Source code for jinwu.physics.gr

from IPython.display import display, Math, Latex



class GeneralRelativity:
    """基础相对论/多普勒与辐射变换工具类"""

    def __init__(self):
        self._v = None

    @property
    def v(self):
        return self._v

    @v.setter
    def v(self, value):
        if hasattr(value, 'unit'):
            if value.value < 0:
                raise ValueError("速度必须大于等于0")
            self._v = value.to(u.meter/u.second)  # type: ignore
        else:
            if value < 0:
                raise ValueError("速度必须大于等于0")
            self._v = value * u.meter/u.second  # type: ignore



    def time_dilation(self, t_rest, frame_from="静止系", frame_to="运动系"):
        result = self.lorentz_factor * t_rest
        print(f"时间膨胀: 从 {frame_from} 到 {frame_to}，输入 {t_rest}，输出 {result}")
        return result




    def length_contraction(self, l_rest, frame_from="静止系", frame_to="运动系"):
        result = l_rest / self.lorentz_factor
        print(f"长度收缩: 从 {frame_from} 到 {frame_to}，输入 {l_rest}，输出 {result}")
        return result


    @property
    def beta(self):
        if self._v is None:
            raise ValueError("速度未设置")
        return 0.0  # 占位实现

    @property
    def lorentz_factor(self):
        beta = self.beta
        return 1 / np.sqrt(1 - beta ** 2)



    @classmethod
    def show_formula(cls, formula_type="all"):
        formulas = {
            "lorentz": r"\\text{洛伦兹因子:}\\quad \\gamma = \\frac{1}{\\sqrt{1-\\beta^2}}",
            "doppler": (r"\\text{Doppler因子:}\\quad "
                        r"\\mathcal{D} = \\frac{1}{\\gamma (1 - \\beta \\cos\\theta)}"
                        r"= \\gamma (1 + \\beta \\cos\\theta')"),
            "volume": r"\\text{体积变换:}\\quad ds = \\mathcal{D}\\,ds',\\quad dV = D\\,dV'",
            "length": r"\\text{长度变换:}\\quad ds = \\mathcal{D}\\,ds'",
            "time": r"\\text{时间变换:}\\quad dt = \\mathcal{D}^{-1} \\,dt'",
            "energry": r"\\text{能量变换:}\\quad E = \\mathcal{D}E'",
            "dcos_theta": (r"\\text{微分余弦变换:}" r"\\quad d\\cos\\theta = \\frac{d\\cos\\theta'}{\\gamma^2(1 + \\beta\\cos\\theta')^2} = D^{-2} d\\cos\\theta'"),
            "cos_theta": r"\\text{余弦变换:}\\quad \\cos\\theta = \\frac{\\cos\\theta' + \\beta}{1 + \\beta\\cos\\theta'}",
            "sin_theta": r"\\text{正弦变换:}\\quad \\sin\\theta = \\frac{\\sin\\theta'}{\\gamma(1 + \\beta\\cos\\theta')}",
            "tan_theta": r"\\text{正切变换:}\\quad \\tan\\theta = \\frac{\\sin\\theta'}{\\gamma(\\cos\\theta' + \\beta)}",
            "solid_angle": r"\\text{立体角变换:}\\quad d\\Omega = \\mathcal{D}^{-2} d\\Omega'",
            "time_ratio_simple": (r"\\Delta t_{\\text{eng}} : \\Delta t_e : \\Delta t_e' : \\Delta t_{\\text{obs}} \\simeq 1 : 2\\gamma^2 : 2\\gamma : 1."),
            "time_ratio_full": (r"\\Delta t_{\\text{eng}} : \\Delta t_e : \\Delta t_e' : \\Delta t_{\\text{obs}} = "
                                 r"\\frac{1-\\beta}{1-\\beta\\cos\\theta} : \\frac{1}{1-\\beta\\cos\\theta} : \\frac{1}{\\gamma(1-\\beta\\cos\\theta)} : 1."),
            "tobs_teng": (r"\\Delta t_{\\text{obs}} = \\frac{1-\\beta\\cos\\theta}{1-\\beta} \\Delta t_{\\text{eng}}."),
            "intensity": (r"\\text{辐射强度变换:}\\quad I_\\nu(\\nu) = \\mathcal{D}^3 I'_{\\nu'}(\\nu')"),
        }
        header = r"\text{带'}\text{的是共动系，不带的是近邻观测者系}\\"
        note = r"\text{尤其需要特别注意的事情是: 近邻观测者系仍然需要经过宇宙学的变换才能得到观测的结果}"
        note2 = r"\text{另外由于视超光速效应,引擎系下两束光的间隔在辐射过程中会导致间隔观测到的信号间隔变短,这完全不涉及相对论}"
        if formula_type == "all":
            display(Math(header))
            display(Math(note))
            for key in formulas:
                display(Math(formulas[key]))
        else:
            display(Math(header))
            display(Math(note))
            display(Math(formulas.get(formula_type, r"\\text{未知公式类型}")))




    @classmethod
    def show_radiation_transform(cls, formula_type="all"):
        """展示常用辐射变换公式"""
        formulas = {
            "flux1": (r"F_\\nu(\\nu_{\\text{obs}}) = \\frac{(1+z)\\mathcal{D}^3 j'_{\\nu'}(\\nu')V'}{D_L^2}."),
            "flux2": (r"F_\\nu(\\nu_{\\text{obs}}) = \\frac{(1+z)L_{\\nu,\\text{iso}}(\\nu)}{4\\pi D_L^2},"),
            "l_iso": (r"L_{\\text{iso}}(\\nu) = \\nu L_{\\nu,\\text{iso}}(\\nu) = \\mathcal{D}^4 (\\nu' L'_{\\nu'}(\\nu'))."),
            "l_nu_iso": (r"L_{\\nu,\\text{iso}}(\\nu) = \\mathcal{D}^3 L'_{\\nu'}(\\nu')."),
            "l_nu": (r"L_\\nu(\\nu) = \\mathcal{D} L'_{\\nu'}(\\nu')."),
            "l": (r"L(\\nu) = \\mathcal{D}^2 L'_{\\nu'}(\\nu')."),
            "intensity": (r"I_\\nu(\\nu) = \\mathcal{D}^3 I'_{\\nu'}(\\nu'),"),
            "emissivity": (r"j_\\nu(\\nu) = \\mathcal{D}^2 j'_{\\nu'}(\\nu'),"),
            "absorption": (r"\\alpha_\\nu(\\nu) = \\mathcal{D}^{-1} \\alpha'_{\\nu'}(\\nu')."),
        }
        header = r"\\text{带'}\\text{的是共动系，不带的是近邻观测者系}\\"
        if formula_type == "all":
            display(Math(header))
            for key in formulas:
                display(Math(formulas[key]))
        else:
            display(Math(header))
            display(Math(formulas.get(formula_type, r"\\text{未知公式类型}")))




    @classmethod
    def show_grmhd_equations(cls):
        """显示理想磁流体的GRMHD方程组（MHD守恒形式）"""
        eqs = [
            r"\\frac{\\partial (\\gamma \\rho)}{\\partial t} + \\nabla \\cdot (\\gamma \\rho \\mathbf{v}) = 0",
            r"\\frac{\\partial}{\\partial t} \\left( \\frac{\\gamma^2 h}{c^2} \\mathbf{v} + \\frac{\\mathbf{E} \\times \\mathbf{B}}{4\\pi c} \\right)"\
            r"+ \\nabla \\cdot \\left[ \\frac{\\gamma^2 h}{c^2} \\mathbf{v} \\otimes \\mathbf{v} + \\left( p + \\frac{E^2 + B^2}{8\\pi} \\right) \\mathbf{I} - \\frac{\\mathbf{E} \\otimes \\mathbf{E} + \\mathbf{B} \\otimes \\mathbf{B}}{4\\pi} \\right] = 0",
            r"\\frac{\\partial}{\\partial t} \\left( \\gamma^2 h - p - \\gamma \\rho c^2 + \\frac{B^2 + E^2}{8\\pi} \\right)"\
            r"+ \\nabla \\cdot \\left[ (\\gamma^2 h - \\gamma \\rho c^2) \\mathbf{v} + \\frac{c}{4\\pi} \\mathbf{E} \\times \\mathbf{B} \\right] = 0",
            r"\\frac{\\partial \\mathbf{B}}{\\partial t} + c \\nabla \\times \\mathbf{E} = 0"
        ]
        display(Math(r"注意方程组中\\otimes表示张量积,通过假设E=B=0, GRMHD方程可以演化为一般的广义相对论流体力学方程"))
        for eq in eqs:
            display(Math(eq))