If you imagine a photon as a miniature cannonball, of course it cannot. But this is a prime example why you should not try to imagine a photon, or other elementary particles, as miniature cannonballs; indeed, why intuition usually fails when trying to comprehend quantum physics, and why it is important to study the math.
Photons are excitations of the electromagnetic field. The fundamental object is the one-and-only electromagnetic field, obeying a quantized form of Maxwell’s equations. A direct consequence of quantization is that at any given frequency, the field’s energy will increase or decrease in steps. These “excitations” are what we call photons.
So suppose something emits a photon. What actually happens is that an excitation is generated in the electromagnetic field. This excitation has certain properties, including energy and momentum. The equations that tell us how these excitations propagate in the field also tell us the likelihood of observing them at various places. In the end, when we observe a photon, it means that we are extracting an excitation from the field.
A way to interpret, or comprehend, the governing equations is by imagining every possible path that an imaginary “miniature cannonball” photon might take and assigning a probability to it. But this is all in our minds. It does not mean that an actual, physical photon goes every direction simultaneously. It does not even mean that an actual, physical photon exists as a miniature cannonball. It is just a mental image; a convenient mental tool, that’s all.
The physical reality, at least in the best theory that we have that actually works (quantum field theory) is that the physical object is the quantum field and its excitations; particles are an illusion, the way we perceive the field’s excitations in experiments where the interaction with the field is localized.
