[jeffreyH (OP)]

Since photons are considered massless does this mean that 2 of them can occupy the same space at the same time? Could they even travel an identical path simultaneously?

[Colin2B]

They are bosons, so I thought that meant exclusion principle doesn't apply? However, can they have a position well enough defined so you could say they occupy the same space, or even follow exactly the same path?

[agyejy]

Answering this question is going to require some pretty basic questions. First what do we mean by photon (or a particle in general)? Second what do we mean when we say "occupy the same space"? Third how do we define the path of a photon (or a particle in general)?

Currently the best answer we have to the first one is that you just have to take the square of the wave function expressed in terms of spatial coordinates as determining the extent of the particle. As such there isn't a really good way to define a precise location for a particle. The answer to the second question comes when you bring two or more particles close together. The wave functions of the particles will start to overlap as they get closer. Now if the objects are electrically charged and have the same charge they will repel but this has nothing to do with the wave functions. If you push them together with enough force to overcome the electrostatic repulsion the wave functions will overlap. For bosons there are no restrictions to occupancy so boson wave functions will overlap happily and there is even a small attraction that arises completely from the fact they are bosons. Fermions on the other hand must occupy different quantum states which results in a repulsion between fermions in precisely the same quantum state.

The thing to note is that quantum states of say electrons are also labeled with the spin of the electron. For example in He there are two 1s electrons. Both of these electrons have precisely identical spatial wave functions and occupy precisely the same region in space with the same kinetic energy and momentum. However, they have different spin quantum numbers which is enough to make the Pauli exclusion principle happy. So in something as simple as He we have an example of two particles (the electrons) existing in exactly the same space. To be clear we are treating the electrons as being everywhere their wave function is non-zero because to do otherwise is to introduce hidden variables and there is currently little reason to believe hidden variables exist. Besides all we can measure is the wave function probabilities anyway. As you move to heavier atoms you find that in addition to the complete overlap of spin up and spin down electrons in the same energy level and orbital the s,p,d, and f electron orbitals of all energy levels spatially overlap somewhat with the s,p,d, and f electron orbitals of all other energy levels.

The path of a photon or particle is then just the over path of the wave function (though sometimes this can get very complicated). But as we just discussed photons are bosons and are thus perfectly happy to be in the same quantum state and thus can very easily be completely overlapped spatially and have identical energy and momentum. Thus they would also have exactly the same path through space. A spin up and spin down electron could do the same exact thing as well assuming something is overcoming their electrostatic repulsion and they aren't traveling through a strong magnetic field.

The entire concept of matter occupying space and things being solid is an illusion primarily caused by electrostatic repulsion with some influence from Pauli exclusion in some situations. Quantum Mechanics is about waves and all waves are happy to be in the same place at the same time. It just so happens that some waves in Quantum Mechanics have other properties (i.e. charge, Pauli exclusion which is basically about symmetry) that cause the waves to repel.

[jeffreyH (OP)]

Interestingly, this relates back to black body radiation and so to quantization of the electromagnetic field. I found this link to be a very good description.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/phodens.html

[lightarrow]

Since photons are considered massless does this mean that 2 of them can occupy the same space at the same time? Could they even travel an identical path simultaneously?

Two photons can have the same exact location on a detector only, because from source to detector they don't have an exact location at all.

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[evan_au]

does this mean that 2 of them can occupy the same space at the same time?

Photons don't interact very much with each other (especially in a vacuum), which makes them ideal for long-distance communications.

Photons can cross paths and pass straight through each other, continuing undisturbed. Here they are in the same place, but traveling in different directions.

Could they even travel an identical path simultaneously?

The core of single-mode optical fiber is just wide enough for an infra-red photon to pass along the center. So all photons follow the same path through the fiber.

To communicate reliably, you need to receive a couple of photons "at once" (or at least within 0.1 nanoseconds, if you are to communicate at 10Gbps). In this case, the photons travel an identical path, practically simultaneously. The photons travel as a wave, so the exact time the photon is emitted, and its exact position in the fiber isn't known exactly, until you detect it at the end of the fiber.

If you try to put too much power down an optical fiber (eg in industrial lasers), you can get the photons to interact with the fiber and each other, producing photons at different frequencies than the original photons.

Green laser pointers use a special non-linear crystal which turns two infra-red photons into one green photon, through interactions between the crystal and the photons.

[lightarrow]

Could they even travel an identical path simultaneously?

The core of single-mode optical fiber is just wide enough for an infra-red photon to pass along the center. So all photons follow the same path through the fiber.

It's as stating that an ant on Earth and another on Pluto follow the same path since they are both in the solar system...

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[evan_au]

It's as stating that an ant on Earth and another on Pluto follow the same path since they are both in the solar system...

I would rather say that an ant in an ant tunnel, and another ant in the same tunnel follow the same path because they are both in the same tunnel.

Of course, single-mode optical fiber is not entirely lossless, and a small fraction of the photons will hit some impurity and be absorbed or scattered in a given km. But those that do make it to the end have followed the same basic path, in that the core is typically about 9 μm in diameter, and I understand that the wavefunction fills the core cross-section (but I haven't seen the solution to Maxwell's equations that proves it...).

See: http://en.wikipedia.org/wiki/Single-mode_optical_fiber#Characteristics

[lightarrow]

It's as stating that an ant on Earth and another on Pluto follow the same path since they are both in the solar system...

I would rather say that an ant in an ant tunnel, and another ant in the same tunnel follow the same path because they are both in the same tunnel.

But stating that the entire wavefunction of the photons (which don't have a wavefunction  []) is spread inside all of the tunnel/optical fiber it's exactly the same as stating that the photons don't have a precise location at all. If you want to talk about them as "localized corpuscles" then you have to treat them as points with zero dimensions, because when they are detected they don't have any measurable non-zero extension.
But if they are points, then they are infinitelly smaller than any finite diametre of an optical fiber. This is the sense of the comment I made in my previous post. It's analogous to the path of an electron in a bubble chamber: the existence of such a path doesn't mean that the electron have a precise trajectory, since the path's transversal dimensions are much greater than the electron's (almost point-like) dimensions.

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[JoeBrown]

I think they resist sharing physical locality quite vigorously.

This is evidenced by varying wave lengths.  Atoms that are smashed together release photons.  The more photons released in the same time & locality produce shorter wave lengths.  Shorter wavelength == higher energy. 

There must be a limit to the number of photons exiting a locality.  When this number is exceeded the photon crowding must compact the wave length.

*** I reserve the right to be completely wrong, here, but when I contemplate energy release, this seems like logical reasoning under the physics. ***

[chiralSPO]

I think they resist sharing physical locality quite vigorously.

This is evidenced by varying wave lengths.  Atoms that are smashed together release photons.  The more photons released in the same time & locality produce shorter wave lengths.  Shorter wavelength == higher energy. 

There must be a limit to the number of photons exiting a locality.  When this number is exceeded the photon crowding must compact the wave length.

*** I reserve the right to be completely wrong, here, but when I contemplate energy release, this seems like logical reasoning under the physics. ***

More photons does NOT mean higher frequency. You can have a 5mW/cm² laser that shines at 1064 nm wavelength, or you can have a 50W/cm² laser that shines at 1064 nm, the difference between the two is just that one is pumping out 10000 more photons per second in a given area, but the frequency is the same. You can also have a 10 mW/cm² laser that shines at 532 nm wavelength. This one will produce the same number of photons per second in a given area as the first laser, but each photon has twice the energy (twice the frequency).

[JoeBrown]

More photons does NOT mean higher frequency. You can have a 5mW/cm² laser that shines at 1064 nm wavelength, or you can have a 50W/cm² laser that shines at 1064 nm, the difference between the two is just that one is pumping out 10000 more photons per second in a given area, but the frequency is the same. You can also have a 10 mW/cm² laser that shines at 532 nm wavelength. This one will produce the same number of photons per second in a given area as the first laser, but each photon has twice the energy (twice the frequency).

What is the underlying cause of the wavelength emitted by a laser?  Is it the confines of atoms from which the photons are released or the structure of the apparatus?

[chiralSPO]

What is the underlying cause of the wavelength emitted by a laser?  Is it the confines of atoms from which the photons are released or the structure of the apparatus?

It depends on the laser.

For some lasers like Ruby lasers or Nd:YAG lasers, it is determined by fairly localized electronic structures. Mostly around a single atom, and its nearest neighbors. The distance between the energy levels determines the frequency of the laser light.
https://en.wikipedia.org/wiki/Nd:YAG_laser
https://en.wikipedia.org/wiki/Ruby_laser

Very common cheap lasers these days are diode lasers, for which the wavelength is determined by the electronic structure of the semiconductors used to create them--slightly larger than atomic scale, but essentially the same idea, instead of having one nucleus with its own electrons in energy levels around it, there are zillions of atoms all working together to support a delocalized structure in the electrons around them.
https://en.wikipedia.org/wiki/Laser_diode

Some lasers use chemical reactions to generate specific frequencies, like excimer lasers. The frequency is determined by the combination of gases in the laser.
https://en.wikipedia.org/wiki/Excimer_laser

There are also lasers where the output frequency can be determined more by the macroscopic construction of the laser:
https://en.wikipedia.org/wiki/Helium%E2%80%93neon_laser

And even tunable lasers, where the electronic structures can generate a comparatively wide range of frequencies, and the laser frequency can be adjusted using diffraction gratings or other physical devices.
https://en.wikipedia.org/wiki/Dye_laser

There are also ways to "mix" photons together (sum frequency generation), for instance the doubling crystal in a green laser pointer, which can produce one 532 nm photon from 2 1064 nm photons.
https://en.wikipedia.org/wiki/Second-harmonic_generation
https://en.wikipedia.org/wiki/Sum-frequency_generation

[evan_au]

I think (photons) resist sharing physical locality quite vigorously.
This is evidenced by varying wave lengths.

Photons are "Bosons". Inside a laser, the photons all have essentially the same wavelength, and they occupy essentially the same volume. They form a "Bose-Einstein condensate", where all of the photons can have the same energy and fill the same volume. (Unlike the other class of subatomic particles, the "Fermions", where they are forbidden from having the same energy and filling the same space.)

PS: Of course, if you pump too much energy into a laser crystal, it can shatter due to thermal stresses. But that is due to the behavior of the atoms in the crystal, not due to antisocial photons.

[evan_au]

What is the underlying cause of the wavelength emitted by a laser?  Is it ... the structure of the apparatus?

In the free-electron laser, the mechanical structure of the "undulator" produces a periodic magnetic field, which triggers laser action. You can change the laser wavelength by changing the physical structure of the undulator, or by changing the velocity of the electrons.

Because these electrons are traveling in a vacuum, at very close to the speed of light, they experience time dilation; by changing the velocity, you change the time dilation factor, and this changes the frequency of the light that they emit.

[JoeBrown]

Well, seems we've gotten quite a bit off topic w/lasers, tho I find the discussion intriguing.

It seems photons resist sharing locality, with e=mc² is an indicator of resistance toward sharing locality.

Atoms are points where photons share locality, so the original supposition isn't terribly exotic, as I initially suspected, there a lot of atoms.

The medium from which photons are released has a bearing on the frequencies produced, which may lend credence to my earlier hypothesis.  w/regard to the free-electron laser,  crowding of electrons by changing the undulator config or velocity of electrons and e=mc², further suggest they don't like being in the same place.

Speculating Gamma ray bursts, lead to consider my earlier hypothesis.

Atoms are the closest photons exist.  Because they possess limits of quanta in their valance organizational structure, it seems they cannot exist at exactly the same point, tho near enough they are essentially considered the same point.

[chiralSPO]

Atoms are the closest photons exist.  Because they possess limits of quanta in their valance organizational structure, it seems they cannot exist at exactly the same point, tho near enough they are essentially considered the same point.

No. Atoms and photons are very different! Atoms have mass; photons do not. Atoms are made of many types of smaller particles (the smallest atom is made of three quarks and one electron); a photon appears to be an elementary particle (cannot be divided into smaller particles). Because atoms are made of little bits, there are many types of atoms (made of different combinations of these bits), and each combination can exist in multiple states; and photons really only have two variables: frequency and polarization.

Atoms are also certainly not considered "pointlike." They have significant sizes, and can be up to a few Ångstroms wide.

Some atoms are bosons, and in that regard are like photons,

[JoeBrown]

Some atoms are bosons, and in that regard are like photons,

Argh, what does that have to do with photons existing at the same point?

I didn't say atoms are photons.  I said they were are a (I meant like a) point where photons exist.  However, it's understood that there is a quantum limit to how much energy can exist within valance capacity of such points.  To me, that suggests they cannot share the exact same physical locality.  Tho an atom is about the closest to a point we might expect a pair of photons to exist.

chairlSPO you seem to have a strong understanding of the composition of atoms...

This topic has me questioning the composition of electrons and/or positrons.  Can you elaborate on their makeup?  Do they contain multiple photons?  Seems to me they must, but I'm ignorant in that regard.