C-0004 Verified MODERATE certainty

For the original Alcubierre metric with the tanh shape function, the total negative energy scales as |E| ~ v_s^2 R^2 / d, where R is the bubble radius and d the wall thickness. There is no wall thickness that makes the requirement small.

Standing our derivation · derivation under assumptions · TRL 1 Assumes the tanh shape function of eq. 3, with wall thickness identified as 1/sigma; r_c = r_s in eq. 16 — no longer an assumption: derived independently in compute/verify_energy_density.py and recorded as C-0006; classical general relativity, no quantum corrections and no backreaction; energy density as measured by Eulerian observers; no quantum inequality constraint is applied, so these are a lower bound on the difficulty rather than an estimate of it Stops applying any construction that is not the original 1994 metric with this shape function; in particular Van Den Broeck-type volume tricks and Natario-class metrics are not covered Computed in compute/warpkit/alcubierre.py, compute/energy_budget.py, tests/test_energy_budget.py

What it rests on

E-0009 · S-0002 — The warp drive: hyper-fast travel within general relativity · equation

…pidly a "top hat" function: With the above definitions, the metric () can be rewritten as:

d s^2 = - d t^2 + ( d x - v_s f ( r_s ) d t )^2 + d y^2 + d z^2 .

It is easy to understand the geometry of our spacetime from the previous expressions. Firs…

EXACT · re-found in source

E-0010 · S-0002 — The warp drive: hyper-fast travel within general relativity · equation

…metric that has this property is given by (G = c = 1): where: and where f is the function:

f ( r_s ) = \frac{\tanh ( \sigma ( r_s + R ) ) - \tanh ( \sigma ( r_s - R ) ) }{ 2 \tanh ( \sigma R )} ,

with R>0 and sigma>0 arbitrary parameters. Notice that for large sigma the function f(r) a…

EXACT · re-found in source

E-0012 · S-0002 — The warp drive: hyper-fast travel within general relativity · equation

…s is given by: then one can show that these observers will see an energy density given by:

T^{\alpha \beta} n_{\alpha} n_{\beta} = \alpha^2 T^{ 0 0} = \frac{1}{8 \pi} G^{ 0 0} = - \frac{1}{8 \pi} \frac{v_s^2 \rho^2}{4 {r_c}^2} ( \frac{d f}{d r_s} )^2 .

The fact that this expression is everywhere negative implies that the weak and dominant en…

EXACT · re-found in source

Attacks run against it

X-0014 SURVIVED span overreach · by straz

Attacked the scope: if the exponents in |E| ~ v^2 R^2 / d were properties of the tanh profile the claim is scoped to, the law would be decoration. Recomputed the radial integral under an unrelated C2 quintic smoothstep by blind midpoint summation: the fitted exponents are 2.00000 in R and -1.00000 in d — profile-generic to five decimals — while the constant is profile-dependent (the smoothstep wall costs 4.29x the tanh wall at equal width). The claim's self-restriction to tanh is therefore honest and conservative: no smooth profile tested is cheaper. No overreach found.

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