Photon Size: Uncertainty Principle & QM Explained

[sophiecentaur]

But in practice there is something special in that photons at 200 nm are already in the UV portion of the EM field. Ordinary light microscopes hit the diffraction limit of visible light just above the 200 nm limit or at 1 PHz. AFAIK 200-300 nm is exactly the diffraction limit of visible light.

What you seem to be talking about is the probability amplitude of finding an electron which is different from photons wavelength. Or are you saying they are related?

This seems to imply that my impression was correct in stating that -

Different parts of the Em spectrum(you mean?) will diffract differently for a given obstruction, of course; their wavelengths are different and so the structure is a different size in wavelengths. Also, the energy of the photons will be different so the effect of the material may be different (absorption / refractive index etc.) . But what has that got to do with the Quote "Width".

When I use the term probability, I mean that the classical optics of diffraction (the pattern) give the probability that photons will be detected in different locations (the light and dark areas). But this has nothing to do with the 'size' of the photon.
Try reading Cthugha's last post if you want to go further than the elementary level.

 

[Maui]

Different parts of the Em spectrum(you mean?) will diffract differently for a given obstruction, of course; their wavelengths are different and so the structure is a different size in wavelengths. Also, the energy of the photons will be different so the effect of the material may be different (absorption / refractive index etc.) . But what has that got to do with the Quote "Width".

Length and width are dimensions and properties of size and volume. I don't see how Cthugha's post supports your evasive explanations so far. Certain wavelengths are diffracted by certain widths. What is there to explain?



What do you mean by 'structure of photons'? If they have a structure and based on this structure they are diffracted below a certain limit(measured in nm as are all spatially extended objects), how is that not a practical limit for photons of visible light?

 

[sophiecentaur]

Length and width are dimensions and properties of size and volume. I don't see how Cthugha's post supports your evasive explanations so far. Certain wavelengths are diffracted by certain widths. What is there to explain?



What do you mean by 'structure of photons'? If they have a structure and based on this structure they are diffracted below a certain limit(measured in nm as are all spatially extended objects), how is that not a practical limit for photons of visible light?

Chuga's post is at a much higher level than what we are discussing. I am pointing out that your ideas are not (even) consistent with elementary ideas about diffraction. (The specifically 200nm bit is a total red herring, for instance as it rerfers to one particular circumstance. As I said, diffraction occurs at all wavelengths). It is you who are suggesting (by implication) a structure for a photon. Follow up on what Chuga's references if you want to talk about 'extent'; it certainly has nothing to do with any ideas of "width" of a photon to explain diffraction. You are trying to over simplify things. I am being evasive, if you like, because all I can do is to point out the inconsistencies of what you are saying. If you cannot see that then how can you move on to the more meaty stuff that Chuga and others are writing about?

 

[Maui]

Chuga's post is at a much higher level than what we are discussing. I am pointing out that your ideas are not (even) consistent with elementary ideas about diffraction. (The specifically 200nm bit is a total red herring, for instance as it rerfers to one particular circumstance. As I said, diffraction occurs at all wavelengths).

Yes, it occurs at all wavelengths and I never ever questioned that(I wonder why you mention it at all). I did say the plain obvious though - diffracton occurs at all wavelengths at specific slit widths corresponding to light's wavelength.

It is you who are suggesting (by implication) a structure for a photon. Follow up on what Chuga's references if you want to talk about 'extent'; it certainly has nothing to do with any ideas of "width" of a photon to explain diffraction. You are trying to over simplify things. I am being evasive, if you like, because all I can do is to point out the inconsistencies of what you are saying. If you cannot see that then how can you move on to the more meaty stuff that Chuga and others are writing about?

I see no coherent statement in Cthugha's on the relationship between a photon's lack of spatial extension and its practical wavelength implications -- he admits there are different scales of length all valid for photons(if I understood correctly). I have stumbled upon similar discussions in the past and they end inconclusively which seems to highlight that quantum theory is obviously neither perfect nor complete theory and a more fundamental theory would better explain photon behavior and have fewer conceptual issues(which all seem to spring from attempts at realism in the micro realm). That's hardly surprising given that the person who discovered the duality of photons said the following:


"All the fifty years of conscious brooding have brought me no closer to answer the question, “What are light quanta?” Of course today every rascal thinks he knows the answer, but he is deluding himself" - AE

 

[sophiecentaur]

I am beginning to see part of your problem here. Diffraction occurs for all wavelengths and with all sizes of obstacles. There is always a pattern (never an abrupt transition) whichever combination you choose; truncation in space will result in a variation in the amplitude of the beam (Fourier). You seem to be claiming otherwise. This is in a classical context but you really should clear that up first.
I also repeat my earlier question which is - where does the "width" of the photon, to which you referred earlier, come into the formation of a diffraction pattern? Can we please clear this up before moving on?

You see, I have never read anything of substance that suggests that the extent / width / length of a photon has any real meaning. It has either zero size or unbounded extent, depending on where you are considering it. Nowhere have I found anyone who shows it has a particular 'size', related to its wavelength.

However clever Albert was, he died a long time ago and things have actually moved on a bit since his time. He was very right about many things but that is as far as it goes. He was fallible (and treated his wife very badly, I believe.)

 

[Cthugha]

It seems most physicists think of photons as part of the EM field which is of infinite extent and 'photons' with definite and detectable properties as excitations of that field upon measurement.

The meaning of the term 'photon' has unfortunately undergone several changes over the decades and the same term has been used for two rather different concepts which is unfortunate.
In the old days of QM, Dirac and others used the term photon for the modes you get in a spectral decomposition of the light field into monochromatic modes with discrete occupation number and fixed energy (and thus of course infinite extent in time). With the arrival of quantum optics in the sixties, a photon rather is an eigenstate of the photon number operator. That means pretty much every state which contains EXACTLY one photon (or one photon per pulse for pulsed light). These can be polychromatic and have pretty much any spatial and temporal shape. Two very different concepts, but unfortunately a single name. The first concept is a useful tool for theorists (but not a state actually realized due to the infinite extent). The second concept is what people actually realize in the lab when they speak of single photon states.

Yes, it occurs at all wavelengths and I never ever questioned that(I wonder why you mention it at all). I did say the plain obvious though - diffracton occurs at all wavelengths at specific slit widths corresponding to light's wavelength.

The problem I see with trying to attribute the diffraction limit to a property of photons is that the diffraction limit is usually rather considered to be a description of the imaging system used. It gives the minimum diameter of an Airy disk in imaging which is the wavelength divided by two times the numerical aperture of the system, where the latter depends on the refractive index of the material and the focusing angle with an optimal value of roughly lambda/2.7 to lambda/2.9 (which roughly gives the mentioned 150-200 nm). However, there are several material and design parameters entering here. Even further, the diffraction limit applies to a certain imaging technique: confocal microscopy. You can easily get better resolution by going to a 4 pi microscope. Alternatively, one can also use STED microscopy or go to near field techniques like total internal reflection microscopy to get sub-wavelength resolution. Each technique gives its own limit.

Also, one can use interferometric techniques and show that for some states - even classical ones - several photons can be way better localized than one photon alone (see e.g. Phys. Rev. A 70, 041801(R) (2004), "Subwavelength coincidence interference with classical thermal light"). In a nutshell, the point I tried to make is that there are many different types of states of the light field and while it might seem attractive to connect some characteristic length scales (like wavelength) of the field with some "true" spatial extent for some special states, it usually does not work out in the general case.