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

  1. Sep 8, 2017 #1
    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
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  3. Sep 8, 2017 #2


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

  4. Sep 8, 2017 #3


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    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.
    That, at least avoids the risk of wanting to attribute an extent to a photon.
    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. :smile:
  5. Sep 8, 2017 #4
    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.
  6. Sep 10, 2017 #5


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    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.
  7. Sep 11, 2017 #6
    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

    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:


    "... 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:


    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
  8. Sep 11, 2017 #7
    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.
  9. Sep 11, 2017 #8
    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
  10. Sep 11, 2017 #9
    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.
  11. Sep 11, 2017 #10
    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
  12. Sep 11, 2017 #11


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    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?
    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)
  13. Sep 12, 2017 #12

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    And yet here we are.
  14. Sep 13, 2017 #13


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    Yes, but...
    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.
  15. Sep 13, 2017 #14


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    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.
  16. Sep 20, 2017 at 10:32 PM #15
    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
  17. Sep 20, 2017 at 11:10 PM #16
    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
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