Time is energy

Energy-time uncertainty relation

The Energy-time uncertainty relation describes a relation between energy and time in quantum mechanics. The relation is comparable to Heisenberg's uncertainty relation and is also obtained from this, but is based on fundamentally different considerations. It is of a principle nature and not a consequence of inaccuracies in a measurement. She surrenders to


in which the Dirac constant, H is Planck's quantum of action and π is the circle number.


Since time cannot be represented as an eigenvalue of an observable, the uncertainty relation does not result directly from the structure of quantum mechanics, as is the case with Heisenberg's uncertainty relation. Since the energy can in principle also be measured precisely at any time, the interpretation of the equation depends on the meaning of the variables.

The simplest mathematically correct explanation results from the general uncertainty relation, if for ΔE. the ΔH is used, and Δt is obtained from the time derivative of the second observable with the help of Ehrenfest's theorem.

A clear interpretation emerges when looking at a wave packet: because of the positional uncertainty, the time can only be determined with an inaccuracy. The difference between the energies that are precisely this time apart is then ΔE..

See also

  • Lifetime (physics) (formulas for quantum mechanical interpretation)
  • Wolfgang Nolting: Basic course Theoretical Physics 5/1; Quantum Mechanics - Basics. 6th edition. Springer-Verlag, Berlin Heidelberg New York 2004, ISBN 3-540-40071-0.

Category: quantum mechanics