Christian H. Cooper

Christian H. Cooper

Christian H. Cooper

@christiancooper

20 Jan 2025

The code: ~~~ from manim import * from manim.mobject.three_d.three_dimensions import Surface import numpy as np class StarField(VGroup): def __init__(self, is_3D=False, num_stars=200, **kwargs): super().__init__(**kwargs) for _ in range(num_stars): x = np.random.uniform(-7, 7) y = np.random.uniform(-4, 4) z = np.random.uniform(-3, 3) if is_3D else 0 star = Dot(point=[x, y, z], color=WHITE, radius=0.02) self.add(star) class QEDJourney(ThreeDScene): def construct(self): # Configuration self.camera.background_color = "#000000" self.set_camera_orientation(phi=70*DEGREES, theta=-30*DEGREES) # 1. Cosmic Introduction star_field = StarField(is_3D=True) title = Text("Quantum Field Theory:\nA Journey into QED", font_size=48, gradient=(BLUE, YELLOW)) subtitle = Text("From Maxwell to Feynman", font_size=36) title_group = VGroup(title, subtitle).arrange(DOWN) self.play(FadeIn(star_field), run_time=2) self.play(Write(title), FadeIn(subtitle)) self.wait(2) self.play(title_group.animate.scale(0.5).to_corner(UL), run_time=2) # 2. Spacetime Foundation axes = ThreeDAxes(x_range=[-5,5], y_range=[-5,5], z_range=[-4,4]) spacetime_grid = Surface( lambda u,v: axes.c2p(u,v,0), u_range=[-5,5], v_range=[-5,5], resolution=(25,25), fill_opacity=0.1, stroke_width=1, stroke_color=BLUE_E ) light_cone = Surface( lambda u,v: axes.c2p(v*np.cos(u), v*np.sin(u), v), u_range=[0,2*PI], v_range=[0,3], resolution=(24,12), fill_opacity=0.15, color=YELLOW ) self.play( Create(axes), Create(spacetime_grid), run_time=3 ) self.begin_ambient_camera_rotation(rate=0.1) self.play(Create(light_cone), run_time=2) self.wait(2) # 3. Electromagnetic Waves Visualization wave_group = VGroup() for direction in [LEFT, RIGHT]: em_wave = ParametricFunction( lambda t: axes.c2p( direction[0]*t, 0, np.sin(3*t)*0.5 ), t_range=[0,5], color=RED ) wave_group.add(em_wave) b_field = ArrowVectorField( lambda p: [0, np.sin(3*p[0]),0], x_range=[-5,5], y_range=[-5,5], z_range=[-4,4], colors=[BLUE] ) maxwell_eq = MathTex( r"\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}", r"\nabla \times \mathbf{B} = \mu_0\mathbf{J} \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}" ).arrange(DOWN).to_edge(DR) self.play( Create(wave_group), Create(b_field), Write(maxwell_eq), run_time=4 ) self.wait(3) # 4. QED Lagrangian Revelation qed_lagrangian = MathTex( r"\mathcal{L}_{\text{QED}} = \bar{\psi}(i \gamma^\mu D_\mu - m)\psi - \tfrac{1}{4}F_{\mu\nu}F^{\mu\nu}", substrings_to_isolate=[r"\psi", r"D_\mu", r"\gamma^\mu", r"F_{\mu\nu}"] ).scale(0.8).to_corner(UR) qed_lagrangian.set_color_by_tex(r"\psi", ORANGE) qed_lagrangian.set_color_by_tex(r"D_\mu", GREEN) qed_lagrangian.set_color_by_tex(r"\gamma^\mu", TEAL) qed_lagrangian.set_color_by_tex(r"F_{\mu\nu}", GOLD) self.play( Transform(maxwell_eq, qed_lagrangian), run_time=3, path_arc=PI/2 ) self.wait(2) # 5. Feynman Diagram Unfoldment feynman_diagram = VGroup( Line(LEFT*3, ORIGIN, color=BLUE), Line(ORIGIN, RIGHT*3, color=BLUE), ArcBetweenPoints(LEFT*3, RIGHT*3, angle=PI/2, color=YELLOW) ).shift(UP*2) vertex_dot = Dot(color=WHITE).scale(1.5) labels = VGroup( MathTex(r"e^-", color=BLUE).next_to(feynman_diagram[0], LEFT), MathTex(r"e^-", color=BLUE).next_to(feynman_diagram[1], RIGHT), MathTex(r"\gamma", color=YELLOW).next_to(feynman_diagram[2], UP) ) self.play( Create(feynman_diagram), GrowFromCenter(vertex_dot), FadeIn(labels), run_time=3 ) self.wait(2) # 6. Coupling Constant Evolution alpha_plot = Axes( x_range=[0, 20], y_range=[0.005, 0.03], x_length=6, y_length=4 ).to_edge(DL) curve = alpha_plot.plot( lambda x: 0.007297 0.0001*x, color=RED ) plot_labels = VGroup( alpha_plot.get_x_axis_label(r"\text{Energy Scale (GeV)}"), alpha_plot.get_y_axis_label(r"\alpha") ) self.play( Create(alpha_plot), Create(curve), Write(plot_labels), run_time=3 ) self.wait(2) # 7. Grand Finale self.stop_ambient_camera_rotation() final_text = Text("QED: Light & Matter United", font_size=48) self.play( FadeIn(final_text, shift=UP), *[FadeOut(mob) for mob in self.mobjects], run_time=5 ) self.wait(3)

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