Wormhole Visualization
Interactive 3D simulation of traversable wormholes based on the Morris–Thorne metric, with real astronomical datasets and gravitational lensing.
Simulation Features
Visualize the wormhole throat as a curved surface embedded in 3D space. The characteristic 'flared tube' geometry follows the exact Ellis embedding function.
Null geodesics are integrated using 4th-order Runge–Kutta in the equatorial plane. Rays are color-coded by outcome: through, deflected, or orbiting.
Background star field uses real coordinates from the Hipparcos Catalogue (ESA 1997) and Yale Bright Star Catalogue, with spectral class colors.
30 galaxies from the Messier and NGC catalogues are gravitationally lensed by the wormhole, showing magnification and position distortion.
Spacetime Physics
where the radial coordinate and proper distance are related by the Ellis formula:
The throat at has radius (the minimum radial extent). Both sides of the wormhole are asymptotically flat as .
where is the impact parameter (angular momentum per unit energy). The effective potential is:
Integrating yields the characteristic catenoid (flared-tube) shape:
This shape is identical to a catenoid — the minimal surface formed by a soap film stretched between two rings. The wormhole also satisfies a minimal surface condition, connecting this geometry to differential geometry.
The Einstein field equations require an energy density that violates the Weak Energy Condition (WEC):
The total exotic matter required scales as:
For , this is — the Casimir effect and quantum fields can produce local negative energy densities, though whether this scales to macroscopic wormholes remains an open question.
Gravitational Lensing
Numerically integrated for each impact parameter. Near-critical rays (b → b₀⁺) are deflected by many multiples of π, producing photon rings.
When a source, wormhole, and observer are perfectly aligned, the source appears as a complete ring (Einstein ring) at angular radius θ_E.
Two images form on either side of the wormhole. At u = β/θ_E = 0 (perfect alignment), magnification diverges → Einstein ring.
Traversal Physics
A traveler at velocity v = 0.1c crossing a 1-AU wormhole experiences about 8 minutes of proper time. Relativistic time dilation compresses this for faster travelers.
Theoretical Wormhole Models
| Model | Type | Throat Radius | Exotic Matter | Tidal Force | Reference |
|---|---|---|---|---|---|
Morris–Thorne (1988) First detailed proposal for a human-traversable wormhole | Traversable | ~1 AU | ~1 M☉ negative | Zero (Φ=0) | Morris & Thorne 1988, Am. J. Phys. 56, 395 |
Ellis Drainhole (1973) First exact traversable wormhole solution with scalar field source | Traversable | Arbitrary b₀ | Scalar field | Zero | Ellis 1973, J. Math. Phys. 14, 104 |
Einstein–Rosen Bridge (1935) The original wormhole solution — connects two Schwarzschild geometries but cannot be traversed | Non-traversable | Rs = 2GM/c² | None required | Infinite at horizon | Einstein & Rosen 1935, Phys. Rev. 48, 73 |
Thin-Shell Wormhole Constructed by cutting and gluing two Schwarzschild spacetimes at a thin shell | Traversable (exotic shell) | a > Rs | Negative surface energy | Finite | Visser 1989, Phys. Rev. D 39, 3182 |
ER=EPR Conjecture Proposed connection between Einstein–Rosen bridges and Einstein–Podolsky–Rosen entanglement | Quantum (speculative) | Planck scale | Quantum entanglement | N/A | Maldacena & Susskind 2013, Fortschr. Phys. 61, 781 |
Astronomical Datasets
50 bright stars with real equatorial coordinates (J2000.0), parallax distances, and spectral classifications. Used for the background star field.
50 stars
Supplementary stellar data including spectral classes and visual magnitudes for the brightest stars in the night sky.
9,096 stars (subset used)
30 galaxies including M31, M87, M51 and NGC objects, with redshifts, distances from NED, and morphological types.
30 galaxies
Galaxy distances computed from the NED cosmological calculator with H₀=70, Ω_m=0.3, Ω_Λ=0.7.
Cosmological distances
Cross-matching and validation of catalog data, spectral classifications, and coordinate transformations.
Reference catalog
Physical constants used in all calculations: c, G, solar mass, solar radius, AU — all from CODATA 2018 / IAU 2015 nominal values.
Physical constants
Explore the Wormhole
Launch the interactive 3D simulation to explore the wormhole geometry, adjust parameters, and trace light rays through curved spacetime.
Open 3D Simulation