{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9b668ad4",
   "metadata": {},
   "source": [
    "# Length contraction\n",
    "\n",
    "Alice has a very fast car. She passes Bob, who is standing on the ground, at a speed of 0.99 light-seconds per second. In Alice's frame, the car is 10 meters long. Is the car also 10 meters long in Bob's frame, or does it change?\n",
    "\n",
    "Let's first plot the situation in Alice's frame of reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7f57de0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import spacetimelib as st\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_worldline(ax, w_plot_data, label):\n",
    "    out = ax.plot(*w_plot_data, label=label, marker='.')\n",
    "    ax.set_xlabel('x-axis')\n",
    "    ax.set_ylabel('t-axis')\n",
    "    ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n",
    "    return out"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e72a0ec9",
   "metadata": {},
   "source": [
    "Let's say that at time `t = 0`, the back of Alice's car is at `x = 0` and the front is at `x = 10`. Both the front and back of the car are not moving, since they are stationary with respect to Alice, so they have velocity `dx/dt = 0`.\n",
    "\n",
    "Also at `t = 0`, Bob is standing at `x = 0`. He moves at a velocity of `dx/dt = -0.99`.\n",
    "\n",
    "We can create worldlines to describe the scenario like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "73f9da86",
   "metadata": {},
   "outputs": [],
   "source": [
    "car_front_0 = st.Worldline(\n",
    "    vertices=[\n",
    "        # (t, x)\n",
    "        (0, 10)\n",
    "    ],\n",
    "    ends_vel_s=(0,))\n",
    "\n",
    "car_back_0 = st.Worldline(\n",
    "    [(0, 0)],\n",
    "    (0,))\n",
    "\n",
    "bob_0 = st.Worldline(\n",
    "    [(0, 0)],\n",
    "    (-0.99,))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a94af233",
   "metadata": {},
   "source": [
    "The API documentation describes the `ends_vel_s` argument, but in brief, it allows you to specify the velocity of the worldline at its past and future ends, so that we can define worldlines that span infinitely into the past and future at a fixed velocity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f5ecaff3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10.0, 20.0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4+Hjs3bsXAKBQKLT6b/lPXLMXWUXwW1u3xo0HNxASH8I1fCKip7h8+TIEQUDbtm2fueyUKVPQt29ftGzZEv369cMHH3yAr776qtIyJSUlWLduHXr27AlPT8/HdjJkaGio2Qe9QqGAUqnU7MEOABYsWICBAweiVatWkMvlWL9+PZYtW4agoCC0b98emzZtgqmpKWJjYyvd7sKFC9G7d2+0b98eM2fOxJEjR1BYWAhTU1NYWFigSZMmUCqVj91fTXDNXgfYmtpic8BmjN49unwNPyEEW1Rb4GLlIvZoRNTImBoZ4twClVbXyc4txIDlB1D2yFZ4AxmwN6I3lAoTre67OrTZ3L93715ER0fj/PnzUKvVePjwIQoLC1FQUKCJurGxMby9vat9m//UtWtXzddpaWkoKSnBc889pznPyMgI3bt3R2pqaqXrPXqfFfu3v3HjBlxc6v53P9fsdURF8Ftbt8aNghsYlTAKGeqMZ1+RiKgOyWQymBk30erkbmeB6MFeMPxrj26GMhmiB3vB3c5Cq9up7h7hPDw8IJPJcP78+acul56ejpdeegne3t7YuXMnTp06hZiYGABAcXGxZjlTU9Na7UWwqpcSqsPIyEjzdcX9P+nNgbXF2OuQiuC3UrTCjYIbCEkIQaY6U+yxiIieaWg3Fxya2Refj+mBQzP7Ymi3+tsyaWNjA5VKhZiYGOTn5z92ecXhek+dOoWysjJ89NFH6NGjB9q0aYPr16/X21wA0KpVKxgbG+Pw4cOa80pKSnDixAm0b9++2rdjbGyM0tLSOpuLsdcxtqa22KwqD35OQQ5GJYxi8IlILzgqTOHfyhaOitq9vlwdMTExKC0tRffu3bFz505cunQJqampWL16Nfz9/QEArVu3RklJCdasWYMrV65g+/bt2LBhQ73OZW5ujgkTJmD69OmIj4/HuXPnMGbMGBQUFCA0NLTat9OyZUtcvXoVycnJuHXrFoqKimo1F2Ovg5qZNsNm1Wa4K9yRU5CDkN0hyLzP4BMRVXB3d8fp06fRt29fTJs2DR07dsTAgQORmJiI9evXAwB8fHywfPlyLFmyBB07dsRnn32G6Ojoep9t8eLFGDJkCIYPH47OnTvj8uXLSEhIQNOmTat9G0OGDEFgYCD69u0LOzs7fP7557WaSSZo804HAJmZmZDJZGjRogUA4Pjx49ixYwfat2+PsWPH1moYXaBWq6FQKJCbmwsrKytRZ7n14BZCEkJwNfcqlOZKxKni4GzpLOpMoinOBxY5lX/93nXAuGavkVHdKyh+qPmoVnU/OkUN60m/1woLC3H16lW4ubnBxKT6b6Qj3aDN86f1mv1///tf7Nu3D0D5rgoHDhyI48ePY9asWViwYEHNJqYqNTNthjhVHNwUbsjOz0ZoQiiu3b8m9lhERKRntI59SkoKunfvDgD46quv0LFjRxw5cgSfffZZve8ruDFqZtoMsQGxaGnVEln5WQhJCGHwiYhIK1rHvqSkBHK5HED55xdffvllAEDbtm2RlZVVt9MRAMDOzA5xqjhN8EMTQvFn3p9ij0VERHpC69h36NABGzZswC+//II9e/YgMDAQAHD9+nXY2trW+YBU7tHgX8+/jpD4EAafiIiqRevYL1myBBs3bkSfPn0wbNgw+Pj4AAB++OEHzeZ9qh92ZnaIVcUy+EREpBWt3zbbp08f3Lp1C2q1utLHCMaOHfvY/oSp7tmb2SNWFVt+WFx1OkITQhGnioOThZPYoxERkY6q0efsDQ0NH/u8YMuWLR87UhDVj4rgu1q54s+8PxGSEILrefW7VygiItJf1Vqz79y5MxITE9G0aVN06tTpqfsQPn36dJ0NR09mb2aP2IBYhO4OxR/qPzQHz3G0cBR7NCIi0jHViv0rr7yieQf+oEGD6nMe0oKDuQNiA2IRkhCCjPsZGJUwisEnIqLHVCv2UVFRVX5N4nMwd0Csqjz4mfczy9fwA7dAaa4UezQiIsnYv38/+vbti7t378La2rpe7iM9PR1ubm749ddf4evrW6e3rfVr9hV7z6vKxo0bazUM1cyju9K9lncNo+JHITs/W+yxiIjqVXZ2NsLDw+Hu7g65XA5nZ2cEBwcjMTFR7NF0jtaxDwwMxPTp01FSUqI579atWwgODsbMmTPrdDhtzZs3DzKZrNKpbdu2os7UUCqC38KiBa7lXUNIQgiDT0QNK/dP4OrB8n/rWXp6Orp06YKff/4Zy5Ytw9mzZxEfH4++ffsiLCysxrdbWlpab8eUF1ON1uy//fZbdOvWDefOncP//vc/dOzYEWq1GsnJyfUwonY6dOiArKwszenQoUNij9RglOZKbAncghYWLTSb9Bl8ItKKIJQfeErb0/FNwMqOwLbg8n+Pb9L+NrQ4LtvEiRMhk8lw/PhxDBkyBG3atEGHDh0QERGBo0ePapZbvnw5vLy8YG5uDmdnZ0ycOBF5eXmay7du3Qpra2v88MMPaN++PeRyOTIyMp54v4cPH4a3tzdMTEzQo0cPpKSkaC67ffs2hg0bhubNm8PMzAxeXl6PHa2urKwMS5cuRevWrSGXy+Hi4oKFCxdWeV+lpaUICQlB27ZtnzpTdWj9OfuePXsiOTkZ48ePR+fOnVFWVob3338fM2bMeOq79BtKkyZNoFQ23terK9bwRyWMQub9TM3n8B3MHcQejYj0QUnB30eYrCmhDPjpnfKTNqp5RMs7d+4gPj4eCxcuhLn548s/+pq6gYEBVq9eDTc3N1y5cgUTJ07EjBkzsG7dOs0yBQUFWLJkCTZv3gxbW9unfox8+vTpWLVqFZRKJd577z0EBwfj4sWLMDIyQmFhIbp06YJ3330XVlZW+N///ofhw4ejVatWmp3ORUZGYtOmTVixYgWef/55ZGVl4fz584/dT1FREYYNG4b09HT88ssvsLOze+Z/l6ep0efsL168iJMnT6JFixZo0qQJLly4gIKCgloNUlcuXboEJycnuLu744033njmX0NFRUVQq9WVTvrO0cIRW1Rb0NyiOTLuZyAkIQQ5+Tlij0VEVCcuX74MQRCq9TLtlClT0LdvX7Rs2RL9+vXDBx98gK+++qrSMiUlJVi3bh169uwJT0/Pp+4gLioqCgMHDoSXlxe2bduGnJwcfPvttwCA5s2b45133oGvry/c3d0RHh6OwMBAzf3dv38fq1atwtKlSzFixAi0atUKzz//PEaPHl3pPvLy8vDiiy/i5s2b2LdvX61DD9RgzX7x4sWIiorC2LFjsWzZMly+fBnDhw+Ht7c3Pv30U/j7+9d6qJry8/PD1q1b4enpiaysLMyfPx//+te/kJKSAktLyyqvEx0djfnz5zfwpPXP0cIRcao4zcfyQneHIjYglmv4RPR0Rmbla9jaUF8HYrqXr9FXkBkCYccAKy22EhhVby+sghab+/fu3Yvo6GicP38earUaDx8+RGFhIQoKCjRRNzY2hre3d7Vu79HG2djYwNPTE6mpqQDKN7svWrQIX331Ff78808UFxejqKhIcz+pqakoKipC//79n3ofw4YNQ4sWLfDzzz/D1NS02o/1abRes1+1ahW+++47rFmzBiYmJujYsSOOHz+OwYMHo0+fPnUyVE0FBQXhtddeg7e3N1QqFX766Sfcu3fvsb/iHhUZGYnc3FzNKTMzswEnrl9OFk6IU8WhuUVz/KH+A6G7Q7mGT0RPJ5OVb0rX5tTMAwheVR54oPzf4JXl52tzO9V8KdjDwwMymazKzd+PSk9Px0svvQRvb2/s3LkTp06dQkxMDACguLhYs5ypqWmdvAy9bNkyrFq1Cu+++y727duH5ORkqFQqzX1VN9wvvPACfvvtNyQlJdV6pgpax/7s2bMICgqqdJ6RkRGWLVuG3bt319lgdcHa2hpt2rTB5cuXn7iMXC6HlZVVpZOUVBX8GwU3xB6LiKSm81vAlLPAiF3l/3Z+q97uysbGBiqVCjExMcjPz3/s8nv37gEATp06hbKyMnz00Ufo0aMH2rRpg+vXa7dr8Uff/Hf37l1cvHgR7dq1A1D+5r1XXnkFb775Jnx8fODu7o6LFy9qlvfw8ICpqekzPxo4YcIELF68GC+//DIOHDhQq3kraB37Zs2aPfGy3r1712qYupaXl4e0tDQ4OjbuPco5WTghVhULJ3On8uAnMPhEVA8UzQG3f5X/W89iYmJQWlqK7t27Y+fOnbh06RJSU1OxevVqzab21q1bo6SkBGvWrMGVK1ewfft2bNiwoVb3u2DBAiQmJiIlJQUjR45Es2bNNHuW9fDwwJ49e3DkyBGkpqZi3LhxyMn5e2uqiYkJ3n33XcyYMQOffPIJ0tLScPToUcTGxj52P+Hh4fjggw/w0ksv1cmnyrR+zR4ATp48ia+++goZGRmVNoUAwDfffFProWrqnXfeQXBwMFxdXXH9+nVERUXB0NAQw4YNE20mXdHcojniAuMQEh9S6Wh5dma1f+MHEVFDc3d3x+nTp7Fw4UJMmzYNWVlZsLOzQ5cuXbB+/XoAgI+PD5YvX44lS5YgMjISvXr1QnR0NN56q+ZbHRYvXoy3334bly5dgq+vL3788UcYGxsDAGbPno0rV65ApVLBzMwMY8eOxaBBg5Cbm6u5/pw5c9CkSRPMnTsX169fh6OjI8aPH1/lfU2ZMgVlZWV44YUXEB8fj549e9Z4bpmgzTsdAHzxxRd46623oFKpsHv3bgQEBODixYvIycnBv//9b2zZsqXGw9TW66+/joMHD+L27duws7PD888/j4ULF6JVq1bVvg21Wg2FQoHc3FzJbdIHgD/z/sSo+FHIys9CS6uW+hP84vy/Pw5UzY/nUMMoKH6I9nMTAADnFqhgZlyjdQiqR0/6vVZYWIirV6/Czc0NJiYmIk5INaHN86f1ZvxFixZhxYoVmr9mVq1ahfPnz+M///kPXFxcajx0Xfjiiy9w/fp1FBUV4dq1a/jiiy+0Cn1j0NyiOeJUcXA0dyxfw98dilsPbok9FhER1SOtY5+WloYXX3wRQPnHFfLz8yGTyTB16lR8/PHHdT4g1b0Wli0Qq4qF0lyJq7lXEZIQwuATEUmY1rFv2rQp7t+/D6B8BwIVuwq8d++ezuxYh57N2dIZcao4TfBDE7iGT0QkVVrHvlevXtizZw8A4LXXXsPbb7+NMWPGYNiwYc/cUQDpFmdLZ8QFxMHBzAFXcq8w+EREEqV17NeuXYvXX38dADBr1ixEREQgJycHQ4YMqfLjA6TbnK2csUW1RRP80QmjGXwiIonR+m2zNjY2mq8NDAxEP6wt1V5F8EcljEJabhpGJ4xGrCoWtqa2Yo9GRER1oEYHwqnw4osvIisrq65mIRE5W5W/hm9vZo+03DSEJoTi9oPbYo9FRER1oFaxP3jwIB48eFBXs5DIXKxcsEW1RRP80btHM/hERBJQq9iT9LhYuZSv4Zva4/K9yxi9ezTuFN4Reywiojo3cuRIza5upU7r2GdkZGgOL+jq6gojIyMA5YccfNax40k/uFq5Ii7w7+CHJoQy+ESkU0aOHAmZTKY52draIjAwEL/99pvYo+kkrWPv5uaGmzdvAgBSUlLg7OwMALhz5w7c3NzqdjoSjauVK2JVsbAzteMaPhHppMDAQGRlZSErKwuJiYlo0qQJXnrpJbHH0klax14QhCqP+5uXl8d9K0tMS8Vf+843tcOlu5cwevdo3C28K/ZYRKSjsvOzcTzrOLLzsxvk/uRyOZRKJZRKJXx9fTFz5kxkZmZqVkjPnj2Lfv36wdTUFLa2thg7dizy8vIeu5358+fDzs4OVlZWGD9+/GMHeJOCan/0LiIiAgAgk8kwZ84cmJmZaS4rLS3FsWPH4OvrW+cDkrhaKloiVhWL0IRQTfA3B2xGU5OmYo9GRPVAEAQ8eKj9G69/SPsB0ceiUYYyGMAAkX6ReLnVy1rdhmkT0ypXJqsjLy8Pn376KVq3bg1bW1vk5+dDpVLB398fJ06cwI0bNzB69GhMmjQJW7du1VwvMTERJiYm2L9/P9LT0zFq1CjY2tpi4cKFNZpDV1U79r/++iuA8v8Rzp49qzmkH1C+j3wfHx+88847dT8hic5N4YZYVSxCEkJw8e5FjNk9BpsDNsPaxFrs0Yiojj14+AB+O/xqdRtlKMPCYwux8Jh2wTz232MwMzJ79oJ/2bVrFywsLAAA+fn5cHR0xK5du2BgYIAdO3agsLAQn3zyCczNy4+SuXbtWgQHB2PJkiVwcHAAUN6vuLg4mJmZoUOHDliwYAGmT5+O999/HwYG0nkPe7Vjv2/fPgDAqFGjsGrVKkke/pWerCL4oQmhuHD3gmYNn8EnIrH07dtXc+z6u3fvYt26dQgKCsLx48eRmpoKHx8fTegB4LnnnkNZWRkuXLigib2Pj0+lLdX+/v7Iy8tDZmYmXF1dG/YB1SOt96An5vHqSVzuCvfyNfz4EFy4ewFj9ozBpoGbGHwiCTFtYopj/z2m1XVyCnIw6LtBKEOZ5jwDmQG+e+U7OJg5aHXf2jA3N0fr1q0132/evBkKhQKbNm3S6nYaA+lso6AG4a5wR1xgHGxNbHH+znmM3TMWuUW5Yo9FRHVEJpPBzMhMq5Obwg1RPaNgICtPioHMAFH+UXBTuGl1OzV9vf7R2Q0MDPDgwQO0a9cOZ86cQX5+vubyw4cPw8DAAJ6enprzzpw5U2nncEePHoWFhYXmk2ZSwdiT1twV7ohTlQc/9U4qxuwew+ATNXKDPQYjYUgC4lRxSBiSgMEeg+v9PouKipCdnY3s7GykpqYiPDwceXl5CA4OxhtvvAETExOMGDECKSkp2LdvH8LDwzF8+HDNJnwAKC4uRmhoKM6dO4effvoJUVFRmDRpkqRerwcYe6ohd+vyTfo2JjYMPhEBAJTmSnRTdoPSXNkg9xcfHw9HR0c4OjrCz88PJ06cwNdff40+ffrAzMwMCQkJuHPnDrp164ZXX30V/fv3x9q1ayvdRv/+/eHh4YFevXph6NChePnllzFv3rwGmb8hyYSK3eERAECtVkOhUCA3N5dvQqyGtHtpCEkIwZ3CO2hn0w6bAjZBIVfU/R0V5wOLnMq/fu86YGz+9OWpwRQUP0T7uQkAgHMLVDAz1vqtQFTPnvR7rbCwEFevXoWbmxv3k6KHtHn+uGZPtdLKuhViA7iGT0Skyxh7qrXWTVtXCj7ftEdEpFsYe6oTrZu2xuaAzbAxscG52+cwbs84qIvVYo9FRERg7KkOeTT1KN+Vrrwpfr/9O8buHsvgExHpAMae6pRHUw9sVv0d/HG7uYZPpOv4Pm39pM3zxthTnWvTtA02BWyCtdwaKbdTMH7PeNwvvi/2WET0D0ZGRgCAgoICkSehmqh43iqex6fhZ2SoXnjaeGJzwGaM3j0aZ2+dxbg947Bx4EZYGluKPRoR/cXQ0BDW1ta4ceMGAMDMrPZ7saP6JwgCCgoKcOPGDVhbW8PQ0PCZ12Hsqd78M/jj94zHhoEbGHwiHaJUlu8ApyL4pD+sra01z9+zMPZUrx4N/m+3fsP4veOxccBGWBhbiD0aEaF8f/KOjo6wt7dHSUmJ2ONQNRkZGVVrjb4CY0/1riL4obtD8dvN3zBu7zgGn0jHGBoaahUP0i98gx41iIrgK+QKTfDzivPEHouIqFFg7KnBtLVpi00DN8HK2Aq/3SzfpM/gExHVP8aeGlQ723bYHLAZVsZWOHPzDCbsnYD8kvxnX5GIiGqMsacG1862/Oh4VsZWSL6ZjPF7xjP4RET1iLEnUbS3bY9NAZtgaWyJ5JvJXMMnIqpHjD2J5tHg/3rjV0zcO5HBJyKqB4w9iaqDbQdsGlge/NM3TmPi3okoKOGuO4mI6hJjT6Lr0Oyv4BuVB3/C3gkMPhFRHWLsSSd0aNahfJP+X8GfmMg1fCKiusLYk87o0KwDPg74GJZGljiVc4rBJyKqI4w96ZSOzTpi48CNsDCywKmcUwhLDGPwiYhqSZKxj4mJQcuWLWFiYgI/Pz8cP35c7JFIC152Xvh44MewMLLAyZyT5cF/+EDssYiI9JbkYv/ll18iIiICUVFROH36NHx8fKBSqXj4Rj3jZeelWcM/mXMSkw5Mw9UmTXDcRI7snN/EHo+eIDu3UOwRiKgKMkEQBLGHqEt+fn7o1q0b1q5dCwAoKyuDs7MzwsPDMXPmzGdeX61WQ6FQIDc3F1ZWVvU9Lj3DmZtnMG7PuPLP3wsCIJPBQBAQ1SIQgwd8KPZ4BGB7UjrmfP87AMBABkQP9sLQbi4iT0WP4u81ktSafXFxMU6dOoUBAwZozjMwMMCAAQOQlJRU5XWKioqgVqsrnUh3+Nj5YFHndzShB4AymQzzr8UjOztZ3OEIWbkPEPXD75rvywTgvW9SkJXLl12IdImkYn/r1i2UlpbCwcGh0vkODg7Izs6u8jrR0dFQKBSak7Ozc0OMSlqweHBPE/oKZTIZMrNOiTMQaVy9lY+yf2wbLBUEpN/imyqJdImkYl8TkZGRyM3N1ZwyMzPFHon+wcWxKwz++WqTIMDOrqM4A5GGWzNzGFT+OwyGMhlaNjMTZyAiqpKkYt+sWTMYGhoiJyen0vk5OTlQKpVVXkcul8PKyqrSiXSLUumLKKcBfwf/r036C89tRuFDviFMTI4KU8x/uYPmewMZsGhwRzgqTEWcioj+SVKxNzY2RpcuXZCYmKg5r6ysDImJifD39xdxMqqtwX0WIiHzOuKycrCyy7swa2KGo1lHEf5zOIMvsiFdWmi+3hvRm2/OI9JBkoo9AERERGDTpk3Ytm0bUlNTMWHCBOTn52PUqFFij0a1pCwtRbfCIvT3HIwNAzdogj/558kMvo5QKkzEHoGIqiC52A8dOhQffvgh5s6dC19fXyQnJyM+Pv6xN+2Rfutk3wnrB6yHaRNTJGUl4e19bzP4RERPILnYA8CkSZPwxx9/oKioCMeOHYOfn5/YI1E96OzQGRsGbIBpE1McuX4EU/ZNQVFpkdhjERHpHEnGnhqPzg6dNWv4h68fxts/v83gExH9A2NPeq+LQxes67+OwSciegLGniShq7Jr5eDvY/CJiCow9iQZXZVdEdM/pjz4fx7ma/hERH9h7ElSuim7aYJ/6M9DmLpvKopLi8Uei4hIVIw9SU5F8E0MTfDLn79gyr4pDD4RNWqMPUnSP4M/dT/X8Imo8WLsSbK6O3bH2v5rYWJogoPXDiJifwSDT0SNEmNPkubn6Ic1/dfAxNAEB64dwLT90xh8Imp0GHuSvB6OPbCm/xrIDeXYf20/pu2fhpLSErHHIiJqMIw9NQo9HHtgbf+1muBHHIhg8Imo0WDsqdHo4dgDa/r9tYafyeATUePB2FOj4u/kj9X9VmuCP+0AN+kTkfQx9tTo9HTqidV9V8PYwBj7MvfhnQPvMPhEJGmMPTVKPZv3xJp+a2BsYIyfM3/G9IPTUVLG4BORNDH21Gj1bN4Tq/uVr+EnZiRi+gEGn4ikibGnRu255s9hVb9VmuDPODCDwSciyWHsqdF7vvnzWNVvFYwMjLA3Yy/ePfgug09EksLYE+Gv4PctD/6eP/Yw+EQkKYw90V/+1eJfWNl3pSb4Mw/OZPCJSBIYe6JH9GrRSxP83X/sxsyDM/Gw7KHYYxER1QpjT/QPvVr0woo+K/4O/i8MPhHpN8aeqAq9nXtjRZ8VaGLQBAnpCQw+Eek1xp7oCXo798bKPis1wY/8JZLBJyK9xNgTPcWja/jx6fF475f3GHwi0juMPdEz9HHug+W9l6OJQRP8X/r/4b1DDD4R6RfGnqga+rr0xUe9PyoP/tX/w6xDsxh8ItIbjD1RNfVz6VcefFkT/HT1J8w6NAulZaVij0VE9EyMPZEW+rn0w4d9Pvw7+IcZfCLSfYw9kZb6u/THh73Lg/+/K//D7MOzGXwi0mmMPVEN9Hftj2W9l6GJrAl2XdmFOYfnMPhEpLMYe6IaGuA6AEt7L4WhzBA/XvkRc4/MZfCJSCcx9kS1MNB1IJb1XgZDmSF+SPuBwScincTYE9XSQNeBWNprKYNPRDqridgDEElBQMsAAMCMgzPwQ9oPkEGG+T3nw9DAUOTJiIgYe6I6E9AyAAIEvHvwXXyf9j1ksvLgG8i4AY2IxMXYE9UhVUsVBAiYeXAmvrv8HQAw+EQkOsaeqI4FtgwEBGDmL+XBl0GGeT3nMfhEJBrGnqgeBLoFAgDe/eVdfHv5W8hkMkT5RzH4RCQKxp6ongS6BZZv0v9lJr659A1kkGGu/1wGn4gaHGNPVI+C3IIgCAIiD0Vi56WdAMDgE1GDk9RvnJYtW0Imk1U6LV68WOyxqJF7wf0FLHp+EQxkBth5aSfeP/o+yoQyscciokZEcmv2CxYswJgxYzTfW1paijgNUbkX3V+EAAGzDs3C/7v4/yCDDLN7zOYaPhE1CMnF3tLSEkqlstrLFxUVoaioSPO9Wq2uj7GI8JL7SxAEAbMPz8bXF78GAAafiBqE5H7LLF68GLa2tujUqROWLVuGhw8fPnX56OhoKBQKzcnZ2bmBJqXGKLhVMD547gPIIMPXF7/GwqMLuUmfiOqdpNbsJ0+ejM6dO8PGxgZHjhxBZGQksrKysHz58ideJzIyEhEREZrv1Wo1g0/1KrhVMABg1qFZ+OriV5DJZJjlNwsymUzkyYhIqnQ+9jNnzsSSJUueukxqairatm1bKdre3t4wNjbGuHHjEB0dDblcXuV15XL5Ey8jqi/BrYIhQMDsQ7Px5YUvAYDBJ6J6o/OxnzZtGkaOHPnUZdzd3as838/PDw8fPkR6ejo8PT3rYTqimnu51csAwOATUb3T+djb2dnBzs6uRtdNTk6GgYEB7O3t63gqorrxcquXIQgC5hyegy8vfAkZZHjP7z0Gn4jqlM7HvrqSkpJw7Ngx9O3bF5aWlkhKSsLUqVPx5ptvomnTpmKPR/REr7R+BQIEzD08F19c+AIymQyR3SMZfCKqM5KJvVwuxxdffIF58+ahqKgIbm5umDp1aqXX8Yl01aDWgyAIAqKOROHz859DBhlmdp/J4BNRnZBM7Dt37oyjR4+KPQZRjf3b498AgKgjUdhxfgdkMhne7fYug09EtSa5z9kT6bN/e/wb83vOBwB8lvoZlp5YCkEQRJ6KiPQdY0+kYx4N/qepnzL4RFRrjD2RDhrsMRjz/OcBYPCJqPYYeyIdNaTNEET5RwEoD/6yk8sYfCKqEcaeSIe92uZVzPWfCwDYfm47Pjz5IYNPRFpj7Il03GttXsOcHnMAAJ+c+wQfnfyIwScirTD2RHrgP57/0QR/27ltWH5qOYNPRNXG2BPpiUeDv/X3rVhxagWDT0TVwtgT6ZH/eP4Hs/1mAwC2/L4FK04z+ET0bIw9kZ4Z2nYoZvnNAgBsSdmCladXMvhE9FSMPZEeer3t63jP7z0AQFxKHFadXsXgE9ETMfZEempY22Ga4MemxGL1r6sZfCKqEmNPpMeGtR2GyO6RAIDNZzcz+ERUJcaeSM/9t91/MbP7TADlwV/z6xoGn4gqYeyJJOCNdm9ogr/p7CYGn4gqYeyJJOKNdm/g3W7vAigP/trktQw+EQFg7Ikk5c32b2JGtxkAgI9/+xgxyTEMPhEx9kRSM7z9cEzvOh0AsPG3jVh3Zp3IExGR2Bh7Igl6q8NbeKfrOwCADWc2YF0yg0/UmDH2RBI1osMITfDXn1mP9cnrRZ6IiMTC2BNJ2KPBX3dmHdafYfCJGiPGnkjiRnQYgWldpgEA1iWvw4YzG0SeiIgaGmNP1AiM7DgSEV0iAAAxyTEMPlEjw9gTNRKjOo7C1C5TAZQHf+OZjSJPREQNhbEnakRCOoZgSucpAIC1yWvx8W8fizsQETUIxp6okQn1CsXbnd8GAKz5dQ02/bZJ5ImIqL4x9kSN0Giv0Zrgr/51NTaf3SzyRERUnxh7okZqtNdoTO40GQCw6vQqBp9Iwhh7okZsjPcYhHcKB1Ae/NizsSJPRET1gbEnauTGeo/FJN9JAICVp1ciLiVO5ImIqK4x9kSEcT7jEOYbBgBYcWoFtqRsEXkiIqpLjD0RAQDG+4zHRN+JAIDlp5Zja8pWcQciojrD2BORxgSfCZrgf3TqI2z7fZvIExFRXWDsiaiSCT4TMNGnPPgfnvyQwSeSAMaeiB4zwXcCJvhMAMDgE0kBY09EVZroOxHjfcYDKA/+J79/IvJERFRTjD0RPdFEn4kY5z0OALDs5DIGn0hPMfZE9EQymQxhvmEY6z0WQHnwt5/bLvJURKQtxp6Inkomk2GS7ySM8RoDAFh6Yik+PfepyFMRkTYYeyJ6JplMhvBO4ZrgLzmxBJ+lfibyVERUXXoT+4ULF6Jnz54wMzODtbV1lctkZGTgxRdfhJmZGezt7TF9+nQ8fPiwYQclkqiK4I/2Gg0AWHx8MYNPpCeaiD1AdRUXF+O1116Dv78/YmMfP1hHaWkpXnzxRSiVShw5cgRZWVl46623YGRkhEWLFokwMZH0yGQyTO40GYIgIDYlFouPL8bDUgFAU7FHI6Kn0Js1+/nz52Pq1Knw8vKq8vLdu3fj3Llz+PTTT+Hr64ugoCC8//77iImJQXFxcQNPSyRdMpkMb3d+GyEdQwAAH55aAqOmSSJPRURPozdr9s+SlJQELy8vODg4aM5TqVSYMGECfv/9d3Tq1KnK6xUVFaGoqEjzfW5uLgBArVbX78CkneJ8oEgo/1qtBoxLxZ2HENI6BIV5hdieuh1Gim9QVlgEtdofD40l82tFMip+nwmCIPIkJBbJ/FRmZ2dXCj0AzffZ2dlPvF50dDTmz5//2PnOzs51OyDVncVOYk9AVUqF47wPxR6CnuL27dtQKBRij0EiEDX2M2fOxJIlS566TGpqKtq2bVtvM0RGRiIiIkLz/b179+Dq6oqMjAy9/6FQq9VwdnZGZmYmrKysxB6n1vh4dJeUHgsgvceTm5sLFxcX2NjYiD0KiUTU2E+bNg0jR4586jLu7u7Vui2lUonjx49XOi8nJ0dz2ZPI5XLI5fLHzlcoFJL4IQcAKysryTwWgI9Hl0npsQDSezwGBnrzNi2qY6LG3s7ODnZ2dnVyW/7+/li4cCFu3LgBe3t7AMCePXtgZWWF9u3b18l9EBER6SO9ec0+IyMDd+7cQUZGBkpLS5GcnAwAaN26NSwsLBAQEID27dtj+PDhWLp0KbKzszF79myEhYVVueZORETUWOhN7OfOnYtt2/4+zGbFu+v37duHPn36wNDQELt27cKECRPg7+8Pc3NzjBgxAgsWLNDqfuRyOaKioiTxB4KUHgvAx6PLpPRYAD4ekh6ZwM9iEBERSRrfrUFERCRxjD0REZHEMfZEREQSx9gTERFJHGP/F6kfQrdly5aQyWSVTosXLxZ7rGqLiYlBy5YtYWJiAj8/v8d2oKQv5s2b99jzUJ97iKxrBw8eRHBwMJycnCCTyfDdd99VulwQBMydOxeOjo4wNTXFgAEDcOnSJXGGrYZnPZ6RI0c+9nwFBgaKM+wzREdHo1u3brC0tIS9vT0GDRqECxcuVFqmsLAQYWFhsLW1hYWFBYYMGaLZ+RhJG2P/l4pD6E6YMKHKyysOoVtcXIwjR45g27Zt2Lp1K+bOndvAk9bcggULkJWVpTmFh4eLPVK1fPnll4iIiEBUVBROnz4NHx8fqFQq3LhxQ+zRaqRDhw6VnodDhw6JPVK15efnw8fHBzExMVVevnTpUqxevRobNmzAsWPHYG5uDpVKhcLCwgaetHqe9XgAIDAwsNLz9fnnnzfghNV34MABhIWF4ejRo9izZw9KSkoQEBCA/Px8zTJTp07Fjz/+iK+//hoHDhzA9evXMXjwYBGnpgYjUCVbtmwRFArFY+f/9NNPgoGBgZCdna05b/369YKVlZVQVFTUgBPWjKurq7BixQqxx6iR7t27C2FhYZrvS0tLBScnJyE6OlrEqWomKipK8PHxEXuMOgFA+PbbbzXfl5WVCUqlUli2bJnmvHv37glyuVz4/PPPRZhQO/98PIIgCCNGjBBeeeUVUeaprRs3bggAhAMHDgiCUP5cGBkZCV9//bVmmdTUVAGAkJSUJNaY1EC4Zl9NTzqErlqtxu+//y7iZNW3ePFi2NraolOnTli2bJlevARRXFyMU6dOYcCAAZrzDAwMMGDAACQl6ecx1C9dugQnJye4u7vjjTfeQEZGhtgj1YmrV68iOzu70nOlUCjg5+ent88VAOzfvx/29vbw9PTEhAkTcPv2bbFHqpaKw3VXHPzm1KlTKCkpqfT8tG3bFi4uLnr9/FD16M0e9MRW00Po6orJkyejc+fOsLGxwZEjRxAZGYmsrCwsX75c7NGe6tatWygtLa3yv/358+dFmqrm/Pz8sHXrVnh6eiIrKwvz58/Hv/71L6SkpMDS0lLs8Wql4uegqudKH35GqhIYGIjBgwfDzc0NaWlpeO+99xAUFISkpCQYGhqKPd4TlZWVYcqUKXjuuefQsWNHAOXPj7Gx8WPvSdLn54eqT9Kx14VD6NYnbR7fo4fx9fb2hrGxMcaNG4fo6GjuQrMBBQUFab729vaGn58fXF1d8dVXXyE0NFTEyagqr7/+uuZrLy8veHt7o1WrVti/fz/69+8v4mRPFxYWhpSUFL16PwjVL0nHXhcOoVufavP4/Pz88PDhQ6Snp8PT07MepqsbzZo1g6Gh4WPvGM7JyRHtv3tdsra2Rps2bXD58mWxR6m1iucjJycHjo6OmvNzcnLg6+sr0lR1y93dHc2aNcPly5d1NvaTJk3Crl27cPDgQbRo0UJzvlKpRHFxMe7du1dp7V4qP0v0dJKOvdQPoVubx5ecnAwDAwPNY9FVxsbG6NKlCxITEzFo0CAA5ZsoExMTMWnSJHGHqwN5eXlIS0vD8OHDxR6l1tzc3KBUKpGYmKiJu1qtxrFjx574KRd9c+3aNdy+fbvSHzO6QhAEhIeH49tvv8X+/fvh5uZW6fIuXbrAyMgIiYmJGDJkCADgwoULyMjIgL+/vxgjUwOSdOy1IeVD6CYlJeHYsWPo27cvLC0tkZSUhKlTp+LNN99E06ZNxR7vmSIiIjBixAh07doV3bt3x8qVK5Gfn49Ro0aJPZrW3nnnHQQHB8PV1RXXr19HVFQUDA0NMWzYMLFHq5a8vLxKWyGuXr2K5ORk2NjYwMXFBVOmTMEHH3wADw8PuLm5Yc6cOXByctL8oaZrnvZ4bGxsMH/+fAwZMgRKpRJpaWmYMWMGWrduDZVKJeLUVQsLC8OOHTvw/fffw9LSUvM6vEKhgKmpKRQKBUJDQxEREQEbGxtYWVkhPDwc/v7+6NGjh8jTU70T++MAumLEiBECgMdO+/bt0yyTnp4uBAUFCaampkKzZs2EadOmCSUlJeINXU2nTp0S/Pz8BIVCIZiYmAjt2rUTFi1aJBQWFoo9WrWtWbNGcHFxEYyNjYXu3bsLR48eFXukGhk6dKjg6OgoGBsbC82bNxeGDh0qXL58Weyxqm3fvn1V/pyMGDFCEITyj9/NmTNHcHBwEORyudC/f3/hwoUL4g79FE97PAUFBUJAQIBgZ2cnGBkZCa6ursKYMWMqffxWl1T1OAAIW7Zs0Szz4MEDYeLEiULTpk0FMzMz4d///reQlZUl3tDUYHiIWyIiIonj5+yJiIgkjrEnIiKSOMaeiIhI4hh7IiIiiWPsiYiIJI6xJyIikjjGnoiISOIYeyIiIolj7Il0XJ8+fTBlyhSxxyAiPcY96BHpuDt37sDIyEjvj3dPROJh7ImIiCSOm/GJqunmzZtQKpVYtGiR5rwjR47A2NgYiYmJVV7nxIkTGDhwIJo1awaFQoHevXvj9OnTmsv3798PY2Nj/PLLL5rzli5dCnt7e+Tk5AB4fDP+unXr4OHhARMTEzg4OODVV1+t40dKRFLD2BNVk52dHeLi4jBv3jycPHkS9+/fx/DhwzFp0iT079+/yuvcv38fI0aMwKFDh3D06FF4eHjghRdewP379wH8HfLhw4cjNzcXv/76K+bMmYPNmzfDwcHhsds7efIkJk+ejAULFuDChQuIj49Hr1696vVxE5H+42Z8Ii2FhYVh79696Nq1K86ePYsTJ05ALpdX67plZWWwtrbGjh078NJLLwEAiouL4efnhzZt2iAlJQXPPfccPv74Y811+vTpA19fX6xcuRLffPMNRo0ahWvXrvE1fCKqNq7ZE2npww8/xMOHD/H111/js88+g1wuR0ZGBiwsLDSnik39OTk5GDNmDDw8PKBQKGBlZYW8vDxkZGRobs/Y2BifffYZdu7cicLCQqxYseKJ9z1w4EC4urrC3d0dw4cPx2effYaCgoJ6f8xEpN+aiD0Akb5JS0vD9evXUVZWhvT0dHh5ecHJyQnJycmaZWxsbAAAI0aMwO3bt7Fq1Sq4urpCLpfD398fxcXFlW7zyJEjAMrfeX/nzh2Ym5tXed+WlpY4ffo09u/fj927d2Pu3LmYN28eTpw4AWtr63p5vESk/7gZn0gLxcXF6N69O3x9feHp6YmVK1fi7NmzsLe3r3J5S0tLrFu3DsOHDwcAZGZmwsXFBStWrNC86S4tLQ2+vr5YvXo1vvzySxQXF2Pv3r0wMCjf8PboZvx/ys/Ph7W1Nb788ksMHjy4Xh4zEek/rtkTaWHWrFnIzc3F6tWrYWFhgZ9++gkhISHYtWtXlct7eHhg+/bt6Nq1K9RqNaZPnw5TU1PN5aWlpXjzzTehUqkwatQoBAYGwsvLCx999BGmT5/+2O3t2rULV65cQa9evdC0aVP89NNPKCsrg6enZ709ZiLSf3zNnqia9u/fj5UrV2L79u2wsrKCgYEBtm/fjl9++QXr16+v8jqxsbG4e/cuOnfujOHDh2Py5MmVtgIsXLgQf/zxBzZu3AgAcHR0xMcff4zZs2fjzJkzj92etbU1vvnmG/Tr1w/t2rXDhg0b8Pnnn6NDhw7186CJSBK4GZ+IiEjiuGZPREQkcYw9ERGRxDH2REREEsfYExERSRxjT0REJHGMPRERkcQx9kRERBLH2BMREUkcY09ERCRxjD0REZHEMfZEREQS9/8B7A6nLFjn0RYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(4, 4))\n",
    "\n",
    "plot_worldline(\n",
    "    ax,\n",
    "    car_front_0.plot(end_extension_time=100),\n",
    "    \"Car front\")\n",
    "\n",
    "plot_worldline(\n",
    "    ax,\n",
    "    car_back_0.plot(end_extension_time=100),\n",
    "    \"Car back\")\n",
    "\n",
    "plot_worldline(\n",
    "    ax,\n",
    "    bob_0.plot(end_extension_time=100),\n",
    "    \"Bob\")\n",
    "\n",
    "ax.set_xlim(-10, 20)\n",
    "ax.set_ylim(-10, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4282a4b7",
   "metadata": {},
   "source": [
    "We can see that Alice's car remains 10 meters long the whole time. Now let's boost to Bob's frame to see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "41d26031",
   "metadata": {},
   "outputs": [],
   "source": [
    "car_front_1 = car_front_0.boost(-0.99)\n",
    "car_back_1 = car_back_0.boost(-0.99)\n",
    "bob_1 = bob_0.boost(-0.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bc596eca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5.0, 10.0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(4, 4))\n",
    "\n",
    "plot_worldline(\n",
    "    ax,\n",
    "    car_front_1.plot(end_extension_time=100),\n",
    "    \"Car front\")\n",
    "\n",
    "plot_worldline(\n",
    "    ax,\n",
    "    car_back_1.plot(end_extension_time=100),\n",
    "    \"Car back\")\n",
    "\n",
    "plot_worldline(\n",
    "    ax,\n",
    "    bob_1.plot(end_extension_time=100),\n",
    "    \"Bob\")\n",
    "\n",
    "ax.set_xlim(-5, 10)\n",
    "ax.set_ylim(-5, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d95a384e",
   "metadata": {},
   "source": [
    "We can clearly see that in Bob's frame, Alice's car is no longer 10 meters long."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "35954bd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "car_back_1.eval(time=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fd983f00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.       , 1.4106736])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "car_front_1.eval(time=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fec00772",
   "metadata": {},
   "source": [
    "At `t = 0` in Bob's frame, the back of the car is at `x = 0` and the front is as `x = 1.41`, so Alice's car has contracted to 1.41 meters."
   ]
  }
 ],
 "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
}