Simple question with a not so simple answer probably: Why can't photons be thought of as solitons? Assuming for a moment that there is some kind of a space-time medium, could a photon not be a soliton in such a setup? I have read something against it, which stated that there are no processes that could produce such a wave. For instance an electron giving up energy in the form of a photon does not oscillate in the right way or at all. Would such a solition produce the kind of effects one sees with the double slit experiment? I would think that the idea of photons as solitons would be a straight forward idea to come up with, but I couldn't easily find anything relating to this idea on the internet (probably because I had been searching for "wave packet"). That makes we think that there is probably a pretty obvious reason that it fails. I am working from the premise that a space-time medium exists, but this is not the accepted model, so is this then the primary reason that it fails? Also, would a light beam made up of individual soliton-photons give the same result with the double slit experiment? Here are two links I found that discusses the idea. HERE and HERE. They are both from ten or more years ago though, so how did they fail? The first one is just an abstract, but the second link is a more comprehensive treatment of the subject.
In order for solitons to arise, the medium in question has to be both nonlinear and dispersive, and AFAIK there is no evidence that this is generally the case with photons (hard to see how vaccum is nonlinear or dispersive, for example). You can indeed produce electromagnetic solitons in nonlinear dispersive media, but these are much more specific beasts than photons generally.
IIRC, nonlinear means that the phase velocity increases with the amplitude of the wave, and dispersive means that the phase velocity decreases with frequency. These two effects work to balance each other (the first tends to sharpen wavefronts, while the second tends to smooth them out), which results in a stable solution called a soliton. Unless the medium has both of these properties, and in the correct proportions, you don't get solitons. I am not familiar with superfluids, so I couldn't say anything about that. It's been quite a while since I dealt with solitons, for that matter.
ok, thanks. Anyone else maybe? Would a superfluid medium show dispersive properties as well as nonliniear speeds depending on wavelength?
From Wikipedia: I can create and destroy photons, so this seems to violate the first criterion? From the particle physics point of view, solitons are objects which cannot be captured in perturbation theory. They are specific solutions to the equations of motion of the theory, and have very specific properties on the boundary at infinity. Photons do not satisfy these criteria, either: they are completely understandable within perturbation theory, and a photon gives none of the properties we ascribe to solitons at the boundary of the theory.
This review looks a bit technical, but it turned up in a google search: http://physics.usc.edu/~vongehr/solitons_html/solitons.pdf
Can I maybe ask for a bit of a laymans explanation of this? Please Register or Log in to view the hidden image! Wiki defines perturbation theory thus: "Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem. Perturbation theory is applicable if the problem at hand can be formulated by adding a "small" term to the mathematical description of the exactly solvable problem." Are both groups of photons and single photons only solvable using perturbation theory? What is the limitation that renders them not solvable exactly? I hope my questions make sense. That link is unfortunately waaaay to technical for me.Please Register or Log in to view the hidden image!
Probably true, but in many cases solitons can ONLY be understood in terms of perturbation of the characteristics of the medium they are traveling thru. I think Quadraphonics in post 2 & 4 is fully correct. I was in a special 5 year experimental program at Cornell as undergraduate and had Lynn M. as my friend. He later went to Bell Labs and spent most of his many years there working to understand and develop photon solitons in optical fibers. The typical glass has dispersion dominate, and since all photons are of finite length, they have Fourier frequency components that travel at different speeds. This limits the minimum spacing between photon bits in ordinary optical fibers. Lynn over came this limit. He may have been the most famous* of my class mates in that special, very tough program called Engineering Physics. (Too tough so Cornell dropped it a few years later. It met all the requirements of both the engineering and liberal art schools for graduation.) *Bell Labs management wanted him to drop idea - he refused and they did not want to fire him. There were several long articles in the WSJ and others about all this. At least some high data rate optical fibers do now use Lynn's solitons.
I think that you and Pete are referring to different things by "perturbation" here. I won't go into the gory details, but I think that all three of us basically agree. ??? Last I heard, Cornell still had Engineering Physics??? I came close to going to that program as an undergrad, but opted for college in a warmer, sunnier climate instead. Or perhaps it's a different program under the same name...
For soliton like structures in modern field theories, I thoroughly recommend David Tong's notes: http://www.damtp.cam.ac.uk/user/tong/tasi.html Enjoy.
Yes, it continues as 4 year program in the Engineering College only now, but there may be a slight difference in the offical name. You would have fit in well - we were an already talented group, I less so than most, as I came from the the public schools of West Virginia. I think part of the reason I got in was there was a regional scholarship not used for several years and my SATs at least equaled their minimiums. They expected me to be in the nearly 50% that busted out or transferred to easier course of study, but I worked like two dogs, and made it thru.)
They just reorganized things. Cornell has both a Department of Physics (http://www.physics.cornell.edu/home/) and a School of Applied and Engineering Physics (http://www.aep.cornell.edu). The former is in the College of Arts and Sciences and the latter is in the College of Engineering. Both are tough as all get-out. My best man at my wedding many years ago is a Cornell Physics grad. Me, A&EP.
Allrighty then.:shrug: How about a superfluid? I mean, they show the ability to form quantised vortices under certain circumstances. Also, if no internal friction occurs in the superfluid, would a wave then propagate indefinitely through it or would it still dissipate (soliton or no)?
What do you mean? I don't really understand your question... One can draw analogies between various aspects of condensed matter physics and quantum field theory.
BillyT said: My question is if the perturbation characteristics of a superfluid would allow for solitions? Then a separate question: If no superfluid of any kind could allow for solitons in the traditional sense, would standard waves be able to propagate indefinitely through a superfluid without dissipating? If the answer is yes to the second part, then how does that differ from a soliton? I am sorry, it must be pretty obvious that I know next to nothing about this stuff, so please be patient with my ignorance. Thanks for the replies so far (on topic or not).
to Kalster: I do not know much about super fluids but think the quantized vortex does not travel.* They may be remarkable in lack of disipation; but that is not a characteristic of solitons. I think all solitons do have some disipation AND TRAVEL. (Certainly it is often possible to restore the energy loss to a soliton) The heart of the soliton idea, AFAIK is a constant shape disturbance of some medium that travels. Thus, I would need some re-education before I could consider calling a quantized vortex a "soliton." ---------- *Perhaps it can? If so, does it constantly change the atoms that are in it (like a sound wave pulse) or do the same atoms "plow thru" with zero friction?
As far as I understand it, no. The topological properties that make superfluids exhibit quantum vortices are exclusive of those required for solitons, in my very limited understanding. Look for the Wikipedia page on "topological defects" for more info... I may be wrong, but I think such a property is what makes superfluids "super" in the first place, no? Depends on what definition of "soliton" you use, but most of them include the properties that the pulse shape does not change (which is stronger than the *energy* not dissipating), and that they only exhibit certain specific interactions with other solitons. More technical definitions of solitons define them simply as certain solutions to certain classes of nonlinear partial differential equations, and so if your system is not described by some such set of equations, you can't call what comes out of it a "soliton."
