1

**Physics, Astronomy & Cosmology / Re: Do photons contradict momentum equations?**

« **on:**31/12/2016 00:29:36 »

A very non-rigorous and not at all complete explanation from the point of view of field theory goes something like this:

All particles are excitations of one of a large number of fields. In certain cases these fields couple strongly enough that we can detect the field itself. For example the photon is an excitation of the electromagnetic field and we can detect the field by how it impacts other things. Electrons on the other hand are excitations of an "electron" field and while electrons couple to the electromagnetic field nothing couples strongly to the "electron field" in a way that allows us to measure it (other than to say that electrons exist). When an excitation in a field propagates without any interference caused by interactions with other fields it follows a very simple propagation rule. This very simple rule is the one that photons follow in free space (i.e. photons travel at one speed which is the speed of light). Now if the excitation of the field is interacting with other fields that changes the rule. It turns out that there is this field called the Higgs and when excitations (i.e. particles) interact with this field the rule that governs their motion changes and suddenly the rule gets a term sometimes called rest mass or invariant mass. The particles no longer travel at one speed but many different speeds and can no longer travel at the speed of light.

Basically the interaction with the Higgs field adds an extra energy term to the equation of motion for the excitation. The equation of motion without the Higgs interaction doesn't have this term. Now energy and mass are equivalent so even without the extra Higgs term there is still mass. However the mass without the Higgs term behaves differently than the mass with the Higgs term and so does the energy. In short since the electron interacts with the Higgs field and the photon doesn't the motion of the electron is different and not everything that happens to an electron in terms of energy and motion has an exact analog for a photon.

All particles are excitations of one of a large number of fields. In certain cases these fields couple strongly enough that we can detect the field itself. For example the photon is an excitation of the electromagnetic field and we can detect the field by how it impacts other things. Electrons on the other hand are excitations of an "electron" field and while electrons couple to the electromagnetic field nothing couples strongly to the "electron field" in a way that allows us to measure it (other than to say that electrons exist). When an excitation in a field propagates without any interference caused by interactions with other fields it follows a very simple propagation rule. This very simple rule is the one that photons follow in free space (i.e. photons travel at one speed which is the speed of light). Now if the excitation of the field is interacting with other fields that changes the rule. It turns out that there is this field called the Higgs and when excitations (i.e. particles) interact with this field the rule that governs their motion changes and suddenly the rule gets a term sometimes called rest mass or invariant mass. The particles no longer travel at one speed but many different speeds and can no longer travel at the speed of light.

Basically the interaction with the Higgs field adds an extra energy term to the equation of motion for the excitation. The equation of motion without the Higgs interaction doesn't have this term. Now energy and mass are equivalent so even without the extra Higgs term there is still mass. However the mass without the Higgs term behaves differently than the mass with the Higgs term and so does the energy. In short since the electron interacts with the Higgs field and the photon doesn't the motion of the electron is different and not everything that happens to an electron in terms of energy and motion has an exact analog for a photon.