- Why are the axes for a moving frame tilted, and why do they appear symmetric around the light cone?
- The axes tilt because, in relativity, simultaneity is relative. The x'-axis (line of simultaneity for the moving frame) and ct'-axis (worldline of the moving frame's origin) must satisfy the Lorentz transformation. Their symmetry around the light cone is a direct geometric consequence of the invariance of the speed of light. The angle between an axis and the light line is related to the frame's velocity, ensuring that light rays always bisect the angle between the t' and x' axes, preserving c for all observers.
- What does the light cone actually represent?
- The light cone defines the boundary of causal connectivity for an event at its vertex. Events inside the future cone can be influenced by the vertex event; events inside the past cone could have influenced it. Events outside the cone are spacelike separated—no signal, even light, can travel between them and the vertex, meaning they cannot be causally connected. This structure is absolute and identical in all inertial frames.
- How does this 1+1D diagram relate to our 3+1D universe?
- The simulator's 1+1D model (one space, one time) captures the essential relativistic effects like time dilation, length contraction, and relativity of simultaneity. In the full 3+1D universe, the light 'cone' is actually a 3D surface in 4D spacetime. The simplified diagram is a cross-section, omitting two spatial dimensions to make the geometry and transformations visually clear and plottable on a 2D screen.
- What is the physical meaning of the Lorentz factor γ (gamma) shown in the simulator?
- The Lorentz factor γ = 1/√(1 - v²/c²) is a dimensionless quantity that quantifies the magnitude of relativistic effects. It determines the rate of time dilation (moving clocks tick slower by a factor of γ) and length contraction (moving lengths are shortened by a factor of 1/γ). As v approaches c, γ increases without bound, explaining why reaching the speed of light requires infinite energy.