If we imagine a photon as a miniature nucleus, then, of course, it is not able to move in all directions at once.
This is a vivid example of why we should not visualize a photon and other elementary particles in the form of tiny nuclei. Normally, intuition fails when trying to understand quantum physics, and in such cases, mathematics is needed.
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Photons are excitations of an electromagnetic field. The fundamental object is the only electromagnetic field obeying the quantum form of Maxwell’s equations.
A direct consequence is that the quantization, that at any given frequency, the energy field is changed, increased or decreased by certain steps (discontinuously). Such disturbances are what we call photons.
Suppose something emits a photon. In fact, at such a moment, the generation of a disturbance in an electromagnetic field occurs. This disturbance has certain properties, including energy and momentum.
The equations that determine the propagation of disturbances in the field also indicate the probability of their observation in various places. As a result, when we observe a photon, we extract the disturbance from the field.
The modern concept of a photon was gradually developed by Albert Einstein at the beginning of the 20th century to explain experimental observations that do not correspond to the classical wave model of light.
The advantage of the photon model is that it takes into account the frequency dependence of light energy and explains the ability of matter and electromagnetic radiation to be in thermal equilibrium.
Many experiments, starting with Compton scattering of single electrons, have confirmed Einstein’s hypothesis that light is quantized.
In December 1926, American physicist Gilbert Lewis coined the now widely used name “photon.” After Arthur Compton won the Nobel Prize for scattering studies in 1927, most scientists recognized that light quanta exist independently and adopted the term.
The way of interpreting or understanding the governing equation is to present all possible paths along which an imaginary photon could pass in the form of a miniature nucleus and assign them probabilities.
This does not mean that a real physical photon moves in all directions simultaneously. This does not even mean that the photon exists in the form of a tiny nucleus. This is just an image, a convenient mental tool, nothing more.
In physics, quantum is the minimum amount of any physical object or property involved in the interaction. Quantization implies that the value of a physical property takes only discrete values consisting of integer multiples of one quantum.
Physical reality, at least in the best theory that we have (quantum field theory), is that a physical object is a quantum field and its perturbations.
Particles are an illusion, an analog for perceiving a field perturbation in experiments where the interaction with the field is localized.