I Properties of Photons: Orange vs. Green

[Jeff Root]

How are the photons in a monochromatic beam of orange light
(for example) different from the photons in a monochromatic
beam of green light? I'm trying to understand the properties of
individual photons.

-- Jeff, in Minneapolis

 

[drvrm]

A photon is an elementary particle, the quantum of all forms of electromagnetic radiation including light. It is the force carrier for electromagnetic force, ...
see https://en.wikipedia.org/wiki/Photon

one can visit popular sites on photons to get a picture.

How are the photons in a monochromatic beam of orange light
(for example) different from the photons in a monochromatic
beam of green light?

as regards the essential difference -the color of the photons characterise its frequency and in turn give its range of energy/momentum as its energy is proportional to frequency.
and its behaviour in different media changes .

 

[jtbell]

Different energy, momentum, frequency and wavelength. $$E = pc = hf = \frac {hc} \lambda$$

 

[Jeff Root]

So, you both believe that the individual photons in a beam
of monochromatic light have the same energy, momentum,
frequency, and wavelength?

Can you explain what is meant by the wavelength of a
single photon?

-- Jeff, in Minneapolis

 

[sheaf]

So, you both believe that the individual photons in a beam
of monochromatic light have the same energy, momentum,
frequency, and wavelength?

Can you explain what is meant by the wavelength of a
single photon?

-- Jeff, in Minneapolis

There are a number of subtleties in this post:

1) When you use the word "beam", it suggests that this is the light from a laser, or thermal source. In this case, the electromagnetic field constituting the beam is not in a state which has a definite number of photons.

2) The word "individual" applied to one of a bunch of monochromatic photons can be tricky - since photons are bosons.

3) In asking about the wavelength of a single photon, perhaps the best thing to envisage is the photon produced from a single-photon-source (rather than a beam). Such photons can be sent through double slits, and, if the experiment is repeated over time, will build up an interference pattern whose geometry is consistent with the photon's wavelength.

 

[bhobba]

Can you explain what is meant by the wavelength of a
single photon?

Its related to its momentum by a well known formula.

That said its much more subtle in QED because the number of photons is itself an observable so the concept of a single photon is rather ill defined.

Thanks
Bill

 

[vanhees71]

The concept of a single photon is very clearly defined as a Fock state with photon number 1. It is important to note that a classical light source or a laser emits electromagnetic fields that cannot be depicted as a stream of particles (a photon has not even a position observable!). It's a coherent state, i.e., a superposition of many-photon states, i.e., the photon number is not determined in such a state, which is called coherent state.

It is a much better intuitive picture of electromagnetic phenomena to think in terms of classical waves, obeying Maxwell's equations. Only when it comes to interaction with matter you often need the photon picture as in the photoelectric effect, which one should not depict as Einstein did in his ground-breaking work of 1905, which however was a predecessor theory to modern quantum theory, which was discovered in 1925 (the modern picture of photons is due to Dirac shortly thereafter). In modern quantum theory the phenomenology described correctly in terms of the naive photon picture of "old quantum theory" is treated in 1st-order timedependent perturbutation theory as the interaction of a quantized bound electron with a classical electromagnetic waves. See

https://www.physicsforums.com/insights/sins-physics-didactics/

 

[Jeff Root]

The idea that the light is in the form of a "beam" was not essential
to my question. It seemed useful to specify monochromatic light,
which suggested laser light, which suggested beams.

Offhand, I'd think that if the light is monochromatic, and has a
beginning and end in time, from a specific source, then it would
or at least could consist of a definite number of photons. I don't
know if that has any significance for my question.

How does the fact that photons are bosons mean that applying the
word "individual" to one of a bunch of monochromatic photons can
be tricky?

A single-photon source instead of a beam sounds fine, although it
isn't obvious how that is different from an extremely feeble beam.
I think you are just saying the photons are spaced far enough apart
that they can be looked at one at a time.

I agree that the widely-spaced photons of monochromatic light,
passed through a pair of slits, will gradually build up an interference
pattern, and that the pattern is indicative of a wavelength associated
with those photons. I'm trying to understand whether the wavelength
can reasonably be said to describe each of the individual photons,
or if it applies only to a statistically large number of photons taken
together as a group. A large enough number that the pattern can be
detected and measured. Obviously, the larger the number of photons
observed, the more precise the measurement can be.

I presume that individual photons could land anywhere on the screen,
but are most likely to land close to certain lines, with something like a
sharply-peaked gaussian distribution of the photons forming each line.
I also presume that the gaussian spread is not due to the photons
having a distribution of wavelengths, but is instead due to the slits
producing a distribution of directions that the photons go, in proportion
to the uncertainty in the photons' wavelength.

I could interpret that to mean that a single photon has a definite
wavelength which cannot be measured with anything better than
extreme uncertainty. Maybe *total* uncertainty. Only with a large
enough sample of photons can the wavelength really be measured.

Bill,

Why do you say that the concept of a single photon is ill-defined
because the number of photons is an observable?

-- Jeff, in Minneapolis

 

[bhobba]

Why do you say that the concept of a single photon is ill-defined because the number of photons is an observable?

Well I didn't express myself well - Vanhees corrected me.

The point I was trying to get across is a quantum field is a Fock space:
https://en.wikipedia.org/wiki/Fock_space

It was in relation to 'I'm trying to understand the properties of individual photons.'.

In general for a quantum field the concept of individual photons is tricky. States do exist where the number is known - but in general it isn't.

Thanks
Bill

 

[A. Neumaier]

A single-photon source instead of a beam sounds fine, although it
isn't obvious how that is different from an extremely feeble beam.
I think you are just saying the photons are spaced far enough apart
that they can be looked at one at a time.

To understand single photons and beams, and how they relate to modes of the electromagnetic fields (which may be quasi-monochromatic), try my slides on photons and on beams, or Chapter B2 of my theoretical physics FAQ.

 

[sheaf]

I'm trying to understand whether the wavelength
can reasonably be said to describe each of the individual photons,
or if it applies only to a statistically large number of photons taken
together as a group.

I would say that, yes, the wavelength attribute can be reasonably said to apply to a single photon. A photon is a single excitation of a mode of the electromagnetic field. A mode is a solution of Maxwell's equations satisfying whatever boundary conditions are appropriate. So for a single photon in a double slit experiment, this mode would be a propagating wave constrained by the slits. It has a wavelength.

 

[Nugatory]

How are the photons in a monochromatic beam...

Offhand, I'd think that if the light is monochromatic, and has a
beginning and end in time, from a specific source, then it would
or at least could consist of a definite number of photons. I don't
know if that has any significance for my question.

It is natural to think that photons are very small things that form a beam of light the same way that a river is a bunch of water molecules flowing by; there's almost no other way way of understanding the commonly-heard statement that a photon is "particle" of light. That's the mental picture is pretty much implied when we speak of light "consisting of" photons, or of the photons "in" a monochromatic beam.

However, as vanhees71 points out in the second paragraph of post #7, this picture is actually very misleading. Light is an electromagnetic wave governed by Maxwell's equations, and photons only appear when the electromagnetic waves interact with matter - the energy is always deposited in discrete chunks at single points, and wherever that happens we say "a photon landed there".

Thus, the best answers I have for your original question:

How are the photons in a monochromatic beam of orange light
(for example) different from the photons in a monochromatic
beam of green light?

are:
1) The photons associated with the orange light deliver less energy and momentum per photon to the surface illuminated by the light.
2) All photons have properties called "wavelength" and "frequency" which are related to their energy and momentum by the formulas provided by jtbell in post #3. These properties have very little to do with the classical notions of wavelength as distance between peaks of a wave and frequency as number of peaks passing per unit time, although they are directly related (in the ideal case of pure monochromatic light) to the frequency and wavelength of the electromagnetic radiation. The photons associated with the orange light have a lower frequency and longer wavelength than those associated with the green light.

 

[Nugatory]

Why do you say that the concept of a single photon is ill-defined
because the number of photons is an observable?

Are you familiar with the quantum mechanical definition of "observable"? In formal quantum mechanical terms, every observable/measurable property of a system corresponds to a Hermitian operator called an "observable". The system state describing a beam of monochromatic light is a superposition of many different states which will give different results when acted on by the number-of-photons operator, so there's no meaningful way of describing such a state as containing one (or any other exact number) of photons. As vanhees points out, there are single-photon states, and Bhobba's point is that a beam of light is not one of these.

A single-photon source instead of a beam sounds fine, although it
isn't obvious how that is different from an extremely feeble beam.
I think you are just saying the photons are spaced far enough apart
that they can be looked at one at a time.

Nope - if you're thinking in terms of the photons being "spaced apart", you're making the mistake discussed earlier of thinking that photons are to a beam of light as water molecules are to a river, and assuming that they exist as recognizable entities with a position and a speed except at the moment that the light is interacting with whatever surface it is illuminating.

 

[Jeff Root]

I'm going to skip over everything else and reply to Nugatory's
last sentence immediately above.

My understanding -- based on everything I've learned about light
so far -- is that light consists of photons whose behavior can be
described largely in terms of transverse waves. These waves
are unlike the waves on the surface of water in that they do not
depend on the motion of a medium which they disturb. Instead,
the waves are a property of the light itself. That is, a property of
the photons.

We know photons exist because we detect them. We can detect
individual photons of sufficiently high energy with photomultiplier
tubes and CCDs. Photons with lower energy -- less than infrared --
are too weak to be detected individually. They can only be detected
by the aggregated effects of many photons, as in a radio receiver.

A photon can only be detected once. Detecting a photon destroys
it or affects it in such a way that it is not possible to detect it again
and know that it is the same photon. So it is not possible to follow
the path of a photon as it moves from one place to another.

What *can* be done, for example, is to emit a stream of photons
in an otherwise dark chamber, so that the origin of the photons is
known. The photons can be detected when they reach a screen,
lighting it up at the points where they hit it. Like all other particles,
the photons can be assumed to get from the origin to the screen
by crossing the space between. If the photons have to go through
a hole to reach the screen, then we can assume that the path goes
through the hole. Interestingly, if there is more than one hole, it
may not be possible to say which hole any of the photons went
through. They can behave as if each photon went through several
holes simultaneously, then came back together at the screen, like
waves.

All kinds of matter -- all kinds of particles -- behave that way. It is
easier to detect this wavelike behavior in large numbers of coherent
low-energy photons, like radio waves, than it is in higher-energy
particles like gamma rays or atoms or baseballs. For these things
with greater kinetic energy, the energy of each particle is relatively
easy to measure, but the wave properties may be undetectible.

I don't see any problem with this picture of light, but it still isn't clear
to me whether an individual photon has a wavelength or frequency
(as measured by some particular observer). It seems obvious that
each photon in a monochromatic beam should have the same or
very nearly the same wavelength and frequency, and this wavelength
and frequency can be found by measuring the responses of a large
number of the photons to an experimental setup to get a statistical
result. But it also seems possible that wavelength and frequency are
an emergent property of a statistically large number of photons taken
together, such that each individual photon does not have wavelength
or frequency.

-- Jeff, in Minneapolis

 

[sheaf]

But it also seems possible that wavelength and frequency are an emergent property of a statistically large number of photons taken together, such that each individual photon does not have wavelength or frequency.

-- Jeff, in Minneapolis

If you take a source which generates a single photon at a time, and a long time interval between photons, and pass the generated photons through a double slit arrangement, you slowly build up the interference pattern. Unless each individual photon has a wavelike character (including a wavelength), it's hard to see how they could be guided to accumulate in the right places, since each one "acts" individually, without knowledge of any of the ones which went before or after.

 

[bhobba]

is that light consists of photons whose behavior can be described largely in terms of transverse waves

Its more subtle than that:
https://www.physicsforums.com/threads/is-light-a-wave-or-a-particle.511178/

Unfortunately simplistic pictures like what you get in beginner texts fall sort in many ways of what is really going on.

Thanks
Bill

 

[f95toli]

I don't see any problem with this picture of light, but it still isn't clear
to me whether an individual photon has a wavelength or frequency
(as measured by some particular observer). It seems obvious that
each photon in a monochromatic beam should have the same or
very nearly the same wavelength and frequency, and this wavelength
and frequency can be found by measuring the responses of a large
number of the photons to an experimental setup to get a statistical
result. But it also seems possible that wavelength and frequency are
an emergent property of a statistically large number of photons taken
together, such that each individual photon does not have wavelength
or frequency.

-- Jeff, in Minneapolis

It is -as has been repeatedly been pointed out above- much more complicated than that. First of all, individual photons do -at least from practical point of view- have both frequency and wavelength. "Practical" here means that there are -in most cases- very little difference between how coherent light (e.g. a laser) and Fock states (i.e true single photons) interact with linear optical elements. You can for example "trap" a single photon in a resonator with a length equal to half its wavelength and if you map out the amplitude of the E and B fields in the resonators it will look exactly the same as for a coherent state (but you will of course need to repeat the measurement many time) despite the fact that the two types of fields have very different statistics (coherent states do not have a fixed number of photons)

More generally, it is meaningful -at least to some extent- to talk about the "shape" of photons. It is for example possible to encode quite a lot of information in single photons by just using photons from from many different orthogonal modes; I believe the current experimental record is something like 7 bits per photon. If the photon was just a shapeless point-particle where the only property was its energy this would of course be impossible (you could at most encode 1 bit)