✨Sparkly physics magic ahead!✨

• The proper time interval is the time taken for an event to occur, as observed by someone where the event is taking place.
  • Example: If two fireworks go off at the same spot, the proper time is the time measured by someone at that spot.
• Time dilation makes things funky! In a different reference frame (moving differently from the event's location), time appears longer than the proper time.

• Imagine a room with two mirrors facing each other.
• Light bounces between the mirrors.
• For someone sitting in the room (at rest with respect to the mirrors), the time taken for the light to bounce back and forth is Δt0 = 2L/c (where c is light speed!).
• BUT! If someone is zooming past the room (moving with a velocity v), they'll see the light taking a diagonal path, and the time they measure is Δt.
• With some math magic (thanks Pythagoras!): Δt = γΔt0, where γ (the Lorentz factor) = 1/√(1 – v²/c²).
  • Real-world analogy: Think of two people on a train. One bounces a ball up and down. To them, it goes straight up and down. But someone outside sees the ball move in a zigzag, covering more distance!

• As you go faster and approach the speed of light, γ gets bigger.
• For speeds up to 20% of light speed, γ is close to 1 (so things feel "normal").
• Lorentz and Fitzgerald thought objects might shrink in length to account for the weirdness of light speed. They were onto something! Einstein later took these ideas and made his special relativity theory without needing any object shrinking.