04 / INTERACTIVE TIMING LABORATORY
Turn a hypothesis
into a curve.
Explore the conditional prediction that an intrinsic time scale contributes an additional, frequency-dependent loss of Ramsey contrast.
Ramsey spectroscopy prepares a superposition, allows a phase to accumulate, and then reads it with a second pulse. Scanning the readout phase gives a fringe. Its contrast tells us how much coherence survives. The model below adds a hypothetical intrinsic decay rate Γ = ε(2πν)²/2 to a separately specified background rate.
The Ramsey contrast laboratory
Background only Background + hypothetical intrinsic decay. Both curves start at ideal contrast 1. Rounded species frequencies are used.
Pₑ(φ) = [1 + C(T) cos φ] / 2
The fringe shrinks when contrast is lost. This idealized readout omits state-preparation and measurement errors.
How to interpret the presets and long time settings
The visible teaching case deliberately chooses a hypothetical ε large enough to make the effect easy to see. It is not a fitted value or a claim that such a value is compatible with all existing experiments. The Planck-time comparison uses approximately 5.39 × 10⁻⁴⁴ seconds as a reference scale, not a measured tick duration or a value established by DTT.
Interrogation times of 10⁴–10⁵ seconds are mathematical extrapolations in this explorer. They do not assert that continuous coherent interrogation of the selected transition is achievable. Lifetime, laser noise, trapping conditions, dead time, and other limitations must be evaluated experimentally. Long total averaging time is also different from one long coherent interrogation.
What the plot establishes: the consequences of an assumed equation. A visible difference between curves is not evidence that nature follows that equation. Conversely, an imperceptible difference on this plot does not provide an experimental bound.
05 / THE DETECTABILITY QUESTION
A tiny prediction needs
an honest uncertainty budget.
A numerical time scale is not a timing resolution. The crucial question is whether its predicted effect exceeds a defensible measurement limit.
From an excess-rate limit to a time-scale bound
If an experiment establishes an upper limit Γmax on an additional decay rate, this model translates it into ε ≤ 2Γmax/(2πν)². Select a hypothetical rate limit to explore the algebra. No statistical confidence level is implied by this calculator.
A smaller bound requires better evidence for a smaller excess-rate limit. It does not mean that the instrument resolves individual intervals of that duration.
| Quantity | What it means | What must be reported |
|---|---|---|
| Time resolution | The smallest distinguishable interval under a defined measurement procedure. | Bandwidth, detector response, estimator, and uncertainty. |
| Frequency stability | How frequency fluctuations behave over an averaging time. | A stability statistic, averaging time, sampling, and noise model. |
| Frequency accuracy | Agreement with the intended reference after systematic corrections. | A traceable uncertainty budget and evaluation of shifts. |
| Model-parameter bound | An allowed range of ε inferred from the absence of a specified effect. | Model assumptions, nuisance parameters, and confidence procedure. |
A convincing analysis must test whether laser noise, magnetic or thermal shifts, motion, collisions, finite lifetime, measurement errors, or link fluctuations can explain the signal. Frequency-squared scaling alone is insufficient: ordinary timing or phase noise can produce similar scaling. The reference architecture and cross-correlations are part of the physics.