"""A one-space-dimensional slice of a light cone and three event types. Coordinates x and ct are in light-seconds. Output is written to CWD. Tested with Python 3.14, NumPy 2.3.5, Matplotlib 3.10.7. """ from pathlib import Path import matplotlib.pyplot as plt import numpy as np def main(): plt.rcParams.update({"font.size": 12}) fig, ax = plt.subplots(figsize=(9.2, 8.0), dpi=100, facecolor="white") fig.subplots_adjust(left=0.11, right=0.96, top=0.88, bottom=0.20) x = np.linspace(-5, 5, 501) ax.fill_between(x, np.abs(x), 5.2, color="#eef4fc", zorder=0) ax.fill_between(x, -np.abs(x), -5.2, color="#f1f4f8", zorder=0) ax.plot(x, x, color="#29795c", linewidth=2, label="Light-cone boundaries") ax.plot(x, -x, color="#29795c", linewidth=2) ax.axhline(0, color="#7c8692", linewidth=0.8) ax.axvline(0, color="#7c8692", linewidth=0.8) ax.plot([0, 3], [0, 4], color="#275aa0", linewidth=2.3, label="Straight massive-observer world line") ax.scatter([0], [0], color="#273643", s=40, zorder=5) ax.text(-0.55, -0.48, "O", weight="bold") events = [ (3, 4, "#275aa0", "A: (x, ct) = (3, 4)\nTimelike: s² = −7", (1.4, 4.48)), (3, 3, "#29795c", "N: (3, 3)\nNull: s² = 0", (3.22, 3.12)), (3, 2, "#bb6430", "B: (3, 2)\nSpacelike: s² = 5", (3.22, 1.66)), ] for ex, et, color, label, position in events: ax.scatter([ex], [et], s=65, color=color, edgecolor="white", zorder=5) ax.annotate(label, xy=(ex, et), xytext=position, color=color, fontsize=11, arrowprops={"arrowstyle": "-", "color": color}, zorder=6) ax.text(-1.8, 3.7, "Future timelike interior\ns² < 0", color="#275aa0", ha="center", fontsize=12) ax.text(-1.8, -3.8, "Past timelike interior\ns² < 0", color="#526a87", ha="center", fontsize=12) ax.text(-3.6, 0.7, "Spacelike\nexterior\ns² > 0", ha="center", color="#9d5a2b", fontsize=12) ax.set(xlim=(-5.1, 5.1), ylim=(-5.2, 5.2), aspect="equal", xlabel="Spatial coordinate x [light-seconds]", ylabel="Time coordinate ct [light-seconds]") ax.grid(alpha=0.15) ax.legend(loc="lower left", frameon=True, facecolor="white", fontsize=10) fig.suptitle("The sign of the interval determines the causal relation", fontsize=16, y=0.96) fig.text(0.5, 0.055, "s² = x² − (ct)². The cone is its null boundary, not the shaded interior.\n" "From O to A: speed 0.75c and clock time √7 seconds.", ha="center", fontsize=11, linespacing=1.5) fig.savefig(Path.cwd() / "minkowski-light-cone-events.png", facecolor="white", transparent=False) plt.close(fig) if __name__ == "__main__": main()