I am not aware of the specific experiment you mentioned regarding photons exhibiting wave behavior in the "double slit of time" or any implications of parts of the wave arriving ahead of the photon.
However, I can provide some general information about the double-slit experiment and wave-particle duality, which might help clarify the concept.
In the classic double-slit experiment, when particles such as electrons or photons are sent through two parallel slits onto a screen, an interference pattern is observed, suggesting wave-like behavior. This phenomenon illustrates the wave-particle duality concept, which states that particles can exhibit both wave-like and particle-like properties.
Wave-particle duality does not mean that parts of a wave arrive ahead of a particle in the direction of travel. Rather, it suggests that particles can display characteristics of waves, such as interference and diffraction patterns, while also exhibiting particle-like behavior, such as localized interactions and momentum transfer.
If the experiment you mentioned does indeed suggest that photons show wave behavior in the "double slit of time," it would be necessary to examine the specific details and findings of the experiment to understand the implications fully. It's important to note that new scientific discoveries often undergo scrutiny, verification, and further experiments to confirm their validity and understand their implications within the broader scientific framework.
To gain a better understanding of the specific experiment and its implications, I recommend referring to the original research paper published in Nature or consulting more recent scientific sources and discussions on the topic.