Heisenberg Uncertainty Calculator
Calculate the minimum uncertainty in position given momentum uncertainty (or vice versa): dx >= hbar / (2 * dp).
Minimum Position Uncertainty (dx)
0.000000000527300 m
Formula
## Heisenberg Uncertainty Principle The uncertainty principle states a fundamental limit on the precision with which position and momentum can be known simultaneously. ### Formula **dx * dp >= hbar / 2** where hbar = h / (2 pi) = 1.0546 x 10^-34 J s. Given dp, the minimum dx is hbar / (2 dp). This is not a measurement limitation but a fundamental property of nature.
Exemplo Resolvido
An electron with dp = 1e-25 kg m/s.
- 01dx_min = hbar / (2 dp)
- 02dx_min = 1.0546e-34 / (2 * 1e-25)
- 03dx_min = 1.0546e-34 / 2e-25
- 04dx_min = 5.273e-10 m = 0.527 nm
Perguntas Frequentes
Does the uncertainty principle apply to energy and time?
Yes. There is an analogous relation: dE * dt >= hbar / 2. This allows virtual particles to briefly exist with borrowed energy.
Is this uncertainty due to imperfect instruments?
No. It is an intrinsic property of quantum mechanics. Even with perfect instruments, you cannot simultaneously know both position and momentum to arbitrary precision.
Why does this not affect everyday objects?
For macroscopic objects, hbar is so tiny that the minimum uncertainty is far below any measurable threshold. Quantum effects only matter at atomic scales.
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