Calculator Inputs
Example Data Table
These examples show how lifetime shrinks as ΔE grows.
| Case | ΔE | Unit | Model | Estimated Δt (order) | c·Δt (order) |
|---|---|---|---|---|---|
| Low energy fluctuation | 1 | eV | ħ/(2ΔE) | ~3.3e-16 s | ~1.0e-7 m |
| Atomic-scale interaction | 1 | keV | ħ/(2ΔE) | ~3.3e-19 s | ~1.0e-10 m |
| Nuclear-scale fluctuation | 1 | MeV | ħ/(2ΔE) | ~3.3e-22 s | ~1.0e-13 m |
| High-energy process | 100 | GeV | ħ/(2ΔE) | ~3.3e-27 s | ~1.0e-18 m |
Formula Used
This calculator uses the energy–time uncertainty timescale: Δt ≈ ħ / (2ΔE).
- ħ is the reduced Planck constant in J·s.
- ΔE is your energy uncertainty in joules.
- Optional scale: Δt ≈ ħ/ΔE for rough estimates.
Travel distance is estimated with d = β·c·Δt, where β = v/c and c is the speed of light.
How to Use This Calculator
- Enter an energy uncertainty ΔE and select units.
- Pick the lifetime model you want to report.
- Set β if you want a reduced travel distance.
- Click Calculate to view results above the form.
- Use Download CSV or Download PDF to export.
FAQs
1) Is this a real decay lifetime?
No. It is an uncertainty-limited timescale for an intermediate fluctuation. Real lifetimes come from interaction rates, widths, and detailed dynamics.
2) Why does larger ΔE imply shorter Δt?
Because the uncertainty relation links energy spread to allowable time localization. Increasing the energy uncertainty permits a process to be confined to a shorter timescale.
3) Which model should I choose?
Use ħ/(2ΔE) for the commonly quoted scale. Use ħ/ΔE when you only need an order estimate. Both show the same inverse dependence on ΔE.
4) What units are best for particle physics?
MeV and GeV are common for particle processes. The calculator converts those units into joules internally before computing Δt.
5) What does the travel distance mean?
It is a rough distance scale over the computed Δt assuming a speed v=βc. It helps compare whether an interaction is more “local” or more “extended”.
6) Why include Δf and Δω?
They express the same uncertainty as frequency or angular-frequency spread using ΔE=hΔf and ΔE=ħΔω. They are useful when thinking in wave or oscillation terms.
7) Can I use this for photons?
Yes. For photons, ΔE relates to spectral width. The resulting Δt can be interpreted as a coherence-time scale associated with that energy spread.
8) What if ΔE is extremely small?
Δt grows very large, and the estimate can exceed realistic physical timescales in your system. In that case, treat the number as a limit, not a prediction.