Measured · cone membership
—
VarWISE rows inside 4 θE
Catalog-complete query over 1,918,082 published sky positions.
Sky data impact · VarWISE
The selected RA/Dec is measured catalog space; the wormhole is a conditional Ellis weak-field lens. The Einstein scale is derived from the live throat radius and lens distance under a shared source-screen assumption, then applied to every VarWISE position in the four-Einstein-radius field.
Derived · local density
—
sources per square degree
The result changes with sky position as well as angular lens scale.
Model · photometry
—
|ΔW1| ≥ 0.05 mag
Uses total magnification of the two Ellis images; it does not overwrite catalog W1.
Model · astrometry
—
|centroid shift| ≥ 0.2″
Flux-weighted photocenter relative to the unlensed VarWISE coordinate.
Model × instrument
—
image pairs wider than 6.1″
WISE W1 resolution is used as a comparison threshold, not a detection claim.
Derived · union
—
rows requiring joint review
Union of the photometric, astrometric, and source-splitting flags.
Boundary condition
—
apparent epoch displacement
Uses the mission’s prescribed mouth-clock offset; lensing alone does not create it.
Interpretation
—
dominant VarWISE class in cone
A dense stellar field can produce a much larger review set than a high-latitude field.
| Nearest catalog coordinate | Class | Separation | β / θE | Modeled ΔW1 | Centroid shift | Image pair | Catalog state |
|---|---|---|---|---|---|---|---|
| Loading the VarWISE sky index… | |||||||
Data contract. RA, Dec, and class are read from the complete VarWISE table at Float32 coordinate precision. Lensing uses a common background screen (D_S=2D_L) because per-source distances are not applied in this view. Photometric and astrometric effects are model outputs; class counts and cone membership are catalog data. No traversable wormhole has been observed.
Mission ledger
Every result below is recomputed from the same metric and traveler path used by the stage. External distance is a declared comparison; gate-to-gate distance, clocks, curvature, and stress-energy come from the wormhole geometry.
Derived · proper distance
—
gate A → gate B through l = 0
Because \(l\) is proper radial distance, the gate-to-gate length is exactly \(2a\).
Derived · elapsed time
—
traveler proper time
Integrated along the selected timelike worldline, not inferred from coordinate speed.
Derived · local measurement
—
γ at the throat
A local static observer measures longitudinal length as \(L_0/\gamma\). This is not optical appearance.
Model requirement
—
∫ negative energy density dV
Exact for this Ellis shape over a complete spatial slice. It is required support, not available technology.
Derived · clock map
—
B external time minus A entry time
Includes the prescribed mouth-clock offset and the coordinate throat transit.
Derived · null route
—
fastest gate-to-gate light time
Computed from \(ds^2=0\) along the radial null geodesic.
Derived · safety
—
max |Δa| across ξ
The larger of the radial and boosted transverse throat tidal eigenvalues.
Boundary audit
—
closed-null-route margin
Positive margin is causal in the prescribed static comparison frame; negative admits a closed causal curve.
Metric and traveler profile
The horizontal coordinate is \(x=l/r_0\). The chart shows exact analytic geometry and the numerically evaluated traveler state. Values are dimensionless except for tidal load, which is reported relative to standard gravity.
One route, four fields
The areal radius reaches its minimum at the throat; the lapse sets clock rate; the traveler velocity and tidal load respond to the same geometry.
r/r₀lapse e^Φv/clog₁₀(1+tide/g)
Equation ledger
Signature \((-+++)\). Stress-energy formulas use SI units where shown; the analytic metric and geodesic equations are evaluated directly in the browser.
EQ 01 · selected spacetime
Redshifted Ellis member of the Morris–Thorne class
$$ds^2=-e^{2\Phi(l)}c^2dt^2+dl^2+r(l)^2d\Omega^2,\qquad r(l)=\sqrt{l^2+r_0^2},\qquad \Phi(l)=\Phi_0\frac{r_0^2}{l^2+r_0^2}$$
The throat is regular because \(r(0)=r_0\), \(r'(0)=0\), \(r''(0)=1/r_0>0\), and finite \(\Phi_0\) creates no horizon. Setting \(\Phi_0=0\) gives the ultrastatic Ellis geometry.
EQ 02 · traveler clock
Invariant proper time
$$d\tau=\frac{1}{c}\sqrt{-g_{\mu\nu}dx^\mu dx^\nu},\qquad d\tau=e^{\Phi}\frac{dt}{\gamma_{\rm local}}$$
Gravitational time dilation \(e^\Phi\) and kinematic time dilation \(1/\gamma\) are shown separately.
EQ 03 · radial geodesic
Free-fall energy and velocity
$$\mathcal E=e^{\Phi(a)}\gamma_A,\quad \left(\frac{1}{c}\frac{dl}{d\tau}\right)^2=\mathcal E^2e^{-2\Phi}-1,\quad \gamma_{\rm local}=\mathcal E e^{-\Phi}$$
The free-fall preset uses numerical quadrature of these exact first integrals. The powered path instead holds \(v_{\rm local}\) constant.
EQ 04 · local length
Lorentz contraction in a tetrad
$$L_{\rm static}=\frac{L_0}{\gamma_{\rm local}}$$
This is a nearby observer’s simultaneous measurement along the direction of motion, not a global contraction of the throat and not the camera image.
EQ 05 · tidal safety
Geodesic deviation
$$\Delta a^{\hat i}=-c^2R^{\hat i}{}_{\hat0\hat j\hat0}\,\xi^{\hat j}$$
At this throat, the radial magnitude is \(2|\Phi_0|c^2\xi/r_0^2\); the moving transverse magnitude is \(\gamma^2\beta^2c^2\xi/r_0^2\).
EQ 06 · required source
Negative energy at the throat
$$\epsilon_0=p_{r,0}=-\frac{c^4}{8\pi G r_0^2},\qquad (\epsilon+p_r)_0=-\frac{c^4}{4\pi G r_0^2}<0$$
The flare-out condition forces radial null-energy-condition violation in classical general relativity for this model.
EQ 07 · ray tracing
Equatorial null rays
$$\left(\frac{dl}{d\lambda}\right)^2=E^2e^{-2\Phi}-\frac{L^2}{r^2},\qquad \frac{d\varphi}{dl}=\frac{b/r^2}{\sqrt{e^{-2\Phi}-b^2/r^2}}$$
The null-ray view integrates this equation. The global crossing threshold is \(b_{\rm crit}=\min_l[r(l)e^{-\Phi(l)}]\).
EQ 08 · chronology audit
Fastest closed causal route
$$\mathcal M_{\rm causal}=\frac{D_{AB}}{c}+\Delta t_{\rm null}-|\Delta T_{AB}|$$
With the page’s explicit clock-map convention, \(\mathcal M_{\rm causal}<0\) means a light signal can traverse the wormhole and return through external space to its own past. This is a boundary-condition audit, not a formation calculation.
EQ 09 · sky lens scale
Ellis angular Einstein radius
$$\theta_E^3=\frac{\pi}{4}\frac{D_{LS}}{D_S}\frac{r_0^2}{D_L^2}$$
The sky view sets \(D_S=2D_L\), so \(D_{LS}/D_S=1/2\). This shared screen is an explicit comparison model, not a per-source distance solution.
EQ 10 · image plane
Two weak-field Ellis images
$$\hat\theta_+^3-\hat\beta\hat\theta_+^2-1=0,\qquad \hat\theta_-^3-\hat\beta\hat\theta_-^2+1=0$$
The browser solves the positive outer-image root and negative inner-image root for every VarWISE coordinate inside \(4\theta_E\), then derives total magnification and the unresolved photocenter.
Live verification
The table recomputes analytic identities and numerical residuals on every parameter change. Green means the selected reduced model passed its own declared check; it does not certify physical realizability.
| Check | Expected | Computed | Status |
|---|
Representation and validity contract
Exact analytic
Static geometry
The selected \(r(l)\), \(\Phi(l)\), throat conditions, curvature components, and stress-energy are exact for the declared metric.
Derived numerical
Worldlines and rays
One-dimensional timelike quadratures and equatorial null-ray families are integrated numerically with convergence checks.
Illustrative projection
Screen geometry
The embedding height and canvas perspective are drawing aids. The ray panel is an unwrapped azimuth diagram, not a camera photograph.
Unknown / speculative
Formation and support
No observed macroscopic traversable wormhole, verified stabilizing material, or accepted construction route supplies these boundary conditions.
Domain. Static, spherical, nonrotating, two-way geometry; radial test traveler; symmetric exterior potentials at the readout gates. The A–B map does not solve cosmological matching, mouth transport, nonlinear stability, quantum backreaction, radiation from accretion, rotation, charge, or the traveler’s self-gravity. A full dynamical formation calculation would require numerical relativity and a physically specified matter model.
Primary sources
- Paz, M. et al. (2026 draft). VarWISE: a catalog of infrared-variable objects from the NEOWISE-Reactivation mission. IRSA manuscript
- Abe, F. (2010). Gravitational microlensing by the Ellis wormhole. Astrophysical Journal 725, 787–793. arXiv
- Toki, Y., Kitamura, T., Asada, H. & Abe, F. (2011). Astrometric image centroid displacements due to gravitational microlensing by the Ellis wormhole. Astrophysical Journal 740, 121. arXiv
- Ellis, H. G. (1973). Ether flow through a drainhole: a particle model in general relativity. Journal of Mathematical Physics 14, 104–118. DOI
- Morris, M. S. & Thorne, K. S. (1988). Wormholes in spacetime and their use for interstellar travel. American Journal of Physics 56, 395–412. DOI
- Morris, M. S., Thorne, K. S. & Yurtsever, U. (1988). Wormholes, time machines, and the weak energy condition. Physical Review Letters 61, 1446. DOI
- Ford, L. H. & Roman, T. A. (1996). Quantum field theory constrains traversable wormhole geometries. Physical Review D 53, 5496. DOI
- Hawking, S. W. (1992). Chronology protection conjecture. Physical Review D 46, 603. DOI
- James, O., von Tunzelmann, E., Franklin, P. & Thorne, K. S. (2015). Visualizing Interstellar’s wormhole. American Journal of Physics 83, 486–499. DOI
- Thorne, K. S. (2014). The Science of Interstellar. W. W. Norton & Company. Reference source for the film-scenario distance and Endurance scale used by the preset.