An article in Science says:
According to the theory of quantum electrodynamics (QED), which describes how electromagnetic fields interact with matter, the vacuum is not as empty as classical physics would have us believe. Over extremely short time scales, pairs of electrons and positrons, their antimatter counterparts, flicker into existence, born of quantum mechanical uncertainty. Because of their mutual attraction, they annihilate each another almost as soon as they form.
But a very intense laser could, in principle, separate the particles before they collide. Like any electromagnetic wave, a laser beam contains an electric field that whips back and forth. As the beam's intensity rises, so, too, does the strength of its electric field.At intensities around $10^{24}$ W/cm2, the field would be strong enough to start to break the mutual attraction between some of the electron-positron pairs, ... . The laser field would then shake the particles, causing them to emit electromagnetic waves—in this case, gamma rays. The gamma rays would, in turn, generate new electron-positron pairs, and so on, resulting in an avalanche of particles and radiation that could be detected.
Ethan Siegel writes about this in his blog "Starts With A Bang":
...you can — through physics — use these electromagnetic properties of empty space to generate real particle/antiparticle pairs.
You ought to notice, right away, that even the dream scenario of the science article gives intensities that are still 100,000 times too small to reach this threshold, and whenever you’re below that threshold, your ability to produce particle/antiparticle pairs is exponentially suppressed. The mechanism at play is quite different than simply the reverse of pair production, where instead of an electron and positron annihilating to create two photons, two photons interact to produce an electron/positron pair. (That process was first experimentally demonstrated way back in 1997.) In the laser setup, no individual photons have enough energy to produce new particles, but rather their combined effects on the vacuum of space causes particle/antiparticle pairs to pop into existence with a particular probability. Unless, however, those intensities approach that critical $10^{29}$ W/cm² threshold, that probability might as well be zero.
But in a reference frame moving in the direction of the beam, the power density would be lower. If it is below the threshold, the effect should not be seen by an observer in that frame. Can you explain this apparent issue?