# The photon model today

#### Prerequisites

Einstein's photon model gave critical hints that led the way to the development of the quantum theory, and his relativity work provided the basis for the creation of a theory of matter that encompasses both electrically charged matter and electromagnetic radiation: ** quantum field theory**.

This theory is our current overarching theoretical model for the behavior of all of everyday matter. (Sub-nuclear processes require an extension of quantum field theory: what is currently called *the Standard Model *of particle physics.) This theory is a grand unified structure that in principle described everything about all matter we typically encounter.

Since it yields Maxwell's equations as an approximation when you have lots of photons and classical systems, it serves as a unifying theory of light as waves and light as photons.

When you try test quantum field theory by calculating things that go beyond classical electromagnetism, In practice, you can only calculate the simplest things. But for those most basic systems, it allows us to calculate properties of systems, say the Hydrogen atom or the Helium molecule, to extraordinary accuracy (12 significant figures). And when we get to photons, it provides the structure that allows us to figure out what some of the interesting and surprising properties lie.

Some weird but well-tested true results are:

- Photons don't interfere with each other; each photon interferes with itself, appearing to know about all possible paths it might take.
- The number of photons is not necessarily a fixed number. Photons can exist in states that are mixed — part of the time there is one number of photons, part of the time there is a different number.
- Photons don’t interact with each other: they just pass right through, like small pulses propagating on an elastic string.*

Right now, the complex properties of photons predicted by quantum field theory are being utilized in biology to probe small systems in extraordinary ways, such as *two-photon confocal microscopy*. There are even possibilities that such basic properties as photosynthesis rely on some of these subtleties. It is likely that the next decade or so that biology will find much value in our sophisticated understanding of the complex nature of light.

* This is the photon version of the statement that the electric field due to multiple sources is just the sum of the fields from the individual sources. The presence of additional fields doesn’t change what electric field a source produces. While these are very good approximations under most circumstances, there are specialized circumstances where there are interesting corrections. An electric field in matter polarizes the matter and this polarization can effect how a second electric field is modified by the matter (dielectric constant). The study of this is called non-linear optics*.* And very high frequency photons (gamma rays) polarize the vacuum slightly, pulling apart electron and positron pairs that travel with them. Two gamma rays can interact (very weakly) through the electric forces between these bits of polarized vacuum.

Joe Redish 5/2/12 and 7/10/19

Last Modified: July 10, 2019