chatgpt helps me out

docs/devlog/v0.2.0.md

@@ -58,3 +58,12 @@ Verdict: **[egui](https://www.egui.rs/) now, [lunex](https://bytestring-net.gith
 - Made a basic UI with egui
 - Added basic entity spawner
 - Added [todo.md](../todo.md)
+
+# 2024-08-06
+
+ChatGPT read https://arxiv.org/abs/2402.11150 and my time dilation notes and
+affirmed that I have a correct understanding and my math is mostly right. The
+suspicious deviation of my results from wikipedia's results is a units error.
+Wikipedia uses microseconds per day, but I show microseconds per second.
+
+ChatGPT helped me make a stupid-simple demo to get started with time dilation.

src/physics/mod.rs

@@ -1,8 +1,13 @@
+mod time_dilation;
+
 use avian2d::prelude::*;
 use bevy::prelude::*;
 
 pub(super) fn plugin(app: &mut App) {
- app.add_plugins(PhysicsPlugins::default().with_length_unit(1.0));
+ app.add_plugins((
+ PhysicsPlugins::default().with_length_unit(1.0),
+ time_dilation::plugin,
+ ));
 
  // we will handle gravity ourselves
  app.insert_resource(Gravity(Vec2::ZERO.into()));

src/physics/time_dilation.rs

@@ -0,0 +1,46 @@
+use bevy::prelude::*;
+use bevy_egui::{egui, EguiContexts};
+
+pub(super) fn plugin(app: &mut App) {
+ app.add_systems(Startup, setup);
+ app.add_systems(Update, (update_time_dilation, update_ui));
+}
+
+#[derive(Component)]
+struct TimeDilation {
+ proper_time: f32,
+ coordinate_time: f32,
+ velocity: f32, // Fraction of the speed of light
+}
+
+fn setup(
+ mut commands: Commands,
+) {
+ commands.spawn(TimeDilation {
+ proper_time: 0.0,
+ coordinate_time: 0.0,
+ velocity: 0.1, // Example value for v/c
+ });
+}
+
+fn update_time_dilation(mut query: Query<&mut TimeDilation>, time: Res<Time>) {
+ for mut time_dilation in query.iter_mut() {
+ time_dilation.coordinate_time += time.delta_seconds();
+ time_dilation.proper_time +=
+ time.delta_seconds() * (1.0 / (1.0 - time_dilation.velocity.powi(2)).sqrt());
+ }
+}
+
+fn update_ui(
+ mut egui_context: EguiContexts,
+ query: Query<&TimeDilation>
+) {
+ let time_dilation = query.single();
+ egui::CentralPanel::default().show(egui_context.ctx_mut(), |ui| {
+ ui.label(format!(
+ "Coordinate Time: {:.2}\nProper Time: {:.2}",
+ time_dilation.coordinate_time,
+ time_dilation.proper_time
+ ));
+ });
+}