Did you know? We owe our GPS accuracy to Einstein’s theory of relativity. If it weren't for corrections based on these concepts, you'd end up a few kilometers away from your desired location!

• Invariant Quantities: These don’t change even if you switch between different frames of motion. Imagine watching a movie. No matter where you sit in the theater, the story doesn't change.

• Example: Proper time, proper length, and spacetime interval.

• Absolute Time & Space: According to Einstein, these aren’t fixed. It's like time can wear different watches in different places.

• Spacetime Interval: Due to the consistent speed of light, time intervals vary based on motion and this introduces the spacetime interval. It’s like adding a 4th dimension to our 3D world.

• Formula for motion in x-direction: Δs² = (cΔt)² – Δx²
• In 3D: Δs² = (cΔt)² – Δx² – Δy² – Δz²

• Galilean relativity: Time is consistent across all frames.

• Einstein's relativity: Time can change, leading to the spacetime interval, which unifies space and time.

• Real-world example: Twins. One stays on Earth, and the other goes on a space journey near light speed. The traveling twin returns younger!

• Instead of just plain 't' for time, we use 'ct' which combines the speed of light and time, adding a spatial dimension. Think of it as adjusting your watch based on how fast you're traveling.

• The spacetime interval remains consistent even between different reference frames due to these transformations. It’s like a universal translator for space and time!