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We examine the dynamical destruction of binary systems in star clusters of different densities. We find that at high densities  (10 4 – 10 5  M ⊙  pc −3 )  almost all binaries with separations  &gt;10 3   au are destroyed after a few crossing times. At low densities [], many binaries with separations  &gt;10 3   au are destroyed, and no binaries with separations  &gt;10 4   au survive after a few crossing times. Therefore, the binary separations in clusters can be used as a tracer of the dynamical age and past density of a cluster.  We argue that the central region of the Orion nebula cluster was ∼100 times denser in the past with a half‐mass radius of only 0.1–0.2 pc as (i) it is expanding, (ii) it has very few binaries with separations  &gt;10 3   au and (iii) it is well mixed and therefore  dynamically  old.  We also examine the origin of the field binary population. Binaries with separations  &lt;10 2   au are not significantly modified in any cluster, therefore at these separations the field reflects the sum of all star formation. Binaries with separations in the range  10 2 – 10 4   au are progressively more and more heavily affected by dynamical disruption in increasingly dense clusters. If most star formation is clustered, these binaries must be overproduced relative to the field. Finally, no binary with a separation  &gt;10 4   au can survive in  any  cluster and so must be produced by isolated star formation, but only if  all  isolated star formation produces extremely wide binaries.

Do binaries in clusters form in the same way as in the field?