Energy-time uncertainty relation

It gives the lower bound on the product of the uncertainty in an energy measurement and the uncertainty in the time interval over which it is made. It explains why energy can appear to fluctuate over short time intervals, such as in quantum vacuum fluctuations.

\Delta E \, \Delta t \geq \frac{h}{4\pi}

What the symbols mean

uncertainty in energy (J)
uncertainty in time (s)
Planck constant (J\cdot s)

About this formula

  • FieldPhysics
  • TopicQuantum mechanics
  • LevelUniversity
  • Also calledenergy time uncertainty principle, time energy uncertainty relation, quantum fluctuation energy time, heisenberg energy time uncertainty, delta E delta t greater than h over 4 pi, vacuum fluctuation uncertainty
  • SourceWikidata Q1193821

Write it in Obsidian

MathLive is a free visual math editor for Obsidian. Run Find a formula, type “energy-time uncertainty relation”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.

Related formulas