Will, is there experimental proof that photons spend some of their time as a particle?

First, a semantic correction:

photons do not

*spend some time* as a particle, then

*some time* as a wave. They

*always* appear to be particles to experiments that measure their particle-like behavior, and

*always* appear to be waves to experiment that measure their wave-like behavior.

Experiments conducted for most of the last half of the 19th century and first decade of the 20th demonstrated the particle nature of photons, leading up to what most people consider the definitive explanation, Einstein’s 1905 paper

“A Heuristic Point of View [Model] of the Creation and Transformation of Light".

These experiments are commonly reproduced in Modern Physics classes. A very simple one involves using a detector with single-photon sensitivity and a monochromatic (or nearly) light source, such as hot filament lamp, uncoated gas vapor lamp, or laser, and many “smoked glass” or similar photographic filters. Adding filters while keeping the light source constant, you eventually reach a step where the detected light drops from low to zero. Plotting this, you find a “notchiness” in the graph, where the energy represented by the smallest notch agrees with the famous formula [math]E = h v[/math], where [math]v[/math] is the photon’s frequency, and [math]h[/math] is the

Planck constant.

It’s important to understand that this “wave-particle duality” is not limited to photons.

*Every* particle with momentum ([math]p[/math]), massless particles such as photons or massive ones such as electrons, has an associated wave nature.

Even big, composite bodies like cannon balls and planets have an associated

de Broglie wave with wavelength give by [math]\lambda = \frac{h}{p}[/math], but it’s so small compared to their size and the associated wavelengths of their constituant particles that it’s physically irrelevant. Thus, the only particles for which experiments show wave-like effects, such as interference, are very small – to the best of my knowledge, nothing larger than the nuclei of metals, such as gold.

If there is why can't we put a mass to them?

In modern particle physics, particles are allowed to have zero or non-zero

*rest mass*. Particles with zero rest mass must travel at the speed of light. Because they have finite, measurable energy and momentum, it’s possible to calculate their relativistic mass. However, because this mass is very small – about [math]10^{-32} \,\mbox{kg}[/math] for a photon of visible light, it’s not significant in most calculations involving mass, so is little discussed.