{ "cells": [ { "cell_type": "markdown", "id": "74be7038", "metadata": {}, "source": [ "# `spacetimelib.Worldline` Tutorial" ] }, { "cell_type": "code", "execution_count": 1, "id": "f798a0fe", "metadata": {}, "outputs": [], "source": [ "import spacetimelib as st\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "f26c539e", "metadata": {}, "source": [ "`spacetimelib.Worldline` allows us to create and manipulate worldlines of particles that change velocity over time, as long as they never exceed the speed of light.\n", "\n", "We can map the worldline into a different reference frame that is moving at some constant velocity with `spacetimelib.Worldline.boost`.\n", "\n", "Let's create a wordline in a 1+1 spacetime that follows $ x = 0.2 sin(4t) $. We'll generate 300 vertices between the times $ t = 0 $ and $ t = 10 $." ] }, { "cell_type": "code", "execution_count": 2, "id": "5dc21c49", "metadata": {}, "outputs": [], "source": [ "t = np.linspace(0, 10, 300)\n", "x = 0.2 * np.sin(4*t)\n", "events = np.stack([t, x], axis=-1)\n", "w0 = st.Worldline(events)" ] }, { "cell_type": "markdown", "id": "669f6e8e", "metadata": {}, "source": [ "Let's plot the worldline we've created." ] }, { "cell_type": "code", "execution_count": 3, "id": "1d6440bd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plotter(ax, w):\n", " out = ax.plot(*w.plot())\n", " ax.set_xlim(-6, 6)\n", " ax.set_ylim(0, 11)\n", " ax.set_xlabel('x-axis')\n", " ax.set_ylabel('t-axis')\n", " return out\n", "\n", "fig, ax = plt.subplots(figsize=(4, 4))\n", "plotter(ax, w0)" ] }, { "cell_type": "markdown", "id": "76cfe7ba", "metadata": {}, "source": [ "This is a space-time diagram of a particle oscillating back and forth.\n", "\n", "Let's see how this worldline gets warped if we observe it in a reference frame that is moving at velocity 0.3 times light speed in the positive x-axis direction with respect to the original reference frame. We'll boost the whole worldline by `0.3`." ] }, { "cell_type": "code", "execution_count": 4, "id": "c648f467", "metadata": {}, "outputs": [], "source": [ "w1 = w0.boost(0.3)" ] }, { "cell_type": "markdown", "id": "e2646d2a", "metadata": {}, "source": [ "Now let's look at the plots of the worldline in the original reference frame and the new reference frame, side by side." ] }, { "cell_type": "code", "execution_count": 5, "id": "38721b25", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(8, 4))\n", "plotter(ax0, w0)\n", "plotter(ax1, w1)" ] }, { "cell_type": "markdown", "id": "274ca8ad", "metadata": {}, "source": [ "TODO: Add a straight worldline that follows the second reference frame." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 5 }