The speed of light is the "spacetime exchange rate" | Hacker News Reader

The speed of light is the "spacetime exchange rate"

twitter.com

6 pointsyashvg4 comments

This thread offers a really elegant way to think about special relativity. The key insight is that everything moves through spacetime at speed c. It's just a question of how that velocity is distributed between spatial and temporal dimensions.

When you're at rest, you're traveling through time at maximum speed (c). Start moving through space, and you "trade" some of that temporal velocity for spatial velocity, which is why time dilation occurs. Light is special only because it's massless. All of its velocity budget goes toward spatial movement, leaving none for temporal movement.

This framing makes time dilation much more intuitive than the usual "moving clocks run slow" explanation. You're not moving slower through time because of some mysterious effect. You're moving slower through time because you're now also moving through space, and your total spacetime speed is conserved.

> The key insight is that everything moves through spacetime at speed c

That's the key error in thinking. The key insight of special relativity is there is no such thing as absolute time or absolute space. You have a perception of your passage of time and moving through space, but it differs from other observers in other inertial frames. There's simply no way to say what your "real" passage of time and movement through space is - that's a meaningless concept. Therefore there is no distribution of your velocity between time and space.

But there is absolute spacetime. Observers will disagree about distance between events in space or time, but they will all agree on the value of the Minkowski metric that includes space and time.

And they'll all disagree on your spatial velocity and how much time has passed for you. The only thing they'll agree on is the spacetime interval between any two events, calculated using the Minkowski metric. That's a fundamental invariant, but it's not absolute spacetime in the sense of a fixed, unchanging background. Instead, it highlights that space and time themselves are relative to the observer's motion.

Reply on news.ycombinator.com