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QED BY RICHARD FEYNMAN

Ricard Feynman was one of the twentieth centuries greatest physicists. Born in New York in 1918, Feynman graduated from M.I.T. in 1939 with a bachelor’s degree before moving to Princeton to complete his doctorate in 1942.  During World War 2, Feynman worked at the Los Alamos laboratories in New Mexico before eventually taking a permanent professorship at the California Institute of Technology in 1959. Feynman shared the Nobel prize for physics in 1965 for his work on quantum electrodynamics (QED). The book was published in 1985; he died, after a long illness, in 1988.
Richard Feynman has always been regarded as a great teacher due to his enthusiasm and his ability to provide fairly simplistic explanations for what are anything but simplistic subjects. Unlike some teachers (and I have met many!), who stand up in front of their audience mainly to prove how clever they are and how stupid the audience is, Feynman wants his audience to understand so that they too can share in the wonder of physics and for this reason, this book, based on a series of four lectures, is eminently readable; even for those among us with only a little prior knowledge.
So, what’s it about? It’s about how light particles called photons interacts with matter, for example how light is reflected from a piece of glass or how light can be made to do something useful by way of a lens. Key to calculating just what the light does when it hits a structure, such as piece of glass, are little arrows, correctly known as “probability amplitudes,” which are used to represent each individual event; such as photons going from the light source to the front layer of glass. The arrows are then combined to provide a final probability of say how much light is reflected back to a detector. Here is how it works (see diagram 1). Each event is timed by an imaginary stop watch, so when the light that is reflected back off the front surface of a piece of glass reaches the detector, the watch stops. For this event, the hand on the watch is reversed from around 8 o’clock to 2 o’clock, as shown. The length of the arrow is 0.2 which comes from the square root of the expected experimental front surface reflection probability, i.e. 0.04 or 4%.  The second part is the reflection from the back surface of the glass. Due to the overall distance being slightly longer, the watch hand rotates a bit more, as shown. This time the arrow is drawn without reversing its direction; again, the length is 0.2. When the two arrows are combined by the “top-to-tail” method, the resultant arrow is found. Once the length of the resultant arrow is squared, the percentage of reflection, here around 5%, is known; in other words 5% of the photons that left the source have interacted with electrons in the glass; the rest went straight through. Feynman admits that this is a simplistic view of what actually happens; only applying to monochromatic light with no interference and mentions, on more than one occasion, that this technique of combining these, ‘damned little arrows,’ is something that undergraduate physics students take around four years to really get the hang of.

 
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In the second chapter, Feynman further extends his theory on the behaviour of photons. This time, the reflection of light from the surface of a mirror is investigated, beginning with an experiment that considers which parts of the mirror contribute most to how much light is reflected. Not surprisingly, the middle part of the mirror (see below) is where most light is reflected; where the angle of incidence is equal to the angle of reflection; however, according to quantum theory, there are millions of different routes that light can take between the source and detector, it is where the time is least, and the arrows point in much the same direction (in the middle of the mirror) that provides the major contribution to the final resultant probability arrow.

An interesting further extension of the experiment above is when most of the mirror above is cut away leaving, say just the three segments on the left (see diagram 2 lower sketch). The three arrows representing this part of the mirror go in a circle like shape so that the start and end are at the same place. This means that the final arrow is more or less zero and there is no reflection. If, however you now scrape away or cover the middle of the three segments, you once again have a decent sized resultant arrow; in other words, there is reflected light. So, there was no reflected light, you scrape away part of the mirror and now you have light! This is called a diffraction grating and it works differently for different colours so that the example above may work for red light but a different pattern diffracting grating will be needed for blue light.

 
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Throughout the book you get a feel for the type of person Feynman was since after all these are lectures spoken by him. As a physicist and, like some other also do, he seems to consider the other sciences, such as chemistry and biology as subsets of physics, declaring that if you understand the interaction between light and electrons that that is pretty much all there is to these other two branches of science; a chemical reaction, for example, occurs due to changes in the position of electrons.  In fact, all that is excluded from this understanding is gravity and nuclear phenomena. Continuing, Feynman, describes three basic rules that cover this:

  1. Photons go from place to place

  2. Electrons go from place to place

  3. An electron emits or absorbs a photon

By now the way that light behaves is beginning to get more complicated, for example: it doesn’t always appear to travel at the speed of light; it doesn’t always go in neat straight lines; virtual electrons, with spin zero, don’t really exist; and partial reflection is really scattering of light by electrons inside the glass.  Also introduced at this point are the famous Feynman diagrams which are used to show the journey particles take in space-time (see below).

 

The mathematical representation of diagram 3 is:

E(1 to 2) * j * E(5 to 3) * E(2 to 6) *j *  E(6 to 4) * P(5 to 6)

Notes: 1. Each event is multiplied because the electrons act at the same time; 2. The ‘j’ operator represents the coupling between an electron and a photon and has a value of -1; 3. Each event e.g. E(1 to 2), has an associated space and time shift – (X2 – X1) and (T2 – T1).

A further diagram, diagram4,  is used to show how electrons are kept in place around atomic nuclei by the interchange of photons between the electrons and protons.

Electrons that exchange fewer photons with protons are more easily dislodged from an atom and it is these electrons that are responsible for electrical current and chemical reactions.

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Also in chapter 3, Feyman talks about polarisation, which to keep things simple, has previously been left out. Photons come in four distinct varieties, or polarisations, that are geometrically based on the three spacial dimensions (x, y, and z) and time. Photons that begin a journey, say from point A, with polarisation X, will still have the same polarisation when it reaches its destination, say at point B. For electrons things are a bit more complicated. Again the electron has four varieties (in fact all ½ and 1 spin particles have this number of varieties), however, this time the polarisation can change between the start and end of a journey, say by the electron absorbing a photon (which could be one the electron has just emitted), giving sixteen possible outcomes between the electrons polarisation at the start and end of a journey. That no electron with the same polarisation can be in the same place at the same time is an example of the exclusion principle – true for electrons and other fermions but not for photons.

In chapter 4, Feynman begins by discussing some of the mathematical difficulties asociated with QED and some of the ‘trickery’ to get calculations to agree with experiments. Four quantities are mentioned; two, ‘m’ and ‘e’, representing the experimental mass and charge of the electron and ‘n’ and ‘j’, corresponding to the same two quantities and which are used for calculation. Calculating ‘m’ involves starting with an electron with no coupling, E(A to B), and then adding further terms for two couplings ( an emission and absorbtion of a photon), four, eiight and so on. A problem arises when when two coupling points occur where one is directly on top of the other such that the distance between them is zero. This is where the mathematics ‘blows up’ and makes no sense. The solution was to give the distance a value; but a very small one! With this problem overcome, people could at last use QED to make accurate calculations, however, he does warn of anomalies at very small distances, possibly due to gravitional effects,  such as probabilities over 100% and negative energy.,


In the final part of chapter 4, Feynman looks at how the rest of the atom works, introducing the theory of QCD (quatum chromo-dynamics), along with an overview of the other main particles (remember this book was written in the early to mid 1980’s). In this theory, as opposed to earlier explanations of how electrons and protons interact by exchanging photons, for the atomic nucleus quarks now interact by exchanging gluons which they are able to emit as well as absorb. This excahnge of gluons effectovely hold the nucleus together. Quarks come in several varieties (which are sub-divided into so called colours - R, G, B – based on their polarisation) but only ‘up’ and ‘down’ quarks exist in the nucleus; the proton consisting of two up quarks and a down quark and the neutron with two down quarks and one up quark. Since an up quark has a charge of 2/3 and a down quark has a charge of -1/3 then the total charge for the proton is +1 and zero for the neutron. Similar diagrams, from above, exist to show quark-gluon, or strong, interactions (see diagram 5).

As chapter 4 continues, other particles are introduced, such as the ‘W’ boson and neutrino. Feynman uses these two particles to explain beta decay whereby a neutron disintegrates into a proton (see diagram 6). This process involves a down quark changing to an up quark. 

Feynman goes on to look at other particles and their interactions in a similar way to that above, introducing the reader to the muon or heavy electron (heavy because it is similar to the electron but with a mass around 200 times greater), the tau particle, different types of neutrino and the five varieties of quark which were known at the time; there is now a sixth quark as well as the Higgs Boson and two Z bosons in the list of elementary particles. He concludes with a short mention of gravity and the difficulties that physicists still have in including gravity in their theories.

So that’s pretty much what I have taken from a first read through and it is fair to say that there is much, much more in this book than I have covered in this review but to cover it all would be futile, time consuming and probably not that successful; instead just read the book! There will be stuff that you know already but everyone will learn something new and, at the end of the day, as Feynman says, don’t worry if there are things you simply don’t get because neither does Feynman and neither does everyone else.