Exploring the Frequency of Photons in Maxwell's Equations

[idea2000]

Hi,


I was wondering what the frequency of a photon is according to maxwell's equations. Does the energy of a photon really oscillate over time? I'm having a hard time picturing what is actually happening. Thanks!

 

[WannabeNewton]

There are no photons in Maxwell's theory. Maxwell's equations are equations of motion of classical electromagnetic fields. Frequencies are associated with normal modes of these fields.

Photons arise from quantizing Maxwell's equations.

 

[Drakkith]

Maxwell's equations are classical in nature and don't actually describe photons. By classical I mean that they were developed prior to quantum theory and the discovery of the photon. The energy of a photon depends solely upon the frequency of the EM wave and something known as plank's constant and does not oscillate over time.

The photon is simply how an EM wave interacts with matter. Einstein showed that light, and by extension all EM waves, can only transfer energy in discrete amounts. This means that if you were to watch an EM wave transferring energy to a detector, you wouldn't see a continuous transfer. Instead, the energy is transferred in lumps that we call photons. You would see the transfer of a lump of energy each time a photon is detected. For an EM wave with a single frequency, each lump of energy is exactly the same amount.

What is "actually" happening is that the EM wave has two components, the electric and magnetic field vectors, that are oscillating as the wave propagates. How fast the oscillations occur is directly linked with how much energy each photon has. Faster oscillations, meaning a higher frequency, result in a larger amount of energy in each photon. This is why extremely high frequency EM waves, such as X-Rays and Gamma Rays, can injure you even when the total energy of the wave is much less than the visible light from the Sun. At those frequencies, each photon deposits so much energy at once that it destroys molecular bonds, damaging DNA and other cell functions.

 

[dauto]

Hi,


I was wondering what the frequency of a photon is according to maxwell's equations. Does the energy of a photon really oscillate over time? I'm having a hard time picturing what is actually happening. Thanks!

Also, the energy of a photon is constant as given by Planck's formula. It does not oscillate over time.

 

[sophiecentaur]

I sometimes consider the problem of reconciling the photon's nature with the simple ideas of energy transitions. There is a kind of paradox which arises from trying to make both QM and classical fit a situation.

It must take a finite amount of time for a photon to be released during an energy transition. Imagine just one photon is released in our observation time. Whilst the energy is being emitted by the (for instance) atom, in a classical sense, you will have an amplitude modulated burst of energy at the frequency, corresponding to E/h. This implies sidebands. The bandwidth associated with the sidebands will relate to the transition time, which will relate to the particular nature of the emitting system (the bandwidth of the transmitter, if you like). Imagine this photon gets detected by another system (different kind of atom, say). The detector system can't be relied on to have a similar 'bandwidth'. So we could have a photon, generated by an emitter with a wide bandwidth, arriving at a detector with a narrow bandwidth. It would not be absorbed if there were not enough energy admitted by the detector. But isn't the energy of the photon, the only parameter that counts here? They must all be identical, for any given frequency or you could tell what sort of system a photon came from.

 

[Drakkith]

I'm not seeing the paradox, Sophie. Could you elaborate?

 

[sophiecentaur]

On the one hand, photons are identical but, on the other hand, they must have different characteristics, depending on their source. That's what I was getting at.

 

[Drakkith]

I'm not seeing it, but perhaps I'm not mixing classical and quantum physics the same way you are.

 

[bahamagreen]

On the one hand, photons are identical but, on the other hand, they must have different characteristics, depending on their source. That's what I was getting at.

Is this what you mean?

I have seen where for the infinite wave the photon is characterized as a mode excitation where E=h*f, f is exact, and the photon is labeled as the energy carrying particle.

And where emission energy measurements E group around h*f for the f of the system showing the f spectrum of the emitter, and the photon is characterized as a mathematical construction used to decompose the emitter's spectrum.

 

[sophiecentaur]

Is this what you mean?

I have seen where for the infinite wave the photon is characterized as a mode excitation where E=h*f, f is exact, and the photon is labeled as the energy carrying particle.

And where emission energy measurements E group around h*f for the f of the system showing the f spectrum of the emitter, and the photon is characterized as a mathematical construction used to decompose the emitter's spectrum.

Yes, I like the idea. The photon is fine as long as it is treated as just that. But there are many well informed Scientists (Feynman, for one) who have given a much more physical interpretation to the photon. That's when I start to have problems.

But Photons really can be treated as particles in many successful models (talk to a Laser or Nuclear expert). As an RF / antenna engineer, I feel easier keeping one foot in the Wave camp. Hence my cognitive conflict.

 

[f95toli]

Yes, I like the idea. The photon is fine as long as it is treated as just that.

Photons are certainly real. We have both single photon emitters and detectors that can be used to emitt single photons that -for most practical purposes- behave like particles.
Part of the problem stems from the fact that quantum optics is both complicated and weird. For example, the "photon as a particle" is only really correct if we are dealing with number states (Fock states). However, these states are difficult to create which means that most light is in thermal or coherent state; and in these type of states we do not have a definite number of photons. Hence, in these cases we can't really talk about one photon (unless we are talking about the average number of photons).

Moreover, there are also situations where one can talk about the spatial shape of a single photon (this can be measured, and can be very long); but this does not directly correspond to e.g. a "photon wavelength".

The point I am trying to make is that quantizing the EM field is just the first step, the "actual" physics of photons (and more generally states of light) is much more complicated than that.

 

[idea2000]

I'm totally confused. So bear with me. I have a ton of questions.

So if the electric and magnetic fields of light has nothing to do with the energy of a light, and the energy only has to do with how fast the electric and magnetic fields are moving back and forth, why even bother characterizing light as an electromagnetic wave? How do we even know the fields are oscillating? Do they interact with something that shows us indirectly that they are oscillating waves? How come they don't interact with the electric and magnetic fields of an electron? How do we even know for certain that light is composed of electric fields and magnetic fields? Have there been any experiments that have shown this? What is the "shape" of a photon? Does a photon have finite length and width? Sorry, I'm just really confused as to how we arrived at the conclusion that light is an electromagnetic wave. Did we just plug in values into Maxwell's equations and pop out an electromagnetic wave? Thanks for any help in advance.

 

[dauto]

I'm totally confused. So bear with me. I have a ton of questions.

So if the electric and magnetic fields of light has nothing to do with the energy of a light, and the energy only has to do with how fast the electric and magnetic fields are moving back and forth, why even bother characterizing light as an electromagnetic wave? How do we even know the fields are oscillating? Do they interact with something that shows us indirectly that they are oscillating waves? How come they don't interact with the electric and magnetic fields of an electron? How do we even know for certain that light is composed of electric fields and magnetic fields? Have there been any experiments that have shown this? What is the "shape" of a photon? Does a photon have finite length and width? Sorry, I'm just really confused as to how we arrived at the conclusion that light is an electromagnetic wave. Did we just plug in values into Maxwell's equations and pop out an electromagnetic wave? Thanks for any help in advance.

One word answer: INTERFERENCE. photons do interfere (with each other and themselves) so they must be treated as waves. Being totally confused by all of the above is an almost unavoidable phase in the learning of quantum mechanics, so don't feel bad about it. We've all been there. That's why the (somewhat outdated) concept of duality was introduced by Bohr to begin with. Only a proper quantum treatment of nature resolves these issues. But the quantum concepts of states being represented by vectors in a space where measurements are related to operators and so on and so forth is just too abstract for most people to grasp at once. It takes time and effort.

 

[UltrafastPED]

But Photons really can be treated as particles in many successful models (talk to a Laser or Nuclear expert). As an RF / antenna engineer, I feel easier keeping one foot in the Wave camp. Hence my cognitive conflict.

As a laser physicist I find that the photon is very useful. Certainly as an RF antenna engineer you do not require the concept of the photon to do your work! But that is because the photons really are the quantized modes of the electromagnetic field, and each one is very miniscule when working with radio waves.

But Maxwell's equations tell us that electromagnetic waves are equally applicable all up and down the scale of wavelengths/frequencies ... and the energy content of a photon becomes significant at some point! For example, the electronic transitions within atoms and molecules fit the photon picture very well; all of spectroscopy is based on this.

And as energy increases you begin to see more and more "particle" behavior, though it is always there: the typical detector always detects over a small region, point-like, even though the "particle" acts as a wave during transit.

For example, my dissertation research was on ultrafast photo-electron diffraction. I can assure you that electrons have wave properties during the diffraction, but are particles at the detector! The same is true for x-rays. I "see" this behavior in the lab, with my very own detectors.

And yet most people are happy with "an electron is a particle" and "a photon is a wave". We even have people on this site who throw a fit when "wave-particle duality" is brought up. As an experienced physicist I prefer to start with the observed physics of the situation, and then apply a theoretical mesh on top which has predictive power.

 

[sophiecentaur]

As a laser physicist I find that the photon is very useful. Certainly as an RF antenna engineer you do not require the concept of the photon to do your work! But that is because the photons really are the quantized modes of the electromagnetic field, and each one is very miniscule when working with radio waves.

But Maxwell's equations tell us that electromagnetic waves are equally applicable all up and down the scale of wavelengths/frequencies ... and the energy content of a photon becomes significant at some point! For example, the electronic transitions within atoms and molecules fit the photon picture very well; all of spectroscopy is based on this.

And as energy increases you begin to see more and more "particle" behavior, though it is always there: the typical detector always detects over a small region, point-like, even though the "particle" acts as a wave during transit.

For example, my dissertation research was on ultrafast photo-electron diffraction. I can assure you that electrons have wave properties during the diffraction, but are particles at the detector! The same is true for x-rays. I "see" this behavior in the lab, with my very own detectors.

And yet most people are happy with "an electron is a particle" and "a photon is a wave". We even have people on this site who throw a fit when "wave-particle duality" is brought up. As an experienced physicist I prefer to start with the observed physics of the situation, and then apply a theoretical mesh on top which has predictive power.

Isn't that the problem? Wouldn't it be better to say that the EM energy can be treated as particles or waves but the two natures are mutually exclusive to the measuring system?

 

[Drakkith]

So if the electric and magnetic fields of light has nothing to do with the energy of a light, and the energy only has to do with how fast the electric and magnetic fields are moving back and forth, why even bother characterizing light as an electromagnetic wave? How do we even know the fields are oscillating? Do they interact with something that shows us indirectly that they are oscillating waves?

Absolutely. We can easily see the effects of an EM wave on an antenna. The EM wave induces a oscillation in the voltage and current in the antenna that are exactly what we'd expect to happen if our wave model is accurate.

How come they don't interact with the electric and magnetic fields of an electron?

They do. In an antenna we repeatedly accelerate electrons one way and then the other to create a changing electric and magnetic field which then propagates outward from the antenna in the form of a wave. This wave is then picked up at another antenna by measuring the current and voltage induced in the antenna when the wave's electric and magnetic fields interact with the electrons in the antenna. Keep in mind that that's an extremely simplified example and there is much more to it than that.

How do we even know for certain that light is composed of electric fields and magnetic fields? Have there been any experiments that have shown this?

Absolutely. However, there are some limitations. Visible light is at such a high frequency that we can't measure the changing electric and magnetic fields in real time using current technology. However, visible light still follows all the rules that other EM waves do. The rules of reflection, refraction, diffraction, and interference describe light equally as well as they do all EM waves. Light and other EM waves such as radio waves and microwaves all travel at the same speed. Every time you take a picture with a digital camera, such as the one in your cell phone, you are using every aspect that I mentioned above and showing that light is an EM wave. To quote a famous physicist who pioneered EM theory:

We have strong reason to conclude that light itself—including radiant heat and other radiation, if any—is an electromagnetic disturbance in the form of waves propagated through the electro-magnetic field according to electro-magnetic laws.

-James Clerk Maxwell

What is the "shape" of a photon? Does a photon have finite length and width?

In the classical idea of size and shape, no, the photon does not have a size or shape.

Sorry, I'm just really confused as to how we arrived at the conclusion that light is an electromagnetic wave. Did we just plug in values into Maxwell's equations and pop out an electromagnetic wave? Thanks for any help in advance.

You should look up information on how James Clerk Maxwell discovered that light is an EM wave. Google should provide plenty of links.

 

[UltrafastPED]

Isn't that the problem? Wouldn't it be better to say that the EM energy can be treated as particles or waves but the two natures are mutually exclusive to the measuring system?

The fact that light (and electrons!) have both characteristics is the physical origin of the term "wave-particle duality".

I think it still holds that "all measurements are classical" ... hence the need for classical concepts!

 

[sophiecentaur]

The fact that light (and electrons!) have both characteristics is the physical origin of the term "wave-particle duality".

I think it still holds that "all measurements are classical" ... hence the need for classical concepts!

I thought I had sorted this out in my mind a long time ago but it's come up again as a result of reading so many questions on PF about it.
I like this idea but is this true directly? (I realize that somewhere we have a 'needle' that points on a scale or a voltmeter in there somewhere.) The Photo electric effect only occurs because of QM - even though we only detect it by classical means.

I remember reading objections to the simple term "wave particle duality" (PF with references iirc) as it implies both natures all the time - rather than the nature depending upon the circumstance. And it's true that the majority of muddled thinking is when the two are used at the same time.

 

[WannabeNewton]

I think it still holds that "all measurements are classical" ... hence the need for classical concepts!

Where did you see that?

 

[UltrafastPED]

I thought I had sorted this out in my mind a long time ago but it's come up again as a result of reading so many questions on PF about it.

Feynman points out that it is always a (probability) wave ... until you look!


The guys that work with quantum field theory don't really use either picture - they just stick to the state space. But that is too abstract for me; I have trouble connecting it to experiments until I revisualize it in terms of wave/particle.

But to each his own. As long as the calculation agrees with the experimental results ... well, then it hardly matters how you think about it.

 

[samgrace]

Hello, in response to a previous response, how do maxwell's equations describe light classically? One person states them as equations of motion for EM waves, does this mean static fields only? the motion of what? the charge?

Thanks
Sam

 

[WannabeNewton]

Hello, in response to a previous response, how do maxwell's equations describe light classically?

As electromagnetic waves.

One person states them as equations of motion for EM waves, does this mean static fields only?

No the fields are fully dynamical.

the motion of what?

Of the electric and magnetic fields.

If you know the formal apparatus of classical EM then let me know and I can answer the above questions in a more detailed manner.

 

[samgrace]

Hey again,

Thank you for your reply, in the time that has passed since you posted it, I have researched maxwell's equations and now have an understand of the apparatus and relationships they state.

Sam

 

[Khashishi]

Photons represent some sort of transaction between a source emitter and a target absorber. They don't have a shape, and there is no way to picture what they look like while traveling between the source and the target. The classical electromagnetic radiation field tells you the probability of these photon transactions. You can think of the electromagnetic wave as moving from source to target. The frequency of a photon is the frequency of the electromagnetic wave that is associated with the photon. That's all you can really say about the photon.

 

[Drakkith]

Photons represent some sort of transaction between a source emitter and a target absorber. They don't have a shape, and there is no way to picture what they look like while traveling between the source and the target. The classical electromagnetic radiation field tells you the probability of these photon transactions. You can think of the electromagnetic wave as moving from source to target. The frequency of a photon is the frequency of the electromagnetic wave that is associated with the photon. That's all you can really say about the photon.

I really, really like this description.