Number of cycles of light per photon

[DarioC]

You can blame Eddington for this one. I'm a retired electronics guy who now has time to read physics history and recent research also and am totally curious about the nature and most basic definitions of light photons.

Eddington mentions in one of his essays in the '20's about "a meters long" burst of light-wave radiation when a electron experiences orbital decay. I know there is recent information relating to the energy involved, but have found nothing on "pulse length/number of cycles."

My question is: If we had a probe that would do it, what does modern theory tell us, if anything, about the number of cycles of light we could observe at the passage of each photon of light from a single photon source?

http://www.sciencemag.org/content/326/5952/550.full

DC

 

[Bill_K]

The wavelength of a photon is determined by the frequency, λ = 2πc/ω. The length of a wave packet is determined by the spread in frequency Δω, roughly 2πc/Δω. So the number of cycles is the ratio of these, n = ω/Δω.

 

[DarioC]

Thanks for the reply. Do you have a online reference for the theory on the spread significance, so I can read more?
What would the result/meaning of this calculation be if the delta frequency was zero (that is a single wavelength/frequency)?

DC

 

[James S Saint]

I'm pretty sure that by definition it is only 1... a "pulse".

A photon is intended to represent the most fundamental entity/packet involved.

 

[Bill_K]

What would the result/meaning of this calculation be if the delta frequency was zero (that is a single wavelength/frequency)?

A pure frequency wave is an idealization. It would have to be of infinite extent in time and space, and such a thing is not possible in nature. Any system that emits a photon must do so in a finite time, and consequently will have a finite linewidth. The sharper the spectral line, the longer the wavepacket.

 

[krd]

Eddington mentions in one of his essays in the '20's about "a meters long" burst of light-wave radiation when a electron experiences orbital decay. I know there is recent information relating to the energy involved, but have found nothing on "pulse length/number of cycles."

It gets worse. It's taken me years to visualise or get an idea of what light is (and I'm probably still wrong). The idea of a light pulse is wrong. It's intuitive - and sometimes you'll see diagrams showing a pulse but they are wrong.

The thing is, your intuition will throw you. All these things you've done in life - like switching on and off a flash lamp. A beam of light with a laser pointer. Those things will throw you - they give you a false idea about what's happening. It's much more counter intuitive. The Double Slits experiment is a good place to look to get and idea of the weirdness - especially the version with the single electron at a time.


If you shine a light from point A to B, divide the distance by the wave length of the light - it will give you the number of cycles. Cycles per second is frequency.

My question is: If we had a probe that would do it, what does modern theory tell us, if anything, about the number of cycles of light we could observe at the passage of each photon of light from a single photon source?

The photon can travel forever until it hits something. Some light from the stars is billions of years old. That's trillions upon trillons of cycles.

 

[edpell]

If I follow, we have say an atom emitting a 5eV photon in 1E-8 seconds so
n=5eV/(h/1E-8)=5/(4E-15/1E-8) = 1.25E7 wave cycles with a wave length of 2475A. So a distance start to stop of 3 meters.

 

[M Quack]

In X-ray and nuclear physics, you get exponential decay with a certain life time. The energy spectrum - and with that the wavelength spread - is the Fourier transform of this exponential. This gives a characteristic Lorentian line shape. The shorter the life time, the broader the line width.

For Mossbauer lines, the life time can be quite long. For 57Fe it is 141 ns, which corresponds to 4.55 neV for a 14.41 keV photon. The number of cycles is huge, as is the length of the corresponding wave train.

 

[jtbell]

Eddington mentions in one of his essays in the '20's about "a meters long" burst of light-wave radiation when a electron experiences orbital decay. I know there is recent information relating to the energy involved, but have found nothing on "pulse length/number of cycles."

The wavelength of light in the visible region is about 400 nm (red) to 700 nm (violet). Take the midpoint of this range for the sake of argument. How many cycles of length 550 nm fit into a pulse that is one meter long?

 

[krd]

The wavelength of light in the visible region is about 400 nm (red) to 700 nm (violet). Take the midpoint of this range for the sake of argument. How many cycles of length 550 nm fit into a pulse that is one meter long?

18x10^5

 

[DarioC]

"Any system that emits a photon must do so in a finite time, and consequently will have a finite line width."

Is that a similar situation as with a RF pulse that would not have an absolutely vertical rise and fall trace? I think there may be a limited similarity.

Could some one give me a reference or even a subject title that I might search that would give me more information on this subject and the derivation and use of these formulas?

Just grasping the dynamics of two cycles of a given frequency propagating through space is seriously difficult. Have to work on that.

Bill K., In reference to the length of a light emission determining the spectral line width, I'm going to have to get some additional information on (spectrometers?)

Use to do field service on them when I first started working in electronics. Funny how things come back around in a different form.

DC

 

[DarioC]

Found it:

http://physics.aps.org/story/v22/st8

DC

After considering the above article at length I am presently thinking that wave packets likely have very little relevance to my question about wave cycles per photon.

I am still wrestling with the concept that a greater number of cycles of a "single" frequency would somehow diminish the Heisenberg Jitters of that emission.

 

[DarioC]

"Researchers have also recently been able to filter a single photon, thereby narrowing the range of frequencies in the wave packet."

"...paired (or “entangled”) photons typically have wave packets that are one tenth of a picosecond long, which is too short for current technology, says Steve Harris of Stanford University in California."

Direct quotes from:

http://physics.aps.org/story/v22/st8

Which seems to be in conflict with information/formulas posted above.

Full/original article here:

http://www.google.com/url?sa=t&rct=...jMDZCQ&usg=AFQjCNGidurVt1rEgqucYxxgOPCThI863w

Using the the above quoted wave packet length I get 600 cycles of visible light (500nm).

DC

Just noticed; above research sponsored by DARPA, and others.

 

[M Quack]

The technique to generate isolated photons is to deposit atoms very sparsely on a substrate - such that you have a single atom in the field of view of a focused laser.
That laser then pumps the single, isolated atom and excites it into a higher state.
From this it decays, emitting a single photon.

The life time and thus energy bandwidth and wavelength spread depend on the type of atom and the transition selected (there may be several). Depending on the experiment you do you may prefer short or long life times.

The net result is that there is no defined length of a photon. It all depends on the circumstances.

I am not familiar with the creation of entangled photons, but I guess the process is the same, selecting atoms that simultaneously emit two coupled photons to conserve some selection rule.

 

[DarioC]

What you summarize is pretty much where my reading and "research" of articles have been leading me.

My wish is to get a understanding of the most basic concepts of the nature of light at it's origin and work "up" from there; if it is possible to get enough of a grasp on the subject to be motivated to continue, as it is simply a hobby for this retired electronics technician.

Most interesting and significant to me is the understanding of orbital decay of electrons and the uptake of energy when they are stimulated by light to a more energetic level. Reading a book by Roger Penrose has enhanced my conviction that real processes are taking place under all the mathematical symbolism even if it is quite at odds with my everyday comprehension of the physical world.

How well someone with my limited knowledge and skills can unearth and comprehend this reality is something that I am in the process of finding out.

Hopefully my knowledge and skills will improve with persistence to the quest on my part.

DC

 

[M Quack]

That is quite a delicate problem. In most models this is just shown as a step. One moment there is an electron in a high level state, the next moment there is the electron in a lower state and the photon is fully formed. Nothing in between. With respect to the spatial extension of the photon that is very very unsatisfactory.

The probability of the transition is given by "Fermi's golden rule". I suggest that you read up on that and then look for theories that go beyond (and that go beyond my humble knowledge :-)

http://en.wikipedia.org/wiki/Fermi's_golden_rule

 

[DarioC]

From what happens when an electron oscillates at lower frequencies (than light) in a radio antenna one might consider that orbital decay transfer is not a single acceleration of the electron with a single deceleration.

Of course this is likely much too mechanical, but I can picture the electron in a Bohr atom as oscillating,upon arrival in the new "orbit," in an elastic manner as a way of radiating the excess energy carried down from the "higher" orbit. I picture this as an inward and outward movement, relative to the nucleus, that would persist through many "orbits" of the electrons normal circulation path. Each cycle of wobble would generate a cycle of EM radiation until the kinetic energy was depleted. The frequency would logically be higher than comes from an antenna due to the strength of forces and the distances involved.

I would suspect that there might be some math that could be done with such a concept, that is using the mass, time, and forces likely involved.

DC

 

[M Quack]

That picture works for hydrogen atoms in very high excited states, called Rydberg atoms.

http://en.wikipedia.org/wiki/Rydberg_atom

For transitions emitting light in the visible or x-ray range that picture does not work (to the best of my knowledge) and you have to dig deeper into the QM of the system.

 

[PhilDSP]

The same question could be asked about other particles. In 1962, de Broglie stated on page 4 of the monograph "Interpretation of Wave Mechanics"

Experiments show that the wave trains corresponding to photons of light are several million wavelengths long (i.e. several meters long), which is very different from $10^{-12}$ or even $10^{-8}$ cm. For electrons, recent experiments (Möllensted in Germany, Faget and Fert in Toulouse) have shown that the wave trains also have a length equal to very many times the wavelength (which is here of the order of $10^{-9}$ cm) and hence the wave train is very much longer than $10^{-12}$ or even $10^{-8}$.

 

[DarioC]

Phil: Thanks for the reference to de Broglie's paper, I just downloaded the PDF and it looks like it will be interesting reading. Do you have any link or title that I could search on the more recent work you mention? The thought of a long wave train for a particle with mass is a real brain twister for me, but the more interesting therefore.

MQ: I think we are pretty much OK in the visual spectrum as that is the area that originally piqued my interest. X-rays are likely to be considerably different if my limited knowledge of their generation has the significance that I think it does.

I am not naive enough to think that the ideas I am tossing around have any value when it comes to calculating outcomes, but rather more for me as a means of perceiving physical realities in the processes that are not blatantly negated by experimental tests.

DC

 

[PhilDSP]

Phil: Thanks for the reference to de Broglie's paper, I just downloaded the PDF and it looks like it will be interesting reading. Do you have any link or title that I could search on the more recent work you mention? The thought of a long wave train for a particle with mass is a real brain twister for me, but the more interesting therefore.

Unfortunately the book I mentioned (English translation) is out of print and hard to get a hold of. You might try a large library, especially at a technical college if possible. An English translation of his book "Introduction to the Study of Wave Mechanics" is easily available and inexpensive but has a strong focus on mathematics rather than being overly conceptual. There is a lot of material by de Broglie in French.