Theory Of Relativity

• Newtonian Mechanics - All motions are relative to a particular frame of reference.
• Frame of reference - object or reference that the observer uses to detect the motion.
• Inertial Frame of Reference - any frame of reference is either at rest or moving at a constant motion/velocity relative to the observer
• Inertial Frame of Reference - constant motion with respect to other frames of reference and obeys the laws of motion by Isaac Newton
• Non-inertial frame of reference - constant acceleration with respect to other frames of reference
• Galilean Invariance (Principle of Relativity) - states that the laws of motion are the same in all inertial frames in a straight line.
• Classical Relativity

  • things move relative to each other
  • no such thing as absolute rest & absolute motion
  • accounts for the effects of gravity on light
• Maxwell's Equation - light is that small part of the electromagnetic spectrum that affects our vision. Light is propagated in space as electromagnetic waves.
• Ether - postulated medium for the propagation of light
• Maxwell's electromagnetic wave - Maxwell's equations do not retain their original expressions from one inertial frame of reference to another
• Special Relativity (STR) - motions of an object are relative to the inertial frame of reference. So, things move relative to each other with no absolute rest & motion.
• Special Relativity (STR) - ignores the effects of gravity because it has no effect in an inertial reference frame
• Einstein's Postulates:

  1. Relativity Principle
  2. The constancy of the speed of light
• Relativity Principle - "laws of motion are the same in every inertial frame of reference"
• The constancy of the speed of light - "speed of light in a vacuum must be the same in all intertial frames"
• 5 consequences of STR:

  1. Relativity of simultaneity
  2. Time dilation
  3. Length contraction
  4. Cosmic speed limit
  5. Mass energy equivalence
• Relativity of simultaneity - not an absolute concept, but depends on the observer's frame of reference
• Relativity of simultaneity conclusion:

  • When two observers are relative to each other,  to the event, and to the identified inertial frames of reference, one observer notices the events as simultaneous, and the other observer notices the events as non-simultaneous.
• Time Dilation: slowing down of a clock as determined by an observer in relative motion with respect to that clock
• Time Dilation: speed of light is the same for everyone
• Time Dilation - if an object is at rest/slow in space, the time moves/covers faster, and vice versa (object moves quickly, time moves slower)
• Time Dilation - time is not absolute and not fixed
• Time dilation conclusion:

  • the time measured by an observer in a stationary or outside intertial frame of reference is greater than that measured by an observer at high inertialor inside their frame of reference
• Length Contraction - the length of an object is relative to the observer's inertial frame of reference

  
• Length Contraction Conclusion:

  • the length measured by an observer outside the frame of reference is less than that measured by an observer inside their frame of reference
• Cosmic speed limit - no ordinary matter/entity in the observable universe can travel faster than 300 million miles per second except light
• Cosmic Speed limit conclusion:

  • if there's 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 - the equivalence between mass and energy
• Mass energy equivalence - 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
• Mass energy equivalence conclusion:

  • For the cosmic speed limit to be consistent with Newton's laws if motion, the relativistic mass of an object must be increased as it continues to travel at a high speed.
• 4 Natures of Time Travelling:

  1. Past can't be changed
  2. Nature prevents "paradoxes" (fixed timeline)
  3. Nature prevents "paradoxes" (dynamic timeline)
  4. Parallel World
• Past can't be changed - you can travel back in time but can;t change the past no matter what (broken glass can't be the same way it was before)
• Nature Prevents "Paradoxes" (Fixed timeline) - when parties travel back in time, the future they left can't be changed. All events are fixed points in time. The actions of the traveler have already become part of history.
• Nature Prevents "Paradoxes" (Dynamic timeline) - Altered events in the past have definite impacts on the present and the loop of events will continue infinitely, creating a paradox.

  
• Parallel World - an infinite no. of parallel universes traveling into the past causes divergent timelines from the first. Hence, the traveler can do anything with impunity and only the new timeline will be affected.
• Arrows of Time - always move forward
• 3 types of Arrows of time:

  1. Thermodynamics arrow
  2. Psychological arrow
  3. Cosmological arrow
• Thermodynamics arrow - inevitable, to a more disastrous/random situation in timeline
• Psychological Arrow - we know everything we did in the past but we're not sure what'll happen in the future
• Cosmological arrow - aligned with the thermodynamics arrow; product of the Big Bang