Photon Width: What Have I Missed?

[padraighaz]

When thinking about the double-slit experiment, I realized - even after having a degree in physics - that I never learned about how wide a photon is? Yes I learned about wavelengths, but amplitude was used to measure intensity, and was never expressed in units of length. What have I overlooked/forgotten/never-learned! here?

 

[HallsofIvy]

If you are imagining a photon as being a little "sphere", that's an error. At the quantum level, such things as shape and size have no meaning.

 

[padraighaz]

If you are imagining a photon as being a little "sphere", that's an error. At the quantum level, such things as shape and size have no meaning.

Not at all.

If we can assign a scale length (wavelength) in one direction, shouldn't there be others for the transverse dimensions - otherwise photons would be purely 1 dimensional linear objects?

 

[ZapperZ]

Not at all.

If we can assign a scale length (wavelength) in one direction, shouldn't there be others for the transverse dimensions - otherwise photons would be purely 1 dimensional linear objects?

The reason why you never learned about this while in school is because photons were never defined to have a definite size in space. It is only defined as quanta in energy dimensions. While there is a characteristic length associated with a collection of photons, which is the wavelength, a single photon was never defined to have a size in real space.

Zz.

 

[padraighaz]

The reason why you never learned about this while in school is because photons were never defined to have a definite size in space. It is only defined as quanta in energy dimensions. While there is a characteristic length associated with a collection of photons, which is the wavelength, a single photon was never defined to have a size in real space.

Zz.

If single photons can interfere with themselves and create double-slit interference results, it would seem that they do indeed have a scale length (wavelength) so this can't be right.

 

[ZapperZ]

If single photons can interfere with themselves and create double-slit interference results, it would seem that they do indeed have a scale length (wavelength) so this can't be right.

But associating a "wavelength" to a photon doesn't mean that the "size" of the photon is that wavelength.

The problem here is that we are used to the concept of "wavelength", which is a classical wave concept. We then try to adapt that to "single photons", which certainly are not classical waves. Now, is the 2-slit interference a unique feature of "waves", even when you shoot one photon at a time? I can show you the Feynman path integral approach that would invoke no waves. Even in Marcella's paper where he derieved the single, double, and multi slit interference using purely QM and not classical wave, you'd be hard pressed to come up with a "wavelength" associated with a classical wave (the QM wavefunction isn't it).

So no, there still isn't a "size" of a photon. Even if you use the interference phenomenon, you'll never find any books or papers claiming that there's anything associated with the size of a photon. This is why you didn't read about it while in school.

Zz.

 

[padraighaz]

But associating a "wavelength" to a photon doesn't mean that the "size" of the photon is that wavelength.

...
So no, there still isn't a "size" of a photon. Even if you use the interference phenomenon, you'll never find any books or papers claiming that there's anything associated with the size of a photon. This is why you didn't read about it while in school.

Zz.

To argue there is no size to photons and that wavelengths are just abstract properties would seem to totally undermine arguments explaining interference fringes. How could there be interference if there is no size?

 

[ZapperZ]

To argue there is no size to photons and that wavelengths are just abstract properties would seem to totally undermine arguments explaining interference fringes. How could there be interference if there is no size?

I never said they were "abstract properties", whatever that is. You did. I said they came from archaic description of light based on the classical wave property. It got carried over into the photon picture.

You can easily falsify what I just said by pointing out valid physics papers that have made claims about photon sizes.

BTW, where, even in wave decription, is "size" of the wave is required to describe interference? The slit size has to be comparable to the wavelength for a clear interference pattern, sure. But this has nothing to do with the size of "light". That concept is undefined in wave theory. I could get the same interference pattern for the current in SQUIDs devices. What "size" do we consider there now?

Zz.

 

[padraighaz]

BTW, where, even in wave decription, is "size" of the wave is required to describe interference? The slit size has to be comparable to the wavelength for a clear interference pattern, sure. But this has nothing to do with the size of "light". That concept is undefined in wave theory. I could get the same interference pattern for the current in SQUIDs devices. What "size" do we consider there now?

Zz.

Indeed. But if the slit size has to be comparable to wavelength, then maybe single-slit and double-slit experiments are telling us something about the transverse dimensions of photons? While this is not the perspective from which we learn about these experiments, nor is it the intent with with they are conducted, I wonder if there's something useful here to be learned if they were analyzed from this approach also?

 

[ZapperZ]

Indeed. But if the slit size has to be comparable to wavelength, then maybe single-slit and double-slit experiments are telling us something about the transverse dimensions of photons? While this is not the perspective from which we learn about these experiments, nor is it the intent with with they are conducted, I wonder if there's something useful here to be learned if they were analyzed from this approach also?

No. I've described several times on here that the "single slit" diffraction is easily explained via the HUP.

Do a search on here for "marcella". He has a terrific paper on Eur. J. Phys. that derived ALL of the interference pattern without having to resort to any classical wave picture. Out of it, the HUP falls right onto your lap.

If you want to speculate that such a thing has anything to do with a "size" of a photon, then there's nothing to stop you, except that you have to at least realize that you are making nothing more than speculation that isn't shared by professionals in this field. You just have one heck of an explanation to provide on why the slit size can easily be SMALLER and smaller and smaller without somehow squeezing out the individual photon. How does this reconcile with it having a "size"?

Zz.

 

[cesiumfrog]

Perhaps buckyball interference, in the limit of small slits, would provide insight. I was surprised (initially) that interference can be seen even when the wavelength is smaller than the diameter.

 

[padraighaz]

No. I've described several times on here that the "single slit" diffraction is easily explained via the HUP.

Do a search on here for "marcella". He has a terrific paper on Eur. J. Phys. that derived ALL of the interference pattern without having to resort to any classical wave picture. Out of it, the HUP falls right onto your lap.

If you want to speculate that such a thing has anything to do with a "size" of a photon, then there's nothing to stop you, except that you have to at least realize that you are making nothing more than speculation that isn't shared by professionals in this field. You just have one heck of an explanation to provide on why the slit size can easily be SMALLER and smaller and smaller without somehow squeezing out the individual photon. How does this reconcile with it having a "size"?

Zz.

There are lots of references to, but no easily accessible sources, of the Marcella paper. But to a large extent, I'd probably consider it irrelevant unless it provided some terrific new insight into quantum phenomena. QM's curse seems to be that it has great and very precise equations that no one understands. Yet another formalism or path to the same results doesn't address my interests unless it casts some light onto the basics.

I think while physicists use an appropriate level of rigorous control of words and concepts when dealing with very tricky fundamentals they sometimes hide or retreat into these, and hence have a kind of dogmatism to shut out questions that are quite rational and reasonable that they feel uncomfortable with.

As for the single slit diffraction case, since the FWHM respond to the slit width, this is consistent with the photon being distorted or affected and hence having a size. The elephant in the room here is that interference and diffraction strongly suggest photons have transverse extent and therefore I don't see it as being unreasonable to ask about it.

 

[ZapperZ]

As for the single slit diffraction case, since the FWHM respond to the slit width, this is consistent with the photon being distorted or affected and hence having a size. The elephant in the room here is that interference and diffraction strongly suggest photons have transverse extent and therefore I don't see it as being unreasonable to ask about it.

But there is a difference here between asking and INSISTING that what you asked makes sense. I can ask you, for example, for the flavor of blue, or the sharpness of charge. Just because I can put together a valid sentence to ask a question, doesn't mean the question has any degree of validity.

You are asking for the property of something in which that thing were never defined with in the first place. Yet, you still insist that there has to be an answer. So tell me what is the degree of happiness of a neutrino?

Zz.

 

[Gelsamel Epsilon]

I heard neutrinos were loners.

 

[padraighaz]

But there is a difference here between asking and INSISTING that what you asked makes sense. I can ask you, for example, for the flavor of blue, or the sharpness of charge. Just because I can put together a valid sentence to ask a question, doesn't mean the question has any degree of validity.

You are asking for the property of something in which that thing were never defined with in the first place. Yet, you still insist that there has to be an answer. So tell me what is the degree of happiness of a neutrino?

Zz.

So you consider a question concerning fundamental physical properties (the size/scale-lengths) of photons as being comparable to asking about a neutrino's happiness or the flavor of a color. Whatever.

 

[Office_Shredder]

a photon is about a quarter of an inch wide

So you consider a question concerning fundamental physical properties (the size/scale-lengths) of photons as being comparable to asking about a neutrino's happiness or the flavor of a color. Whatever.

So what is the spin of your computer?

 

[padraighaz]

a photon is about a quarter of an inch wide



So what is the spin of your computer?

.25 inches... Sounds reasonable. Any idea if this is wavelength dependent?

As for my computer: S1 = 7200rpm for the disk, s2 = 600rpm for the fan - a guess, and Sz is 23mins 56 secs.

 

[tim_lou]

i think the question is not really unreasonable... I guess what padraighaz means is the "localization" of photon. How can I know where a photon is approximately at with certain probability? and how "wide" would this probability density be? i mean what is the shape of this distribution, is it like a normal curve or what? from what I know, in order to "localize" a light wave, one would need a Fourier summations of varies wave functions with different frequencies... so does the probability density of "one photon" exists? or is it non-sense to ask such question since photons can never be consisted of one frequency solely?

 

[ZapperZ]

i think the question is not really unreasonable... I guess what padraighaz means is the "localization" of photon. How can I know where a photon is approximately at with certain probability? and how "wide" would this probability density be? i mean what is the shape of this distribution, is it like a normal curve or what? from what I know, in order to "localize" a light wave, one would need a Fourier summations of varies wave functions with different frequencies... so does the probability density of "one photon" exists? or is it non-sense to ask such question since photons can never be consisted of one frequency solely?

If this is true, then it contradicts experimental observations. We DO have "single photon sources". However, if such a thing is simply a "wavepacket" consisting of a Fourier sum of a series of wavelength, then it is no longer a monochromatic "photon", and thus, has no single, characteristic wavelength. This means that using a single, unique wavelength to describe a photon is meaningless. Not only that, applying such a thing to something like the photoelectric effect would be wrong!

In other words, in trying to offer the possibility of a photon being defined to have a 'size', something that it was never defined to have, you have thrown out other verifiable experimental evidence.

Zz.

 

[padraighaz]

If this is true, then it contradicts experimental observations. We DO have "single photon sources". However, if such a thing is simply a "wavepacket" consisting of a Fourier sum of a series of wavelength, then it is no longer a monochromatic "photon", and thus, has no single, characteristic wavelength. This means that using a single, unique wavelength to describe a photon is meaningless. Not only that, applying such a thing to something like the photoelectric effect would be wrong!

In other words, in trying to offer the possibility of a photon being defined to have a 'size', something that it was never defined to have, you have thrown out other verifiable experimental evidence.

Zz.

How does the photon having a size contradict experimental evidence?

 

[ZapperZ]

How does the photon having a size contradict experimental evidence?

Pay attention on what he said as in "... I know, in order to "localize" a light wave, one would need a Fourier summations of varies wave functions with different frequencies..."

Now use that and tell me what is the "energy" of a single photon. Did you have to do a "fourier summation" to pick up a "wavelength"? Would there be a "threshold" in the photoelectric effect if it is really composed of a number of different frequencies?

Think about it. If you accept such a scenario, you're throwing out a whole slew of very well-verified experiments JUST to satisfy your assertion that a photon has a "size", something that has no experimental verification. Is this something that you would like to do?

Zz.

 

[delton]

I have always had the same problem of visualizing the size and 'shape' of photons: which we all know have particle properties. There are many confusing diagrams in textbooks which show photons as little "blobs" or wave packets with definite dimensions, or as points even. I am a college freshman and based the infromation I know so far I picture light as spherical waves eminating from a source, so the photons don't have a definate transverse size.. but they do have a definite longitudinal size, or length. Each phonton is a length or "packet" of wave with enough energy to meet the Planck law for a photon E=hf.. so the sperical waves have gaps in them. I would love to hear how my model could be improved, I know it probably has conflictions with higher level quantum stuff... If my my idea of photon length is right, how would you determine the length?

 

[padraighaz]

Pay attention on what he said as in "... I know, in order to "localize" a light wave, one would need a Fourier summations of varies wave functions with different frequencies..."

Now use that and tell me what is the "energy" of a single photon. Did you have to do a "fourier summation" to pick up a "wavelength"? Would there be a "threshold" in the photoelectric effect if it is really composed of a number of different frequencies?

Think about it. If you accept such a scenario, you're throwing out a whole slew of very well-verified experiments JUST to satisfy your assertion that a photon has a "size", something that has no experimental verification. Is this something that you would like to do?

Zz.

Of course I don't want to contradict observation but I don't see how a photon having dimensional scale-lengths contradicts observation as has been asserted. How could this possibly be refuted by the photoelectric effect? As I recall, the photoelectric effect refers to electrons escaping from metals as a result of photons having frequencies greater than a certain threshold. Since there is a blend of frequencies or wavelengths in a packet, and there is a band of electron energies in metals, there is plenty of slack in the system to work with real work distributions of frequencies as opposed to the PHY101 simplistic single frequency infinitely perfect incident waves.

 

[Zelos]

photons can't have size since relativity (i know this is mostly QM stuff but still something from there) would say it has 0 width and with it no radius no size

 

[padraighaz]

photons can't have size since relativity (i know this is mostly QM stuff but still something from there) would say it has 0 width and with it no radius no size

If photons have zero width how could there be double-slit interference if this requires photons to pass through both slits simultaneously? Surely this implies photons are at least as wide as the slits are apart; from this perspective it's not a big deal to say a photon can go through both slits at once like a gust of wind entering a room's windows (a very crude analogy - I know.)

Perhaps the width of photons is not defined because it is something the optical train can set? For example, if the optics for the double-slit light source produces too fine a beam, only one slit is illuminated and no effect occurs; broaden the beam and the interference effect happens? But not being defined is not the same as not existing.

 

[ZapperZ]

Of course I don't want to contradict observation but I don't see how a photon having dimensional scale-lengths contradicts observation as has been asserted. How could this possibly be refuted by the photoelectric effect? As I recall, the photoelectric effect refers to electrons escaping from metals as a result of photons having frequencies greater than a certain threshold. Since there is a blend of frequencies or wavelengths in a packet, and there is a band of electron energies in metals, there is plenty of slack in the system to work with real work distributions of frequencies as opposed to the PHY101 simplistic single frequency infinitely perfect incident waves.

Please note that having a SIZE alone does NOT contradict anything.

This is specific to the notion that it is composed of a Fourier component of frequencies. If a photon indeed is made up of such a thing, then there isn't a "threshold" that corresponds to a WELL-DEFINED energy. Your photon will now have a RANGE of frequencies. You will not have a threshold.

I used to do angle-resolve photoemission spectroscopy for my postdoctoral work. A photon having such a range WILL show up in the spectroscopy. I would NOT have seen a sharp, distinct "coherent peak" either at the Fermi energy or at the Fermi wavevector. The evidence here is too overwhelming.

Zz.

 

[padraighaz]

Please note that having a SIZE alone does NOT contradict anything.

This is specific to the notion that it is composed of a Fourier component of frequencies. If a photon indeed is made up of such a thing, then there isn't a "threshold" that corresponds to a WELL-DEFINED energy. Your photon will now have a RANGE of frequencies. You will not have a threshold.

I used to do angle-resolve photoemission spectroscopy for my postdoctoral work. A photon having such a range WILL show up in the spectroscopy. I would NOT have seen a sharp, distinct "coherent peak" either at the Fermi energy or at the Fermi wavevector. The evidence here is too overwhelming.

Zz.

As I recall, in order to have a finite wave packet, and not a sinusoid of infinite duration, a blend of frequencies (df) is necessary. The narrower the frequency range the longer the packet will be, so lasers, which have a very narrow f-range (df/f is very small) have very long packets compared to photons from other sources. So, you can have a meaningful threshold if the blend refers to a narrow range of frequencies clustered about the mean. Your observations of a sharp peak only means df/f is very small also, not that df/f is zero, i.e. an infinitely long sinusoidal photon.

Therefore, df != 0 which is required for finite packets is not in conflict with observation and is consistent with a packet having size or scale length in the direction of motion and hence it is meaningful to talk about photon/packet size in at least one direction, and therefore it is not absurd to ask about transverse dimension scales/sizes.

 

[ZapperZ]

As I recall, in order to have a finite wave packet, and not a sinusoid of infinite duration, a blend of frequencies (df) is necessary. The narrower the frequency range the longer the packet will be, so lasers, which have a very narrow f-range (df/f is very small) have very long packets compared to photons from other sources. So, you can have a meaningful threshold if the blend refers to a narrow range of frequencies clustered about the mean. Your observations of a sharp peak only means df/f is very small also, not that df/f is zero, i.e. an infinitely long sinusoidal photon.

Therefore, df != 0 which is required for finite packets is not in conflict with observation and is consistent with a packet having size or scale length in the direction of motion and hence it is meaningful to talk about photon/packet size in at least one direction, and therefore it is not absurd to ask about transverse dimension scales/sizes.

Let me get this right. You are actually, seriously, claiming that each photon should be a mixture of SEVERAL different frequencies JUST so you could make a 'wavepacket' to signify its size?

OK, try this. Consider that I have a photon of size of 1 micron. Can you tell me, for example, all the necessary Fourier components to make a wavepacket of that size if I have, let's say, 250 nm wavelength that I have SELECTED via an inteferometer. Remember, all I have in is a cw light source here coming from, let's say, a synchrotron beamline undulator.

Secondly, the "spread" that I observe of my coherent peak is also temperature dependent of my sample. In other words, as I cool the material down to 5K, the coherent peak gets sharper and sharper. Now, even AFTER I deconvolve thermal effects out of the spectral, I STILL get a result that has the peak becoming sharper with temperatures. Yet, cooling my sample should do NOTHING to the "spread in frequency" of my light source. Your insistance that the spread in my spectra is indicative of the spread in my light source doesn't wash here. As I cool the temperature of the material, it should not affect the width of the coherent peak at all IF this is due to the light source. In fact, if I also deconvolve the finite detector resolution, the sharp peak that I get at 5K at the Fermi wavevector is almost a delta function!

In all of this, we have gone through a rather moot argument. You started out by using the 2-slit as your "evidence", and now you're arguing that photoemission can, somehow, contain photons in which, each INDIVIDUAL PHOTONS can in fact be made up of a Fourier sum of frequencies. Nowhere in here did you define what you meant by "size". Is it the size of the slit? But the size of the slit isn't unique! If I see diffraction effects when it is 2 microns, I can also see it when it is 0.5 microns, 0.1 microns! So how does this define a "size"? A ping pong ball cannot go through a slit when the slit is smaller than its "size".

You will notice that you would have the SAME problem, not just with photons, but also with electrons. For example, look at what is known as the 'scattering cross section' in high energy physics. You will see that it isn't a unique number! It depends on the energy of the electrons themselves.

When we DO have some definition of a "size", we have to do it very carefully. We define a "size" for an atom in such a way that we estimate the range of overlap of the valence atomic orbitals. In solid state physics, we measure the crystal lattice constant and use solid spheres as estimates. In other words, we have to DEFINE what we mean by a "size". You can't just use that word as freely as you can with a football or a rock.

If you go back to the photon, you'll notice that THAT DEFINITION is missing! You don't have to believe what I just said. You can go and look it up yourself. Now, considering that we use light in a gazillion different ways in doing our research (synchrotron sources are nothing more than giant facilities of light sources), don't you think that if such a definition has any meaning, that someone would have done it and settle this question once and for all? After all, we tabulate almost everything else about the universe that we know, why not a photon?

For some reason, this issue of the size of a photon seems to be a big deal for you. I thnk I've done everything I can to answer that question. If you thnk a photon has a size dispite the lack of literature support, then there's nothing I can do. At some point, you believe in what you believe.

Zz.

 

[jtbell]

If photons have zero width how could there be double-slit interference if this requires photons to pass through both slits simultaneously? Surely this implies photons are at least as wide as the slits are apart;

This reasoning doesn't work with electrons. High-energy scattering experiments so far have failed to show any finite size for the electron. They are consistent with the electron being a point-like particle, with a tiny upper limit on the possible value of the electron radius. Nevertheless, two-slit interference experiments have been done with electrons, with a finite slit spacing that is much larger than the upper limit on the electron radius.

 

[padraighaz]

Let me get this right. You are actually, seriously, claiming that each photon should be a mixture of SEVERAL different frequencies JUST so you could make a 'wavepacket' to signify its size?

Zz.

Not so I can make a wavepacket to signifiy its size; the fact is you yourself assume they have a size/length otherwise you'd still be sitting at your spectroscope until the end of time waiting for a photon to finish passing through the equipment. If they are finite in time (dt), they are finite in length since s=c*dt. If they are finite in length, then the simple sinusoid is incorrect since it must be at least convoluted with a profile. Even the simplest topphat profile convoluted with a sinusoid will produce a Fourier decomposition with multiple wavelengths; the longer the extent or width of the tophat function, the fewer Fourier components of different wavelengths needed. Either way, a finite packet is actually a blend of components. Since Fourier components tend to be integer fractions of the primary, they would not show up as a broadening of a line in your spectroscope and so I was wrong there - some of the cobwebs are clearing from my memory...



That's what I recall when I got my degree in Theoretical Physics decades ago, so forgive me if I'm a little rusty here. The point being that if a photon is to have finite extent, and not stretch from New York to London, then you need to view it as something like a Gaussian mix of pure sinusoids. So a wave packet is actually a blend of different wavelengths even though it is assigned one through E=hc/lambda.

OK, try this. Consider that I have a photon of size of 1 micron. Can you tell me, for example, all the necessary Fourier components to make a wavepacket of that size if I have, let's say, 250 nm wavelength that I have SELECTED via an inteferometer. Remember, all I have in is a cw light source here coming from, let's say, a synchrotron beamline undulator.

Zz.

But I think your cw assumption is breaking down at the level we are analyzing photons since in the best case scenario for your position, you still have to conceed that even though the device is producing very coherent and pure sources of photons, they are still finite (otherwise they'd have infinite energies) and hence must involve convoluting a shaping function (gaussian/tophat, or other) with a sinusoidal component, and the existence of the shaping wil;l cause any Fourier decomposition to result in many different frequencies.

...

When we DO have some definition of a "size", we have to do it very carefully. We define a "size" for an atom in such a way that we estimate the range of overlap of the valence atomic orbitals. In solid state physics, we measure the crystal lattice constant and use solid spheres as estimates. In other words, we have to DEFINE what we mean by a "size". You can't just use that word as freely as you can with a football or a rock.
Zz.

I agree.

...

For some reason, this issue of the size of a photon seems to be a big deal for you. I thnk I've done everything I can to answer that question. If you thnk a photon has a size dispite the lack of literature support, then there's nothing I can do. At some point, you believe in what you believe.

Zz.

Perhaps. But it seems to me there is some confusion in general understanding of what photons are and their properties, and the reason it's such a 'big deal' to me is that some aspects of physics have always fascinated me even after I left professional research decades ago, and recently I started thinking more about them - the double-slit experiment in particular - and was trying to come to grips with the notion of "particles" taking two different paths simultaneously - hence my interest in how wide a photon is. However, as I've grown older, I'm much less willing to settle for a "that's just the way it is" kind of argument, and I believe such arguments are frequently indications of areas that deserve further consideration.

 

[ZapperZ]

Not so I can make a wavepacket to signifiy its size; the fact is you yourself assume they have a size/length otherwise you'd still be sitting at your spectroscope until the end of time waiting for a photon to finish passing through the equipment. If they are finite in time (dt), they are finite in length since s=c*dt. If they are finite in length, then the simple sinusoid is incorrect since it must be at least convoluted with a profile. Even the simplest topphat profile convoluted with a sinusoid will produce a Fourier decomposition with multiple wavelengths; the longer the extent or width of the tophat function, the fewer Fourier components of different wavelengths needed. Either way, a finite packet is actually a blend of components. Since Fourier components tend to be integer fractions of the primary, they would not show up as a broadening of a line in your spectroscope and so I was wrong there - some of the cobwebs are clearing from my memory...

No I don't. I make zero assumption about its size because I'm NOT detecting it's location, but rather its ENERGY! That has been what you seem to be missing so far - that it is defined as a quanta of energy, not as a quanta of object with definite boundary in space!

Look, we don't have to drag this into utter absurdity. I can easily tell when light has a pencil-beam profile. In fact, I do laser profiling often as part of my job. And if you bother to check the papers of people who do single-photon emission "on demand", you can easily check what processes are involved in such emission to STILL produce "plane wave" states even when the emission of one photon versus another isn't a CW process. Yet, in ALL of these, no where was it ever mentioned about the actual "SIZE" of the photon. Of course, we can make narrow guesses on the PROBABILITY of where it would be within a certain time, but we do this everywhere, even with conduction electrons! Try it! Look at the Bloch wavefunction of the conduction electrons and try to find the "average position" of it at any given time, assuming you find a scheme to normalize the wavefunction in the first place.

That's what I recall when I got my degree in Theoretical Physics decades ago, so forgive me if I'm a little rusty here. The point being that if a photon is to have finite extent, and not stretch from New York to London, then you need to view it as something like a Gaussian mix of pure sinusoids. So a wave packet is actually a blend of different wavelengths even though it is assigned one through E=hc/lambda.

OK, now consider this. If I make a "wavepacket", of light, I actually make a Fourier sum of various other wavelengths, no? HOwever, this assumes that there are MONOCHROMATIC sources of single wavelengths in which I can sum up to produce that wavepacket. Where did these monochromatic sources come from? Other photons? What are the sources that produced such monochromatic sources? What exactly is "mixing"?

And we haven't exactly explore the glarring omission here where you actually produce peer-reviewed papers that support your assertion. Have you read any papers that actually have made any claims that a "photon" is actually a wavepacket consisting of a mixture of a number of different frequencies of... something?

If you think this is not requried on PF, please re-read the PF Guidelines that you have explicitly agreed to, especially on speculative personal theories.

Perhaps. But it seems to me there is some confusion in general understanding of what photons are and their properties, and the reason it's such a 'big deal' to me is that some aspects of physics have always fascinated me even after I left professional research decades ago, and recently I started thinking more about them - the double-slit experiment in particular - and was trying to come to grips with the notion of "particles" taking two different paths simultaneously - hence my interest in how wide a photon is. However, as I've grown older, I'm much less willing to settle for a "that's just the way it is" kind of argument, and I believe such arguments are frequently indications of areas that deserve further consideration.

But you also made a gross misjudgement that the rest of my profession is settling down with the "just the way it is" scenario. Nothing could be further from the truth. As physicists, we are EMPLOYED not to verify things that already work, but to study things that don't, or currently have no explanation. We know A LOT about light and photons. Do we know everything? No. But we do know what we don't know!

Ironically, I think you should listen to your own advice. Remember, I DID NOT SAY a photon has NO SIZE. I said a photon was NEVER DEFINED to have a size. YOU, on the other hand, INSISTED that it MUST have a size. It appears that in this transaction, it is you who have a priori made a decision on the property of a photon (i) before there are any evidence and (ii) before there are any theoretical development out of it. You have decided to ask and study thing with a prejudice already in mind.

I attended a seminar last week on the possible structure of a photon given by a theorist here in our division. Again, this explores the outer boundaries of light beyond what we currently know, including possible results from a photon-photon collider. You see the possibility of photons coupling to gluons via hadronic interaction even though it doesn't have any hadronic content. There are many exotica such as these being explored almost every day! And I can easily tell you that in such a picture, your "fourier sum of various frequencies" would be blown out of the water! So you don't need to tell me about all the boundaries of physics that are out there. I can easily tell you that you don't know the half of what I have come across just within the hallway of my office.

Yet, we must keep in mind of what we DO know already, because those have brought us a huge amount of understanding AND applications. We know quite a bit of the characteristics of light within the range that we work with and what we encounter. No where in any of these is the "size" of a photon is defined. You may not like that, but that is so far the reality. If you think you can make a definition for it, and come up with a measurement of its size, then you may either submit it to a peer-reviewed journal, or do this in the IR forum. It doesn't belong in the main physics forum.

Zz.

 

[padraighaz]

...
Look, we don't have to drag this into utter absurdity.
...
Zz.

Yes indeed. In any case thanks for the effort you put into your responses.

 

[Chaos' lil bro Order]

My guess is that if a photon had a definite size, it would have a rest mass and therefore its speed would be limited to sub C. Since photons travel at C in vacuo, is this not proof that photons have no dimensional size?

 

[Edgardo]

Hi padraighaz,

the photon must not be considered
as a tiny sphere as pointed out by HallsofIvy in the second post, but I think this is not what you thought of, right?

Now, with respect to your question "how wide is a photon?",
in a certain sense you could call the "coherence length" of a photon as your width.

Let me try to explain (The numbers in the brackets refer to the references at the end of my post):
A photon can be described as a single-photon wave packet (probability density, $$|\Psi|^2$$) [1,2],
and you can actually measure the width of a the wave packet. This is done in experiments with interferometers [13], where the coherence length of a photon is measured, and the coherence length corresponds to the width of the photon-wavepacket [3,4,5].

See for example this pdf (ref [3]):
http://departments.colgate.edu/physics/research/Photon/root/P371/lab2wavepackets.pdf
Galvez and his students conducted experiments and you can also view the results here (ref [5]):
http://departments.colgate.edu/physics/research/Photon/root/P371/lab2results.jpg

Basically, Galvez takes a Mach-Zehnder interferometer, which consists of
two arms with two beamsplitters. He sends photons through the interferometer and then measures the count rate. He does this several times, each time changing the length of one arm.

It is in fact possible to describe the photon wavefunction by a Fourier transformation, see [4].
And as you stated correctly, the photon does not have a definite, pre-existing energy before measurement.
You can read this in paper [1] and in other science discussion groups [6,7,8].

The photon is in a superposition of energy eigenstates [2] which implies that the photon's energy is spread and does not have definite value.
The superposition of plane waves leads to the wave-packet.

How wide is the photon actually and is its width constant?

The width $$\Delta x$$ of your photon wave-packet depends on the energy spread, or better to say the spread of the k-vectors $$\Delta k$$.
See this paper by Galvez (this paper is highly recommended!):
http://departments.colgate.edu/physics/faculty/EGalvez/articles/ajpph.pdf (see ref [3]).
Galvez shows experimentally that the photon can have different coherence lengths. In his experimental setup he uses the Mach-Zehnder interferometer, in which he splits up the photon wave packet into two wave packets. These wave packets are then overlapped again at the second beam splitter. Furthermore, he uses bandpass filters, that is filters which let through only certain frequencies (or wavelengths or k-values).
Thus, by using the bandpass filter he is choosing the spread $$\Delta_k$$.
In the paper Galvez gives values for the spreads for two different bandpass filters (see right side of page 132 of the Galvez paper,
in section D):

$$\Delta k = 2 \pi * \Delta \lambda/ \lambda_0^2$$
where $$\Delta \lambda$$ is specified by the two different bandpass filters as $$\Delta \lambda= 10 \rm{nm}$$ and $$\Delta \lambda=0.1 \rm{nm}$$

which leads to coherence lengths of 84 micrometers and 8400 micrometers respectively.

Note that the spread $$\Delta k$$ also leads to an energy spread of $$\Delta E = c \hbar \Delta k$$
(see page 132 bottom left side).

Why does this new spread of $$\Delta k$$ change the length $$\Delta x$$ of the wave-packet?
This becomes clear if you keep in mind the Fourier transformation. Also Galvez writes in his paper the relation between $$\Delta k$$ and the spatial spread $$\Delta x$$ of the wave-packet.

$$\Delta x = 1/ \Delta k$$
(see page 132 top left side, uncertainty principle)

Thus, the smaller your $$\Delta k$$, the bigger your $$\Delta x$$.

Why is it important to have a small spread $$\Delta k$$? A small $$\Delta k$$ results in a great value for $$\Delta x$$, thus your wave-packet becomes long.
This is good, because in order to have interference both packets from the
two arms of the interferomter must overlapp [9,10].

In figure 3a of Galvez's paper you can see what happens if the wave-packets overlap quite well, and
in figure 3b if they do not overlap.

Let me note that another way to interpret the wave-packet of the photon is the count rate, see ref [11,12]

Hopefully, this post was helpful for you.

Cheers,

Edgardo

-----------------

References:

[1] "Heisenberg's Introduction of the Collapse of the Wavepacket into Quantum Mechanics",
Raymond Y. Chiao , Paul G. Kwiat, Fortschritte der Physik Volume 50, Issue 5-7 , Pages 614 - 623.
A preprint of the paper is available here: http://arxiv.org/abs/quant-ph/0201036

[2] "Pure-state single-photon wave-packet generation by parametric down conversion in
a distributed microcavity", M. G. Raymer and Jaewoo Noh, K. Banaszek and I. A. Walmsley.
Phys. Rev. A 72, 023825 (2005). A preprint of this paper is available here:
http://arxiv.org/ftp/quant-ph/papers/0504/0504062.pdf

[3] "“Interference with correlated photons: Five quantum mechanics experiments for undergraduates,” E. J. Galvez, C. H. Holbrow, M. J. Pysher,* J. W.

Martin,* N. Courtemanche,* L. Heilig,* and J. Spencer,*” American Journal of Physics 73, 127-140 (2005). You can download the paper here:
http://departments.colgate.edu/physics/faculty/EGalvez/articles/ajpph.pdf

[4] http://departments.colgate.edu/physics/research/Photon/root/P371/lab2wavepackets.pdf

[5] http://departments.colgate.edu/physics/research/Photon/root/P371/lab2results.jpg

[6] http://lists.nau.edu/cgi-bin/wa?A2=ind0205&L=phys-l&P=48869
[7] http://www.lepp.cornell.edu/spr/1999-02/msg0014640.html
[8] http://www.lepp.cornell.edu/spr/1999-02/msg0014733.html

[9] ieeexplore.ieee.org/iel5/9181/29129/01314185.pdf?arnumber=1314185
"Experimental test of the delayed single-photon self-interference effect", Nicklas Ohlsson,
mattias Nilsson and Stefan Kröll

[10] "Delayed single-photon self-interference", R. Krishna Mohan, Baozhu Luo, Stefan Kröll and Alois Mair,
Phys. Rev. A 58, 4348–4358 (1998) [Issue 6 – December 1998 ]

[11] "Single-photon and two-photon wavepackets in spontaneous parametric
down-conversion", Yoon-Ho Kim, ieeexplore.ieee.org/iel5/8993/28536/01276170.pdf

[12] "Measurement of one-photon and two-photon wave packets in spontaneous parametric downconversion",
Yoon-Ho Kim, JOSA B, Vol. 20, Issue 9, pp. 1959-1966

[13] "Coherence length of photons from a single quantum system", Jelezko et. al,
Physical review A 67 (2003)

 

[Chaos' lil bro Order]

Great post Edgardo, well thought out and fully referenced, a true gem!