13.1 The beginnings of relativity

Reference frames

• Relative perspective in Physics clarifies different points of view.

• Example: Car velocity varies based on the observer's frame.

• Reference frame: Defines an object's position using coordinates and time events.

  • Your current sitting position is a reference frame.

  • Despite Earth's motion, you feel stationary.

Examples of reference frames

• Everyday examples illustrate perspectives.

• Car moving down a road:

  • People on opposite sides perceive its direction differently.

• Train leaving a station:

  • Person A (platform) sees Person B (train) moving right.

  • Person B (train) sees Person A (platform) moving right.

Inertial frames of reference

• Inertial reference frame:

  • Non-accelerating frame.

  • All inertial frames move at constant velocity relative to each other.

• No absolute reference frame:

  • Nothing is completely stationary in the Universe.

  • Everything is in motion relative to each other.

Newton’s Postulates of Time and Space

• Inertial reference frames are employed due to consistency with Newton's laws.

• Galilean Relativity encompasses this principle.

• Example: An object in an inertial frame moves in a straight line with constant velocity unless acted upon by force.

  • Corresponds to Newton's first law.

• Laws of Physics remain consistent across frames if moving at constant velocity.

• Cartesian coordinate system is commonly used for reference frames.

  • Represents points in space in 3D and 2D.

• Infinite inertial frames in the Universe; methods to transition between them exist.

13.2 Lorentz transformations

Lorentz transformations

• Observers moving relative to each other may differ in numerical values of space and time coordinates for events, and yet they unanimously agree on the numerical value of the speed of light in a vacuum.

• The Lorentz transformation equations establish the connection between values in one reference frame and those in another.

• These equations supersede the Galilean transformation equations, which become inadequate when dealing with speeds approaching that of light.

The Postulates of Special Relativity

• Galilean relativity: Newton's laws are applicable in all inertial frames.

• Newton treated space and time as fixed and absolute.

• The time interval between events in one frame equals that in another.

• Exception at speeds close to light's: Space and time become relative.

• The length of the object or time interval depends on the frame of reference.

• Velocity addition is applicable at much lower speeds than light's (c).

• Doesn't work for speeds approaching c.

• Example: Rocketship traveling at 0.7c releasing probe at 0.5c results in 1.2c, violating the light speed limit.

Einstein’s Two Postulates of Relativity

• First Postulate

  • The laws of physics are the same in all inertial frames.

  • In its own reference frame, an object is always stationary.

  • Conducting a physics experiment produces the same results on a moving train or stationary platform.

• Second Postulate

  • The speed of light (c) in vacuum is constant in all inertial frames.

  • Different observers measure the speed of light as c, irrespective of their motion.

  • The runner holding the flashlight measures the speed of light as c.

  • A stationary observer sees the speed of light as c, not affected by the runner's velocity.

  • Applies only to the speed of light, not to any other speed.

Simultaneity in Special Relativity

• "Simultaneous" denotes occurring at the same time.

• Relativity of simultaneity:

  • Whether events are simultaneous depends on the observer's reference frame.

• In one frame, events at different points in space appear simultaneous.

• In another frame moving relative to the first, events seem sequential.

• Contrast with Galilean relativity where simultaneity was absolute.

Illustrative Example

• Person B in the moving train carriage switches on a lamp.

  • Observe light reaching points X and Y simultaneously.

• Person A stationary on the platform observes the train passing.

  • Sees light move to both ends of the carriage at speed c (Einstein's second postulate).

  • Light reaches point X before point Y due to the carriage's motion.

• The difference in arrival times is exaggerated in the diagram; the actual difference is very small and depends on the train's speed.

Visualization using Space-Time Diagrams

• Diagrams aid in understanding simultaneity in different frames of reference.