Light: Waves and Particles

Question

I have three questions:

a. How do pictorial representations of electromagnetic waves translate to real life? They're shown as having perpendicular fields in phase, but how can the strength of a given field, be it magnetic or electrical, be perpendicular to the other. Basically, how does this wave actually propagate through space?

b. Einstein theorized that the energy of a single photon increases with raised frequency. Frequency? What charicteristic of a photon makes it periodic so as to possess a frequency? Does its amount of energy fluctuate, or does this refer to the number photons per second, etc?

c. How do photons propogate through space, this is almost a parellel question to my inquiry in point a.

Answer 1

(a) Obviously the pictures we draw of light are a bit misleading. The electric and magnetic fields are perpendicular because a changing electric field produces a magnetic field and vice versa. The direction of these generated fields need to be perpendicular. The direction of propagation (the direction the light travels) is then perpendicular to both of those waves.

(b) Since light is made up of EM waves, those waves will have a specific wavelength and frequency. The frequency of light is related to the speed at which the particle/wave travels through space by the relation: c = $\lambda\nu$, where $\lambda$ is the wavelength and $\nu$ is the frequency.

(c)As mentioned before, photons propagate in a straight line perpendicular to the propagation of the electric and magnetic fields.

Answer 2

a. Here is an instructive picture from Wikipedia of an electromagnetic wave showing the electric and magnetic field strengths (they're vectors).

b. The photon you are referring to is just an amount of energy in the wave. The energy in the wave comes in discrete packets of $hf$. The photon you are picturing in your mind is probably a localized particle. This actually does not have an exact frequency. It is actually spread over frequencies according to

$$\Delta p \Delta x \geq \frac{h}{4\pi}$$

and here $p = hf$, and $\Delta x$ is the spread in space. However, provided $\Delta x$ is large enough, it will have an approximate, average frequency. You can think of an electromagnetic wave as containing a certain number of these particles. In general, however, the number of particles will also not be exactly defined because we also have

$$\Delta E \Delta n \geq ({\rm something}).$$

That is, you cannot have both an exact number of photons and an exact field strength. You can still have average values, though, as above.

Answer 3

Well, you asked the 6 million dollar question. I am not a physicist. I respect them greatly. They have equations for EM radiation that work. This enables them to make accurate predictions and create cool stuff, but beyond that I think the answer to your question is nobody really knows. Particles act like waves and waves act like particles. Photons have no mass, but they kind of do. Weird things happen that seem to defy common sense. I guess that's what makes physics so interesting.

Answer 4

On question (a) the field is the force per unit charge. Force is mass $\times$ acceleration. Acceleration is the rate of the rate of change of position over time. And since you can change position in more than one direction, this quantity has to tell us about direction. As such, the force and the field also have to be directional quantities and two different forces can be perpendicular.

The wavelength of a single photon refers to something that will take some setting up. Suppose you shine a laser beam at a filter that blocks some of the light. This will reduce the amount of light in the beam after the filter. As your put more filters in front of the beam you might think the amount of light in the beam will decrease gradually, but that's not what happens in reality. In the real world, if you have a sensitive enough detector there will come a point at which the detector sometimes goes off and sometimes shows doesn't. And for intensities above that level the detector will go off as if the energy comes in chunks.

Now, let's suppose you shine just one photon at a time through a pair of narrow slits a suitable distance apart. So if you put a detector in front of each slit at most one of them will go off at any given time. If you shine many photons through the two slits one at a time you will see a pattern of bars. Light bars will have lots of photons arriving, dark bars will see few photons. If you block one of the slits, you see a different pattern of bars. This means that by unblocking one of the slits you prevent photons from going to places that go from being a light bar to being a dark bar. So there is something going through both slits that changes the pattern of bars. You can perform experiments to test how the thing going through both slits behaves. It is deflected by lenses and mirrors as a photon would be. It is blocked by opaque objects as a photon would be. It is a photon in every respect except that you don't see it. A photon exists in multiple versions and you only ever see one of them directly. There is a wave like thing called the wave function that consists in part of the multiple versions of the photon whose intensity is related to the probability of seeing a photon at a given location. The fact that the probability can decrease as a result of allowing another source for the wave function is a sign that there is something more complicated going on than just the existence of many versions of the photon. The more complicated stuff is called by various names like phase and entanglement that I won't go into further here.

Now the different versions of a photon are affected by lenses and mirrors and other stuff. The effect of the lenses and mirrors is local: it affects the wave function in its vicinity. And in general changes in the wave function propagate by affecting the wave function first near the disturbance and only later does it change the parts of the wave function further away. That's how the wave function propagates. Changes in a particular region gradually spread out over time by affecting the wave function in nearby regions.

There is much more to say about this, for which you should read "The Fabric of Reality" by David Deutsch, especially chapters 2,9,11 and "The Beginning of Infinity" by Deutsch chapters 11 and 12.