diagrama_de_minkowski.ipynb

{
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"
    }
   },
   "cell_type": "markdown",
   "id": "30344614",
   "metadata": {},
   "source": [
    "# Diagrama de Minkowski\n",
    "**Feito por:** Luiza Valezim\n",
    "\n",
    "**Última data de modificação:** 28/10/2022\n",
    "\n",
    "#### Descrição \n",
    "\n",
    "Esse notebook apresenta um diagrama de Minkowski interativo e as explicações dos cálculos para chegar nos devidos valores. Para simplificações futuras, foram adotadas as unidades de medida relativas a velocidade da luz, portanto foi considerado $c = 1$.\n",
    "\n",
    "Esse diagrama considera dois eventos: **A** e **B**, no qual consideramos que o A (representante das coordenadas x, ct) seria o nosso referencial parado e B (com as coordenadas x', ct') como sendo referencial em movimento. No nosso caso, estamos simulando a dilatação do tempo e do espaço quando o observador B passa com velocidade $v$ pelo observador A. \n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cededd79",
   "metadata": {},
   "source": [
    "**Importando as bibliotecas**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "93f23c96-8528-4cb0-b53f-7f7bfccc6b1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import numpy as np\n",
    "import math\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import FloatSlider\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "049dc8f6",
   "metadata": {},
   "source": [
    "**Declarando as variáveis globais**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "566a8837-e650-47c8-9530-0e8fa5f19304",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = 3*1e8"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a2daa5d",
   "metadata": {},
   "source": [
    "### Funções Auxiliares"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9b09e5f",
   "metadata": {},
   "source": [
    "**Fator de Lorentz (gamma)**\n",
    "\n",
    "$$ \\gamma = \\frac{1}{\\sqrt{1 - \\frac{v^2}{c^2}}}  $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "96f6b46c-9593-4508-a879-77946dbd889a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calcula_gamma(v):\n",
    "    gamma = 1 / (1 - (v**2/c**2))**0.5\n",
    "    return gamma"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a89f5d5b",
   "metadata": {},
   "source": [
    "**Transformações de Lorentz**\n",
    "\n",
    "$$ \n",
    "x = \\gamma \\cdot (x' + v \\cdot t') \\\\\n",
    "t = \\gamma \\cdot (t' + \\frac {v}{c^2} \\cdot t')\n",
    "$$\n",
    "\n",
    "$$\n",
    "x' = \\gamma \\cdot (x - v \\cdot t) \\\\\n",
    "t' = \\gamma \\cdot (t - \\frac {v}{c^2} \\cdot t) \n",
    "$$\n",
    "\n",
    "Para simplificações de contas, consideramos a velocidade da luz ($c$) como sendo igual a 1, já que a unidade de medida utilizada para distância é proporcional à essa velocidade (como $sluz$).\n",
    "\n",
    "Assim, obtivemos as seguintes fórmulas simplificadas:\n",
    "$$\n",
    "x = \\frac{(x' + v \\cdot t')}{\\sqrt{1-v^2}} \\space \\space \\space \\space \\space\n",
    "t = \\frac{(t' + v \\cdot x')}{\\sqrt{1-v^2}} \n",
    "$$\n",
    "\n",
    "\n",
    "$$\n",
    "x' = \\frac{(x - v \\cdot t)}{\\sqrt{1-v^2}} \\space \\space \\space \\space \\space\n",
    "t' = \\frac{(t - v \\cdot x)}{\\sqrt{1-v^2}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "19e2a58f-fea6-4ddc-92b8-c3338165ec31",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Para descobrirmos x e t\n",
    "def transf_lorentz(x_linha, t_linha, v):\n",
    "    x = (x_linha + t_linha*v) / (1-v**2)**0.5\n",
    "    t = (t_linha + x_linha*v) / (1-v**2)**0.5\n",
    "    return x, t\n",
    "\n",
    "# Para descobrirmos x_linha e t_linha\n",
    "def transf_lorentz_linha(x, t, v):\n",
    "    x_linha = (x - t*v) / (1-v**2)**0.5\n",
    "    t_linha = (t - x*v) / (1-v**2)**0.5\n",
    "    return x_linha, t_linha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2553e10",
   "metadata": {},
   "source": [
    "**Intervalo invariante**\n",
    "\n",
    "O intervalo invariante é o que consideramos como uma medida de “distância” que não muda, relacionada ao intervalo de tempo e ao deslocamento no espaço. Como o próprio nome diz, ele sempre deverá ser igual caso estejamos comparando dois eventos.\n",
    "\n",
    "$$\n",
    "i^2 = {ct}^2 - x^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "29e53a00-5a67-431a-99c3-0c4f5f6c76b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcula o intervalo invariante de um sistema\n",
    "def calcula_intervalo_invariante(x, t, l):\n",
    "    int_inv = round(t**2 - x**2, 2)\n",
    "    print(\"O intervalo invariante é de {0}: {1}\".format(l, int_inv))\n",
    "\n",
    "# Compara o intervalo invariante dos dois sistemas\n",
    "def compara_intervalo_invariante(x_a, t_a, x_b, t_b):\n",
    "    int_a = calcula_intervalo_invariante(x_a, t_a)\n",
    "    int_b = calcula_intervalo_invariante(x_b, t_b)\n",
    "    \n",
    "    if (int_a == int_b):\n",
    "        return True\n",
    "    else:\n",
    "        return False"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63d035eb",
   "metadata": {},
   "source": [
    "**Encontra o ângulo da reta**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7fb9c1cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def findAngle(M1, M2):\n",
    "     \n",
    "    # Store the tan value  of the angle\n",
    "    angle = abs((M2 - M1) / (1 + M1 * M2))\n",
    " \n",
    "    # Calculate tan inverse of the angle\n",
    "    angle_radians = math.atan(angle)\n",
    " \n",
    "    # Convert the angle from\n",
    "    # radian to degree\n",
    "    angle_degrees = math.degrees(angle_radians)\n",
    "    \n",
    "    # Print the result\n",
    "    #print (\"O ângulo formado é de: {0}\".format(round(angle_degrees, 4)))\n",
    "    \n",
    "    return angle_radians"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e890a4d",
   "metadata": {},
   "source": [
    "**Desenha ponto e legenda**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "88f3d2f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_point(x, y, color):\n",
    "    plt.scatter(x, y, color=color)\n",
    "    txt_a = '('+ str(round(x,3)) + ', '+ str(round(y,3)) + ')'\n",
    "    plt.text(x + 0.3, y + 0.3, txt_a)    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8d61f27",
   "metadata": {},
   "source": [
    "### Função Principal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "72e67426",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def diagram(v, x, ct, zoom):\n",
    "    \n",
    "    # Definindo os dominios de x\n",
    "    eixo_x = np.linspace(-zoom, zoom, num=1000)\n",
    "    \n",
    "    # Calculando o ângulo formado pelo eixo x'\n",
    "    angle = findAngle(0, v) \n",
    "    # Calculando a tangente do eixo ct'\n",
    "    tg = math.tan(angle)\n",
    "    inverted_tg = math.tan((2*math.pi/4) - angle)\n",
    " \n",
    "    # Retas formadas pela velocidade desejada\n",
    "    plt.plot(eixo_x, eixo_x*v, c=\"blue\", label=\"eixo x'\")\n",
    "    plt.plot(eixo_x, eixo_x*inverted_tg, c=\"blue\", label=\"eixo ct'\")\n",
    "    \n",
    "    # Retas formadas pela velocidade da luz\n",
    "    plt.plot(eixo_x, eixo_x, c=\"orange\", label=\"v = c\")\n",
    "    plt.plot(eixo_x, -eixo_x, c=\"orange\")\n",
    "    \n",
    "    # Desenha reta entre eixo e evento B    \n",
    "    #plt.plot(eixo_x, eixo_x*v + ct - x*tg, c=\"yellow\", linestyle='--')\n",
    "    #plt.plot(eixo_x, (eixo_x - x)*inverted_tg + ct, c=\"yellow\", linestyle='--')  \n",
    "    \n",
    "    # Descobrindo os pontos para x' = 0 e ct' = 0\n",
    "    x_linha, ct_linha = transf_lorentz_linha(x, ct, v)\n",
    "    x1, ct1 = transf_lorentz(x_linha, 0, v)\n",
    "    x2, ct2 = transf_lorentz(0, ct_linha, v)\n",
    "    plt.plot([x, x1], [ct, ct1], c=\"purple\", linestyle='--')\n",
    "    plt.plot([x, x2], [ct, ct2], c=\"purple\", linestyle=\"--\")\n",
    "    plt.scatter(x1, ct1, color=\"purple\")\n",
    "    plt.scatter(x2, ct2, color=\"purple\")\n",
    "    \n",
    "    # Desenhando o evento em A em relação à A (sempre nulo)\n",
    "    draw_point(0, 0, 'red')\n",
    "    \n",
    "    # Desenhando o evento B (input)\n",
    "    draw_point(x, ct, 'purple')\n",
    "    \n",
    "    # Desenhando o evento em B em relação à A\n",
    "    print(\"\\nx = {0}, ct = {1}\".format(round(x,3), round(ct,3)))\n",
    "    print(\"x' = {0}, ct' = {1}\\n\".format(round(x_linha,3), round(ct_linha,3)))\n",
    "    \n",
    "    # Calcula o intervalo invariante\n",
    "    calcula_intervalo_invariante(x, ct, \"A\")\n",
    "    calcula_intervalo_invariante(x_linha, ct_linha, \"B\")\n",
    "    \n",
    "    plt.title('Diagrama de Minkowski')\n",
    "    plt.grid()    \n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"ct\")\n",
    "    plt.ylim(-zoom, zoom)\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "dc694190",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "efc887b4d8854d8b8723292b3991ef2c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description='v', max=1.0, step=0.01), FloatSlider(value=10.0, des…"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interactive_plot = interactive(diagram, v=(0.0, 1.0, 0.01), x=(0, 20, 0.1), ct=(0, 20, 0.1), zoom=(5, 25, 1))\n",
    "output = interactive_plot.children[-1]\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fde27761",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "# Gráfico do comportamento do gamma dependendo da velocidade\n",
    "\n",
    "Como adicional, achei interessante plotar o gráfico do comportamento do gamma quando aumentamos a velocidade"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 516,
   "id": "9b2a7e42-f264-4a48-9bf3-8bd7e7f82321",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Quanto maior o \"step\" do eixo x, mais dá para notar que o gamma tende à infinito \n",
    "step = 1e-5\n",
    "velocidades = np.arange(0*c, 1*c, step*c)\n",
    "gammas = []\n",
    "\n",
    "for vel in velocidades:\n",
    "    gamma = calcula_gamma(vel)\n",
    "    gammas.append(gamma)\n",
    "    \n",
    "# Plotando gráfico do gamma por velocidade\n",
    "plt.plot(velocidades, gammas)\n",
    "plt.title('Fator de Lorentz por Velocidade')\n",
    "plt.xlabel('Velocidade')\n",
    "plt.ylabel('Gamma')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5a318bc",
   "metadata": {},
   "source": [
    "**Conclusões:**\n",
    "- Quanto menor a velocidade, $\\gamma$ tende à 1;\n",
    "- Quanto maior a velocidade, $\\gamma$ tende à infinito;\n",
    "- Quanto menor for o step, maior será a aproximação para infinito quando a velocidade tender à $c$. Isso se deve pela limitação computacional que temos ao lidar com números muito grandes.\n",
    "\n",
    "---"
   ]
  }
 ],
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