How could the "size" of a photon be measured?

[Jeff Root]

I'm looking at the possibility of trying to measure the length
of photons as a Science Fair project. I know that photons are
often considered to be "point particles", and I know there are
fundamental limits on measurements due to uncertainty in
position and momentum. I also know that according to
special relativity, length is a relative measurement, and that
light is different from virtually everything else in that it is
always moving relative to every observer.

How can I define the "length" of a photon? I suspect that there
might be several different ways to define the length, and they
might each have advantages and disadvantages.

How might I go about measuring the length? One tool you
might suggest is an interferometer. I can probably build one
if I need to, but I doubt I could build a very good one. Visible
light would be easiest to use in some ways, but the wavelength
is awfully small. Radio waves have a much more convenient
wavelength, but they are invisible, and can't be detected one
at a time. So the two best choices both seem very bad.

I'm looking for any measurement than can be practically done,
even if it isn't very precise, that would tell me something about
the length of the photons I'm measuring. I might use a laser of
known wavelength/frequency (that I could also measure myself)
and do something to the beam that would have an effect that
would depend on the lengths of the individual photons.

-- Jeff, in Minneapolis

 

[CWatters]

This is the nearest I think you can get. Vary the gap and plot a distribution curve.

 

[sophiecentaur]

If you are thinking of Photos as little bullets - or even big bullets then you are doomed to failure. They are referred to as 'particles' but that description is dangerously misleading. They have nothing to do with the Corpuscules that were proposed before EM Waves were introduced. Many decades ago the notion of The Duality Of Light emerged and that light (EM) was both particles and waves. This has long been rejected and it is now acknowledged that EM energy transfer is best described in terms of Waves and EM interactions, best described in terms of Quanta of Energy - (photons). Quantum Mechanics and the later Quantum Electrodynamics are not classical models and you cannot use classical ideas as a way into those subjects; they are NEW and have moved on from Science up until the 19th Century.

"point particles",

That, at least avoids the risk of wanting to attribute an extent to a photon.

One tool you
might suggest is an interferometer

Interference (diffraction) is a wave phenomenon so all your interference experiment will do is to tell you about wavelength. If you want to think in terms of particles and probability functions, you end up with exactly the same equations as you get from wave theory so why bother?
You should read around a bit about QED. This Wiki Article is a fair start. There is an interesting passage, referring to the famous Feynman Diagram:
"It is important not to over-interpret these diagrams. Nothing is implied about how a particle gets from one point to another. The diagrams do not imply that the particles are moving in straight or curved lines. They do not imply that the particles are moving with constant speeds. The fact that the photon is often represented, by convention, by a wavy line and not a straight one does not imply that it is thought that it is more wavelike than is an electron. The images are just symbols to represent the actions above: photons and electrons do, somehow, move from point to point and electrons, somehow, emit and absorb photons."
You are going against that advice, I think and, along with many before you, you will end up chasing your tail.

 

[Gigaz]

The closest thing to the size of a photon is the coherence length L. https://en.wikipedia.org/wiki/Coherence_length

L is used to describe the probability, that the electromagnetic field at point x1, x2 are in phase. Typically you have p=exp( -|x1-x2|/L ) for Lasers (I will describe more complicated cases later)
Now why is it reasonable to call this the "size" of the photon? Because if you do something like a double slit experiment, you will only get interference if the path difference is much smaller than L. Otherwise, the wave field does not overlap and you only see particle properties.
Photons in a Laser beam typically have a small transversal coherence length (typically ~100 Lambda or so) and a very large longitudinal coherence length (Can be kilometers easily, with state of the art research it can be of astronomical size). You are probably more interested in the latter. You should be able to find a few ways to determine it from the Internet.

Now to the more complicated cases:
A photon can be in more than one position at once (As for example seen in the double slit experiment). You can essentially create funny Quantum states with photons which make the concept of photon "size" totally meaningless.

 

[sophiecentaur]

the concept of photon "size" totally meaningless

There is a probability of a photon turning up 'anywhere' so that implies it is 'smeared out' over all space. A pretty useless thing to know, really.

 

[Jeff Root]

I had in mind something like the way distance can be measured by
the time it takes a light pulse to travel to a target and return,
but configured to reveal the lengths of the photons rather than
the distance they travel.

The distance of the Moon is regularly measured by observation of
laser pulses aimed at the Apollo and Lunokhod retroreflectors from
telescopes at McDonald Observatory in Texas and Apache Point in
New Mexico. They typically detect only one photon per detected
return pulse. McDonald sends 10 pulses per second, Apache Point
sends 20. Over a period of about a minute, enough photons are
detected to make a useable dataset from which a distance can be
calculated. Of course, the distance changes a lot in a minute,
which complicates the calculation.

The important point for me is that each measurement is typically
of a single photon. As few as 10 photons provide sufficient data
for a distance measurement precise to 2 centimeters. 3000 photons
can give precision better than 1 millimeter. The largest source
of error is in not knowing which part of the retroreflector any
individual photon was reflected by, since the retroreflector is
not exactly perpendicular to the beam. The next largest source
of error appears to be variations in the atmosphere. Both are
irrelevant to my investigation since they are limited in lab
experiments.

Apache Point transmits pulses 100 picoseconds long of laser light
with a wavelength of 532 nanometers. So in vacuum, each pulse is
about 3 centimeters or 56,350 wavelengths long.

Which suggests to me that each photon of green light is at most
56,350 wavelengths long.

From this web page on The Basics of Lunar Ranging:

http://tmurphy.physics.ucsd.edu/apollo/basics.html

"... we don't know if a particular photon was in the leading or
trailing edge of the beam, or right in the middle."

Which suggests to me that the experimenters believe the photons
are significantly less than 56,350 wavelengths long.

And this Wikipedia page on Apache Point laser ranging:

https://en.m.wikipedia.org/wiki/Apache_Point_Observatory_Lunar_Laser-ranging_Operation

says that using the new SPAD technology, multiple consecutive
photons within each pulse can be separately detected and timed.

The lunar ranging lasers need to be relatively powerful in order
to get a detectable return from the Moon. That isn't needed in
the experiment I'm proposing. So pulses much shorter than
100 picoseconds might be possible.

I wonder how much more tightly the lengths of individual photons
can be constrained. Maybe to a single wavelength?

-- Jeff, in Minneapolis

 

[Gigaz]

I think you have wrong ideas about the "length" of a photon.

At the beginning of the Lunar Laser ranging, the photon is created by the pulsed laser. The photon has at this point a particular quantum state with a length, which is probably the size of the pulse. The length also coincides with the coherence length, iirc.
The photon them travels to the moon and back, and during all this time the length along the direction of travel is constant, but the length of the quantum state perpendicular increases significantly.
When the photon arrives at the detector, an arrival time is measured. This measures the position of the photon, but not the length of its quantum state. The photon is also destroyed in the process.
As far as you are concerned, the position of a photon at one particular point in time can be determined with any precision, there is no limit. But that does not tell you much about the photon. Unlike macroscopic objects, particles have no length by themselves. Each individual particle resembles more a cloud of gas which can be compressed, expanded or split in many little parts.

 

[Jeff Root]

It appears that I neglected to say anything about the window
at the receiving end. McDonald used a rotating disk and I think
Apache Point uses some other mechanism to limit the time
window in which light is allowed to reach the detectors. The
windows are on the order of one nanosecond long. Individual
photons can be detected anytime in the window, but photons
which are part of the transmitted beam are strongly bunched
around a specific time. The point is, the entire photon has to
pass through the window, or it will not be detected. There's no
such thing as "part of a photon". So each detected photon has
to be smaller than the window. It's only an upper limit, but it is
a real limit on the length. I'm essentially wondering how much
farther the limit can be reduced.

-- Jeff, in Minneapolis

 

[Gigaz]

If you send the photons through a rotating disk mechanism, the number of photons which arrive at the detector will ultimately be proportional to the size of the window. There is no lower limit.

 

[Jeff Root]

The lower limit is zero. The detectors only detect photons in
an extremely narrow range of wavelengths around 532 nm.
Measurements of zero were the norm at McDonald. Apache
Point has a larger aperture telescope so one or two photons
per window are more common than zero. But if the scope is
pointed the slightest bit off target, zero becomes the norm
there, too.

-- Jeff, in Minneapolis

 

[sophiecentaur]

The problem that I have with discussions like the last few posts is that it implies that photons of a given frequency are not identical but their nature would depend on the method by which they were 'created'.
If you detect a photon then the detector should somehow be able to tell what the source of that electron was. Is that valid?

If you send the photons through a rotating disk mechanism, the number of photons which arrive at the detector will ultimately be proportional to the size of the window. There is no lower limit.

Why doesn't that just involve the phase error of a pulse that has only one quantum of energy? (A purely classical interpretation which basically involves an oscillator, a switch and a receiver)

 

[Vanadium 50]

If you are thinking of Photos as little bullets - or even big bullets then you are doomed to failure.

And yet here we are.

 

[Nugatory]

The point is, the entire photon has to pass through the window, or it will not be detected.

Yes

There's no such thing as "part of a photon".

Yes, but...

So each detected photon has to be smaller than the window.

That does not follow. It would if photons were like little bullets moving from one point to another, but they aren't.
All you have here is a constraint on the time and place at which the photon might be detected.

 

[sophiecentaur]

All you have here is a constraint on the time and place at which the photon might be detected.

Exactly. The only place and time that the photon has a 'location' is where / when it is detected. To describe a photon that has no particular place and time as a 'particle' for all its life is questionable. The nature of this 'particle' would have to depend upon the detecting mechanism and that (for light arriving from the Andromeda Galaxy, for instance) would be challenging causality, I think.
I know that there are some branches of Physics which use the particle nature of photons in assumptions and calculations and, if it works in a particular context then why not? But, as Feynman himself said - and we cannot argue with his statements - the meaning of the word 'particle' has to be treated carefully. This Wiki link discusses it and uses many different sources.

 

[Jeff Root]

The problem that I have with discussions like the last few posts
is that it implies that photons of a given frequency are not identical
but their nature would depend on the method by which they were
'created'.
If you detect a photon then the detector should somehow be able
to tell what the source of that electron was. Is that valid?

Are you referring to my posts? If so, are you referring to how the
photons returned from the Moon can be identified as originating
in the transmitted laser beam? If so, it is statistical.

When the laser is turned off, or the telescope is not aimed exactly
at the retroreflector, or the time window is not correctly aligned
with the returning light, there might be one photon detected every
minute, on average. When the laser is on and everything is well
lined up, there might be ten or twenty photons detected each
second, and they will be bunched very closely in time within a
very small part of the time window. So although it isn't possible
to say whether any individual detected photon was part of the
transmitted beam, it is possible to say that the vast majority of
them were.

Apologies if that isn't what you meant.

-- Jeff, in Minneapolis

 

[Jeff Root]

The point is, the entire photon has to pass through the window,
or it will not be detected.

Yes

There's no such thing as "part of a photon".

Yes, but...

So each detected photon has to be smaller than the window.

That does not follow. It would if photons were like little bullets
moving from one point to another, but they aren't.
All you have here is a constraint on the time and place at which
the photon might be detected.

Why does it not follow? Certainly there are many ways in which
photons are not like little bullets moving from one point to another,
but in some ways they *are*. My intent is to design experiments
to measure certain properties of individual photons. Maybe the
results will be that the experiments don't reveal those properties.
Maybe that will be because photons don't have those properties.
I think the Michelson-Morley experiment was worth doing even
though it failed to detect what it was trying to measure.

If the time window is shorter than the time required for the length
of the photon to pass through the window, then it indicates a lower
limit on the length of the photon. I have no reason to assume that
isn't true. I have no reason to think it might not be true, since it
appears to be true of everything else. But I'd like to find out by
performing well-designed experiments.

-- Jeff, in Minneapolis

 

[Nugatory]

but in some ways they *are*.

Such as?

 

[Jeff Root]

Photons are like little bullets moving from one point to another
in that they are both little. (You specified little bullets; photons
are little in that photons of visible light are able to go through
what I consider to be small holes, and they're able to go through
shutters that are opened and closed what I consider to be very
rapidly, so they can't be terribly long.)

Photons move from one place to another, like bullets. A bullet is
fired from a gun in one place and hits a target in another place.
A photon of visible light is emitted from a source in one place
and illuminates a surface in another place.

Bullets and photons both transport energy and momentum. They
both move very fast, along fairly straight lines.

They are both physical things. They can both be created and
destroyed. They can both pass through some objects but not
through others. Both can affect objects they hit, changing the
objects. Both can carry information.

-- Jeff, in Minneapolis

 

[sophiecentaur]

Photons are like little bullets moving from one point to another
in that they are both little.

That is a very naive model that can never explain interference patterns built up from single photons (and several other wave phenomena).

My intent is to design experiments
to measure certain properties of individual photons.

You could save a lot of time and money by reading about the thousands of experiments that have already been done and the well informed explanations of the results.

 

[Jeff Root]

Photons are like little bullets moving from one point to another
in that they are both little.

That is a very naive model that can never explain interference
patterns built up from single photons (and several other wave
phenomena).

Saying that photons are little is all it takes to define a model
of them? I would have thought there would be far more to a
model than that. I wouldn't expect such a model to have any
predictive power at all. At least, not without defining "little".

-- Jeff, in Minneapolis

 

[Jeff Root]

Another possibility of something that could be measured is the
delay when light travels through a medium. Photons travel at c
in vacuum but are delayed each time they interact with matter.
If a photon can only interact with one other particle at a time,
then it must completely disengage from a particle before it can
begin to engage with another. It can't be absorbed by a particle
while still being emitted by another particle. So measuring a
minimum time between interactions could say something about
the size of the photon.

-- Jeff, in Minneapolis

 

[Nugatory]

Photons are like little bullets moving from one point to another
in that they are both little. (You specified little bullets; photons
are little in that photons of visible light are able to go through
what I consider to be small holes, and they're able to go through
shutters that are opened and closed what I consider to be very
rapidly, so they can't be terribly long.)

Photons move from one place to another, like bullets. A bullet is
fired from a gun in one place and hits a target in another place.
A photon of visible light is emitted from a source in one place
and illuminates a surface in another place.

Bullets and photons both transport energy and momentum. They
both move very fast, along fairly straight lines.

They are both physical things. They can both be created and
destroyed. They can both pass through some objects but not
through others. Both can affect objects they hit, changing the
objects. Both can carry information.

When you hear that a photon is a "particle of representing a quantum of light" or some such it's natural to think that they act as you describe above, but in fact almost none of that is even close to how photons behave. Probably the most important thing to understand is that light moving from point A to point B does not mean that photons are moving from A to B; they do not move from place to place like bullets (or anything else). Light waves move at $c$ in a vacuum, but it's not clear that photons move at all, at least not the way you're imagining.

A better way of thinking about photons (at least in a B-level thread, and I'm open to suggestions about better ways of explaining it) is that light always moves as electromagnetic waves; that's what light is. Photons only come into the picture when the electromagnetic waves interact with matter: even though the wave is spread out in space, when it transfers energy to whatever it is illuminating, the energy is always delivered in discrete amounts at single points in space. When this happens we say that a photon appeared at that point. Thus, light moving from point A to point B cannot be modeled as photons moving from point A to point B. Instead, the light source is transferring energy and momentum to the electromagnetic field in its vicinity; with sufficiently accurate instruments we could observe that the energy is being transferred in discrete amounts. At some later time we observe that the electromagnetic field in the vicinity of whatever object is being illuminated is transferring energy to that object, again in discrete amounts landing at single points. However, there is (except under very controlled conditions that don't apply to a flash of light) no relationship between the energy transfers at the source and the target so it doesn't work to think of the photons at the source having moved through space to the target.

 

[DrGreg]

Photons travel at c
in vacuum but are delayed each time they interact with matter.
If a photon can only interact with one other particle at a time,
then it must completely disengage from a particle before it can
begin to engage with another. It can't be absorbed by a particle
while still being emitted by another particle.

You might like to read the Insights FAQ "Do Photons Move Slower in a Solid Medium?" which explains why this model is an oversimplification of what really happens, and is further evidence that photons don't really behave like particles.

 

[Drakkith]

I think the Michelson-Morley experiment was worth doing even
though it failed to detect what it was trying to measure.

True, and that negative result (not failure) was immensely important. But the problem is that there is no possible experiment you could do on your own to determine a property of a photon with greater accuracy or precision than we already know.

Bullets and photons both transport energy and momentum. They
both move very fast, along fairly straight lines.

Not quite. While bullets and photons both transport energy and momentum, bullets don't diffract around barriers or through gratings. You literally cannot explain most of the properties of light with a bullet-like model.

 

[sophiecentaur]

@Jeff Root There is very little point in trying to jump in at this late stage with a 'personal interpretation' of the nature of such an established entity. That is unless you have already read all that's available about the conventional situation so far. Science is not something that works the way you think it should work. Science moves on after there's enough Evidence for the next step. From your comments, it seems you have underestimated the complexity of the topic and also the amount of work that's been done on it so far. Take any successful and celebrated Scientist and you will find someone who went through all the rigorous stuff that had already been done before making their own significant contribution. No one ever makes a successful change without building on a firm background of knowledge.
Your picture of a photon really doesn't agree with what's already known about the topic and no amount of 'bending' of facts can make them fit your view.