# What is the trajectory of a photon moving through a vacuum?

Since electromagnetic energy is carried by photons and moves in forms of waves, does it mean that a single photon when propagating through space doesn't follow the straight path but instead always moves up and down, up and down like a wave. If so another question arises the speed of propagation of light in vacuum is fixed meaning that it will always take the same amount of time for it to travel from point A to point B, but if a photon always moves up and down it will also mean that it travels longer distance than the distance between A and B and so it ill travel faster than light propagates, is it even possible, could you please clarify these concepts for me?

• For a nice visualtization see en.wikipedia.org/wiki/Electromagnetic_radiation. Notice that the wave does not have any motion perpendicular to the direction of the propagation, but what oscillates is the intensity of the magnetic and electric fields (as mentioned in the answer by Michael. – user83548 Dec 22 '15 at 22:25
• Electromagnetic fields are quantum fields, i.e. they are continuous phenomena, at least at the scale that we have access to. What is not continuous are the possible measurements we can do on them. All measurements on a quantum field will always return quantized values for energy and angular momenta. That's what photons are: quanta. They are not particles that travel on or with the field. Photons show up when the field interacts with matter and only then. – CuriousOne Dec 23 '15 at 0:29

Since electromagnetic energy is carried by photons and moves in forms of waves, does it mean that a single photon when propagating through space doesn't follow the straight path but instead always moves up and down, up and down like a wave.

The term photon belongs to the realm of quantum mechanics. The photon is a fundamental elementary particle in the standard model of particle physics. Electromagnetic energy is defined well in classical electrodynamics and it does move this energy as a wave in time and space.

A single elementary particle propagating through space is mathematically modeled by a wavefunction which is a solution of a quantum mechanical equation. This is a complex number function, it has a sinusoidal form but the only physically measurable effect is the probability of getting a "photon" signal at a specific (x,y,z,t). It is the probability that has a sinusoidal dependence in space time, not the photon, as can be seen in the answer here. The energy of the photon is h*nu, where nu is the frequency of the classical wave which will emerge from a large number of such energy photons.

So it is not possible to talk of a trajectory of a single photon at the microscopic quantum level. It is only macroscopically, when the atomic source is known, and the interaction footprint of the photon is detected on a screen or a camera that a straight line can be drawn which in effect is the optical ray of the classical em wave.

If so another question arises the speed of propagation of light in vacuum is fixed meaning that it will always take the same amount of time for it to travel from point A to point B, but if a photon always moves up and down it will also mean that it travels longer distance than the distance between A and B and so it ill travel faster than light propagates, is it even possible,

No, it is not possible in vacuum. The photon does not propagate as you imagine, and can only be described by its energy=h*nu and its spin direction. It always travels at c.

In the complicated quantized environment of a medium with an index of refraction the way the photon wavefunctions are related to the emergent classical wave, shows that the individual photon paths, which at the microscopic level are always in vacuum and travel with velocity c, can not be an optical ray. An individual photon impinging on a transparent medium will interact by elastic scatterings with the atoms of the lattice and certainly its path cannot be one straight line. In coherence with the zillions of photons in a classical em wave it is better to discuss the classical paths and let quantum mechanics take care of the individual interactions. A true analysis quantum mechanically needs quantum field theory and is unnecessarily complicated.

Your confusion comes from combining two different concepts (although they are related). Photon is a discrete particle. A wave is a continuous. You can look at light as a discrete particle or a wave, but if you think of them the way you are thinking of them, things get confusing.

• A photon does not travel among the wave's amplitude function. It travels in all possible paths and we observe one path at a time (And usually if the path from A to B is simple, the many possible paths cancel out).
• A photon always travels at speed c.
• The up and downs of a electromagnetic wave are the consequences of a photon moving. They are self inducing oscillations in the electromagnetic field.
• You can also think that the ups and downs of an electromagnetic wave can be represented as a photon, which is carrying information about a change in the electromagnetic field at speed c. (A change caused perhaps by moving a charged particle like an electron.)

By the way, if I didn't answer your question, try to think about why we started thinking of light as particles. (The problems that lead to the concepts you are studying). You can start at the photo-electric effect.

• Photons don't travel, at all. A photon is an initial state prepared by a measurement and a final state of a second measurement. There are no "particles" between those states. The only thing "there is" is the quantum field, which is continuous. No offense, but particles that travel all possible paths are about as physical as Santa Clause visiting all houses trough the chimneys during one night. It's not a good physical picture and one should avoid teaching QM that way. – CuriousOne Dec 23 '15 at 0:25
• Would you elaborate in saying "photons don't travel at all" in an answer? @CuriousOne – jackskis Jul 31 '16 at 2:41
• There is an answer like that here: physics.stackexchange.com/questions/247093/…. I am glad not many people looked at it, otherwise it would have been voted into oblivion, already. People just can't seem to let go of the photon as an object interpretation. – CuriousOne Jul 31 '16 at 3:20