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Name: Fred
Status: student
Grade: 9-12
Country: Canada
Date: Winter 2011-2012

Photons exhibit wave-particle duality, and i am trying to grasp what that term really means. I understand yes it behaves both as a particle and as a wave, but my question is, will one photon follow a sinusoidal path as it travels through space? That is, instead of traveling in just a straight line, will it instead travel say, at 3.00x10^8 m/s [right] and at the same time be going up and down then up then down as it does this, like the graph of a transverse wave?

Fred, A wave does NOT travel a sinusoidal path. A wave travels a straight path. The medium through which the wave moves is what oscillates like a sine function. For light waves, this "medium" is a combination of electric and magnetic fields. The fields do not move. The field strength at a position just gets weaker and stronger, often reversing the direction that it points. The sine wave graph of such a wave shows the electric and magnetic fields at a specific time. The up and down curvature on the graph indicates the strength of the electric field, not the motion of the wave.

A model easier to imagine could be based on color. Consider a horizontal string with many tiny lights along it. When a light is red, the field points upward. When the light is blue, the field points downward. When the light is brighter, the field is stronger. Build a field by setting the lights in sequence as bright red, dim red, no light, dim green, bright green, dim green, no light, dim red, bright red, and so on. Now, move the string horizontally. The wave moves horizontally. At some point through which the string moves, color goes from red to no light, to green, and so on. At that point, the field goes from upward to no strength, to downward, and so on. The field, however, moves horizontally. The motion of the field is the motion of the string.

Dr. Ken Mellendorf Physics Instructor Illinois Central College

Fred -

Photons are generally not imagined as traveling in a wiggling sinusoidal path. More like they _are_ a certain amount of jiggling of the whole general area where they are passing through at the moment. It is a wave, so yes it is a time-varying transverse electric and orthogonal transverse magnetic field both extending over some largish volume with very blurred boundaries. Exactly how those boundaries are defined in time or space depends on how the wave was shaped as it was launched, how well specified it's energy or how short its launch-time was, and any material structures around it at present.

People who do laser beams think in "modes". Examples of wave-modes are: - a plane-wave in free-space (cannot ever really exist, but approximations from distant objects happen often) - a Gaussian beam-waist and expanding cone of light in free-space. - a dipole-radiated field such as from a radio half-wave dipole antenna - a characteristic captive wave-mode in a metal wave guide - a characteristic captive wave-mode in a glass optical fiber Of course those are mostly wave-nature descriptions of the shape and path of a stream of photons. When you get one photon, its association with a particular mode is often less clear.

So then we weigh the photon's particle nature. I think the particle nature only shows up at discrete instants and points, such as the instant the photon is launched or absorbed or changed. So it is not really possible to trace some narrow path that "the particle" traveled. It can suddenly exert a particle effect at any point in the blurry-boundaried wave-field, or not. If it does, then it is no longer the same photon. It is gone, or at least it has a different energy and direction and wave-shape. So a path with sinusoidal wiggle is pretty much meaningless or at least un-verifiable. (Deducing where it "must have" traveled is always basically conjecture, and is also usually has a range of plausible answers.)

It is a little like those bleach-white sword-villains in the movie series Matrix, who cannot touch or be touched until they suddenly choose to materialize and swipe. Or like a large cloudy ghost that suddenly turns into a small, hard fly and bites something. Quantum mechanics plays this kind of game. It _is_ evasive, concealing, frustrating. There are rules for probability of when/where the bites occur, and that is all there is. That the rules are mostly wave-like seems queer to us. The rules are enough to result in averages which are nearly deterministic, so in the large scale we still get to do science and engineering.

Jim Swenson

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