There are emerging tools such as Remotion, which allow users to create videos based on their instructions. However, when it comes to professional-grade mathematics and physics, Remotion lacks the rigor and accuracy that Manim offers, a library originally developed by 3Blue1Brown. I conducted a test using Manim to produce a video that illustrates the Mills-Yang theory at a very high, generic level.
"""Yang-Mills Equations - YouTube VideoA single continuous animation combining all scenes with smooth transitions.Optimized for YouTube upload (1080p60).Render command: manim -qh yang_mills_youtube.py YangMillsYouTube"""from manim import *class YangMillsYouTube(Scene): """Complete Yang-Mills explanation video for YouTube.""" def construct(self): # ==================== INTRO ==================== self.intro_section() # ==================== EQUATIONS ==================== self.equations_section() # ==================== EXPLANATION ==================== self.explanation_section() # ==================== VISUALIZATION ==================== self.visualization_section() # ==================== OUTRO ==================== self.outro_section() def intro_section(self): """Opening title and hook.""" # Fade in title title = Text("Yang-Mills Equations", font_size=72, color=YELLOW) self.play(Write(title), run_time=2) self.wait(1) # Subtitle subtitle = Text( "The Mathematics Behind the Universe", font_size=36, color=WHITE ) subtitle.next_to(title, DOWN, buff=0.5) self.play(FadeIn(subtitle, shift=UP)) self.wait(1) # Hook text hook = Text( "One of the 7 Millennium Prize Problems", font_size=28, color=GOLD ) hook.next_to(subtitle, DOWN, buff=0.8) self.play(Write(hook)) self.wait(1) prize = Text("$1,000,000 unsolved!", font_size=24, color=GREEN) prize.next_to(hook, DOWN, buff=0.3) self.play(FadeIn(prize)) self.wait(2) # Transition out self.play( FadeOut(title), FadeOut(subtitle), FadeOut(hook), FadeOut(prize), run_time=1 ) self.wait(0.5) def equations_section(self): """Show the main equations.""" # Section title section_title = Text("The Equations", font_size=48, color=BLUE) section_title.to_edge(UP) self.play(Write(section_title)) self.wait(0.5) # Field Strength Tensor eq1_label = Text("Field Strength Tensor", font_size=28, color=BLUE) eq1_label.next_to(section_title, DOWN, buff=0.8) eq1 = Text( "F\u03BC\u03BD = \u2202\u03BCA\u03BD - \u2202\u03BDA\u03BC + ig[A\u03BC, A\u03BD]", font_size=36 ) eq1.next_to(eq1_label, DOWN, buff=0.3) self.play(Write(eq1_label)) self.play(Write(eq1), run_time=2) self.wait(1.5) # Yang-Mills Field Equation eq2_label = Text("Yang-Mills Field Equation", font_size=28, color=GREEN) eq2_label.next_to(eq1, DOWN, buff=0.6) eq2 = Text( "D\u03BC F\u03BC\u03BD = J\u03BD", font_size=40 ) eq2.next_to(eq2_label, DOWN, buff=0.3) self.play(Write(eq2_label)) self.play(Write(eq2), run_time=1.5) self.wait(1.5) # Expanded form eq3_label = Text("Expanded Form", font_size=28, color=RED) eq3_label.next_to(eq2, DOWN, buff=0.6) eq3 = Text( "\u2202\u03BC F\u03BC\u03BD + ig[A\u03BC, F\u03BC\u03BD] = J\u03BD", font_size=36 ) eq3.next_to(eq3_label, DOWN, buff=0.3) self.play(Write(eq3_label)) self.play(Write(eq3), run_time=2) self.wait(2) # Highlight the key term highlight_box = SurroundingRectangle(eq3, color=YELLOW, buff=0.2) note = Text( "This term makes it non-Abelian!", font_size=24, color=YELLOW ) note.next_to(highlight_box, DOWN, buff=0.3) self.play(Create(highlight_box), Write(note)) self.wait(2) # Transition out self.play( FadeOut(section_title), FadeOut(eq1_label), FadeOut(eq1), FadeOut(eq2_label), FadeOut(eq2), FadeOut(eq3_label), FadeOut(eq3), FadeOut(highlight_box), FadeOut(note), run_time=1 ) self.wait(0.5) def explanation_section(self): """Step-by-step explanation.""" # Section title section_title = Text("Understanding the Physics", font_size=48, color=GREEN) section_title.to_edge(UP) self.play(Write(section_title)) self.wait(0.5) steps = [ ("1. Gauge Field", "A\u03BC represents the force carrier", BLUE), ("2. Field Strength", "F\u03BC\u03BD measures field curvature", GREEN), ("3. Non-Abelian", "Fields interact with themselves!", RED), ("4. Applications", "Strong & weak nuclear forces", PURPLE), ] step_groups = [] prev_group = section_title for i, (title, desc, color) in enumerate(steps): step_title = Text(title, font_size=32, color=color) step_desc = Text(desc, font_size=24, color=WHITE) step_group = VGroup(step_title, step_desc).arrange(DOWN, aligned_edge=LEFT, buff=0.15) step_group.next_to(prev_group, DOWN, buff=0.5, aligned_edge=LEFT) step_group.shift(RIGHT * 0.5) self.play(Write(step_title)) self.play(FadeIn(step_desc)) self.wait(1) step_groups.append(step_group) prev_group = step_group self.wait(2) # Transition out all_steps = VGroup(*step_groups) self.play(FadeOut(section_title), FadeOut(all_steps), run_time=1) self.wait(0.5) def visualization_section(self): """Visual representation of gauge fields.""" # Section title section_title = Text("Visualizing Gauge Fields", font_size=48, color=PURPLE) section_title.to_edge(UP) self.play(Write(section_title)) self.wait(0.5) # Create grid of arrows arrows = VGroup() for i in range(-4, 5): for j in range(-2, 3): arrow = Arrow( start=ORIGIN, end=0.35 * RIGHT, color=BLUE, buff=0, stroke_width=2 ) arrow.move_to([i * 0.7, j * 0.7 - 0.5, 0]) arrow.rotate(0.25 * (i + j)) arrows.add(arrow) self.play(Create(arrows), run_time=2) self.wait(1) # Label label1 = Text("Electromagnetic field (Abelian)", font_size=24, color=BLUE) label1.to_edge(DOWN, buff=1) self.play(Write(label1)) self.wait(1) # Transform to show non-Abelian self.play( arrows.animate.set_color(RED), FadeOut(label1), run_time=1 ) label2 = Text("Yang-Mills field (non-Abelian)", font_size=24, color=RED) label2.to_edge(DOWN, buff=1) self.play(Write(label2)) # Animate self-interaction for _ in range(2): self.play( Rotate(arrows, angle=PI/8, about_point=ORIGIN), run_time=1.5 ) self.play( Rotate(arrows, angle=-PI/8, about_point=ORIGIN), run_time=1.5 ) interaction_note = Text( "Fields interact with themselves!", font_size=28, color=YELLOW ) interaction_note.next_to(label2, UP, buff=0.3) self.play(Write(interaction_note)) self.wait(2) # Transition out self.play( FadeOut(section_title), FadeOut(arrows), FadeOut(label2), FadeOut(interaction_note), run_time=1 ) self.wait(0.5) def outro_section(self): """Closing summary and call to action.""" # Summary summary_title = Text("Summary", font_size=56, color=YELLOW) self.play(Write(summary_title)) self.wait(1) self.play(summary_title.animate.to_edge(UP)) points = VGroup( Text("Yang-Mills equations describe fundamental forces", font_size=28), Text("Non-Abelian structure = self-interacting fields", font_size=28), Text("Foundation of the Standard Model", font_size=28), Text("Mass gap problem remains unsolved", font_size=28, color=GOLD), ).arrange(DOWN, buff=0.4, aligned_edge=LEFT) points.next_to(summary_title, DOWN, buff=0.8) for point in points: self.play(Write(point)) self.wait(0.8) self.wait(2) # Fade to final card self.play(FadeOut(summary_title), FadeOut(points)) # End card thanks = Text("Thanks for watching!", font_size=48, color=WHITE) subscribe = Text("Like & Subscribe for more physics!", font_size=28, color=BLUE) subscribe.next_to(thanks, DOWN, buff=0.5) end_group = VGroup(thanks, subscribe) self.play(Write(thanks)) self.play(FadeIn(subscribe)) self.wait(3) # Final fade out self.play(FadeOut(end_group)) self.wait(1)if __name__ == "__main__": print("=" * 50) print("Yang-Mills YouTube Video") print("=" * 50) print() print("Render command:") print(" manim -qh yang_mills_youtube.py YangMillsYouTube") print() print("For 4K:") print(" manim -qk yang_mills_youtube.py YangMillsYouTube")
Naixian Zhang 