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Getting to grips with Feynman

  1. Oct 21, 2007 #1
    Hello all.
    Firstly, know that I need a little handholding.

    We are told that in the detail, the actual behavior of matter is better modeled with quantum theory concepts, apparently to a impressively proven accuracy, even if the mathematical aids involve counterintuitive, though useful, notions. Even so, I do expect the concepts to model everything, even large scale slow moving lumps at huge distances. I am happy to reach for Mr. Newton's handy handbook if the Quantum Theory effects become small enough to ignore.

    Hence my first Feynman diagram. An electron approaches another, and they repel because as they get close, a photon passes between them with enough energy to give it momentum in a new direction. Here
    The little photon, shoving off from one electron, changes its direction, and then hits the other electron, and sends it aside also.

    I know I can launch a couple of charged balloons together, and they repel. I can hang them up from a single hook in the ceiling, and they stand apart for hours. I do not notice any photons passing between them, even if I start shoving them about. Is there really any radiation passing between them at some frequency hard to observe? Does it actually happen?

    I observe electronic forces repulsion in large masses (balloons) at huge distances (many centimetres) from billions of these together, presumably furiously repelling each other (and exchanging photons) on the same balloon. But the other balloon is a bit further away! How is this scenario represented in using Quantum concepts?
    Last edited: Oct 21, 2007
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  3. Oct 21, 2007 #2


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    those photons you see in those Feynman diagrams are virtual photons.
  4. Oct 21, 2007 #3


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    To expand a little on the above answer, these virtual photons are what "mediate" the electromagnetic force. To take your example, two electrons repel each other due to the electromagnetic force, and we say that there is an exchange particle or mediator of the electromagnetic force (the virtual photon) transferred between the two electrons.

    The most important things to understand on Feynman diagrams are the things that things that are there to being with, and the products of the interaction. We know less about what goes on during the actual interaction, since it is far more difficult to observe what is going on, than what the results are.
  5. Oct 21, 2007 #4


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    I think every photon is virtual if you extend the diagram to the whole universe.
  6. Oct 21, 2007 #5
    I thank you folk for the replies. :smile:

    So are we saying that close up to the region of a impending collision, we enter this 'virtual world' where there is some (low) probability almost anything could be the outcome, and one (quite high) probability that electrons repel in ways we can often see?

    More.. that there is this uncertain period, and region, where we don't know, and can't look, but we can postulate 'virtuals' like virtual photons, that can greatly aid us in calculating the later outcome?

    If quantum concepts are to be applied in explaining matter behaviour, they must not be bounded by caveats that only bring them into existence when the distance is small, or the speed exceptional, or (astonishingly!) that we must not be looking at the time. The charged balloons repel, and I am asking, even qualitatively, why?

    The Feynman graphs are, I think, very very clever, in providing a way of diagrammatically keeping track of a bunch of tortuous calculations, and they lead the mind to a (sort of) physical explanatory landscape. I still have an awkward time trying to see the charged balloons in terms of quantum concepts.
  7. Oct 21, 2007 #6
    Good questions.
    See if this helps
    Also, the nature of a photon alone gets very tricky,but there are some relevant points here: http://www.math.ucr.edu/home/baez/photon/schmoton.htm.

    Some key points:
    * Electrons can exchange arbitrary numbers of photons of arbitrary energy in quantum mechanics. The quantum "probability amplitude" requires the amplitude for each possible type of exchange (0 photons, 1 photon, etc) to be calculated separately and then added according to the standard rules of QM.

    * In the above picture, you can think of Heisenberg uncertainty as explaining away the lost/gained energies of the electrons in these exhanges over short periods of time.

    * The dominant contribution to brief interactions interactions between electrons comes from the quantum interference of a 0-photon exchange and a 1-photon exchange.

    * The picture described here is the "perturbative picture": the idea of adding 0-photon exchange + 1-photon +... is a "perturbative series expansion", which is used in approximating the full calculations that we wish to avoid, and this series must be cut off in practical calculations. Therefore the *way* in which these "virtual" photons are appearing is an artifact of this approximation scheme; nevertheless, we still say that the electrons interact with quanta of the Maxwell field (photons).

    * As you said, we know electrons are supposed to be sources of classical electric potentials, etc satisfying the classical Maxwell equations. A potential can be formed between charged objects by a "coherent state" of a large number of photons, a state in which there is an uncertainty in the number of photons. EM radiation (light) is also a coherent state.

    * Energy conservation is tricky to get used to. In the perturbative picture, electron A at rest emits a virtual photon, which is absorbed by electron B at rest (by rest I mean the expectation value of momentum is zero). After adding the 0-photon exchange amplitude (see 1st link above for details), electron B's wavefunction is shifted in momentum space, which results in a shift of the position space wavefunctions seen as repulsion. The problem: B now in an non-zero energy state, while the overall system seemed to initially have none. The resolution to this problem is that we are looking at the approximation scheme of the perturbation picture, and there will be a process in which a photon is exhanged the other way, from B to A, with the same energy so that, within the time allowed by Heisenberg uncertainty, the (expectation value of) energy of B goes back to zero. So, one cycle can be thought of as: B goes into a non-zero energy state with wavefunction shifted in position space, then B returns to its initial energy state within the allowed time uncertainty (but not position state). The same can be thought of for A. This cycle is iterated for each 0+1-photon exchange so that the electrons iteratively move away from each other, while energy is "iteratively conserved". This strange picture of energy conservation arises because, again, we are looking at a strange picture of the actual quantum mechanical process (i.e., the perturbative approximation picture in which virtual photons are exchanged). The QM of an electron interacting with a classical potential is more familiar to us, where we say "energy conservation follows since the expectation values of kinetic + potential energies are constant up to allowed uncertainty". But to get the calculation of an electron sitting in a non-classical background, we resort to this whole approximation scheme.

    * Even though the way virtual photons appear in our calculations is a bit artificial, we can hand-wave the following. Virtual photons being exchanged between electrons, e.g. between those in the light-detecting molecules of the eye and some outside electrons, cannot be seen since they are not increasing the energy of the electron (exciting it) in these molecules outside of the usual temporal uncertainty. A feature of "real" photons, in contrast, is that when emitted from an electron, e.g., they lower the energy of that electron for a longer period than the uncertainty principle admits, and if enough of these photons are of the right energy they can go excite enough electrons in our eye molecules so that we detect light.
  8. Oct 21, 2007 #7
    I have a question, if a photon is exchanged between the two electrons as in the diagram, why is it that the e- emitting the photon recoils only when it is close to another e-? Or, why is it that it emits a photon only when it come close to another e-? This doesn't make sense to me as according to this theory an e- should be continuously emitting photons regardless of how close it is to another e- and therefor be continuously loosing energy. Do we observe a decrease in energy for the e- which emitted the photon and a gain in the absorbing e-?

    Edit: I just read your post javierR and it explains some of this(sorry should have read the entire thread first) but it doesn't answer why charged particles emit these virtual photons only when they are close to another charged particle. Or maybe you did and i just don't understand as some of your explanations are still a little beyond my current knowledge base of QM.
    Last edited: Oct 21, 2007
  9. Oct 21, 2007 #8


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    Above all, Feynman loved simple. As my professors used to tell me, the less math you need for an argument, the better. And that's exactly what Feynman did with his diagrams. His Nobel compatriot, Julian Schwinger, solved the same problems as Feynman with a highly difficult, highly mathematical approach. Feynman's diagrams cut the work done in the Schwinger style by half or so. Feynman made the math, relatively speaking, easy.

    Like a systems engineer's block system diagrams or a programmer's flow charts, Feynman diagrams are visual aides, metaphorical images, figurative language in fact. In no way do they directly describe how the world really works; in QED, for example,they provide a clear way to get to the integrals required to compute a matrix element. A diagram, for example, shows initial and final states, and it can be decomposed, graphically into multiple diagrams, each with differing states intermediate between initial and final states. So one diagram can be equal to several diagrams; and then there are "partial summation" diagrams, and on and on. The diagrams are shorthand for perturbation terms.

    The entire business of "virtual" is an artifact of perturbation theory. Where, for example are the virtual particles in the exact solutions for the Coulomb scattering of an electron from a massive positive charge? (Well, almost. If the system describes a resonant scattering state, for example, always with a complex mass --the imaginary part must be positive(the resonant state has time dependence dominated by, exp(-s t). The resonant state can be and is called virtual, as it is in many parts of physics. Again, "virtual" is a great piece of figurative language, a sound-bite if you will.
    Reilly Atkinson
  10. Oct 21, 2007 #9
    Wow - huge food for thought. Thanks also to you folk who don't mind that I am in a steep learning curve here.

    Probably the most difficult thing to find a satisfying conceptual model for is any situation involving 'force at a large distance', experienced as electrostatic and magnetic. [We are all happy to set gravity aside for the present!] The balloons repel because allegedly traveling between them are quantum 'force carrier particles'. I wish they were more obvious! Also, of the 6 (12?), which are likely to be doing the work?

    Another thing that I wondered about when considering the electrons about to collide was .. is it only one energetic photon that thrusts them apart? If so, how is it decided which electron gets to launch it, and accept the recoil? Maybe its a whole blizzard of photons, going both directions. Do each deserve a new Feynman diagram? OK then - I jest a little, but I am at the stage where I still need to read lots from the links you folk provided earlier. I am asking if this photon is postulated as real - or is it a calculation aide artifice? Have we found a stunningly accurate mathematical fairytale fantasy analogy - or are we serious that this is the way all is made? I am guessing that the term 'virtual' is the clue that this photon is an intermediate math aid, and not of the sort that lights up a room.

    The force on the balloons is real and substantial. My hair rises and sticks out when I get charged to more than about 90kV while standing on a polystyrene tile! There is nothing "virtual" about these things. If the virtual photon exchange was a useful calculation concept, then we are still left with "From where comes the force and what is its nature? This is different to " I know how strong it is, and what direction it acts, and what other stuff might eventually appear".

    In considering these conceptual models, I am struck by how strongly they preserve the mechanical collision imagery. A Feynman diagram starts out like a billiard table scenario. Even so, the more I mess with them, the more impressed I get.
    Last edited: Oct 21, 2007
  11. Oct 21, 2007 #10


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    We will always only be sure about the second part, and the first part has always some extra philosophical input to it.

    In fact, one can even find a 'degree of real-ness' for them: the measure by which the intermediate particles are "on shell" or are "off-shell" (virtual) ! The more the intermediate particle is on shell, the more a Feynman graph can be considered as a kind of billiard table scenario, and the more the intermediate particle is off-shell, the more you have to see it as "a contribution to an interference phenomenon".

    In order to help understand the last part, think of a (classical) light wave going through a parallel-plate piece of glass (a Fabry-Perrot interferrometer). The right way to find out the reflected and transmitted waves is by solving the Maxwell equations with the correct boundary conditions at the interfaces air-glass and glass-air, right ? Out will come that with an incoming plane wave with wavevector k and amplitude Ai, you'll find a transmitted wave amplitude At and a reflected wave amplitude Ar.

    But you can also approximate that solution, by considering only a single boundary at a time, using (I think they are called) Fresnell's equations: at a single boundary, you have a transmission T and reflection R coefficient. And now, you can say that the incoming light with amplitude Ai is first reflected at the first boundary: R Ai is a contribution to the reflected wave, and T Ai continues in the glass. It evolves through the glass (phase factor f = exp(i 2 pi d/lambda) ) and then hits the second boundary: reflection f R' T Ai and transmission f T' T Ai.
    The reflected part goes back again to the first boundary, where it can be transmitted, and contribute to the overall reflected wave (contribution f^2 T' R' T Ai ) and is reflected back (f^2 R' R' T Ai) to go again to the second boundary etc...

    So you can see that there are different "processes" in this where the light gets through directly, where the light makes one bounce, where the light makes 2 bounces, ... You can make a simple drawing of each of these terms, and call the propagator "f", and the boundary interactions "R'" and "T'". You hence write down your "Feynman graphs" for each contribution.

    In the end, you have to sum all these contributions in order to find the right amplitude and phase of the transmitted and reflected waves.

    Now, did the light really bounce several times around ? Or did the EM field just follow the Maxwell equations (where no such bouncing appears!) and we found a mathematical trick to solve the Maxwell equations ? Who'll tell ?
  12. Oct 22, 2007 #11
    If anyone could answer this question of Sneills I'd be greatly interested in the answer...

    So either Sneills point about how does the electron know when to emit a virtual photon, or the electron is continuously emitting virtual photons (I'm not too worried about the energy thing as I assume QM finds some way around that), but yes, how does the electron "know" which virtual photons to recoil from, as if it were continually emitting them in every direction the net force would be zero. This indicates some other form of field that tells the virtual photons either where to point or the like, to describe the change in motion...again back to a field. Also how does one photon "know" the speed to be emitted so as to cause an equal change in momentum for both electrons? I don't like using the term "know" but there is little else for it.

    And is it, or will it ever be possible to measure an EM force to the degree so as to see if it is quantised to the degree predicted by QM? Millikan got some fairly accurate measurement going on, and that was a wee while ago...

    Also am I correct to assume that the reason the EM force decreases with distance is there will be less virtual photons hitting the electron?


  13. Oct 22, 2007 #12


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    In classical mechanics, how does the Sun know when to emit a force ?
  14. Oct 22, 2007 #13


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    Those are Stokes's relations. That's a nice analogy, anyway! You can even carry it out a bit further: if the refiection coefficient, R, is small, you get a very good approximation by considering just the first "bounce" of the wave between the two surfaces, and ignoring the following "higher order" ones. This is similar to being able to get away with considering just the first-order Feynman diagrams, for some purposes.
  15. Oct 22, 2007 #14


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  16. Oct 22, 2007 #15


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    Now that I'm in the office, I can check my optics books (Hecht, pp. 136-37, and Pedrotti^3, pp. 184-185). The Stokes relations are

    [tex]tt^{\prime} = 1 - r^2[/tex]

    [tex]r = -r^{\prime}[/tex]

    The Fresnel equations are the ones that relate r (for waves polarized parallel or perpendicular to the surface) to the angles of incidence and refraction.
  17. Oct 22, 2007 #16


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    Allegedly is a good word, in this context. The argument goes something like: QED is, we presume, the most basic of E&M theories. It's key factors are an assumed three-point interaction between photons and charged particles -- making Bohr's idea central to QED, and standard quantization of fields -- shortcuts to avoid tons of Fock Space manipulations.

    Wish they were more obvious? Why do you see the balloons?

    There are at least a few approaches that can get you from the QED-photon approach to good ''ol Maxwell" approach; or should I say alleged approaches. A quick and dirty approach is to do everything in momentum space, in which case the classical and quantum versions of the equations of motion are quite similar. Use the density matrix of you choice, but one that gives a good account of the statistical properties of the environment and you are home free. You can also go there via coherent fields, via the WKB method, and so forth. Yours is an excellent question, but one that has been asked and answered many times over the past 80 years or so.

    First, you should be impressed by Mr. Feynman's diagrams and approach; they totally revolutionized physics, in quite a short period of time -- just look back at the pre- and post- Feynman literature. The differences are nothing short of amazing.

    Photons are postulated, period.(They allegedly have something to do with reality.) And yes, they are indeed calculational aides, AS WELL AS conceptual aides, and the harbinger of 20th century physics.

    Your idea of "virtual" as an intermediate math aide is correct, as I discussed in my earlier post.

    Maybe times have changed. When I learned and taught this stuff, the word was "These diagrams are seductive, but their lure of reality must be overcome by the practicality of computations and theoretical explorations." Nobody, as far as I know, claims that each term in a perturbation theory expression describes realty; only the sum does.
    the same is true for diagrams; only the sum represents reality.

    I guess by your ascription of "fairytale fantasy" to QFT, Feynman, ..., you would say the same for Newton, Maxwell, Carnot, Planck,. Boltzman, Einstein,.......... I would certainly hope so.

    Most of the answers you want are discussed, perhaps not always directly, in the literature, including in lots of texts.

    Reilly Atkinson
  18. Oct 22, 2007 #17
    I don't have to post anything much more here. This site is so packed with tutorials and information, its going to keep me absorbed for awhile. Especially, its good information! I have had to waste time untangling turgid phraseology in patents (patentese?), which turned out to be fantasies of a less useful sort than a valid mathematical abstract.

    About the photons warding off the impending electron collision.. :smile:
    The photons coming from the balloons that allow me to see them, and appreciate the colours, are of the same sort that would light up a room. With the illumination level low enough, I could display individual photons arriving, as speckles on an image intensifier, steadily building up until the balloon shapes become obvious. I hope they are not 'virtual' !
    What I was after was those responsible for the substantial force, operating over a huge (!) distance of many centimetres, made by these 'virtual' photons that aim very accurately.

    However - I have taken on board the point about 'virtual' photons, and I accept that they are mathematically useful in much the same way as Maxwell's 'displacement current'. A friendly conceptual fiction thrown in 'to make the equations come out right'. When the result is seen to accurately model physical experience, we begin to need a better story, or maybe we just live with its usefulness. I think Omega(-) started out as an equation filler, until it got found for real!
    Caution though. We once had phlogiston invented with the property of having 'negative weight', and Tycho Brahe had tables of celestial data so accurate he had a right to believe planetary motions involved epicycles.

    Esp. the replies from reilly and vanesch and javierR are really helpful - many thanks.
  19. Oct 23, 2007 #18
    I assume you're meaning gravity here. In classical mechanics theres a gravitational field that acts on mass. There is no emitting or gravitons or the like that causes gravity i don't believe.

    Anyways gravity is attractive and although same principle as repulsive I think, it'd be easier for me if we talk about say two electrons coming together...like charges repelling. You do know what Sneill and I are asking don't you? I just don't see a feasible explanation to this...


  20. Oct 24, 2007 #19
    a question

    why do people say virtual particles come (only) from pertubation calculation, what about free fields? In the free propagator the integration goes over the whole momentum as well, including 'off shell' momentum.
  21. Oct 26, 2007 #20

    There is this book by Anthony Zee "QFT in a nutshell", where the author couples a free quantum field to a classical source, gets a propagator and integration goes over all momentum. No pertubation theory, no Feynman diagrams, but off-shell, 'virtual' particles.

    Why the claim of others virtual particles come only from pertubation theory?
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