PDA

View Full Version : Quantized Photons



peterdrowan
2008-Sep-16, 11:38 AM
One thing I have never understood is that atomic particles are quantized e.g only allowed to have certain energy values e.g. electrons and spin but photons have a completely continuous energy spectrum. Is this because force exchanging particles (the photon is the force exchanging particle for the em force) are allowed any value. Or is there some theory that says these are also quantised in terms of energy level.

ToSeek
2008-Sep-16, 12:19 PM
Moved from General Science to Q&A.

Ken G
2008-Sep-16, 12:33 PM
There are really two meanings to the words "quantized energy" that often get confused. The "first quantization" says that if you have a "particle in a box", like an electron in an atom or a photon in a similarly sized box, then the energy levels are themselves quantized, like you are talking about. That is just as true for photons as for electrons, but it is less common to find photons in such "boxes". Nevertheless, there is still a type of quantization, "second quantization", that applies to completely free photons of an unspecified number, which is that you have to end up with an integer number of them as the result of any energy measurement, but that number can vary at different (continuous) energies as long as energy is conserved. So even though the possible frequencies can be continuous for free photons, you always get a discrete number of photons at each frequency, so the quantization is within each photon energy.

peterdrowan
2008-Sep-16, 01:22 PM
It is more that a photon seems to have any energy allowed by a continuous spectrum not fixed amounts with steps in between. Are you saying a constrained photon would only have certain allowed levels but a free photon can have any. I do understand that a sum of all of the quantized photons makes a total energy. I am thinking about the photon itself and its possible energy values and that those values are continuous.

Ken G
2008-Sep-16, 01:36 PM
Are you saying a constrained photon would only have certain allowed levels but a free photon can have any. Right, and for the same reasons that electrons in atoms have certain allowed levels. The wave function must interferere coherently inside the box, which constrains the allowable energies. The main difference between electrons and photons in this regard is that the electron has charge, so can be confined more easily into tiny boxes (atoms).

Lepton
2008-Sep-16, 01:40 PM
It is more that a photon seems to have any energy allowed by a continuous spectrum not fixed amounts with steps in between. Are you saying a constrained photon would only have certain allowed levels but a free photon can have any. I do understand that a sum of all of the quantized photons makes a total energy. I am thinking about the photon itself and its possible energy values and that those values are continuous.

Read about the photoelectric effect.

Gigabyte
2008-Sep-16, 02:53 PM
Umm, I almost hate to bring this up. But isn't light itself quantized? I'm pretty sure the quanta of light are photons.

That something can vibrate at different frequencies doesn't mean it isn't quantum.

Gigabyte
2008-Sep-16, 03:00 PM
http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html#c3


Analysis of data from the photoelectric experiment showed that the energy of the ejected electrons was proportional to the frequency of the illuminating light.

Yes, I thought so. Photons are quanta, just like electrons. Electrons have different amounts of energy when ejected, just as light has different amounts of energy. Still quanta however.

Quantum doesn't mean a particle can't have an variable amount of energy.

Ken G
2008-Sep-16, 04:03 PM
Recall from the OP:

One thing I have never understood is that atomic particles are quantized e.g only allowed to have certain energy values e.g. electrons and spin but photons have a completely continuous energy spectrum.
So the issue here is not whether or not there are particles like electrons and photons, but rather, under what circumstances their energies are quantized. For both electrons and photons, in some situations their energy forms a discrete spectrum, and in other situations, it is allowed to be continuous. There has always been some ambiguity in what is meant by the "quantum" in "quantum mechanics". Is it the mechanics of particles, whose existence was known long before quantum mechanics was devised, or does it require the further constraint, to be considered "quantum mechanics", that the particles have "quantized" attributes (like angular momentum in discrete multiples of h)? I think the OP is basically asking around the fact that there is indeed ambiguity in the meaning of "quantum" in "quantum mechanics", because sometimes observables have discrete eigenvalues, and sometimes they are continuous, yet it is still called quantum mechanics either way.

Theophage
2008-Sep-16, 04:39 PM
Umm, I almost hate to bring this up. But isn't light itself quantized? I'm pretty sure the quanta of light are photons.

That something can vibrate at different frequencies doesn't mean it isn't quantum.

Robinson, I didn't know you were a member of this forum too. Nice to see you're carrying your avatar over from the JREF. Sorry about your banning there.

Anyway, if you'd read the OP, it said that quanta of light are photons, so you aren't "bringing up" anything new in the thread.

The problem the OP was having was harmonizing the idea of a quantum, with the idea that a photon can have a continuous set of energies depending on its frequency. The idea of "quantum" is antithetical to the idea of "continuous", get it? But I think Ken G did a pretty good job of explaining.

Gigabyte
2008-Sep-16, 05:34 PM
Banning? What banning? I never heard anything about a banning!

In regards to the essential OP conundrum: "One thing I have never understood is that atomic particles are quantized e.g only allowed to have certain energy values e.g. electrons and spin but photons have a completely continuous energy spectrum."

Quantized does not mean "only allowed to have certain energy values".

It means -to subdivide (as energy) into small but measurable increments. So that there are discrete packets or particles or something, rather than a nebulous field.

Electrons are not limited to "allowed to have certain energies" anymore than photons are. An electron is a quanta, like a photon is a quanta.

Beta particles (fast moving electrons) certainly have different energy levels that electrons in an atom, or free electrons, or electrons flowing in a cathode tube, or electrons that are braking, or electrons in a plasma, etc etc

Quantum Theory does not propose electrons are limited to certain energy levels.

Gigabyte
2008-Sep-16, 05:45 PM
Which may seem redundant at this point.

The confusion may arise from electrons being "forced" into energy levels around a nucleus, when part of an atom.

antoniseb
2008-Sep-16, 07:29 PM
Sorry about your banning there.

We generally frown on posting things like this here. Technically you are attacking the person, not the idea... we presume in some effort to discredit him/her. Because this is a special case, I am warning you publicly in the thread to avoid this kind of ad hom attack in the future, or you will be suspended.

Note to all: being banned elsewhere does not mean you are unwelcome here. It is your behavior here that gets you in trouble with us.

Gigabyte
2008-Sep-16, 07:30 PM
Thinking more on the electron and quantum energy states, it appears that electrons, which give rise to most EM radiation (or light), must have the same variations in energy as photons, or how else could they create all the different wavelengths of light?

korjik
2008-Sep-16, 07:34 PM
Photons are quantized because they are packets of energy. Why they have a continous spectrum is due to how photons can interact with the environment.

Photons due to atomic transitions are only specific values because the electrons of nucleons that cause the emission are limited to fixed values.

Other methods can create photons with arbitrary energy values. Any accelerated charged particle will emit photons with a wavelength dependent on the acceleration of the particle. This will give you a fixed wavelength at a fixed acceleration, but if you have a continously varying acceleration, then you will have a continously varying emission.

Then there is scattering. A photon that 'collides' (technically, it is passes nearby) with a charged particle may end up exchanging energy with the particle. Compton scattering IIRC. If you have a monochromatic beam of photons passing through a beam of electrons, you will get some random scattering and end up with a continous spectrum scattered component to the photons.

Gigabyte
2008-Sep-16, 07:39 PM
Other methods can create photons with arbitrary energy values. Any accelerated charged particle will emit photons with a wavelength dependent on the acceleration of the particle. This will give you a fixed wavelength at a fixed acceleration, but if you have a continuously varying acceleration, then you will have a continuously varying emission.


Speak more on this.

How does the sun create all the different types of light?

The visible spectrum for example. Don't those photons come from electrons?

If so, then the electrons have all kinds of different energies, to be able to produce all those frequencies.

If not, then what is creating the light?

ToSeek
2008-Sep-16, 07:41 PM
We generally frown on posting things like this here. Technically you are attacking the person, not the idea... we presume in some effort to discredit him/her. Because this is a special case, I am warning you publicly in the thread to avoid this kind of ad hom attack in the future, or you will be suspended.

Note to all: being banned elsewhere does not mean you are unwelcome here. It is your behavior here that gets you in trouble with us.

Let me add that posting links to pages with adult language is frowned upon here as well. I have deleted the offending post.

phunk
2008-Sep-16, 08:01 PM
Speak more on this.

How does the sun create all the different types of light?

The visible spectrum for example. Don't those photons come from electrons?

If so, then the electrons have all kinds of different energies, to be able to produce all those frequencies.

If not, then what is creating the light?

Correct me if I'm wrong but I believe it's because the sun is made up of plasma, which is ionized and contains 'free' electrons. Electrons are only limited to specific energy levels when they are bound within atoms.

Gigabyte
2008-Sep-16, 08:04 PM
That's what I thought.

So electrons are like photons, in that they can have any kind of energy level. When free.

HenrikOlsen
2008-Sep-16, 08:44 PM
So electrons are like photons, in that they can have any kind of energy level. When free.
And completely unlike photons in almost every other way, one has an electrical charge the other doesn't, one has rest mass the other doesn't, one has spin , the other has spin 1, etc.

DrRocket
2008-Sep-16, 09:19 PM
There are really two meanings to the words "quantized energy" that often get confused. The "first quantization" says that if you have a "particle in a box", like an electron in an atom or a photon in a similarly sized box, then the energy levels are themselves quantized, like you are talking about. That is just as true for photons as for electrons, but it is less common to find photons in such "boxes". Nevertheless, there is still a type of quantization, "second quantization", that applies to completely free photons of an unspecified number, which is that you have to end up with an integer number of them as the result of any energy measurement, but that number can vary at different (continuous) energies as long as energy is conserved. So even though the possible frequencies can be continuous for free photons, you always get a discrete number of photons at each frequency, so the quantization is within each photon energy.

This is a mathematical description of the issue that may or may not appeal to one's physical intuition. Nevertheless, it does describe what is going on.

When you take a measurement in quantum mechanics you are applying a Hermitian operator to an element in a Hilbert space (the "wave function") and you recover an eigenvalue. In a finite-dimensional space the eigenvalues are computed by finding roots of the characteristic polynomial for a matrix, and there are usually n of them where n is the dimension of the space involved. Physicists tend to avoid the case where eigenvalues have multiplicity greater than 1. But in any case the eigenvalues are discrete, and one can decompose the finite-dimensional Hilbert space into a direct sum of eigenspaces.

In the infinite dimensional case the spectrum of an operator is a bit more complicated, and the decomposition requires a relatively sophisticated integral. It becomes more complicated when the operator is not bounded. In any case, the spectrum in the infinite-dimensional case splits into a discrete part and a continuous part, depending on details of the model and of the operator. In some physical circumstances the continuous part of the spectrum applies, and the result is a continuum of allowable values for the measurement, energy being one such possible measurement.

The explanation above is, of necessity, rather simplified. If you want to see the mathematics in detail and in rigorous form a good book on Functional Analysis is recommended. Functional Analysis by Walter Rudin is my personal favorite. Unbounded Linear Operators: Theory and Applications by Goldberg is another good reference.

Gigabyte
2008-Sep-16, 09:24 PM
When is an electron ever at rest? :)

slang
2008-Sep-16, 09:35 PM
When is an electron ever at rest? :)

(with that avatar in sight I read the 4th word as election...)

korjik
2008-Sep-16, 09:47 PM
Speak more on this.

How does the sun create all the different types of light?

The visible spectrum for example. Don't those photons come from electrons?

If so, then the electrons have all kinds of different energies, to be able to produce all those frequencies.

If not, then what is creating the light?

Note:Things get a bit fuzzy when talking about this. I will be talking like a photon goes from the center of the sun to the surface, but that isnt really true. It dosent make a difference for the examples tho.

Most of the energy in the sun is initally released as gamma rays. As the photons try to reach the surface of the sun, they are repeatedly scattered by the free charged particles in the sun. Some photons get scattered more, some less. The average of this scattering ends up giving you a thermalized distribution, more commonly known as a blackbody distribution.

Gigabyte
2008-Sep-17, 02:48 AM
Most of the energy in the sun is initially released as gamma rays.

OK, I understand that is the current theory, but we don't actually know what is going on inside the sun. But, going with that theory, something odd seems to be taking place.



As the photons try to reach the surface of the sun, they are repeatedly scattered by the free charged particles in the sun. Some photons get scattered more, some less. The average of this scattering ends up giving you a thermalized distribution, more commonly known as a blackbody distribution.

Going with that explanation, it seems like you are saying Gamma rays, produced by fission of course, turn into all the other kinds of EM radiation, by passing through the plasma of the sun.

Now it might be simplistic, but that sounds like all kinds of redshifting going on. We have very high energy radiating from the core, which turns into all kinds of lower energy radiation, by passing through plasma.

So somehow, electrons and protons and hydrogen atoms turn Gamma rays into all the other kinds of EM we know is radiating from the sun.

By "scattering" Gamma, plasma can turn Gamma into everything else? That sounds, I don't know, sort of, hmm.... I'm not sure what the word is.

Is that really what is happening in the sun? Gamma rays are being shifted down to all the other frequencies? By scattering through plasma?
What happens to all the energy? Wouldn't Gamma turning into infrared, or visible light, be a huge loss of energy? Where does that lost energy end up?

Is there a topic about this already?

Gigabyte
2008-Sep-17, 03:05 AM
I know it isn't really "redshifitng", but what do you call it? When high energy "light" turns into lower energy light?

This whole thing has got me thinking now. How does the filament in a tungsten lamp create all those different frequencies of visible light? The photons are coming from "excited" electrons. So the electrons are at all kinds of different frequencies themselves? If not, what mechanism is producing the continuous spectrum of photons?

This is weird. I never really thought about this matter before.

alainprice
2008-Sep-17, 03:58 AM
It's blackbody radiation, plain and simple.

Ken G
2008-Sep-17, 04:03 AM
I know it isn't really "redshifitng", but what do you call it? When high energy "light" turns into lower energy light?
Absorption and re-emission. The energy is conserved-- it's just more lower-energy photons.

So the electrons are at all kinds of different frequencies themselves? Yes, high density objects subject the electrons to many kinds of conditions, so they can have a continuous range of energies. That's what you need for "blackbody radiation".

korjik
2008-Sep-17, 05:05 AM
OK, I understand that is the current theory, but we don't actually know what is going on inside the sun. But, going with that theory, something odd seems to be taking place.

We have a really good idea about what goes on inside the sun. Fusion is not an unknown effect, it has actually been done here on Earth. Going with that theory, exactly nothing strange is going on.



Going with that explanation, it seems like you are saying Gamma rays, produced by fission of course, turn into all the other kinds of EM radiation, by passing through the plasma of the sun.

Produced by fusion. Yes, trying to get photons to pass through extremely dense extremely hot plasma for half a million kilometers is going to cause rather large amount of scattering.



Now it might be simplistic, but that sounds like all kinds of redshifting going on. We have very high energy radiating from the core, which turns into all kinds of lower energy radiation, by passing through plasma.

Scattering and absorption and reemission, but no redshiftng.


So somehow, electrons and protons and hydrogen atoms turn Gamma rays into all the other kinds of EM we know is radiating from the sun.

By "scattering" Gamma, plasma can turn Gamma into everything else? That sounds, I don't know, sort of, hmm.... I'm not sure what the word is.

Actually, almost any material that a photon passes through causes some scattering. It is called optics.


Is that really what is happening in the sun? Gamma rays are being shifted down to all the other frequencies? By scattering through plasma?
What happens to all the energy? Wouldn't Gamma turning into infrared, or visible light, be a huge loss of energy? Where does that lost energy end up?

Is there a topic about this already?

The scattering of gamma rays down to the sun's blackbody spectrum is the exact same effects that warm the Earth's ocean when the sun shines on the water. There is no even remotely strange physics here. Light getting scattered generally creates more photons. Back of the envelope calculation for fusion in the sun is that every gamma is split into a few million photons at the surface of the sun