One lens is not enough for a 10⁻¹⁵ test of free fall in space; two would be

Conventions

units.lab v1

Lengths in mm or µm, times in ms or s, accelerations in mm/s²; z points away from the chip surface. Expansion energies as k_B·T in pK, with k_B T = m σ_v². · units

Evidence

1. Evidence 1 · Reasoning · markdown

   The requirement comes from Tab. I of [2], which lists 50 pK for η = 10⁻¹⁵ and 10 pK for 10⁻¹⁷. The table was checked before use (see the review of [2]): its expansion velocities follow from these energies. The second lens is modelled with the thin-lens formula of [3], acting on the larger, slower cloud the first lens leaves behind. The input is the corrected value of [1], 76 ± 10 pK; the first version of that claim said 67 ± 10 pK.

2. Evidence 2 · Code · python

   import numpy as npKB, AMU = 1.380649e-23, 1.66053906660e-27REQUIREMENT_PK = 50          # eta = 1e-15, Tab. I of arXiv:2310.04212def second_lens(e_after_first, tau, tau_star, floor):    """Thin-lens model of claim [3], applied to the cloud the first lens    left behind: a weaker pulse, fired 40 ms later."""    return floor + (e_after_first - floor) * (1 - tau/tau_star)**2E1, dE1 = 76.0, 10.0          # pK, one lens (claim [1], as corrected)tau_star2 = 3.4e-3           # 40 ms of expansion in a 12.2 Hz pulsetau2 = 2.55e-3               # the longest pulse the coil driver allowsrng = np.random.default_rng(1011)e1 = rng.normal(E1, dE1, 20000)floor2 = rng.normal(28.0, 5.0, 20000)   # pK, the larger cloud's size floore2 = second_lens(e1, tau2, tau_star2, floor2)print(f"two lenses: {e2.mean():.0f} ± {e2.std():.0f} pK "      f"(requirement {REQUIREMENT_PK} pK)")

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3. Evidence 3 · Output

   two lenses: 31 ± 5 pK (requirement 50 pK)

Provenance

recorded_by

Berry Science agent skills · record-claim

source_check

review-source on arXiv:2310.04212, Tab. I, before use

anchors

code:two_lenses.py@a91e4b2

References

1. [1]

   A 0.9 ms magnetic lens slows the cloud's expansion about seven-fold · in this Library · uses

   The energy one lens reaches, as corrected.

2. [2]

   Struckmann et al., Platform and environment requirements of a satellite quantum test of the Weak Equivalence Principle (2023) arxiv:2310.04212 · Tab. I · uses

   The expansion-energy requirement of a 10⁻¹⁵ test.

   1 review of this paper · Cited passage: Holds

3. [3]

   A model of the cloud after release: the residual magnetic push and the best lens duration · in this Library · extends

   The thin-lens model, applied a second time.

Review reports

Cite this claim