DO single photons display sine curve??

Question

Electromagnetic waves are shown as the charge (and magnetic fields) waving as a smooth sine curve. Is there experimental verification of such smooth sine curve?--or does it come out of the fact that maxwell equation derivation resembles a wave equation.

If an individual photon is moving (and not a train of photons) will the charge curve still be a smooth sine wave? If not what does it look like.

Have experiments with single photon been carried out to verify the shape of charge/magnetic waves for individual photons? Do they show a smooth curve or gaps??

Answer 1

Neither the time nor space dependence of a macroscopic (classical) electromagnetic wave has to be sinusoidal. In fact any solution of the form f(x-ct) satisfies the wave equation for any component of the electromagnetic field, with f any function whatsoever. The form of the wave depends on the source (charges and currents) which produced it.

On the other hand it's relatively easy to calculate the radiated EM field for charges and currents which have a sinusoidal time dependence and it's always possible to write any current density as a linear superposition of such fields. That's why these types of fields are important theoretically. Also, for some applications, like radio waves, the fields do vary more or less sinusoidally near the constant (carrier) frequency.

Now, with respect to a single photon (rather than a macroscopic EM field): that's described by a complex valued wavefunction which does not have to be a sine wave either; it only needs to have the general form f(x-ct).

The interaction of a photon and matter has to be analyzed using quantum mechanics. Even for a photon which does happen to have a definite energy (i.e. has a sinusoidal time dependence), the picture of an oscillating electric field of the classical type, that is, a charge being pushed back and forth by an electric field, is inapplicable.

Even though the wavefunction is known, the electric and magnetic fields have to be treated as operators, and their expectation values turn out to be zero everywhere in space. If you try to measure the electric field of a single photon at a point in time, the result will always be unpredictable except for the polarization direction (orientation) for a linearly polarized photon. In other words the phase (whether it's pointing along the polarization vector or in the diametrically opposite direction) is unmeasurable. In any case it's impossible to measure any observable connected to the photon without destroying it.

Answer 2

The wave function of a photon is sinusoidal, but it's not just a simple A*sin(Bx+c) type of function. An EM wave is made up of an Electric field and a Magnetic field. Think of it this way. If the wave is propagating along the z-axis, the Electric field and the Magnetic field will be sinusoids along the x- and y-axis. This is for linearly polarized light, which means that the Electric field oscillates parallel to the x-axis. For other polarizations, the Electric field vector oscillates in a sinusoidal fashion, but it also rotates around the z-axis. This can be circular or elliptical, which basically just means that the length of the Electric field vector is constant (circular) or variable (elliptical). Ultimately, though, the Magnetic field vector is always perpindicular to the Electric field vector which are bot perpindicular to the direction of propagation of the photon. There are no "gaps", as the functions are all smooth. I don't know how much of this has been verified experimentally (or how), but I know that this is what the theory (and Maxwell) states.

Answer 3

i think photons prefer smooth curves since photographers prefer smooth lines on jeans rather than gap jeans which sometimes can be unsmooth, although they are great jeans nonetheless. i just bought a pair of gap jeans and they're my favorite pair of jeans i've ever bought in my life. go gap! they have awesome stuff. i think the gap sign is very memorable, although the gap sign is not curved like the sony sign is curved. quiksilver has a wave on their signs and so that is a memorable sign as well. i've taken the train once but there were no photographers on the train, and the train was pretty straight and did not curve, but i wasn't reading the signs on the train, i was just looking at my gap jeans. so i don't know what it looks like. i have a friend who had to have a co-signer on their lease because she didn't have a job at the time. so co-signers are important. did you ever consider the answer to your question may lie with a co-signer wearing gap jeans who does photography on the side? she does a number on my imagination, so she can be an imaginary number sometimes. but that's besides the point.

hope this helps.

Answer 4

The probabilty of a single photon existing at a particular place at a particular time is a sine function.

Answer 5

Photons do some odd things when 'measured' one at a time...but only if you measure them somehow.