ASTR Lecture Notes 10/15

Albert Einstein (1879-1955): Pioneered the theories of special and general relativity.
- 1905: Introduction of Special Relativity.
- 1915: Introduction of General Relativity, changing perceptions of gravity.

Common Sense in the 1800s:
- Velocity Addition: It was believed straightforward to add velocities.
- Wave Behavior: It was assumed light waves behaved like all other known waves.

Scenario: A train moving at 50 m/s with a ball thrown at 10 m/s (in opposite directions).
- Observer watching the ball on the train sees:
- Ball moving at 50 + 10 = 60 m/s (forward)
- Ball moving at 50 - 10 = 40 m/s (backward)

Assumption: Just like sound and water, light waves were thought to require a medium (luminiferous ether).

Objective: To detect the motion of Earth through the luminiferous ether by measuring speed variations of light.
Findings:
- Observation: No changes in speed regardless of Earth's motion direction.
- Conclusion: There is no luminiferous ether; light can propagate through a vacuum. The speed of light is constant at c = 3 × 10^8 m/s.
- Implication: Preceded Einstein's concept that light’s speed remains constant regardless of source movement.

Scenario: Mavis on a moving train sets off a firecracker; Stanley observes.
Observation: Light reaches the train's ends simultaneously for Mavis, but Stanley does not see it as simultaneous due to the train’s motion.
- Questions posed:
- Does he see one end first? A. Both ends at once; B. The left end; C. The right end.
Conclusion: Time is relative; different observers can perceive events differently.

Relativity of Simultaneity: Observers may disagree on simultaneity of events based on their reference frames.
Time Dilation: The faster an object moves, the more significant the time difference as perceived by observers stationary relative to that object.

Length Contraction: Objects appear shorter in the direction of motion at relativistic speeds.
Mass Increase: An object’s mass increases as its speed approaches light speed.
Ultimate Speed Limit: No mass-bearing object can travel faster than the speed of light.
Energy-Mass Equivalence: Expressed as $E=mc^2$ .

Newton’s laws hold as approximations valid under slow speeds ( $v ext{ is much less than } c$ ).

Time and space are not absolute; they depend on the observer’s perspective.
Distinction between scientific relativity (physics) and philosophical relativism (morality).
Cultural impact through the 1920s had misconceptions of relativity linked with moral relativism.

Spacetime links three spatial dimensions and one time dimension:
- Spatial Dimensions: 3D (up/down, left/right, forward/backward).
- Temporal Dimension: 1D (time).
- Total: 4D spacetime.
Quote by Taylor & Wheeler: "Space is different for different observers. Time is different for different observers. Spacetime is the same for everyone."

Newton’s View: Gravity as action at a distance.
Einstein’s View: Gravity emerges from curvature in spacetime; a mass causes the curvature, hence influencing movement.

Ensure to revisit all chapters mentioned for detailed understanding of topics; especially focusing on the construction of spacetime and implications of relativity through Einstein’s theories.