# Is light's path a wave?

In a lot of textbooks I see a schematic of light drawn as a squiggly line. I have even heard that some things are too small to be seen because they are smaller than the wavelength of light (and therefore light wiggles around them.)

But now I think that light actually travels in a perfectly straight line and that no particles will feel any force from this light when they are not on this line.

My friend says I'm wrong, and that if you increase the amplitude of the light, the ray will wiggle into the particle. To back it up, he linked me to a video about the single photon double slit experiment, where a single photon seems to interfere with itself. I'm not sure that this experiment proves him right, but it does seem to say that light wiggles around.

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– Keep these mind May 14 '13 at 6:55
I'm reminded of Feynman's "path integral" where everything takes every possible path, weighted by probability. en.wikipedia.org/wiki/Path_integral_formulation – Brandon Enright May 14 '13 at 7:26

In general light propagates in a straight line in situations where its wavelength is much smaller than the other linear dimensions of the problem. As light in the visible range has wavelengths of about a half micron, this covers most everyday circumstances, but there are exceptions. (For example, shine a laser pointer on a human hair in a dark room and you'll get double-slit interference fringes.)

Light is a wave regardless of the existence of photons, and regardless of its amplitude. It is only in the 'geometric optics' limit of small wavelength that you can even begin to talk about light rays.

(On the other hand, the squiggly line you see in schematics need not be wrong, but you need to take it carefully. It is not a spatial squiggle, but it's the electric field that makes up the light which goes one way and then another as you traverse the light's path.)

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What did you mean about the geometric optics limit? Will a light ray hit a charged particle off to the side if I increase its amplitude enough? – Mark May 14 '13 at 0:50
I get the impression that the final paragraph is what the OP really wanted to know about. It may help to note that (a) this representation is a graph, and (b) the graph has different units on the two axes: meters on one and newtons/coulomb on the other (assuming that it's $E$ being graphed -- if it's $B$, then tesla). – Ben Crowell May 14 '13 at 1:00
@BenCrowell you are right. I was also thinking about the units as well. This means that no increase in amplitude will cause nearby charges to feel a force. They must be exactly on the line of the ray. – Mark May 14 '13 at 1:33
@Mark: My point about the units was simply that it shows that your friend is obviously wrong to think of the graph as a wiggling path through space. – Ben Crowell May 14 '13 at 2:39

You and your friend are confusing two aspects of the nature of light:

1) the classical, which represents successfully light as a sinusoidal variation of the electric and magnetic fields that compose the radiation

2)the quantum mechanical one where light is built up by an innumerable number of particles called photons.

The classical case holds down to dimensions of fractions of microns and optics and interference of light are phenomena observed and explained with classical electrodynamics. Your straight lines belong to the geometrical optics part of the case. In this framework amplitude increase means to increase the energy the light carries in the field, the amplitude is the height of the electric and magnetic field. Increasing the energy content will not add wiggles :). The path will follow the same classical optical rays.

In the quantum mechanical /particle case the photon is characterized by its frequency nu, the same as the frequency of the classical wave, but its existence has only two variables, spin (+/-1) and energy=h*nu where h is the Planck constant. There exists no amplitude to increase, but the interference pattern observed in the two slit experiment even when one photon at a time goes through is the effect of the quantum mechanical nature of particles ( and all of nature at the micro level). The paths of particles at the quantum mechanical level do not obey the laws of classical mechanics but are dependent on solutions of the quantum mechanical equations describing the dynamics of the problem. These solutions give probability waves, i.e. sinusoidal dependencies on space (x,y,z) and time to find the particle/photon at a specific space point. Note it is a probability to find it there, not a variation in the space distribution of the particle/photon, its energy is not spread out. You either see it at a point or not, with a calculable probability.

Thus in the quantum mechanical case there is no amplitude to be changed to see the interference pattern. The change in the boundary conditions of the problem ( one slit/two slits) changes the solution/probabilities and the interference appears. It characterizes the quantum mechanical nature of all phenomena at this scale ( electrons do that too).

The statement :

I have even heard that some things are too small to be seen because they are smaller than the wavelength of light (and therefore light wiggles around them.)

There are also the two frameworks in this case too. Too small and too large have to be quantified. Take radio waves, their wavelengths are so large that they do not see the atomic structure of some walls, for example , and can propagate through classically with a loss of energy. They do not wiggle, they might be deflected or reflected, but that can follow optical paths too.Visible light goes through glass, it does not "see" the atomic structure of glass, but it does not wiggle ( there would be great distortions), it follows calculable optical paths. When we go down to photons, the quantum mechanical nature will interact with the atomic structure and displacements may appear, governed by the probability for the quantum mechanical solution of the problem.

Too small to be seen by a given optical frequency means that the electromagnetic field does not interact as it passes the "small" but keeps its optical path.

For completeness the two, classical and quantum, merge smoothly when large numbers of photons are involved, as in the classical electromagnetic wave. How the classical is built up from the quantum is given here, but it needs a lot of physics background to understand.

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