It is well-known that the Heisenberg-Euler-Schwinger effective Lagrangian predicts that a vacuum with a strong static electromagnetic field turns birefringent. We propose a scheme that can be implemented at the planned FCC-ee, to measure the nonlinear effect of vacuum birefringence in electrodynamics arising from QED corrections. Our scheme employs a pulsed laser to create Compton backscattered photons off a high energy electron beam, with the FCC-ee as a particularly interesting example. These photons will pass through a strong static magnetic field, which changes the state of polarization of the radiation - an effect proportional to the photon energy. This change will be measured by the use of an aligned single-crystal, where a large difference in the pair production cross-sections can be achieved. In the proposed experimental setup the birefringence effect gives rise to a difference in the number of pairs created in the analyzing crystal, stemming from the fact that the initial laser light has a varying state of polarization, achieved with a rotating quarter wave plate. Evidence for the vacuum birefringent effect will be seen as a distinct peak in the Fourier transform spectrum of the pair-production rate signal. This tell-tale signal can be significantly above background with only few hours of measurement, in particular at high energies.
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