Thread: Photon wavelength

What's the easiest way to understand the concept of "wavelength" as applied to a photon? This is one of those things that I've always assumed I knew until I thought about it more deeply. For example, if I had a photon with a wavelength of 100,000 km, then what does this actually mean?

I hope I'm right in assuming that my example photon is not actually smeared out over 100,000 km of space? Since I'm visualising some kind of weird particle (with wavelike properties) I find myself now struggling to grasp what wavelength is... and don't want to have to learn advanced quantum theory to seek resolution.

I think the best way is to work a few simple problems involving light interference, like here.
http://www.pa.msu.edu/courses/1998sp.../examples.html

If you try to visualize it the way you are doing, you will have the same problem everybody else has with the dual wave-particle nature of light.

My description above is not really the way I'm trying to visualise things - it just came out that way when I tried to describe my thoughts. In truth, I try hard not to mentally visualise what a photon is since such things probably defy human ken.

The examples in the link you gave didn't provide much enlightenment for me. I'm still confounded as to what wavelength actually means in the context of a single photon. I suspect most people are in the same situation and don't realise it.

I find it's easier to think of it in terms of time. At any point in the photon's path, the frequency is how long it takes for magnetic & electric fields that you (the observer) are experiencing to shift from positive to negative, and back again.

Light is the way it is just because there's propagation delay. Some event is happening very far away from you, and you're finding out about it late. Imagine if you were listening to a sports announcer describing a soccer game, but instead of hearing it on the radio, the information was getting to you by a continuous stream of carrier pigeons. The sequence of events is still unfolding to you in real time, at the rate at which it happened, but late. Light is not that different. A charged particle somewhere just accelerated toward you, then decelerated away from you, and did so in an amount of time equal to the frequency of the light. The first carrier pigeon arrives telling you that a particle somewhere has begun acceleration toward, then another carrier pigeon arrives telling you it's going faster, then faster, then faster,,, then one arrives telling you it's starting to slow down..... etc. The longer the event takes, the longer the stream of carrier pigeons, and less change in circumstances each of them has to report.

Originally Posted by Zwirko

I find myself now struggling to grasp what wavelength is... and don't want to have to learn advanced quantum theory to seek resolution.

In that case you are pretty much out of luck.

I don't know if this is what you meant but in terms of light and other EM waves:

Light travels through space at the speed of light. (about 3x10^8m/s)

Electromagnetic waves have a certain frequency.

The period of the wave is the time taken for the wave to complete one cycle at this frequency.

The wavelength is the distance travelled by the wave during the time taken by one period.

You could apply this to anything periodic nature travelling some distance e.g:

A car has a flashing light on the top. The light flashes on and off at 0.5 hz.(once in two seconds) the car is travelling 20m/s therefore the wavelength of the light/car system would be 20/0.5 = 40 metres.

As the frequency of the wave increases the wavelength decreases and vice versa.

Light can be thought of as a bundle of photons or quanta. You don't want to learn about relativity or any sort of Quantum Mechanics, I understand. So, I won't say much more about the nitty gritty of light propogation, but you should also understand that photons are quantized. That means that a photon consists of only whole forms of state, no partials, which is, in a sense, why the comparison of a photon to a particle isn't far-fetched. Although, the crucial thing to remember is that a photon is not a (weird) particle.

A photon with a wavelength of 100,000 km would indeed have a crest span 100,000 km per oscillation! Think about radio waves, which have wavelengths around a meter. Radio waves do span that distance in real space. Even though electromagnetic waves with such ridiculously huge wavelengths aren't normally dealt with, they can exist in theory.

Here's an experimental set up that illustrates the problem I've run in to: Imagine we have a source that emits two photons at the exact same time; one has a wavelength of 100,000 km and the other a wavelength of 100 nm. They travel across a set distance to arrive at an array of detectors.

Now, as I understand things my apparatus will register two simultaneous clicks as both photons arrive at the detectors at the exact same instant. Thinking about this in my befuddled state, I started wondering about the 100,000 km photon - if the photon was physically spanning across a distance of 100,000 km then it must arrive at the detector in piecemeal fashion (that is, the "front" first, followed by a relatively long delay before the "back end" of the photon finally arrives and completes the interaction with the detector). Meanwhile, the 100 nm photon is sitting back with its feet up waiting for the longer one to finish interacting with the detector. Since photons are discrete quanta this clearly makes no sense at all - hence, my question.

If anyone managed to follow that, then you'll perhaps see what it is I'm confused about: what do we mean exactly when we speak of the wavelength of a single photon? If one photon is a 100 billion times "longer" than an another, then how can they be detected at the same instant in my experiment?

Wouldn't the waves arrive at the same time but be hit the detector they would just be at different phase angles. One may reach the detector at an electrical peak and the other 3/4 of its magnetic peak etc.

Originally Posted by Zwirko

What's the easiest way to understand the concept of "wavelength" as applied to a photon? This is one of those things that I've always assumed I knew until I thought about it more deeply. For example, if I had a photon with a wavelength of 100,000 km, then what does this actually mean?

I hope I'm right in assuming that my example photon is not actually smeared out over 100,000 km of space? Since I'm visualising some kind of weird particle (with wavelike properties) I find myself now struggling to grasp what wavelength is... and don't want to have to learn advanced quantum theory to seek resolution.

The simplest way is to forget about photons altogether and to understand that light is a wave.

Originally Posted by Zwirko

Here's an experimental set up that illustrates the problem I've run in to: Imagine we have a source that emits two photons at the exact same time; one has a wavelength of 100,000 km and the other a wavelength of 100 nm. They travel across a set distance to arrive at an array of detectors.

Now, as I understand things my apparatus will register two simultaneous clicks as both photons arrive at the detectors at the exact same instant. Thinking about this in my befuddled state, I started wondering about the 100,000 km photon - if the photon was physically spanning across a distance of 100,000 km then it must arrive at the detector in piecemeal fashion (that is, the "front" first, followed by a relatively long delay before the "back end" of the photon finally arrives and completes the interaction with the detector). Meanwhile, the 100 nm photon is sitting back with its feet up waiting for the longer one to finish interacting with the detector. Since photons are discrete quanta this clearly makes no sense at all - hence, my question.

If anyone managed to follow that, then you'll perhaps see what it is I'm confused about: what do we mean exactly when we speak of the wavelength of a single photon? If one photon is a 100 billion times "longer" than an another, then how can they be detected at the same instant in my experiment?

IIRC, you can't reliably detect a photon with a detector smaller than that photon's wavelength. This is why radio antennas are so big, among other things. Any detection event will still happen at a specific time though.

Originally Posted by Zwirko

Here's an experimental set up that illustrates the problem I've run in to: Imagine we have a source that emits two photons at the exact same time; one has a wavelength of 100,000 km and the other a wavelength of 100 nm. They travel across a set distance to arrive at an array of detectors.

Now, as I understand things my apparatus will register two simultaneous clicks as both photons arrive at the detectors at the exact same instant. Thinking about this in my befuddled state, I started wondering about the 100,000 km photon - if the photon was physically spanning across a distance of 100,000 km then it must arrive at the detector in piecemeal fashion (that is, the "front" first, followed by a relatively long delay before the "back end" of the photon finally arrives and completes the interaction with the detector). Meanwhile, the 100 nm photon is sitting back with its feet up waiting for the longer one to finish interacting with the detector. Since photons are discrete quanta this clearly makes no sense at all - hence, my question.

If anyone managed to follow that, then you'll perhaps see what it is I'm confused about: what do we mean exactly when we speak of the wavelength of a single photon? If one photon is a 100 billion times "longer" than an another, then how can they be detected at the same instant in my experiment?

The solution is simple. Why would your source cut off the 100 nm photon any shorter than the 100,000 km? It wouldn't. Both photons remain the same length. The properties of the photon, such as wavelength, do not physically stretch out the photon length. So, the 100 nm photon does not finish any sooner than the 100,000 km photon.

We first assume that both emitters begin transmitting at the same time. The short-length photon will only be emitted for a short period of time, while the long-wavelength photon (some may disagree as to whether or not a long wavelength wave is a photon) will take a long time to transmit.

The distances from both emitters to the detectors must be the same in order for both signals to arrive at the same time. A question now arises at to how many cycles of energy are transmitted, or in other words the time length of transmission. If those times are equal, which is extremely dubious, then each detector will be receiving the photon signals simultaneously and will both receive signals over that time length.

The next question is in regard to the type of detector for each signal. If the instantaneous level can be detected for both detectors, then the frequencies of the detected signals will be the same as that transmitted from each of the sources.

Your question illustrates the difficulty in describing a photon. If a photon is the energy transmitted by an atom in going from one energy state to another, then the pulse width will be very short. In contrast, the low frequency radiation from an antenna is only limited by the design characteristics of a transmitter.

The real time characteristics of a hydrogen photon were only recently described in a 2005 book on Planck's quantum theory (p.440) by taking the inverse transform of Planck's state space equation:

http://science-site.net/planck.htm

I'm now inclined to assume that two photons of differing wavelengths are actually the same size (that is, particulate in nature) and that wavelength corresponds to something other than what most people assume it does - some shenanigans do with fields most likely.

So, my photon with a wavelength of 100,000 km would not actually physically span across such a distance of space. If it did, wouldn't it interact with electrons in a noticeably different manner than do shorter wavelength photons?

Originally Posted by Zwirko

Here's an experimental set up that illustrates the problem I've run in to: Imagine we have a source that emits two photons at the exact same time; one has a wavelength of 100,000 km and the other a wavelength of 100 nm. They travel across a set distance to arrive at an array of detectors.

Now, as I understand things my apparatus will register two simultaneous clicks as both photons arrive at the detectors at the exact same instant. Thinking about this in my befuddled state, I started wondering about the 100,000 km photon - if the photon was physically spanning across a distance of 100,000 km then it must arrive at the detector in piecemeal fashion (that is, the "front" first, followed by a relatively long delay before the "back end" of the photon finally arrives and completes the interaction with the detector). Meanwhile, the 100 nm photon is sitting back with its feet up waiting for the longer one to finish interacting with the detector. Since photons are discrete quanta this clearly makes no sense at all - hence, my question.

If anyone managed to follow that, then you'll perhaps see what it is I'm confused about: what do we mean exactly when we speak of the wavelength of a single photon? If one photon is a 100 billion times "longer" than an another, then how can they be detected at the same instant in my experiment?

a photon is a point particle.

You are misconstruing the notion of wavelength. Unfortunately you will have to study quantum mechanics, which you say you do not want to do, to understand this.

Of course I'm misconstruing what wavelength is. That's the problem in a nutshell and is what this thread is about.

Originally Posted by Zwirko

Of course I'm misconstruing what wavelength is. That's the problem in a nutshell and is what this thread is about.

Now go learn some quantum mechanics, whether you want to or not. Read a book. Griffiths might be a good place to start. No one can do your thinking for you ans you have not posed a cogent question.

I hope I'm right in assuming that my example photon is not actually smeared out over 100,000 km of space? Since I'm visualising some kind of weird particle (with wavelike properties) I find myself now struggling to grasp what wavelength is... and don't want to have to learn advanced quantum theory to seek resolution.

I cannot answer in terms of QM. You'll get a QM reply anyway.

In EM terms the length it is spread out in space is inversely related to its bandwidth. A wavelength of 100,000 kilometers is irrelevant. An absolutely pure frequency (zero bandwidth) theoretically spans the Universe, regardless of the frequency, would have to have been in existence for infinite time and will exist forever. As such it is a purely theoretical concept.

Equally, an infinite bandwidth is associated with a perfect electromagnetic impulse of zero time and infinite amplitude. Also a purely theoretical concept.

Your 100,000km pulse has a frequency of 3Hz; lets assume a pretty wide bandwidth of 10%, or 0.3Hz. The pulse length would then be 1,000,000 km long. Your energy density in space would have a huge row of zeroes after the decimal point before getting to significant numbers.

Originally Posted by muppet

Equally, an infinite bandwidth is associated with a perfect electromagnetic impulse of zero time and infinite amplitude. Also a purely theoretical concept.

no

This only applies to a uniform spectrum.

In fact any time function of compact support cannot have a Fourier transform of compact support, an elementary consequence of the Paley-Weiner Theorem.

This only applies to a uniform spectrum.

I agree, since the spectrum of a perfect impulse is uniformly zero all the way out to infinity; this is a consequence of the integral being unity - a unity impulse integral spread uniformly across an infinite spectrum is indistinguishable from zero at any point on that spectrum. Paley-Weiner does not handle this condition.

Originally Posted by muppet

This only applies to a uniform spectrum.

I agree, since the spectrum of a perfect impulse is uniformly zero all the way out to infinity; this is a consequence of the integral being unity - a unity impulse integral spread uniformly across an infinite spectrum is indistinguishable from zero at any point on that spectrum. Paley-Weiner does not handle this condition.

The spectrum of a unit impulse is uniformly one.

do we use photons in fiber optics? to push/store data?

like a compact disc or dvd for example... are the lasers that read or write them based on photons that are concentrated in lasers sending/receiving data via scanning the surface of discs?

Originally Posted by FuturePasTimeCE

do we use photons in fiber optics? to push/store data?

like a compact disc or dvd for example... are the lasers that read or write them based on photons that are concentrated in lasers sending/receiving data via scanning the surface of discs?

light is photons

OP

picture a water wave, the way it ripples, well the path of a photon does the same where it "wiggles" as oppose to going perfectly straight, this is due to angular velocity, (much like an AC sin wave in electronics)

the wavelength is a measurement of the two points where the wave peaked(usually)


if you really want to understand waves and wavelengths look at sound, since it is similar(just don't look for traveling particles!)


as for a photon wavelength that is in visible light spectrum the length is 400 - 700 nm,, thats NANOMETERS ( 1 billion nanometers = 1 meter ) (10^(-9))

We have two mathematical models that describe some of the aspects of EM radiation. The wave model, and its associated wavelength, which describes some but not all characteristics of light, and the particle model which describes some others. This is often referred to as wave-particle duality. This does not mean that light is a wave, or a particle, or a combination of both as you implying. You cannot mix apples with oranges; just try to explain the photoelectric effect with the wave theory.

All they are are mathematical models which do a good, but separate, job of describing a reality which could be neither,ie you let circumstances guide you as to which model to use. This is of course for the classical theory of light and not QM.

Originally Posted by MigL

We have two mathematical models that describe some of the aspects of EM radiation. The wave model, and its associated wavelength, which describes some but not all characteristics of light, and the particle model which describes some others. This is often referred to as wave-particle duality. This does not mean that light is a wave, or a particle, or a combination of both as you implying. You cannot mix apples with oranges; just try to explain the photoelectric effect with the wave theory.

All they are are mathematical models which do a good, but separate, job of describing a reality which could be neither,ie you let circumstances guide you as to which model to use. This is of course for the classical theory of light and not QM.

QED is the single model that explains what we know of electrodynamics. There are not two separate models, but only one. The classical Maxwellian wave theory is just a limiting approximation of QED.

In practice the classical equations are much easier to work with, but in principle QED does the whole job.

See the sticky thread "Lectures on Physics (QED)" for interesting lectures on QED by none other than Richard Feynman.

Originally Posted by Zwirko

Here's an experimental set up that illustrates the problem I've run in to: Imagine we have a source that emits two photons at the exact same time; one has a wavelength of 100,000 km and the other a wavelength of 100 nm. They travel across a set distance to arrive at an array of detectors.

If you really want to make sense of the issue, you should look into how radios work. Those are photons that are long enough to examine.

http://www.howstuffworks.com/radio.htm

Now, as I understand things my apparatus will register two simultaneous clicks as both photons arrive at the detectors at the exact same instant. Thinking about this in my befuddled state, I started wondering about the 100,000 km photon - if the photon was physically spanning across a distance of 100,000 km then it must arrive at the detector in piecemeal fashion (that is, the "front" first, followed by a relatively long delay before the "back end" of the photon finally arrives and completes the interaction with the detector). Meanwhile, the 100 nm photon is sitting back with its feet up waiting for the longer one to finish interacting with the detector. Since photons are discrete quanta this clearly makes no sense at all - hence, my question.

If anyone managed to follow that, then you'll perhaps see what it is I'm confused about: what do we mean exactly when we speak of the wavelength of a single photon? If one photon is a 100 billion times "longer" than an another, then how can they be detected at the same instant in my experiment?

I'm pretty sure the detector has to absorb the full energy packet before a photon will register as having arrived, so if the front ends of the waves are emitted simultaneously, then the description you gave should be accurate. If the tail end of the waves are what are traveling simultaneously, then they'd appear to arrive at the same time.

Have a read of How Long Is a Photon? by Drozdov and Stahlhofen. It's an interesting paper.

Originally Posted by Zwirko

What's the easiest way to understand the concept of "wavelength" as applied to a photon? This is one of those things that I've always assumed I knew until I thought about it more deeply. For example, if I had a photon with a wavelength of 100,000 km, then what does this actually mean?

I hope I'm right in assuming that my example photon is not actually smeared out over 100,000 km of space? Since I'm visualising some kind of weird particle (with wavelike properties) I find myself now struggling to grasp what wavelength is... and don't want to have to learn advanced quantum theory to seek resolution.

Well according to Schrödinger's wave function a particle can be both a wave and a solitary particle when they found that electrons give diffraction patterns when passed through a double slit in a similar way to light waves - so you just have to think of a photon as a particle that at it's highest and lowest point connect through the form of an energy wave, and thus becomes inverse when the energy changes.[/img]