notices the events as non-simultaneous
• Time dilation


  The slowing down of a clock as determined by an observer who is in relative motion with respect to that clock
• Time dilation


  • Alex's mirror covered a larger distance than Bill's mirror, and therefore needed more time
• Both distance and time must be directly proportional to each other for the speed of light to remain constant
• Alex experiences dilated time, while Bill experiences proper time
• If you are moving faster in space, you are moving slower in time
• The faster you go through space, the slower you move in time
• The slower you move through space, the faster you move in time
• Time is not absolute, it is relative
• Time is relative


  • A person's 3:00 PM looks different from another person's 3:00 PM
  • Twin paradox
• If you are moving closer to the speed of light, time slows down
• If you are moving at exactly the speed of light, your time freezes or stops
• If you are moving faster than the speed of light, you are going back in time or in the past
• The time measured by an observer in a stationary or outside inertial frame of reference is greater than the time measured by an observer at a high speed or inside his/her frame of reference
• Length contraction


  The length of an object is relative to the observer's inertial frames of reference
• Length contraction


  • An object's length contracts as you move in the speed of light, relative to the object of reference
• The length measured by an observer outside the frame of reference is less than the length measured by an observer inside his/her frame of reference
• Cosmic speed limit


  No ordinary matter or entity known to exist in the observable universe can travel faster than 300 million meters per second except light
• Nothing beats the speed of light, as it is the fastest traveling entity
• Why light is the fastest

  Light has photons, which are massless particles. Only objects with massless quantum particles can travel at the same speed of light
• Speed of dark


  Dark energy is the only thing faster than the speed of light, at double the speed of light. It causes galaxies to move away from each other. However, this is not an entity, that is why light is considered the fastest moving object
• If hypothetically there is an entity discovered that exceeds the speed of light, then it would require an unlimited amount of energy to accelerate it exactly or greater than the speed of light
• Mass-energy equivalence


  It states the equivalence between mass and energy. The product of a large value of the squared speed of light and a small amount of mass corresponds to a tremendous amount of energy released during a nuclear reaction. This is not possible in ordinary chemical reactions, only in special nuclear reactions, in minute or quantum particles
• For the cosmic speed limit to be consistent with Newton's laws of motion, the relativistic mass of an object must be increased as it continues to travel at high speed
• Past can't be changed

  You can't unscramble a scrambled egg, you can't unbreak a broken plate. Whenever you try fixing things that should have already been left in the past, you are adding entropy or disorder to the system. Past can't be changed no matter what