Constraining validity of the Minkowski energy-momentum tensor

Robert N. C. Pfeifer, Timo A. Nieminen, Norman R. Heckenberg, Halina Rubinsztein-Dunlop

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


There exist two popular energy-momentum tensors for an electromagnetic wave in a dielectric medium. The Abraham expression is robust to experimental verification but more mathematically demanding, while the Minkowski expression is the foundation of a number of simplifications commonly found within the literature, including the relative refractive index transformation often used in modeling optical tweezers. These simplifications are based on neglecting the Minkowski tensor's material counterpart, a process known to be incompatible with conservation of angular momentum, and in conflict with experimental results, yet they are very successful in a wide range of circumstances. This paper combines existing constraints on their usage with recent theoretical analysis to obtain a list of conditions that must be satisfied to safely use the simplified Minkowski approach. Applying these conditions to an experiment proposed by Padgett, we find their prediction in agreement with that obtained using the total energy-momentum tensor.

Original languageEnglish
Article number023813
Pages (from-to)1-7
Number of pages7
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
Publication statusPublished - 2 Feb 2009
Externally publishedYes

Bibliographical note

Erratum can be found in Physical Review A - Atomic, Molecular, and Optical Physics, Volume 79(2), 029903(E),


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