The Schwinger Exponent: Pair Production From the Vacuum as a Ledger of Field Ratios
Year: 2026
Type: article
Abstract: A sufficiently strong electric field does not merely polarise the vacuum; it tears pairs from it. Schwinger's 1951 formula gives the production rate, and its defining feature is an exponential in the inverse field. This paper tabulates that formula across field ratios from a thousandth of the critical field to the critical field itself. The rate at the critical field is 4.698e+54 pairs per cubic metre per second, while at a tenth of the critical field the exponential suppression alone has removed thirteen orders of magnitude, and at a hundredth it has removed over a hundred. Laboratory fields, including the strongest laser foci expressed as equivalent static fields, sit at ratios of a few thousandths, where the static rate is zero for every practical purpose; real laser pair production proceeds by multiphoton and radiation-mediated routes instead. The ledger is computed from Schwinger's leading term, not measured, and it quantifies why the vacuum's breakdown, though exactly predicted, remains unobserved in its pure form.
Author: Aldred, William Alexander
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225779858
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