To the extent I understand this (which is limited), the existence of the photon was calculated from theory (having already been discovered by experiment earlier) by assuming that the magnitude of the electromagnetic field was not, at the quantum level, simply a value (at some point in space and time), but was rather a "coordinate" to which the Schroedinger hypothesis is applicable. And the Schroedinger hypothesis says that whenever classical physics presents us with a quantity such that an energy depends upon it and its time rate of change (or more correctly, its conjugate momentum, which is essentially the same thing), then quantum mechanically the value of the quantity appears as a probability distribution governed by a solution to the corresponding Shroedinger equation which is constructed out of the classical discription by replacing terms in it with differential operators, such that the square of the magnitude of the resulting solution, for each possible value of the solution, gives the probability that a measurement designed to measure the value would return that value. Applying this to the electromagnetic field produced the reasult that the probability distribution for observable values of the magnitude of the field would follow the same law as for the permissible positions of a classical harmonic oscillator, which had the result that the possible steps in energy level of the electromagnetic field are in integer multiples of something, so that energy can be emitted or absorbed into the field only in such integer steps -- photons. The "something" that the steps are proportional to turns out to be the classical frequency of the field. One interesting consequence of this is that the lowest possible state of the field turns out to be not zero, but half a photon. That matters considerably in view of the fact that the calculation applies independently to each possible combination of frequency, direction of propagation, and polarization-- that is, every possible independent electromagnetic wave state. How many possible modes of electromagnetic vibration exist in the universe? Well, the universe is very large and the shortest possible wavelength is not even known with certainty, which by any calculation leads to an immense number of possible wave states. Each of them independently, according to this calculation, possesses, even when totally "dark", half a photon worth of energy. Even if each half a photon has only a tiny amount of energy, the total of them all is immense.

These ideas are extendable to other forms of subatomic particles also, making virtual particles a signficant fundamental concept of the universe.

Experimental evidence supporting this idea consists in, among other things, the observation that 2 electrical plates placed very close together in a vacuum under circumstances where all electrostatic or other known forces are nullified, will be attracted by a force that turns out to be equivalent to the negative of the radiation pressure that would normally be exerted between them by certain virtual photons (and balanced by like photons on the outside), but which are suppressed by being inpermissible wave solutions between 2 conductors, which causes a lesser radiation pressure between the plates then on them from the outside. Keep in mind that this is in total darkness and relies upon virtual photons only.

Also observed in other experiments are spectroscopic effects that indicate the charge of the electron is not quite what it "ought" to be, but seems to be affected by virtual particles popping in and out of existence due to the interconversion between matter-antimatter pairs and photons, which process is reversible in principle and which appears to be taking place all the time at a subliminal level involving the photons that are thrown off of the electron as part of its charge.

If empty space is filled with virtual particles, one might suppose that space IS in fact an assembly of such particles -- they are what it is made of, and that the appearance of an observable particle simply is the raising of some virtual particle from its minimum possible state to the next higher one. Note that such a change would alter the underlying fabric of space and thus may account for the distortion of space-time that we call gravity, where mass is present.

Mondern expansions on these ideas have led to various string theories.

For a more complete and knowledgeable discussion, the reader is referred to ... where?