Can photons cast a shadow?
At first glance, the answer seems to be trivially negative. But…
Light is made of photons, a fundamental particle that belongs to the so-called bosons, and that don’t have to respect the Pauli exclusion principle. For this reason, two photons do not interact directly, but simply go through each other. This is why sunlight and our radio waves do not shield each other, but travel undisturbed.
The ability of photons to occupy the same physical quantum state (position, energy, momentum, etc …) also makes possible to pack lots of them together in a tiny region, the concept behind black holes made of light:
Black hole created from the concentration of energy In theoretical physics , a Schwarzschild kugelblitz is a concentration of heat , light or radiation so intense that its energy forms an event horizon and becomes self-trapped: according to general relativity and the equivalence of mass and energy , if enough radiation is aimed into a region, the concentration of energy can warp spacetime enough for the region to become a black hole , although this would be a black hole whose original mass–energy had been in the form of radiant energy rather than matter.  In simpler terms, a kugelblitz is a black hole formed from radiation as opposed to matter. Such a black hole would nonetheless have properties identical to one of equivalent mass and angular momentum began more conventionally, following the no-hair theorem . The best-known reference to the kugelblitz idea in English is probably John Archibald Wheeler ‘s 1955 paper “Geons”,  which explored the idea of creating particles (or toy models of particles) from spacetime curvature, called geons . Wheeler’s paper on geons also introduced the idea that lines of electric charge trapped in a wormhole throat might be used to model the properties of a charged particle-pair. Kugelblitz drives have been considered possible future black hole starship engines.   A man-made kugelblitz would only be conceivable with a gamma-ray laser 1 billion times stronger than the current hypothesized ones, and it would have to produce a pulse that was 100 billionth of the current duration of a modern laser ‘s pulse. A single pulse would need to equate to the energy produced by the sun in 1/10 of a second. A kugelblitz of this size would last five years, and a device similar to a Dyson sphere could be constructed around it to harness the energy produced by the Hawking radiation . See also [ edit ] References [ edit ]
If a photon hits an electron, which in turn hits another photon, then the two photons are indirectly interacting. But there is always another particle to act as an intermediary.
Another possibility is that of a high-energy photon that splits into an electron and a positron, which then unite again. When the photon is split, the particles it produces can interact and deflect other photons. So that, for all intents and purposes, two photons can influence each other.
Below, a drawing I made myself:
Colored in black, the high-energy photon that momentarily splits. In red, photons deflected by the ephemeral particles.
Sure, the likelihood of one or two photons splitting and interacting in the tiny space-time window needed is slim, but not zero.
To answer the question: for a photon to cast a shadow, it must deflect other photons, and although the probability of this happening is minimal, and high-energy photons are required, it is absolutely possible.