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Arcane
2008-Aug-21, 08:33 PM
Let me start by stating what I do know about light so there is no confusion.

1) Light is made of photons
2) Photons have no mass
3) Photons are both particles and waves

Does every photon carry all waves of light? Visible light, X-rays, Infrared, etc..

For instance, a red laser beam, I azz-u-me, only carries certain wave lengths of light, otherwise why is it red? Right?

If the answer to that is no, then why do some photons only carry certain wave lengths?

Second question is, how much light does one photon carry? I mean, if you turned on a laser for one second how many photons would be in it? Of course that depends on the size of the beam. But let me rephrase it.

I picture in my mind a beam of light being this really looooong trail of photons, possibly 1000000000000000000000 photons all stacked up behind each other like lemmings in a long line. Of course you have to add in the width of the beam as well.

Lastly, what exactly does one photon consist of? When I imagine light, I imagine a wave, but when I try to imagine one photon I can't picture it.

Simple questions I hope, and thanks for any input.

korjik
2008-Aug-21, 09:04 PM
Light is defined as photons. Technically, light is electromagnetic radiation in a specific frequency band (400-800 nm or so) made up of photons.

All photons have a specific 'wavelength' dependent on the amount of energy the photon has. The energy is the product of the frequency and plancks constant. When you also include that the speed of light is the product of the frequency and the wavelength, then you get that any beam of light where the photons have a specific energy will have a specific color. This is why lasers have specific colors. The He-Ne laser emits at 633nm in the red band.

As for the amount of energy in each individual photon, it is a very small amount. Plank's constant is a very small number. 6.6x10^-34 Js

Multiply this by the frequency of a He-Ne laser 3x10^8m/s/633x10^-9m =4.7x10^14 hz

so each photon is 3.1x106-19 Joules. Your 10^21 photons in your example would be about 310 Joules of energy, or about enough to melt 1 gram of ice.

As for what a photon is, it is a bundle of energy with a quanta of angular momentum and a bit of momentum. Trying to visualise it prolly wouldnt work. I usually visualise photons as little balls that group into waves, but that dosent really make any sense. :)

Hornblower
2008-Aug-21, 10:07 PM
Welcome to the weird and wonderful world of quantum mechanics.

Let me start by stating what I do know about light so there is no confusion.

1) Light is made of photons
2) Photons have no mass
3) Photons are both particles and waves

Does every photon carry all waves of light? Visible light, X-rays, Infrared, etc..No. I think of a photon as a packet of electromagnetic energy. That makes it particle-like in character, and it can have any amount of energy, depending on its source. Its behavior includes a wave characteristic that has a wavelength inversely proportional to the photon's amount of energy.

For instance, a red laser beam, I ***-u-me, only carries certain wave lengths of light, otherwise why is it red? Right? All photons in that laser beam have the same amount of energy, and they form coherent wave action of a single wavelength. They collectively stimulate the retina cones in such a way that we see red.

If the answer to that is no, then why do some photons only carry certain wave lengths?We know that a photon has a characteristic wavelength as stated above. As for the ultimate question of "why", that may be beyond the realm of science to try to answer. Don't take me as gospel. I welcome the opinions of others on that.

Second question is, how much light does one photon carry? I mean, if you turned on a laser for one second how many photons would be in it? Of course that depends on the size of the beam. But let me rephrase it.

I picture in my mind a beam of light being this really looooong trail of photons, possibly 1000000000000000000000 photons all stacked up behind each other like lemmings in a long line. Of course you have to add in the width of the beam as well.
A 1-watt red laser would emit approximately 3x1018 photons per second, each of which would have an energy level of about 2 electron volts. (You may wish to Google such terms as electron volt, joule, watt, etc.)

Lastly, what exactly does one photon consist of? When I imagine light, I imagine a wave, but when I try to imagine one photon I can't picture it.Neither can I. You need to forget much of what you know about classical mechanics and trust the math. This is a topic in advanced college-level physics. I have forgotten much of what I studied 40 years ago. There are many in this forum who can help.

Simple questions I hope, and thanks for any input.

P.S. I see korjik has posted a response while I was writing mine. The more, the merrier.

WaxRubiks
2008-Aug-21, 10:55 PM
I just thought of this analogy(maybe it should go in ATM, :D)

analogy: imagine that you have a castle on a moor and you have a dog that one night goes missing.
It heads off into the night at a set speed and follows a straight path.

When you discover it has gone missing you send out a search party.
And as they look all over the moor for the dog, all that they know is that they have a set probability that the dog is in any particular place.
Eventually they come across the dog and the dog's location goes from being a probability to a fact.

I think that may be a good analogy, I would be interested if this analogy when played out on a computer simulation, involving walls with doors, whether there would be interference patterns of probability, involving the position of the dog.

I think I have read that large objects do behave in this manner, it is just that the frequency is too high, or something, to be able to detect the interference pattern.

eta: yeah, just realised that the dog would obviously have to have a wavelength for interference to happen after any doors in walls. :doh:

Sam5
2008-Aug-21, 11:44 PM
yeah, just realised that the dog would obviously have to have a wavelength for interference to happen after any doors in walls. :doh:

Is that the Fido theory of light, or the Bowser theory? :)

astromark
2008-Aug-22, 01:47 AM
:)its a mongrel half breed.;Frogmarch.

I would avoid the complexity of the higher phiysics... Light is energy showing off.

Ken G
2008-Aug-22, 02:25 AM
Does every photon carry all waves of light?You've had a few answers on this already, but they fall into the standard confusion about what the concept of "photon" means, because there are actually two rather different meanings that concept can have and they are often mistaken for each other. One meaning is the fundamental quantum of electromagnetic energy propagating in vacuum, that is, that which mediates the interaction between two quantum systems that we describe as emission and absorption of light. Thus if we think of a photon as the quantum (i.e., a particle) that mediates that interaction, then its state is described by a "wave function", which in practical situations will always represent many different possible wavelengths at once (i.e., it is described by a "wave packet", not a wave of known wavelength). So if that's the kind of photon you are asking about, the answer to this question is yes, each of these quanta carry all wavelengths of light, though they tend to strongly favor a particular narrow range depending on the generation mechanism of the quanta.

However, this raises the question, what is all that E = h*nu business you hear about? Well, that's the other meaning for "photon", which is not a quantum that you can do real experiments on, but rather an elementary excitation of the electromagnetic field. This latter is a mode of the field, not a "real particle". In music, this type of "photon" would be like talking about the sound frequency of a particular pure tone, while the first meaning above would be like what you actually get when you strike a piano key. The "mode" meaning for "photon" is purely a mathematical conceptualization, and it is quite handy to use in calculations, because you normally take the "wave packet" of a particular quantum of interest (the first meaning of "photon") and you expand it in a series of "Fourier modes", the latter being the second meaning of what a "photon" is. If all that sounds confusing, then you see why answers about what photons "are" often get quite mixed up.

Second question is, how much light does one photon carry?
Again the answer is going to depend on which meaning of "photon" you intend in the question, but basically, the excitation or the quantum has an expectation value for its energy. That's how much energy it "has", so that is in effect "how much light" it carries.

Lastly, what exactly does one photon consist of?It doesn't "consist of" anything, it is a theoretical construct of the human mind that aids us considerably in interpreting and predicting observations.

greatgreekcollector
2008-Aug-22, 02:49 AM
light is only one of many expressions of an energy form.

Photons are simply one of the many of parts of energy that can be detected individually.

If you could "see a photon" it would be a charged energy of varying x,y,z axis energy.

Some "things cannot be seen" but need to be understood through Math and convoluted juggling of theoretical constraints of the mind.

you cant hear light
you cant see sound
you cant weigh gravity
you cant stop time

they are different forms of the energy spectrum and take different skill sets to comprehend.

Jeff Root
2008-Aug-22, 03:17 AM
Light consists of massless particles called photons. Photons have various
properties, including some which can be described in terms of waves. For
example, the probability that a photon will be at a particular location at a
particular time is a wave function. All particles have this property. That
is, all particles behave like waves.

A photon is the smallest possible unit of light. It is not possible to detect
anything less than one whole photon. So either you detect the presence
of a photon, or you don't detect anything at all. You cannot detect just
half of a photon, for example. Once you have detected a particular photon,
you have detected the entire photon, and there is no more of that photon
left to detect.

That means it is impossible to measure the wavelength of an individual
photon. In order to measure the length of something, it is necessary to
make two measurements: the location of one end and the location of
the other end of the thing. But you cannot make two measurements of
an individual photon, so you can't measure its length.

Same for frequency. To measure frequency you need to make two
measurements: the first time that something passes you, and the next
time something passes you. Since you can only make one measurement
of a photon, you cannot measure the frequency of an individual photon.

What you can measure for an individual photon would be, for example,
the angle by which its path is altered by passing through a prism or being
reflected by a spectroscope grating. This measured angle tells you the
wavelength, frequency, and energy of the photon, but... only in a
statistical way. The angle at which a photon is deflected is not exactly
the same for every photon of a particular wavelength, frequency, and
energy. Instead, the probability distribution of a large number of angle
measurements of a large number of photons is the same for photons of
a particular wavelength, frequency, and energy. So if you measure the
deflection angle of a large enough sample of photons from a monochrome
light source, you can measure the wavelength, frequency, and energy
of that light.

The wavelength, frequency, and energy of light is not a property of the
light itself. Instead it is a property of the relationship between the light
and the observer. If the observer is approaching the light source, the
measured wavelength will be shorter than it will be for an observer who
is at rest relative to the light source. The frequency will be higher and
the energy will be higher. If the observer and light source are moving
away from each other, the wavelength will be longer, the frequency will
be lower, and the energy will be lower. This is called Doppler effect or
Doppler shift.

For an observer at rest relative to the source, many light sources have
particular wavelengths, frequencies, and energies that they emit. The
amount of Doppler shift observed in the wavelength, frequency, or energy
of light from such sources can be used to determine the relative speed
between the source and the observer.

In very general terms, the shorter the wavelength, higher the frequency,
and higher the energy of a group of photons, the easier they are to detect.
So individual photons of visible and infrared light can be detected with a
CCD chip or a photomultiplier tube, but detecting radio waves requires
enormous numbers of photons to strike a radio antenna simultaneously,
because each radio photon has so little energy. Humans are reported to
be able to detect as few as six photons of green light striking a spot on
the eye's retina simultaneously.

The number of photons in a beam of light depends on the beam's intensity.
A 60-watt lightbulb puts out more photons per second than a comparable
40-watt lightbulb. A 60-watt red laser puts out more photons per second
than a 40-watt red laser.

-- Jeff, in Minneapolis

Sam5
2008-Aug-22, 03:25 AM
Lastly, what exactly does one photon consist of? When I imagine light, I imagine a wave, but when I try to imagine one photon I can't picture it.

Being interested in history and the history of science, I like to start with early ideas and then move forward. I’ll let the professors move forward on this, but I’ll pass along what was basically Maxwell’s idea of the late 19th Century, which some people still like to use today.

A few years ago, while trying to visualize what a light “photon” or a single EM “wave packet” might look like, I came across an old 1876 book by Maxwell, which published a drawing of his opinion of what a combined electric and magnetic wave pair might look like, if we could draw a picture of it. This is a portion of his picture that would represent one full wave:

http://i34.tinypic.com/hx0m75.jpg

These are supposed to represent waves of magnetic and electrical “fields”. Fields, not particles.

If animated, they would look something like this (scroll down a little at that link):

http://www.astronomynotes.com/light/s2.htm

[edited to add:] A slightly different version of the animation is here:

http://www.olympusmicro.com/primer/java/electromagnetic/index.html

His entire picture is in the next link, and it contains the one full wave, plus about 1/4 of the next wave, to which he has attached the electric and magnetic labels. The parts of the wave that are going more or less up and down represent the magnetic force field, and the parts that are going out to the side represent the electric force field:

http://i37.tinypic.com/2cfz9c5.jpg

I put a bunch of Maxwell waves together to form a Maxwell light “beam”, one photon wide and 4 photons long

http://i35.tinypic.com/a2u35x.jpg

Even though Einstein wrote the so-called “particle” or “quantum” theory of light in 1905, he said this in 1929:

http://www.rain.org/~karpeles/einsteindis.html
”The "field" thus provided a conceptual apparatus which rendered unnecessary the idea of action at a distance. Faraday also had the bold idea that under appropriate circumstances fields might detach themselves from the bodies producing them and speed away through space as free fields: this was his interpretation of light.”

He’s actually paraphrasing Faraday’s idea here, but I personally like this version where the electric and magnetic fields “detach” themselves from the emitting atoms and the waves “speed away through space as free fields”.

Jeff Root
2008-Aug-22, 04:40 AM
I put a bunch of Maxwell waves together to form a Maxwell light
“beam”, one photon wide and 4 photons long

http://i35.tinypic.com/a2u35x.jpg
The idea that a photon is one wavelength long happens to be a
notion I favor, but it is not held by any physicist that I know of.

-- Jeff, in Minneapolis

Ken G
2008-Aug-22, 07:33 AM
A few corrections seem in order:

That means it is impossible to measure the wavelength of an individual
photon. In order to measure the length of something, it is necessary to
make two measurements: the location of one end and the location of
the other end of the thing. But you cannot make two measurements of
an individual photon, so you can't measure its length.Length is not at all the same thing as wavelength. For example, the most natural concept of length for a photon is called its coherence length, which for typical photons includes a vast number of wavelengths (often millions).

Same for frequency. To measure frequency you need to make two
measurements: the first time that something passes you, and the next
time something passes you.No, frequency of light is not measured that way, it is measured by detecting the energy and dividing by h. In principle, you can measure the energy, and therefore frequency, of a photon to arbitrary precision, though of course in practice there are technological limitations.

The idea that a photon is one wavelength long happens to be a
notion I favor, but it is not held by any physicist that I know of.
That's because physicists like to define the concepts they use. How are you defining "length" of a photon, such that you can "favor" any particular value for it? As I mentioned above, one common way to attribute a concept of length to a photon is called the coherence length, which is the length over which the same photon can interfere with itself. But that's usually many many wavelengths, typically, so is apparently different from the length you are imagining.

Jeff Root
2008-Aug-22, 09:21 AM
That means it is impossible to measure the wavelength of an individual
photon. In order to measure the length of something, it is necessary to
make two measurements: the location of one end and the location of
the other end of the thing. But you cannot make two measurements of
an individual photon, so you can't measure its length.
A few corrections seem in order:

Length is not at all the same thing as wavelength. For example, the
most natural concept of length for a photon is called its coherence
length, which for typical photons includes a vast number of wavelengths
(often millions).
You can't measure or detect the coherence length of an individual
photon. I don't think the concept of coherence length even has any
meaning when applied to an individual photon.

Same for frequency. To measure frequency you need to make two
measurements: the first time that something passes you, and the next
time something passes you.
No, frequency of light is not measured that way, it is measured by
detecting the energy and dividing by h.
That isn't a measurement of frequency then. It is a measurement of
energy and use of the theory of the relationship between energy and
frequency to calculate the frequency. That relationship could not
have been established in the first place without actually measuring
frequencies.

In principle, you can measure the energy, and therefore frequency,
of a photon to arbitrary precision, though of course in practice there
are technological limitations.
If you measure the energy of a single photon you will get a value
which can only be predicted statistically. If you measure the energy
of an arbitrarily large collection of photons, then you can measure the
mean energy to arbitrary precision.

The idea that a photon is one wavelength long happens to be a
notion I favor, but it is not held by any physicist that I know of.
That's because physicists like to define the concepts they use. How
are you defining "length" of a photon, such that you can "favor" any
particular value for it?
The minimum length in which all of its energy is contained.

As I mentioned above, one common way to attribute a concept of
length to a photon is called the coherence length, which is the length
over which the same photon can interfere with itself. But that's usually
many many wavelengths, typically, so is apparently different from the
length you are imagining.
You can measure the coherence length of a group of photons, but you
can't measure the coherence length of an individual photon.

-- Jeff, in Minneapolis

Hornblower
2008-Aug-22, 12:20 PM
Ken G's responses are most welcome. I knew my answers were simplistic, but I could not remember enough about the details to elaborate.

Ken G
2008-Aug-22, 03:53 PM
You can't measure or detect the coherence length of an individual
photon.Which definition of "photon" are you using? I grow tired of being forced to ask for a distinction. You see, the "mode" meaning of a photon always has infinite coherence length, and it has a definite wavelength. The "quantum" meaning of photon has a finite coherence length, but only an expectation value for wavelength-- indeed, it can only be described by a wave function, which is not a "property" of the individual particle, but it is all the information we can use to predict the behavior of the individual quantum. So every "problem" you had with the issue of coherence length would also exist for wavelength-- your distinction in no way establishes any advantage of the wavelength over the coherence length in the conceptualization of the length of a quantum.

I don't think the concept of coherence length even has any
meaning when applied to an individual photon.That is exactly like saying the concept of wave function has no meaning when applied to an individual photon. Would you really like to go on the record with that bizarre opinion?

That isn't a measurement of frequency then. It is a measurement of
energy and use of the theory of the relationship between energy and
frequency to calculate the frequency. I'm afraid we do that all the time. No measurement is possible without a theoretical framework to give it meaning; such is also true with the angular measurement you suggested.

That relationship could not
have been established in the first place without actually measuring
frequencies.So? We are talking about how one can determine, to arbitrary desired accuracy, the frequency of a photon-- something you claimed above cannot be done except in a "statistical way". Instead you claimed some strange angular measurement was required. I did not want you to confuse people unnecessarily, such measurements are only one option.

If you measure the energy of a single photon you will get a value
which can only be predicted statistically.Obviously, but we are talking about measurements here, not predictions. See your last post.

If you measure the energy
of an arbitrarily large collection of photons, then you can measure the
mean energy to arbitrary precision.And you can also measure the energy of one photon to a similar precision-- simply reduce the intensity of the ensemble until only one photon at a time is being treated by the exact same observational approach. The point here is that you seem to suggest that more information is somehow available about an ensemble than is available for an individual photon, and that is incorrect. In either case, the wave function is the mathematical entity that organizes all the information we can have about the state of either one photon or an ensemble of photons. The only difference is in intensity.

The minimum length in which all of its energy is contained.Huh? I asked for a scientific definition, that means you have to say how one can tell what it is. Now, how do you tell where "all the energy is contained", and why does it come out one wavelength? Sounds like make believe to me.

You can measure the coherence length of a group of photons, but you
can't measure the coherence length of an individual photon.
Again, the coherence length is a property of the wave function describing the quantum, and emerges from the statistical superposition of the photon modes needed to describe our information about the quantum. If you prepare a quantum in a certain state described by a wave packet, then it has a coherence length and an expectation value for wavelength, but it does not have a definite wavelength. So why is this a problem for the concept of coherence length but not wavelength? I'm afraid I don't see what you are arguing here, but it should probably be a new thread-- either Q&A or ATM.

Sam5
2008-Aug-22, 04:23 PM
The idea that a photon is one wavelength long happens to be a
notion I favor, but it is not held by any physicist that I know of.

-- Jeff, in Minneapolis

Radio scientists tend to think of EM radio signals as being waves. When they speak of “wavelength” they are talking about waves that are long and that have a wave front and a wave end. The length of the waves are calculated by diving the distance light travels in a second by the frequency of the wave. When they talk about a thirty meter wavelength, they mean the wave is thirty meters long.

http://www.1728.com/freqwave.htm

http://cfcp.uchicago.edu/education/explorers/2002summer-YERKES/pdfs-sum02/background.pdf
” All waves have crest (high points), troughs (low points), a wavelength (the distance from one crest to another or one trough to another), amplitude (the height of a crest or trough), and a frequency (the number of complete wavelengths that pass a given point in a second.)”

The way the radio wave gives up its energy to a receiving antenna is through a process they call “resonation”. In effect, it is the bump, bump, bump of successive radio waves that causes a receiving antenna to resonate, and the antenna needs to be the length of a full wave, or some even-fraction of a wavelength, such as a half-wave, quarter-wave, eighth-wave, etc. So while the bump, bump, bump seems to act like “particles” hitting the receiving antenna, radio engineers have explained to me that what actually hits the antenna are successive waves.

Jeff Root
2008-Aug-22, 11:47 PM
You can't measure or detect the coherence length of an individual
photon.
Which definition of "photon" are you using? I grow tired of being forced
It is extremely rare to see a distinction made. In fact, off the top of
my head, I don't recall anyone other than you making this distinction.
No distinction is mentioned in this About.com page:

No distinction is made, as far as I can tell, in the Wikipedia article:
http://en.wikipedia.org/wiki/Photon

Possibly, in the section titled "Second quantization", a bit more than
halfway down the page, is what you are talking about? The section is
about "Fourier modes", but says "The key new step was to identify an
electromagnetic mode with energy E = nhν as a state with n photons,
each of energy hν." So its purpose appears to be to deal with groups
of photons, not individual photons.

You see, the "mode" meaning of a photon always has infinite coherence
length, and it has a definite wavelength.
Since photons are not actually infinitely long, I think it is safe for you
to assume that I am not talking about coherence length when I refer
to the length of a photon, and that I'm not talking about modes.

The "quantum" meaning of photon has a finite coherence length, but
only an expectation value for wavelength-- indeed, it can only be
described by a wave function, which is not a "property" of the individual
particle, but it is all the information we can use to predict the behavior
of the individual quantum.
Yes, that appears to be the same as I said.

So every "problem" you had with the issue of coherence length would
also exist for wavelength--
I didn't say there was any problem, but I did say that the coherence
length of an individual photon cannot be measured, and I said that the
wavelength of an individual photon cannot be measured, so what you
say here agrees with what I said.

over the coherence length in the conceptualization of the length of a
quantum.
The concept of coherence length does not appear to be meaningful as
applied to individual photons. The concept of wavelength, however, is
meaningful even if the wavelength of an individual photon cannot be
reliably measured.

I don't think the concept of coherence length even has any
meaning when applied to an individual photon.
That is exactly like saying the concept of wave function has no meaning
when applied to an individual photon. Would you really like to go on
the record with that bizarre opinion?
No, only what I said.

To measure frequency you need to make two measurements: the
first time that something passes you, and the next time something
passes you.
No, frequency of light is not measured that way, it is measured by
detecting the energy and dividing by h.
That isn't a measurement of frequency then. It is a measurement of
energy and use of the theory of the relationship between energy and
frequency to calculate the frequency.
I'm afraid we do that all the time. No measurement is possible without
a theoretical framework to give it meaning; such is also true with the
angular measurement you suggested.
No need to be afraid. Yes, we do it all the time. Yes, it results in
a determination of the frequency. But NO, it is NOT a measurement
of frequency. It is a calculation of frequency from a measurement
of something else. My comment was about measuring frequency, not
about measuring something else and calculating what the frequency
must be from that measurement of something else.

That relationship could not have been established in the first place
without actually measuring frequencies.
So? We are talking about how one can determine, to arbitrary desired
accuracy, the frequency of a photon-- something you claimed above
cannot be done except in a "statistical way". Instead you claimed some
strange angular measurement was required. I did not want you to
confuse people unnecessarily, such measurements are only one option.
I did not say that an angular measurement is required.
What I said in post #9 was:

What you can measure for an individual photon would be, for example,
the angle by which its path is altered by passing through a prism or being
reflected by a spectroscope grating.
Why you would call that "strange" is beyond my comprehension.

If you measure the energy of a single photon you will get a value
which can only be predicted statistically.
Obviously, but we are talking about measurements here, not predictions.
When you pass a beam of monochromatic light through a spectroscope,
an image of the slit is formed on the screen. The image is fuzzy because
different photons are reflected from the grating at different angles, even
if all the photons are identical. The distribution of photons always gives
a strong centerline where the majority of photons light up the screen.
But because each photon is reflected at an unpredictable angle, no one
photon measurement reliably indicates the photon's actual wavelength,
frequency, or energy.

If you measure the energy of an arbitrarily large collection of photons,
then you can measure the mean energy to arbitrary precision.
And you can also measure the energy of one photon to a similar
precision-- simply reduce the intensity of the ensemble until only one
photon at a time is being treated by the exact same observational
approach.
You can't reliably measure the energy of an individual photon. You
can calculate what the energy of an individual photon must be by
dividing the measurement of the total energy of a large group of
photons by the number of photons in the group.

What technique do you think can be used to measure the energy of
an individual photon with arbitrary precision?

The point here is that you seem to suggest that more information is
somehow available about an ensemble than is available for an individual
photon, and that is incorrect.
An individual photon in a monochromatic beam can hit anywhere on
the spectroscope screen. The location that it hits does not reveal
the wavelength, frequency, or energy of that photon. Only when a
number of photons have hit the screen does the pattern become
visible, enabling the photon's characteristics to be determined.

The idea that a photon is one wavelength long happens to be a
notion I favor, but it is not held by any physicist that I know of.
That's because physicists like to define the concepts they use. How
are you defining "length" of a photon, such that you can "favor" any
particular value for it?
The minimum length in which all of its energy is contained.
Huh? I asked for a scientific definition, that means you have to say
how one can tell what it is. Now, how do you tell where "all the energy is
contained", and why does it come out one wavelength? Sounds like make
believe to me.
I was just pointing out that Sam5's assumption that a photon is one
wavelength long appears to be ATM, but at the same time saying that
I sympathize with the assumption. I have no argument to support the
idea, and I have no particular desire at this time to argue about it.

-- Jeff, in Minneapolis

Jeff Root
2008-Aug-23, 12:31 AM

The image labeled "Light wave" within the graphic, on the right side and
a bit less than halfway down the page, showing the electric and magnetic
fields of light as red sine waves, has the handedness wrong, which I find
is a frequent occurrance on web pages. If the wave is travelling to the
right (the direction of the arrow), then the positive part of the magnetic
field is shown to the left of the positive part of the electric field, instead
of to the right as it should be.

-- Jeff, in Minneapolis

Ken G
2008-Aug-23, 02:14 AM
Radio scientists tend to think of EM radio signals as being waves. When they speak of “wavelength” they are talking about waves that are long and that have a wave front and a wave end.Certainly not.
The length of the waves are calculated by diving the distance light travels in a second by the frequency of the wave. When they talk about a thirty meter wavelength, they mean the wave is thirty meters long.That's ridiculous. None of those links suggest that even in the smallest way. The wavelength is the distance between crests, that is true-- and that's all that's true. Forget that it's the "length of the wave", because waves typically have many many crests. If that weren't true, the wavelength would be very poorly defined (if you don't believe me, take the Fourier transform of a single circuit of a sine wave from 0 to 2*pi).

In effect, it is the bump, bump, bump of successive radio waves that causes a receiving antenna to resonate, and the antenna needs to be the length of a full wave, or some even-fraction of a wavelength, such as a half-wave, quarter-wave, eighth-wave, etc. Hang on, if the wave is only 30 meters "long", where exactly is this "bump, bump, bump" coming from? Gosh, it sure sounds like the wave has to be many wavelengths long for the concept of resonance to apply (it does). This is elementary wave theory.

So while the bump, bump, bump seems to act like “particles” hitting the receiving antenna, radio engineers have explained to me that what actually hits the antenna are successive waves.The "bump, bump, bump" happens even for a single photon-- don't you think single photons require the principle of resonance to be absorbed?

Sam5
2008-Aug-23, 04:22 AM
Hang on, if the wave is only 30 meters "long", where exactly is this "bump, bump, bump" coming from?

Multiple waves in a long stream of a continuous transmission. A "wave train".

Gosh, it sure sounds like the wave has to be many wavelengths long for the concept of resonance to apply (it does).

Right. The continuous radio signal is more than one wavelength long. Radio waves are multiples of waves, one following another. They aren’t just one wave. They are a continuous transmission, and that creates the bump, bump, bump. One wave is one very short bump, hardly enough to allow us to enjoy a full radio broadcast. A continuous transmission of 30-meter waves would generate about 10,000,000 cycles per second (Hz per second). This is about 10 MegaHertz, which would be in the shortwave band of amateur radio.

http://cfcp.uchicago.edu/education/explorers/2002summer-YERKES/pdfs-sum02/background.pdf
”All waves have crest (high points), troughs (low points), a wavelength (the distance from one crest to another or one trough to another), amplitude (the height of a crest or trough), and a frequency (the number of complete wavelengths that pass a given point in a second.) When we talk about frequency the unit that is associated with it is Hertz (Hz). When you say that a wave has a frequency of 1-Hz you are saying that it has one cycle per second. Another way of saying this is that one complete wave passes a given point in one second of time.”

These aren’t “particles.” They aren’t a series of little balls or point-particles thrown at receiving antennas. They are “waves”, with crests, troughs, and length.

Ken G
2008-Aug-23, 06:22 AM
It is extremely rare to see a distinction made. In fact, off the top of
my head, I don't recall anyone other than you making this distinction.And what do you conclude from that? My own conclusion is quite simple: virtually all answers about photons are considerably "dumbed down". That's not a criticism, it is just a fact-- in truth a "photon" is whatever we need it to be in whatever context we are considering, and if you ask a quantum field theorist how they think of photons, you should expect to understand not one single word. Is that what you want "About.com" to say? Please.

My purpose in pointing out the distinction, at a level that both I and most readers can understand, is to straighten the confusion we have seen in this thread, which is that when somone quotes E=h*nu, they are assuming that either an energy or a frequency measurement has been made on the quantum, or they are describing fundamental modes of a field. If instead they are talking about a quantum that has just been created by some standard process, the quantum has neither a definite E nor a definite nu, and that formula only applies to expectation values. Such a quantum can only be described by a wave function that has no definite E or nu value, and that wave function may be used to calculate any expectation value you need to confront observations. The wave function also admits a property of "coherence length", which is the most meaningful concept of "how long" is the photon, other than saying it is a point particle with no internal degrees of freedom not described by its wave function. This applies perfectly well to individual photons-- I'm sorry if "About.com" left that unclear to you, but I frankly don't find it very suprising that they left out a few details that are relevant to this thread.

Possibly, in the section titled "Second quantization", a bit more than
halfway down the page, is what you are talking about? Yes, that is the natural place to look for answers about photons.

The section is
about "Fourier modes", but says "The key new step was to identify an
electromagnetic mode with energy E = nhν as a state with n photons,
each of energy hν." So its purpose appears to be to deal with groups
of photons, not individual photons.So you think "second quantization" is about multiple photons, but doesn't apply to individual photons? No, second quantization is all about photons, and the usual descriptions you find are simply very dumbed down. That's the point I'm trying to tell you-- there's no single particular concept of "a photon", the concept is different in different approaches to treating light, and the distinction I drew above is merely the tip of the iceberg of all those possible ways of thinking about what photons are. Nevertheless, it is a distinction that will avoid some confusions that I have already seen on this thread, and yes, you won't find it in very many places. Want to ignore it? Then be confused.

If you don't, then just note: if one uses the word "particle" or "quantum" that has not just had a an energy measurement on it, one must be talking about a photon as something whose wave function is a wave packet. If one uses the word "mode", then one must be talking about an elementary field excitation, which is a mathematical entity that can be superimposed to generate the wave packets that describe actual particles. This is not special to photons (ergo "second" quantization), it is true of all particles, including electrons.

Since photons are not actually infinitely long, I think it is safe for you
to assume that I am not talking about coherence length when I refer
to the length of a photon, and that I'm not talking about modes.If you are not talking about modes, then when you say E=h*nu, you are talking about expectation values. But why does this not mean you are talking about coherence length? Again, the coherence length comes from the wave function, so it applies perfectly well to quanta, ensembles, and modes-- they all have wave functions. And when one says that photons are modes, then they are infinitely long in the sense that they do require an infinite amount of space-- as conceptual objects.

I didn't say there was any problem, but I did say that the coherence
length of an individual photon cannot be measured, and I said that the
wavelength of an individual photon cannot be measured, so what you
say here agrees with what I said.Well, what you said was "The concept of coherence length does not appear to be meaningful as
applied to individual photons." What I am saying certainly does not agree with that erroneous claim.
But NO, it is NOT a measurement
of frequency. It is a calculation of frequency from a measurement
of something else. Well this is certainly an irrelevant side issue, but still I will point out that all measurements are like that. Without some theories about how things behave, no measurements are possible.

Why you would call that "strange" is beyond my comprehension.
Then I shall explain. I called it "strange" because you are implying that somehow we cannot measure the frequency of a photon because it is quantized and can only be fully absorbed or fully not absorbed. There are two fundamentally wrong claims you have made that I am correcting:
1)you said the coherence length is not meaningful for an individual photon. In fact it is just as meaningful as the particle's wave function, and is thus the most meaningful way to think about "how long" a photon is given that we recognize a photon is a point particle, and
2) you opined that all the energy "contained" in a photon is contained in one wavelength. In fact Sam5 had one thing right-- the crucial principle of resonance applies to individual photons, and requires many "bumps" in the wave function.

But because each photon is reflected at an unpredictable angle, no one
photon measurement reliably indicates the photon's actual wavelength,
frequency, or energy.
Again you are bringing in prediction; I already pointed out we are talking about measurement. I am well aware that prediction is statistical, and can only be verified by an ensemble of particles. That's called the uncertainty principle, and I haven't seen anyone on this thread who is at all confused on that score. The confusion is about what "photon" means, and your strange claims of what limitations appear in the measurements on single photons.

You can't reliably measure the energy of an individual photon. That's an example of what I mean. Perhaps this is your core misconception that will fix the rest. Actually, there is no fundamental limit on how reliably you can measure the energy of an individual photon-- only technological limitations. Nevertheless, the photon (in the quantum meaning you are using, not the mode meaning that many others have used here) is described by a wave packet prior to such a measurement.

What technique do you think can be used to measure the energy of
an individual photon with arbitrary precision?There are quite a few, actually. One is a calorimeter, where you measure how much the photon raises the temperature. Another is to use a resonance of whatever chosen precision is available. In all cases, the limitations are technological, and have nothing to do with the wave function of the individual photon. Photon energies are routinely measured to far higher precisions than the spread in their wave functions, and doing so is called "observing an intrinsic line profile".

An individual photon in a monochromatic beam can hit anywhere on
the spectroscope screen. The location that it hits does not reveal
the wavelength, frequency, or energy of that photon.Actually, that simply depends on the apparatus. It is perfectly possible for that location to reveal all those things to far higher precision than is inherent in the wave function of the photon. That's called a "diffraction grating" or "echelle spectrograph". Of course we get into the usual issues of how the act of measuring selects these quantities from the possibilities available in the wave function.

Only when a
number of photons have hit the screen does the pattern become
visible, enabling the photon's characteristics to be determined.This is definitely your core misconception, and it probably explains all the other problems you are having. It's just plain wrong to say that we need a bunch of measurements to understand the energy of one particular photon. Perhaps you meant photons', not photon's, in which case you would be talking about determining the properties of the ensemble prior to measurement, not the individual photons you are measuring. What you are talking about would be what we do when we are trying to check a prediction, so again you are confusing prediction and measurement, the former only relating to ensembles and the latter being relevant to individual photons.

I was just pointing out that Sam5's assumption that a photon is one
wavelength long appears to be ATM, but at the same time saying that
I sympathize with the assumption.And I was just pointing out that your "sympathies" are pretty irrelevant in Q&A when they are demonstrably wrong. Still, I'm not saying you shouldn't bring them up-- you should bring them up, and get them corrected, which is what's happening.

I have no argument to support the
idea, and I have no particular desire at this time to argue about it.
Then you must also recognize that I might be writing this for someone other than you, say for someone who read your comments and might have thought there was something to them. This is Q&A, after all, and people come here to learn-- I know I do.