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Photon-photon collisions, as one of the fundamental processes in quantum physics, have attracted a lot of attention. However, most effort has been focused on photons energetic enough to create particle-antiparticle pairs. The low energy limit—e.g., optical photons—has attracted less attention because of their extremely low collision cross section. By optical photons we mean UV, visible and infrared, although the cutting edge of extreme lasers is in the near infrared. The Schwinger critical field for pair generation seems not possible, at least directly, with the current laser technology. This often is considered as a problem, but we view this as an asset; the near impossibility of pair production via photon-photon scattering in the infrared is a perfect scenario to study virtual pairs that characterize Dirac’s quantum vacuum. Moreover, it is remarkable that this scenario of photon-photon collisions was already studied in the 1930s by two of the fathers of Quantum Mechanics, among others, at the dawn of this theory. In their respective papers, however, Born and Heisenberg arrived to different conclusions regarding the birefringence of vacuum. This controversy is still an open question that will be solved soon, we hope, with upcoming experiments. Here, we discuss a possible photon-photon collision experiment with extreme lasers, and will show that it can provide measurable effects, allowing fundamental information about the essence of Quantum Electrodynamics and its Lagrangian to be extracted. A possible experimental scenario with two ultra-intense pulses for detecting photon-photon scattering is analyzed. This would need a high-precision measurement, with control of temporal and spatial jitter, and noise. We conclude that such an experiment is barely feasible at $$10^{23}$$ W/cm$^2$ (today’s intensity record) and very promising at 1$$0^{24}$$ W/cm$^2$. 

Abstract In this paper we will show that photon–photon collision experiments using extreme lasers can provide measurable effects giving fundamental information about the essence of QED, its Lagrangian. A possible scenario with two counterpropagating ultra-intense lasers for an experiment to detect scattering between optical photons is analyzed. We discuss the importance of the pulse widths and waists, the best scenario for overlapping the beams and signal detection, as well as ways to distinguish the signal from the noise. This would need a high-precision measurement, with control of temporal jitter and noise. We conclude that such experiment is barely feasible at 10²³ W cm⁻²and very promising at 10²⁴ W cm⁻².