What is a photon?

The naive conception of a photon is as a massless particle, which flows along a light beam at the speed of light and otherwise has no properties, if the experimentalist does not first force it into entanglement with another particle.

But quantum optics paints a completely different picture of a photon. A photon is a complicated thing. Even in a pure state there can be an arbitrary solution of the homogeneous Maxwell equations. (In an impure state - and photons are certainly not always so pure - they are much more complicated objects, namely linear operators on the space of homogeneous Maxwell equations!)

A single photon in a pure state is, from a mathematical point of view, essentially the same as a non-trivial solution of the wave equation! This means that one could in principle prepare a photon corresponding to every such solution!

To say that a photon has a particular frequency or direction already means to restrict its state considerably. In addition, it can be unpolarised, circular polarised, linear polarised, and every possible combination thereof.

In the naive imagination one can also detect the presence of a photon in that one can see a flash on the screen which it hits, or hear a click in a photodetector, and thus count the number of photons.

One has admittedly detected a click or a spot or a flash at some particular place. But to say that one has seen a photon is a euphemism.

For the photoelectric effect one needs quantum matter in the detector, but no quantum radiation; classical light, which is known to be a pure wave, does this just as well as a photon canon! To count photons in classical light, however, is just as crazy as taking photos of a person who is not present!

Many people talk about photons as though they knew all about them. However they are mysterious objects, whose true nature only beings to dawn (if ever) when one attends a lecture about quantum optics. More details can be found in the quantum opticians' bible:
L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, 1995.
and in a simplified but nevertheless very readable presentation:
U. Leonhardt, Measuring the Quantum State of Light, Cambridge, 1997

But this does not yet have anything to do with the the thermal interpretation - the picture of photons presented above was rock-hard orthodoxy!

The new interpretation first comes into play when one wants to talk consistently about what has actually happened objectively in a photon experiment.

The Copenhagen interpretation simply forbids us to speak about it: 'Shhhhh! Otherwise inconsistencies will immediately come to light!' With the consequence that everything microscopic acquires a ghostly nature. As long as one does not measure it, the microscopic admittedly has no properties. They first arise when physicists who understand the art of measurement are on the scene, and can compel matter to reveal itself to be in a determinate state.

The much-loved information theory interpretation adds one more thing; it claims that the state of the system depends on the knowledge or lack of knowledge of the observer.

But this is clearly nonsense. Nature certainly doesn't care what physicists know!

Otherwise, before she was observed by the first physicist (or the first amoeba?) she could not have had any properties. But then how did she develop in such a way as to bring forth physicists (or amoebae)?

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)
A theoretical physics FAQ