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ByMetallurgiston October 17, 2007

Caveat - Be sure to read Professor Zee's introduction as well as Feynman's introduction before you read the rest of the book. More about this at the end of this review.

In my opinion this is one of the best of Feynman's introductory physics books. He does close to the impossible by explaining the rudimentary ideas of Quantum Electro Dynamics (QED) in a manner that is reasonably accessible to those with some physics background. He explains Feynman diagrams and shows why light is partially reflected from a glass, how it is transmitted through the glass, how it interacts with the electrons in the glass and many more things. This is done via his arrows and the rules for their rotation, addition and multiplication.

One reviewer has criticized this book because Feynman does not actually show how to determine the length of the arrows (the square of which is the probability of the action being considered occurring) and the how you determine their proper rotation. True, but as is stated in Feynman's introduction, this was never the intention of the book. If you want to learn how to create the arrows used in a Feynman diagram and use them to solve even the most rudimentary problem, you have to major in physics as an undergraduate, do well enough to get into a theoretical physics graduate program and then stick with the program until the second year, when you will take elementary QED. You will then have to take even more classes before you can solve harder problems. Clearly, it is not possible to do all this in a 150-page book aimed at a general audience. He does, however, give the reader a clear indication of what these calculations are like, even if you are not actually given enough information to perform one on your own. Feynman is fair enough not to hide the difficulties involved in actually computing things. He briefly discusses the process of renormalization (that he admits is not mathematically legitimate), which is required to get answers that agreed with experimental data and the difficulties in determining the coupling constants that are also required. In the end, he admits that there is no mathematically rigorous support for QED. Its virtue lies in the fact that it provides the correct answers, even if the approach to getting them involve a bit of hocus-pocus (again his words).

The last 20 pages of the book show how the approaches used in QED, as strange as they are, were used to create an analogous approach for determining what goes on in the nucleus of an atom. This short section shows complexity of nuclear physics and the role that QED has played in trying to unify a baffling plethora of experimental data. Unfortunately, this last section is largely out of date and is hopelessly complicated. Fortunately, it is only 20 pages long.

As mentioned in the beginning of this review, you should read Zee's introduction as well as Feynman's, before you get into the rest of the book. Zee puts QED into proper perspective. Along with wave and matrix mechanics, the Dirac-Feynman path integral method that is described in this book is another approach to quantum mechanics. Zee also points out that while it is a very powerful approach for many problems, it is unworkable for others that are easily solved by wave or matrix mechanics. Feynman's introduction is very important because he emphatically states that photons and electrons are particles and that the idea of their also being waves stems from the idea that many features of their behavior could be explained by assuming that they were waves. He shows that you can explain these effects using QED, without having to assume that they are waves. This eliminates the many paradoxes that are created when one assumes that photons and electrons exhibit dual, wave/particle behavior. QED is not, however, without its own complications. Some of this behavior depends upon the frequency of the photon or electron. Frequency is generally thought of as a wave property, but it can also be thought of a just a parameter that defined the energy of the photon or electron. This is a fundamental idea separating QED from wave based quantum theories. Feynman does not try to speculate why photons and electrons obey the rules of QED because he does not know why, nor does anyone else and we probably are incapable of knowing why. He is completely satisfied that his calculations agree with experimental data to a degree that is unsurpassed by any other theoretical physics calculation.

I would recommend this book to anyone who is interested in getting an idea of what QED is all about and to those who seek a deeper understanding of physical phenomena. You will learn how QED explains many things, some of which from the basis for the paradoxes discussed at length in books such as "In search of Schrodinger's cat". Reading this book is a good antidote for the head spinning paradoxes described in that book. Feynman believes that they stem from using a poor analogy (that of waves) to explain the behavior of particles. As far as the deeper questions of why photons and electrons obey the ruled of QED, he does not care, so long as he can get the right answer. This may therefore not be the book for you if you are interested in this deepest WHY, but it definitely is if you want to know more about Feynman's powerful approach to quantum mechanics.

In my opinion this is one of the best of Feynman's introductory physics books. He does close to the impossible by explaining the rudimentary ideas of Quantum Electro Dynamics (QED) in a manner that is reasonably accessible to those with some physics background. He explains Feynman diagrams and shows why light is partially reflected from a glass, how it is transmitted through the glass, how it interacts with the electrons in the glass and many more things. This is done via his arrows and the rules for their rotation, addition and multiplication.

One reviewer has criticized this book because Feynman does not actually show how to determine the length of the arrows (the square of which is the probability of the action being considered occurring) and the how you determine their proper rotation. True, but as is stated in Feynman's introduction, this was never the intention of the book. If you want to learn how to create the arrows used in a Feynman diagram and use them to solve even the most rudimentary problem, you have to major in physics as an undergraduate, do well enough to get into a theoretical physics graduate program and then stick with the program until the second year, when you will take elementary QED. You will then have to take even more classes before you can solve harder problems. Clearly, it is not possible to do all this in a 150-page book aimed at a general audience. He does, however, give the reader a clear indication of what these calculations are like, even if you are not actually given enough information to perform one on your own. Feynman is fair enough not to hide the difficulties involved in actually computing things. He briefly discusses the process of renormalization (that he admits is not mathematically legitimate), which is required to get answers that agreed with experimental data and the difficulties in determining the coupling constants that are also required. In the end, he admits that there is no mathematically rigorous support for QED. Its virtue lies in the fact that it provides the correct answers, even if the approach to getting them involve a bit of hocus-pocus (again his words).

The last 20 pages of the book show how the approaches used in QED, as strange as they are, were used to create an analogous approach for determining what goes on in the nucleus of an atom. This short section shows complexity of nuclear physics and the role that QED has played in trying to unify a baffling plethora of experimental data. Unfortunately, this last section is largely out of date and is hopelessly complicated. Fortunately, it is only 20 pages long.

As mentioned in the beginning of this review, you should read Zee's introduction as well as Feynman's, before you get into the rest of the book. Zee puts QED into proper perspective. Along with wave and matrix mechanics, the Dirac-Feynman path integral method that is described in this book is another approach to quantum mechanics. Zee also points out that while it is a very powerful approach for many problems, it is unworkable for others that are easily solved by wave or matrix mechanics. Feynman's introduction is very important because he emphatically states that photons and electrons are particles and that the idea of their also being waves stems from the idea that many features of their behavior could be explained by assuming that they were waves. He shows that you can explain these effects using QED, without having to assume that they are waves. This eliminates the many paradoxes that are created when one assumes that photons and electrons exhibit dual, wave/particle behavior. QED is not, however, without its own complications. Some of this behavior depends upon the frequency of the photon or electron. Frequency is generally thought of as a wave property, but it can also be thought of a just a parameter that defined the energy of the photon or electron. This is a fundamental idea separating QED from wave based quantum theories. Feynman does not try to speculate why photons and electrons obey the rules of QED because he does not know why, nor does anyone else and we probably are incapable of knowing why. He is completely satisfied that his calculations agree with experimental data to a degree that is unsurpassed by any other theoretical physics calculation.

I would recommend this book to anyone who is interested in getting an idea of what QED is all about and to those who seek a deeper understanding of physical phenomena. You will learn how QED explains many things, some of which from the basis for the paradoxes discussed at length in books such as "In search of Schrodinger's cat". Reading this book is a good antidote for the head spinning paradoxes described in that book. Feynman believes that they stem from using a poor analogy (that of waves) to explain the behavior of particles. As far as the deeper questions of why photons and electrons obey the ruled of QED, he does not care, so long as he can get the right answer. This may therefore not be the book for you if you are interested in this deepest WHY, but it definitely is if you want to know more about Feynman's powerful approach to quantum mechanics.

76 people found this helpful

ByTimothy Byrneon April 10, 2007

Yes the book explains QED without any math, but it doesn't really explain it very well. I admire what Feynman is trying to do, but I don't believe he succeeds. I'll give one example. The book is built around using vector addition and multiplication to show how to come up with probability sums and products. So far so good. The problem is that we never get an explanation for why the vectors point the way the do, are rotated just so, etc. Without that it's simply voodoo, and nothing has been explained.

It's not that you'd need math for any of that. You wouldn't. It's not the lack of math that leaves the reader in the dark, it's simply Feynman's not having the time to elaborate given the lecture format. Twenty pages on how waves work and reinforce and cancel etc. would at least provide the frame work for understanding more or less what is going on in the vector voodoo.

Feynman certainly made an amazing use of the time he had in the brief lecture series the book is drawn from, but unfortuantely a brief lecture series aimed at the scientifically illiterate is just not a reasonable forum for presenting even a very basic understanding of QED.

It's not that you'd need math for any of that. You wouldn't. It's not the lack of math that leaves the reader in the dark, it's simply Feynman's not having the time to elaborate given the lecture format. Twenty pages on how waves work and reinforce and cancel etc. would at least provide the frame work for understanding more or less what is going on in the vector voodoo.

Feynman certainly made an amazing use of the time he had in the brief lecture series the book is drawn from, but unfortuantely a brief lecture series aimed at the scientifically illiterate is just not a reasonable forum for presenting even a very basic understanding of QED.

Caveat - Be sure to read Professor Zee's introduction as well as Feynman's introduction before you read the rest of the book. More about this at the end of this review.

In my opinion this is one of the best of Feynman's introductory physics books. He does close to the impossible by explaining the rudimentary ideas of Quantum Electro Dynamics (QED) in a manner that is reasonably accessible to those with some physics background. He explains Feynman diagrams and shows why light is partially reflected from a glass, how it is transmitted through the glass, how it interacts with the electrons in the glass and many more things. This is done via his arrows and the rules for their rotation, addition and multiplication.

One reviewer has criticized this book because Feynman does not actually show how to determine the length of the arrows (the square of which is the probability of the action being considered occurring) and the how you determine their proper rotation. True, but as is stated in Feynman's introduction, this was never the intention of the book. If you want to learn how to create the arrows used in a Feynman diagram and use them to solve even the most rudimentary problem, you have to major in physics as an undergraduate, do well enough to get into a theoretical physics graduate program and then stick with the program until the second year, when you will take elementary QED. You will then have to take even more classes before you can solve harder problems. Clearly, it is not possible to do all this in a 150-page book aimed at a general audience. He does, however, give the reader a clear indication of what these calculations are like, even if you are not actually given enough information to perform one on your own. Feynman is fair enough not to hide the difficulties involved in actually computing things. He briefly discusses the process of renormalization (that he admits is not mathematically legitimate), which is required to get answers that agreed with experimental data and the difficulties in determining the coupling constants that are also required. In the end, he admits that there is no mathematically rigorous support for QED. Its virtue lies in the fact that it provides the correct answers, even if the approach to getting them involve a bit of hocus-pocus (again his words).

The last 20 pages of the book show how the approaches used in QED, as strange as they are, were used to create an analogous approach for determining what goes on in the nucleus of an atom. This short section shows complexity of nuclear physics and the role that QED has played in trying to unify a baffling plethora of experimental data. Unfortunately, this last section is largely out of date and is hopelessly complicated. Fortunately, it is only 20 pages long.

As mentioned in the beginning of this review, you should read Zee's introduction as well as Feynman's, before you get into the rest of the book. Zee puts QED into proper perspective. Along with wave and matrix mechanics, the Dirac-Feynman path integral method that is described in this book is another approach to quantum mechanics. Zee also points out that while it is a very powerful approach for many problems, it is unworkable for others that are easily solved by wave or matrix mechanics. Feynman's introduction is very important because he emphatically states that photons and electrons are particles and that the idea of their also being waves stems from the idea that many features of their behavior could be explained by assuming that they were waves. He shows that you can explain these effects using QED, without having to assume that they are waves. This eliminates the many paradoxes that are created when one assumes that photons and electrons exhibit dual, wave/particle behavior. QED is not, however, without its own complications. Some of this behavior depends upon the frequency of the photon or electron. Frequency is generally thought of as a wave property, but it can also be thought of a just a parameter that defined the energy of the photon or electron. This is a fundamental idea separating QED from wave based quantum theories. Feynman does not try to speculate why photons and electrons obey the rules of QED because he does not know why, nor does anyone else and we probably are incapable of knowing why. He is completely satisfied that his calculations agree with experimental data to a degree that is unsurpassed by any other theoretical physics calculation.

I would recommend this book to anyone who is interested in getting an idea of what QED is all about and to those who seek a deeper understanding of physical phenomena. You will learn how QED explains many things, some of which from the basis for the paradoxes discussed at length in books such as "In search of Schrodinger's cat". Reading this book is a good antidote for the head spinning paradoxes described in that book. Feynman believes that they stem from using a poor analogy (that of waves) to explain the behavior of particles. As far as the deeper questions of why photons and electrons obey the ruled of QED, he does not care, so long as he can get the right answer. This may therefore not be the book for you if you are interested in this deepest WHY, but it definitely is if you want to know more about Feynman's powerful approach to quantum mechanics.

In my opinion this is one of the best of Feynman's introductory physics books. He does close to the impossible by explaining the rudimentary ideas of Quantum Electro Dynamics (QED) in a manner that is reasonably accessible to those with some physics background. He explains Feynman diagrams and shows why light is partially reflected from a glass, how it is transmitted through the glass, how it interacts with the electrons in the glass and many more things. This is done via his arrows and the rules for their rotation, addition and multiplication.

One reviewer has criticized this book because Feynman does not actually show how to determine the length of the arrows (the square of which is the probability of the action being considered occurring) and the how you determine their proper rotation. True, but as is stated in Feynman's introduction, this was never the intention of the book. If you want to learn how to create the arrows used in a Feynman diagram and use them to solve even the most rudimentary problem, you have to major in physics as an undergraduate, do well enough to get into a theoretical physics graduate program and then stick with the program until the second year, when you will take elementary QED. You will then have to take even more classes before you can solve harder problems. Clearly, it is not possible to do all this in a 150-page book aimed at a general audience. He does, however, give the reader a clear indication of what these calculations are like, even if you are not actually given enough information to perform one on your own. Feynman is fair enough not to hide the difficulties involved in actually computing things. He briefly discusses the process of renormalization (that he admits is not mathematically legitimate), which is required to get answers that agreed with experimental data and the difficulties in determining the coupling constants that are also required. In the end, he admits that there is no mathematically rigorous support for QED. Its virtue lies in the fact that it provides the correct answers, even if the approach to getting them involve a bit of hocus-pocus (again his words).

The last 20 pages of the book show how the approaches used in QED, as strange as they are, were used to create an analogous approach for determining what goes on in the nucleus of an atom. This short section shows complexity of nuclear physics and the role that QED has played in trying to unify a baffling plethora of experimental data. Unfortunately, this last section is largely out of date and is hopelessly complicated. Fortunately, it is only 20 pages long.

As mentioned in the beginning of this review, you should read Zee's introduction as well as Feynman's, before you get into the rest of the book. Zee puts QED into proper perspective. Along with wave and matrix mechanics, the Dirac-Feynman path integral method that is described in this book is another approach to quantum mechanics. Zee also points out that while it is a very powerful approach for many problems, it is unworkable for others that are easily solved by wave or matrix mechanics. Feynman's introduction is very important because he emphatically states that photons and electrons are particles and that the idea of their also being waves stems from the idea that many features of their behavior could be explained by assuming that they were waves. He shows that you can explain these effects using QED, without having to assume that they are waves. This eliminates the many paradoxes that are created when one assumes that photons and electrons exhibit dual, wave/particle behavior. QED is not, however, without its own complications. Some of this behavior depends upon the frequency of the photon or electron. Frequency is generally thought of as a wave property, but it can also be thought of a just a parameter that defined the energy of the photon or electron. This is a fundamental idea separating QED from wave based quantum theories. Feynman does not try to speculate why photons and electrons obey the rules of QED because he does not know why, nor does anyone else and we probably are incapable of knowing why. He is completely satisfied that his calculations agree with experimental data to a degree that is unsurpassed by any other theoretical physics calculation.

I would recommend this book to anyone who is interested in getting an idea of what QED is all about and to those who seek a deeper understanding of physical phenomena. You will learn how QED explains many things, some of which from the basis for the paradoxes discussed at length in books such as "In search of Schrodinger's cat". Reading this book is a good antidote for the head spinning paradoxes described in that book. Feynman believes that they stem from using a poor analogy (that of waves) to explain the behavior of particles. As far as the deeper questions of why photons and electrons obey the ruled of QED, he does not care, so long as he can get the right answer. This may therefore not be the book for you if you are interested in this deepest WHY, but it definitely is if you want to know more about Feynman's powerful approach to quantum mechanics.

ByIan J. Milleron July 19, 2008

This book covers four lectures that explains QED in terms of the path integral method, which was developed by the author. Needless to say, this is authoritative on this approach, but it also remarkably clear and comprehensible. Notwithstanding that, I would recommend slow and careful reading, as you may find a small sequence of statements that seem perhaps a little unjustified. Later, Feynman fronts up to some of these, and explains why he oversimplified to get things going. If you see them first, and this is not unreasonable, I believe you will get more from the text. The first lecture is a general introduction that shows how the path of the photon as a particle can be followed in terms of time-of-flight from all possible paths. The assertion is, the photon is a particle, not a wave, however there is no explanation for why there is a term that I would call the phase. The second lecture is a tour-de force and explains in terms of this particle treatment, why light reflects and diffracts, and is particularly interesting in why light behaves as if it is reflected only from the front and back of glass, whereas it is actually scattered by electrons throughout the glass. The third lecture covers electron-photon interactions, and covers Feynman diagrams and shows why QED is the most accurate theory ever proposed. The fourth lecture may seem a bit of a disappointment. The author tries to cover a very wide range of phenomena, which he terms "loose ends", and in some ways this chapter has been overtaken somewhat, nevertheless it also gives a look into Feynman's mind, and that also is well worth the price of the book. It is also here that the issue of renormalization is discussed - if you could call Feynman admitting it is "a dippy procedure" a discussion.

Why buy the book? I suspect this is probably the best chance a non-specialist has of understanding the basis of QED. The biggest disappointment? Feynman dismisses wave theory, which everybody else uses, and replaces it with a monumental raft of integrals. My initial thoughts were that waves are effectively an analogue way of solving those integrals, perhaps a gift from nature, and it is a pity I can't ask Feynman why that option was dismissed.

Why buy the book? I suspect this is probably the best chance a non-specialist has of understanding the basis of QED. The biggest disappointment? Feynman dismisses wave theory, which everybody else uses, and replaces it with a monumental raft of integrals. My initial thoughts were that waves are effectively an analogue way of solving those integrals, perhaps a gift from nature, and it is a pity I can't ask Feynman why that option was dismissed.

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ByM. Greeneon April 16, 2007

When I was a senior in high school, I asked my physics teacher why light bent when it entered a lens. He responded with an analogy about soldiers marching on a field and entering a marsh. The first soldiers entering the marsh would slow down and "bend" the column until all the soldiers were in the marsh.

The analogy made no sense to me because we were talking about light, not soldiers. He responded that light travels in waves and if I viewed the soldiers as a wave front, I could understand his analogy. I left the conversation feeling very stupid for not "getting it." and thinking the analogy had so many holes in it. For example, it didn't explain why the lens was a marsh as far as light goes.

It wasn't until I read QED that I realized I didn't get the soldier analogy because my teacher was wrong - light doesn't travel in waves, it travels in discrete little packets called photons.

In QED, Feynman opens his first chapter by saying a couple of things. First he tells you that the theory he's going to describe to you has been experimentally verified out to 10 decimal places so it's probably right. He then gives you a quick review of what matter is and then tells you "light comes in particles. Not waves, particles." No wavicles, just little bits of light. He tells you that photons go from place to place, an electron goes from place to place and the electron will sometimes either absorb or emit a photon. From that basis, the rest of the book shows how that model explains why light bends when it enters a lens, why mirrors reflect, why oil slicks show different colors, why peacock feathers iridesce along a with host of other phenomena. He also explains why light has wave-like properties despite the fact that light comes in packets.

The first reviewer is right - there are questions left unanswered but that doesn't diminish the book. The framework Feynman develops in four chapters gives you a clear mental image of what's going on. Bohr and Pauli disliked Feynman's approach because it violated the Copenhagen approach of eschewing all models. In their view, only mathematics would suffice to understand quantum mechanics. I for one, am very glad Feynman ignored them, developed his approach and eventually gave the 4 lectures that are the basis of the book.

If you think light travels in waves, read this book. It's truly wonderful. If you're as dumb as I am, you'll have to read it multiple times but it's definitely worth it.

The analogy made no sense to me because we were talking about light, not soldiers. He responded that light travels in waves and if I viewed the soldiers as a wave front, I could understand his analogy. I left the conversation feeling very stupid for not "getting it." and thinking the analogy had so many holes in it. For example, it didn't explain why the lens was a marsh as far as light goes.

It wasn't until I read QED that I realized I didn't get the soldier analogy because my teacher was wrong - light doesn't travel in waves, it travels in discrete little packets called photons.

In QED, Feynman opens his first chapter by saying a couple of things. First he tells you that the theory he's going to describe to you has been experimentally verified out to 10 decimal places so it's probably right. He then gives you a quick review of what matter is and then tells you "light comes in particles. Not waves, particles." No wavicles, just little bits of light. He tells you that photons go from place to place, an electron goes from place to place and the electron will sometimes either absorb or emit a photon. From that basis, the rest of the book shows how that model explains why light bends when it enters a lens, why mirrors reflect, why oil slicks show different colors, why peacock feathers iridesce along a with host of other phenomena. He also explains why light has wave-like properties despite the fact that light comes in packets.

The first reviewer is right - there are questions left unanswered but that doesn't diminish the book. The framework Feynman develops in four chapters gives you a clear mental image of what's going on. Bohr and Pauli disliked Feynman's approach because it violated the Copenhagen approach of eschewing all models. In their view, only mathematics would suffice to understand quantum mechanics. I for one, am very glad Feynman ignored them, developed his approach and eventually gave the 4 lectures that are the basis of the book.

If you think light travels in waves, read this book. It's truly wonderful. If you're as dumb as I am, you'll have to read it multiple times but it's definitely worth it.

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ByAspen Logic, Inc.on October 26, 2000

QED is your guide to the theory of Quantum Electro Dynamics which explains the interaction of light and matter. It is about a 1/4" thick and feels like it was written for the layperson to absorb without being over taxing. It isn't just another "popular science" type book because it provides an accurate explanation of the theory without being watered down by inaccurate metaphors and analogies meant to soften some difficult physics for the uninitiated. The text is a series of lectures Feynman prepared for an english teach friend of his who wanted to know about his theories but was afraid to ask (so to speak).

This book is fun to read and I highly recommend it for the scientist or (most importantly) the non-scientist on your gift list. Fear not, Feynman is the greatest teacher of science America has ever had to offer (imho). You will enjoy this and quite likely a few of his other books such as, "Surely, Your'e Joking Mr. Feynman".

This book is fun to read and I highly recommend it for the scientist or (most importantly) the non-scientist on your gift list. Fear not, Feynman is the greatest teacher of science America has ever had to offer (imho). You will enjoy this and quite likely a few of his other books such as, "Surely, Your'e Joking Mr. Feynman".

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ByJ. Koelmanon February 1, 2009

Quantum Electro Dynamics (QED) is the fundamental theory that explains all the physics you'll ever experience (assuming you're not a nuclear physicist and neither have plans to plunge into a black hole). QED is the result of unifying Einstein's special relativity with quantum mechanics, and forms the leading example for virtually all fundamental physics developed in the second half of the twentieth century.

Can the key ideas and principles of such a deep theory be explained to 'the average interested Joe'?

With this book Feynman demonstrates it is possible.

So is this the book for YOU? It depends. I think the best way to see whether this book matches your expectations is to read Zee's superb introduction. Unfortunately, the 'Look Inside' preview functionality is missing for this book. However, Zee's introduction to QED is available via his website: [...] Have a look, and you'll know whether this book fits your expectations.

Can the key ideas and principles of such a deep theory be explained to 'the average interested Joe'?

With this book Feynman demonstrates it is possible.

So is this the book for YOU? It depends. I think the best way to see whether this book matches your expectations is to read Zee's superb introduction. Unfortunately, the 'Look Inside' preview functionality is missing for this book. However, Zee's introduction to QED is available via his website: [...] Have a look, and you'll know whether this book fits your expectations.

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Byarpard fazakason October 21, 2010

I highly recommend this book to anyone without a formal background in quantum physics or higher math who is interested in learning about the modern explanation for how the world works at the atomic level. Richard Feynman is one of the originators of this worldview, and in this book manages to present an explanation which is at once true to the actual math while avoiding actually delving too deeply into the math. It's all about the math because as someone once said, "mathematics is the language of physics". That Feynman was able to carry off this seemingly impossible feat is evidence of his exceptional teaching ability. As he once said, if you can't explain something to a freshman, you don't really understand it.

In a nutshell, he explains that everything that happens in the world of atoms and light particles is governed by probability and chance. Every event has a certain numerical factor associated with it called an "amplitude", and the probability of the event occuring is the square of the amplitude. He doesn't get into the very complicated math of actually calculating the amplitude, but he explains two fundamental rules about amplitudes: first, if a single event can happen in more than one way, such as a light particle going from point A to point B by more than one path, then you add the amplitudes for each way the event can happen and then square the sum to determine the probability of the event happening. On the other hand, if there is a sequence of events, first event 1 then event 2, for example first a light particle goes from point A to point B, then from point B to point C,you multiply the amplitude for event 1 times the amplitude for event 2 and then square the product to get the amplitude for the sequence of events to occur.

Then he explains that an amplitude can be thought of as an arrow, with both a length and a direction, and that to add amplitudes you line up all the individual arrows tip to tail, draw one big arrow from the first tail to the last tip, and that arrow is the amplitude which is the sum of the individual amplitudes. (I forget how you multiply the arrows.)

Then he gives an example using partial reflection of light from glass, a mystery known since Newton's time which was not solved until the advent of quantum theory. Here light particles are emitted from a source, travel to a glass surface, and a certain percentage bounce off the front side of the glass and go back to a detector, the percentage varying from 0 to 4% based on the thickness of the glass. The mystery has been how the light bouncing off the front surface knows how thick the glass is. He shows that in order to solve the mystery, you have to include an amplitude for every path that a light particle can take from the light source to both the front surface and back surface of the glass and back to the detector, including loop-de-loops that go around Jupiter 15 times, and paths that go to the far end of the universe and back. Since these are all different ways the same event can occur, the rule for amplitudes says you have to add all these amplitudes to get the final amplitude. I.e., you have to add up all the amplitudes for every possible path the particle can take to either surface, no matter how crazy. And then if you do, you find that you end up with an amplitude which is basically the same as if you had the light particle going in the shortest possible path (i.e., a straight line) directly from the source to the front surface of the glass and then back again back by the shortest possible path (i.e., a straight line) to the detector, just like we "know" light does, and varying with the thickness of the glass just as observed. But if you don't include all possible paths in your summing up of the amplitudes, you won't get the right answer for partial reflection!

This is all so cool and fascinating. You end up actually seeing how the mathematical apparatus of quantum electrodynamics explains this phenomenon, without having to know that the arrows are actually complex numbers, and that adding, multiplying, and squaring arrows is just the arithmetic of complex numbers.

As the Guinness man says, "brilliant"!

For those who enjoyed the book, or want to learn more, or are confused, or learn better by listening and watching than by reading, I highly recommend watching a series of four lectures Feynman gave at the University of New Zealand in Auckland in the sixties, which goes over the same material. You get the inimitable Feynman persona, with interesting asides on the Mayans, and astronomy, and all sorts of other tangentially related topics, delivered in a quintessential New York accent, accompanied by diagrams in multi-colored chalk on the blackboard. It's available on the world's most well known Internet video site, which I'm not sure I can mention by name in this review, so I won't. Each lecture is an hour and a half, but in my opinion worth every minute.

In a nutshell, he explains that everything that happens in the world of atoms and light particles is governed by probability and chance. Every event has a certain numerical factor associated with it called an "amplitude", and the probability of the event occuring is the square of the amplitude. He doesn't get into the very complicated math of actually calculating the amplitude, but he explains two fundamental rules about amplitudes: first, if a single event can happen in more than one way, such as a light particle going from point A to point B by more than one path, then you add the amplitudes for each way the event can happen and then square the sum to determine the probability of the event happening. On the other hand, if there is a sequence of events, first event 1 then event 2, for example first a light particle goes from point A to point B, then from point B to point C,you multiply the amplitude for event 1 times the amplitude for event 2 and then square the product to get the amplitude for the sequence of events to occur.

Then he explains that an amplitude can be thought of as an arrow, with both a length and a direction, and that to add amplitudes you line up all the individual arrows tip to tail, draw one big arrow from the first tail to the last tip, and that arrow is the amplitude which is the sum of the individual amplitudes. (I forget how you multiply the arrows.)

Then he gives an example using partial reflection of light from glass, a mystery known since Newton's time which was not solved until the advent of quantum theory. Here light particles are emitted from a source, travel to a glass surface, and a certain percentage bounce off the front side of the glass and go back to a detector, the percentage varying from 0 to 4% based on the thickness of the glass. The mystery has been how the light bouncing off the front surface knows how thick the glass is. He shows that in order to solve the mystery, you have to include an amplitude for every path that a light particle can take from the light source to both the front surface and back surface of the glass and back to the detector, including loop-de-loops that go around Jupiter 15 times, and paths that go to the far end of the universe and back. Since these are all different ways the same event can occur, the rule for amplitudes says you have to add all these amplitudes to get the final amplitude. I.e., you have to add up all the amplitudes for every possible path the particle can take to either surface, no matter how crazy. And then if you do, you find that you end up with an amplitude which is basically the same as if you had the light particle going in the shortest possible path (i.e., a straight line) directly from the source to the front surface of the glass and then back again back by the shortest possible path (i.e., a straight line) to the detector, just like we "know" light does, and varying with the thickness of the glass just as observed. But if you don't include all possible paths in your summing up of the amplitudes, you won't get the right answer for partial reflection!

This is all so cool and fascinating. You end up actually seeing how the mathematical apparatus of quantum electrodynamics explains this phenomenon, without having to know that the arrows are actually complex numbers, and that adding, multiplying, and squaring arrows is just the arithmetic of complex numbers.

As the Guinness man says, "brilliant"!

For those who enjoyed the book, or want to learn more, or are confused, or learn better by listening and watching than by reading, I highly recommend watching a series of four lectures Feynman gave at the University of New Zealand in Auckland in the sixties, which goes over the same material. You get the inimitable Feynman persona, with interesting asides on the Mayans, and astronomy, and all sorts of other tangentially related topics, delivered in a quintessential New York accent, accompanied by diagrams in multi-colored chalk on the blackboard. It's available on the world's most well known Internet video site, which I'm not sure I can mention by name in this review, so I won't. Each lecture is an hour and a half, but in my opinion worth every minute.

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BySheraz Choudharyon July 28, 2010

This is one of my favorite books of all time. This book changed the way I view the world and was inspiring.

Throughout high school and college, we are taught statements that light moves in a straight line as facts. The reality is that this is not a fact but rather a simplification. The real mechanisms which this book explains are not that much harder to understand but a lot more beautiful, interesting and amazing.

I unlearned years of Physics I was taught and am now even more interested in learning more. Feynman not only makes reading this book rewarding but also very easy.

One of the things I greatly appreciate is that Feynman does not simplify without letting you know what he is doing and why. I wish that someone when I was in high school had told me that light appearing to move in a straight line is a simplification of a complex process of interactions of photons with each other. At that age I may not have bother to learn the reality but at least would have kept my mind open.

I recommend this book to everyone curious and interested in how nature works. I am reading my copy for the third time now and it still continues to awe me.

Throughout high school and college, we are taught statements that light moves in a straight line as facts. The reality is that this is not a fact but rather a simplification. The real mechanisms which this book explains are not that much harder to understand but a lot more beautiful, interesting and amazing.

I unlearned years of Physics I was taught and am now even more interested in learning more. Feynman not only makes reading this book rewarding but also very easy.

One of the things I greatly appreciate is that Feynman does not simplify without letting you know what he is doing and why. I wish that someone when I was in high school had told me that light appearing to move in a straight line is a simplification of a complex process of interactions of photons with each other. At that age I may not have bother to learn the reality but at least would have kept my mind open.

I recommend this book to everyone curious and interested in how nature works. I am reading my copy for the third time now and it still continues to awe me.

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ByDavid A. Sharpon September 10, 2008

Even though these lectures are more than 20 years old, Feynman did an incredible job of explaining a fundamental concept in Physics. I can see now why he received the Nobel prize for his work in this area. I would call him the Carl Sagan of Physics, except that Mr. Sagan's popularity came later in time. QED is so bizarre and incredible, yet so accurate and powerful a theory that it boggles the mind! Mr. Feynman's explanation is so complete and articulate that anyone can understand it. This theory explains the physical underpinnings of most of our daily experience, the interactions of photons with matter, yet it is a complete surprise!

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I didn't know exactly what to expect, but bought this based on suggestions from a blog. It is actually a transcript of a series of lectures from Feynman and not specifically a book, per se.

That may be a good thing though, as a lecture is probably a little lighter reading and this is heady stuff.

Quite a bit of the beginning of the book is introductions and anecdotal stories about the various pop-physicists. Once you get into the actual lectures, you jump right into light as a wave vs a particle and it goes straight into the building blocks of the universe and what understand (and don't understand) about them.

The nice thing is that this is intended for the educated reader, but not for the PhD-in-Atomic-Physics reader. So if you have a basic grasp of physics, you will likely be able to follow this book.

If you hated science, this won't magically open the world of particle physics to you.

My only real complaint about the book is the location of the diagrams. Often the text will be talking about something that is two pages away in the diagrams and I found myself looking at the wrong diagram and being confused, or having to flip back and forth between a couple of pages to find the correct diagram once I figured out what was going on. This is distracting and un-necessary.

Overall, highly recommended as a challenging read for anyone who has an interest in physics and the building blocks of our universe and a desire to stretch their brain-muscles a little bit once again.

That may be a good thing though, as a lecture is probably a little lighter reading and this is heady stuff.

Quite a bit of the beginning of the book is introductions and anecdotal stories about the various pop-physicists. Once you get into the actual lectures, you jump right into light as a wave vs a particle and it goes straight into the building blocks of the universe and what understand (and don't understand) about them.

The nice thing is that this is intended for the educated reader, but not for the PhD-in-Atomic-Physics reader. So if you have a basic grasp of physics, you will likely be able to follow this book.

If you hated science, this won't magically open the world of particle physics to you.

My only real complaint about the book is the location of the diagrams. Often the text will be talking about something that is two pages away in the diagrams and I found myself looking at the wrong diagram and being confused, or having to flip back and forth between a couple of pages to find the correct diagram once I figured out what was going on. This is distracting and un-necessary.

Overall, highly recommended as a challenging read for anyone who has an interest in physics and the building blocks of our universe and a desire to stretch their brain-muscles a little bit once again.

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ByFascinated exploreron January 6, 2016

Feynman was a world famous, Nobel Prize winning physicist. He gave four lectures on QED, quantum electrodynamics, to explain the theory to a non scientific friend Alix Mautner, and wrote this book based on these lectures. QED has the best agreement between theory and experiment- accurate to 12 significant figures, of any scientific theory. I read the book first then watched his QED lectures on YouTube. It would have worked better to watch the lecture, read that chapter in the book, then watch the next lecture, etc. The questions and answers at the end of the videos are particularly helpful since the audience asks many of the same questions that I had while reading and watching the lectures.

In his first lecture he starts with light reflecting off a glass surface and puts a detector next to the light source to measure reflected light. For every 100 photons that leave the light source, 96 enter the glass and 4 are reflected. If all the photons are the same, how do 4 of them know to be reflected? Next he considers a very thin piece of glass where again the reflected light is measured but there are two reflecting surfaces, the top and the bottom of the glass. The number of photons reflected now varies from 0 to 16. As the thickness of the glass is increased the number of photons reflected goes up till it reached 16 then decreases to 0 and oscillates between 0 and 16 as the thickness increases.

To explain this variation he uses an arrow with a certain length to represent the reflected photon, where the length squared is the probability that the photon will hit the detector. A stopwatch with a large hand is added to measure how long it takes for the photon to be detected, and the arrow representing the photon is given the same angle as the large hand on the stopwatch. The arrow representing the photon from the front face is reversed in direction from the stopwatch hand, while the bottom surface is given the same direction as the stopwatch hand. The arrows are now vectors with size and direction. To get the probability of a photon reflecting from the top and bottom surfaces you add the arrows for each tail to head. The photons interfere with each other and when their directions are opposite they cancel and no photons are measured. I find it easier to picture the light as sine waves which can interfere constructively and add together, or destructively to go to zero. As a result you can get any percentage between zero and 16 percent for the intensity.

Since 4% of the photons are reflected from a single surface the arrow length is 0.2 (0.2 squared is 0.04 or 4% probability for constructive interference), and if they destructively interfere then 0.2 - 0.2 = 0 no photons are seen. For two reflecting surfaces when both the arrows are in the same direction the squares add to 16% ( 0.2 + 0.2 = 0.4, then squared = 0.16 or 16% ). We calculate the observed 4% reflected photons from the experiment with a single reflecting surface. The interference effect is responsible for changing the percent of reflected light when we have two reflecting surfaces and is confirmed by other experiments. Note that we still do not know why 4% of the photons are reflected from the single glass surface, but using this straightforward method we can make very accurate predictions on the overall behavior of photons. We can only talk about probabilities for individual photons. The individual photons that are going to be reflected cannot be identified beforehand. Only the probability that a photon will be reflected can be measured. You can generalize this procedure for a number of reflecting glass surfaces. QED does not explain why 4% of the photons are reflected, but it does allow us predict what will happen very accurately.

In his second lecture he describes the light that hits a mirror and is reflected at the same angle that the light hit the mirror, i.e., the angle of incidence equals the angle of reflection of the light. He takes into account light reflecting from every part of the mirror, and shows that the contribution of reflection from areas distant from the center of the mirror can be ignored. This is not because no light is being reflected, rather the interfering light cancels itself out. If a large number of parallel lines are etched on the mirror surface, they prevent light from hitting the lines and being reflected. This is a diffraction grating that reflects light separated as different colors, and looks like a rainbow, for example a CD or DVD reflects light this way. Numerous diagrams are used to make his arguments clear, and they help. He winds up the several interesting ideas. Light doesn't really travel only in a straight line, somehow it senses the neighboring paths around it and uses a small core of nearby space. The Heisenberg Uncertainty Principle, that we cannot know both the position and momentum of a photon, is no longer needed under QED. The usual graduate level explanation of this principle is that we need to use light of a certain energy to probe a photon or electron to find its position and in the process we added an unknown quantity of energy so we no longer know the energy of the particle. More advanced explanations consider this insufficient and that there is a basic unavoidable uncertainty in making the measurement.

The way we look at things is usually too simple, such as thinking that light travels in a straight line. It actually travels many ways, most of which cancel each other out, which results in light looking like it is traveling in a straight line. When we take into account all possible paths some problems like the Heisenberg Uncertainty Principle disappear. Feynman is applying the principle of least action that he learned in high school and was first formulated by Pierre- Louis de Maupertuis in 1744. The principal says if you take the trajectory of a particle or artillery shell the most likely path is the one with the least action. To get the least action you measure the difference between the kinetic energy and the potential energy of the particle over the entire path, that is mathematically integrate the least action function over the possible paths of the particle. The path with the smallest difference between the two energies is the least action and is the one that is followed by the particle. Feynman uses this method of least action for many of his breakthrough ideas.

The way a magnifying glass works is that all the light going through the lens will meet at the same point. In order to be in focus, every path must take the same amount of time. A ray of light passing through the edge of a lens to the focal point has a much longer path than one going through the center of the lens to the focal point. The light going through the center has to be slowed down so the times for the two beams are equal. This is accomplished by having a lot of glass at the center of the magnifying lens (it is double convex). The glass always appears to slow the speed of light, and more of the glass in the center slows the light more- the effect is that all the light from various parts of the lens reaches the focal point at the same time.

The probability of an event happening is the absolute square of its arrow, the arrow represents a complex number. When the event can happen in separate, alternative ways you add the complex numbers or arrows. When an event can happen only as a succession of steps you multiply the complex numbers for each step. Most of his explanations are clearer with his diagrams, but they are rather detailed. You can see his reasoning, he breaks the reflection of light into simple steps, then considers in detail what happens at each step and finds a way to combine the different steps to be able to predict what will happen. One of his favorite tricks it Is to simplify the problem by figuring which of the very large number of possibilities cancel each other out or contribute very little so they can be ignored.

In the third lecture he shows that photons don’t bounce off a glass surface, they are absorbed by an electron then reemitted anyplace within the glass. In making a simple graph or model he limits the motion to the x-axis and use time for the vertical axis. He uses solid lines to represent electrons, and wiggly lines for photons. At any point an electron can absorb or emit photons. Electrons and photons can travel forward and backward in time and in space. An electron traveling back in time is a positron (a positive electron). You can begin to see that he is making a model that allows all possibilities, whether a beam of light traveling in an unlikely zigzag pattern to get to the second point, or an electron traveling back in time, everything is possible and is included at first. Then consideration is made as to how likely a given event is and if it is not very likely it is excluded.

At this point Feynman begins to talk about the amplitude of a photon that is moving a certain way or in a certain direction, he is relating this to the amplitude squared which is the probability of the event happening. Although you can predict accurately what will happen for an incoming ray from anywhere and what percent of it will reach a detector by just considering the front and back surface of the glass, what actually happens is that the photons are absorbed by the electrons in the glass and reemitted somewhat randomly. This is called scattering and causes some well known effects such as the sky appearing blue (blue light has a shorter wavelength than other visible colors and scatters the most). Although it is a bit tedious the detailed analysis shows how the repeated application of three simple actions explain the world around us.

The actions are:

A photon goes from place to place. P(A to B)

An electron goes from place to place. E(A to B)

An electron emits or absorbs a photon. j (-0.1) coupling number

It's helps to visualize photons and electrons as waves, like a sine wave. These waves can interfere with each other. When they interfere constructively the waves add together and you get a strong signal since the arrows from the stopwatch are parallel and point in the same direction. When they are out of phase they essentially destroy each other. The arrows are parallel and point in the opposite directions and you get no signal. There can be any degree of interference between these two extremes. He cheats a little, thankfully, by not doing the actual calculation, which could require years of graduate school to understand throughly. There is still a lot of detail to wade through. The reward is that you get to travel along with one of the best minds in the area and learn how he perceives and solves problems.

The agreement between the calculated and experimental values of the Dirac electron magnetic moment, an indication of the validity of QED, is now agreeing to about 12 significant figures. The calculation is difficult since it involves including terms such as j*j*j*j*j which involves hundreds of thousand of calculations.

When arrows representing the amplitude of reflections from a glass surface are attached head to tail, they form a small part of a circle when the glass is thin, and up to a half circle when the glass is thicker. As the glass gets still thicker the arc starts getting smaller till it goes to zero then increases again. The resultant arrow from the first tail to the last head is the amplitude or probability for the whole set of reflections. If you connect the tail of the resultant with a radius from the center of the circle, then to the head of the resultant from the center of the circle you have two amplitudes of 0.2 apiece. Squaring and adding these gives probability 4% for the reflection mentioned in the beginning that agrees with experiment (see Fig 68 p 104). This reflected light is due to photons being absorbed by electrons and reemitted in random directions (this is scattering). This absorption and reemission process takes a small amount of time, causing the reflected photons to take longer traveling through the glass, and making them appear to be going slower. They are still traveling at the speed of light while moving between electrons, but it takes time and causes a pause when being absorbed and reemitted.

In laser materials the electrons in the lasers atoms are held in a higher energy state by an external electric field (or heat). When they absorb a photon of the correct frequency (the energy equal to the difference in energy between the energy level the electron is in and the higher energy state), this photon and another identical photon are then emitted. Each collision of a photon results in an additional identical photon being emitted and traveling in exactly the same direction. After a numerous collisions there are a large number of identical photons traveling together in exactly the same direction. These beams of photons bounce back and forth between two parallel mirrors. One mirror is a perfect reflector, while the other only partially reflective. The beam, after bouncing back and forth between the mirrors, eventually exits through the partially reflective mirror as a laser beam.

There are four types of polarization of light and it is sometimes ignored in general discussions. An important point is made that if two electrons have the same polarization they exhibit destructive interference if they try to occupy the same position. This is the basis of the Pauli Exclusion Principle. It is also the reason we have so many elements in the universe. As protons and neutrons combine to make heavier atoms, electrons are added to keep the atom neutral and stable. Since electrons can’t all have the same energy they have to populate other higher energy levels within atoms, This produces all of the known elements which have different properties. The chemical and physical properties of a given element are mostly due to the number of the outermost electrons. Feynman sees the principle of least action at work in the interaction of electrons and photons with external electric and magnetic fields. This interaction is responsible for all the effects we see around us in our everyday world, and are predicted and explained very accurately by QED.

The renormalization technique that allows calculations with QED is tricky and is based on the odd fact that if you use m and e, the mass and charge on the electron, to determine n and j, the coupling constants in QED, then use these n and j to solve another problem your answer is accurate. If you do it again with another n and j that are close then the answer to the other problem is again close.

In the fourth lecture he mentions chromodynamics which is used to explain the large number of subatomic particles. Unlike QED its ability to predict accurately is very limited - only 2.7 plus or minus 0.3 (2 significant figures) for the magnetic moment, instead of 12 significant figures using QED. It does provide a framework to discuss three of the four main interactions in Nature. The “strong interactions” of quarks and gluons (strong force that holds the paste okaynucleus together), “weak interactions” of W’s (weak force that causes most radiation), and the “electrical interactions” of photons (electromagnetic forces). The fourth interaction, gravity, is so weak at the subatomic particle level that it can be ignored unless you need about 40 significant figures. At the moment we are not capable of experiments to this type accuracy.

The interaction between theoreticians and experimentalists is constantly changing. Sometimes the theoreticians suggest an experiment, such as Dirac predicting the positron. Other times experimentalists find values that force theories to be updated and improved. At the moment the very smallest particles, quarks, cannot be measured. At the very largest objects, the cosmology of universe, no one has been able to think of experiments to test some of the theories. We could use another Feynman.

The lectures on QED, that the book is based on, are available on the internet and Wikipedia has an article on QED that includes good explanations and animations that improve understanding.

In his first lecture he starts with light reflecting off a glass surface and puts a detector next to the light source to measure reflected light. For every 100 photons that leave the light source, 96 enter the glass and 4 are reflected. If all the photons are the same, how do 4 of them know to be reflected? Next he considers a very thin piece of glass where again the reflected light is measured but there are two reflecting surfaces, the top and the bottom of the glass. The number of photons reflected now varies from 0 to 16. As the thickness of the glass is increased the number of photons reflected goes up till it reached 16 then decreases to 0 and oscillates between 0 and 16 as the thickness increases.

To explain this variation he uses an arrow with a certain length to represent the reflected photon, where the length squared is the probability that the photon will hit the detector. A stopwatch with a large hand is added to measure how long it takes for the photon to be detected, and the arrow representing the photon is given the same angle as the large hand on the stopwatch. The arrow representing the photon from the front face is reversed in direction from the stopwatch hand, while the bottom surface is given the same direction as the stopwatch hand. The arrows are now vectors with size and direction. To get the probability of a photon reflecting from the top and bottom surfaces you add the arrows for each tail to head. The photons interfere with each other and when their directions are opposite they cancel and no photons are measured. I find it easier to picture the light as sine waves which can interfere constructively and add together, or destructively to go to zero. As a result you can get any percentage between zero and 16 percent for the intensity.

Since 4% of the photons are reflected from a single surface the arrow length is 0.2 (0.2 squared is 0.04 or 4% probability for constructive interference), and if they destructively interfere then 0.2 - 0.2 = 0 no photons are seen. For two reflecting surfaces when both the arrows are in the same direction the squares add to 16% ( 0.2 + 0.2 = 0.4, then squared = 0.16 or 16% ). We calculate the observed 4% reflected photons from the experiment with a single reflecting surface. The interference effect is responsible for changing the percent of reflected light when we have two reflecting surfaces and is confirmed by other experiments. Note that we still do not know why 4% of the photons are reflected from the single glass surface, but using this straightforward method we can make very accurate predictions on the overall behavior of photons. We can only talk about probabilities for individual photons. The individual photons that are going to be reflected cannot be identified beforehand. Only the probability that a photon will be reflected can be measured. You can generalize this procedure for a number of reflecting glass surfaces. QED does not explain why 4% of the photons are reflected, but it does allow us predict what will happen very accurately.

In his second lecture he describes the light that hits a mirror and is reflected at the same angle that the light hit the mirror, i.e., the angle of incidence equals the angle of reflection of the light. He takes into account light reflecting from every part of the mirror, and shows that the contribution of reflection from areas distant from the center of the mirror can be ignored. This is not because no light is being reflected, rather the interfering light cancels itself out. If a large number of parallel lines are etched on the mirror surface, they prevent light from hitting the lines and being reflected. This is a diffraction grating that reflects light separated as different colors, and looks like a rainbow, for example a CD or DVD reflects light this way. Numerous diagrams are used to make his arguments clear, and they help. He winds up the several interesting ideas. Light doesn't really travel only in a straight line, somehow it senses the neighboring paths around it and uses a small core of nearby space. The Heisenberg Uncertainty Principle, that we cannot know both the position and momentum of a photon, is no longer needed under QED. The usual graduate level explanation of this principle is that we need to use light of a certain energy to probe a photon or electron to find its position and in the process we added an unknown quantity of energy so we no longer know the energy of the particle. More advanced explanations consider this insufficient and that there is a basic unavoidable uncertainty in making the measurement.

The way we look at things is usually too simple, such as thinking that light travels in a straight line. It actually travels many ways, most of which cancel each other out, which results in light looking like it is traveling in a straight line. When we take into account all possible paths some problems like the Heisenberg Uncertainty Principle disappear. Feynman is applying the principle of least action that he learned in high school and was first formulated by Pierre- Louis de Maupertuis in 1744. The principal says if you take the trajectory of a particle or artillery shell the most likely path is the one with the least action. To get the least action you measure the difference between the kinetic energy and the potential energy of the particle over the entire path, that is mathematically integrate the least action function over the possible paths of the particle. The path with the smallest difference between the two energies is the least action and is the one that is followed by the particle. Feynman uses this method of least action for many of his breakthrough ideas.

The way a magnifying glass works is that all the light going through the lens will meet at the same point. In order to be in focus, every path must take the same amount of time. A ray of light passing through the edge of a lens to the focal point has a much longer path than one going through the center of the lens to the focal point. The light going through the center has to be slowed down so the times for the two beams are equal. This is accomplished by having a lot of glass at the center of the magnifying lens (it is double convex). The glass always appears to slow the speed of light, and more of the glass in the center slows the light more- the effect is that all the light from various parts of the lens reaches the focal point at the same time.

The probability of an event happening is the absolute square of its arrow, the arrow represents a complex number. When the event can happen in separate, alternative ways you add the complex numbers or arrows. When an event can happen only as a succession of steps you multiply the complex numbers for each step. Most of his explanations are clearer with his diagrams, but they are rather detailed. You can see his reasoning, he breaks the reflection of light into simple steps, then considers in detail what happens at each step and finds a way to combine the different steps to be able to predict what will happen. One of his favorite tricks it Is to simplify the problem by figuring which of the very large number of possibilities cancel each other out or contribute very little so they can be ignored.

In the third lecture he shows that photons don’t bounce off a glass surface, they are absorbed by an electron then reemitted anyplace within the glass. In making a simple graph or model he limits the motion to the x-axis and use time for the vertical axis. He uses solid lines to represent electrons, and wiggly lines for photons. At any point an electron can absorb or emit photons. Electrons and photons can travel forward and backward in time and in space. An electron traveling back in time is a positron (a positive electron). You can begin to see that he is making a model that allows all possibilities, whether a beam of light traveling in an unlikely zigzag pattern to get to the second point, or an electron traveling back in time, everything is possible and is included at first. Then consideration is made as to how likely a given event is and if it is not very likely it is excluded.

At this point Feynman begins to talk about the amplitude of a photon that is moving a certain way or in a certain direction, he is relating this to the amplitude squared which is the probability of the event happening. Although you can predict accurately what will happen for an incoming ray from anywhere and what percent of it will reach a detector by just considering the front and back surface of the glass, what actually happens is that the photons are absorbed by the electrons in the glass and reemitted somewhat randomly. This is called scattering and causes some well known effects such as the sky appearing blue (blue light has a shorter wavelength than other visible colors and scatters the most). Although it is a bit tedious the detailed analysis shows how the repeated application of three simple actions explain the world around us.

The actions are:

A photon goes from place to place. P(A to B)

An electron goes from place to place. E(A to B)

An electron emits or absorbs a photon. j (-0.1) coupling number

It's helps to visualize photons and electrons as waves, like a sine wave. These waves can interfere with each other. When they interfere constructively the waves add together and you get a strong signal since the arrows from the stopwatch are parallel and point in the same direction. When they are out of phase they essentially destroy each other. The arrows are parallel and point in the opposite directions and you get no signal. There can be any degree of interference between these two extremes. He cheats a little, thankfully, by not doing the actual calculation, which could require years of graduate school to understand throughly. There is still a lot of detail to wade through. The reward is that you get to travel along with one of the best minds in the area and learn how he perceives and solves problems.

The agreement between the calculated and experimental values of the Dirac electron magnetic moment, an indication of the validity of QED, is now agreeing to about 12 significant figures. The calculation is difficult since it involves including terms such as j*j*j*j*j which involves hundreds of thousand of calculations.

When arrows representing the amplitude of reflections from a glass surface are attached head to tail, they form a small part of a circle when the glass is thin, and up to a half circle when the glass is thicker. As the glass gets still thicker the arc starts getting smaller till it goes to zero then increases again. The resultant arrow from the first tail to the last head is the amplitude or probability for the whole set of reflections. If you connect the tail of the resultant with a radius from the center of the circle, then to the head of the resultant from the center of the circle you have two amplitudes of 0.2 apiece. Squaring and adding these gives probability 4% for the reflection mentioned in the beginning that agrees with experiment (see Fig 68 p 104). This reflected light is due to photons being absorbed by electrons and reemitted in random directions (this is scattering). This absorption and reemission process takes a small amount of time, causing the reflected photons to take longer traveling through the glass, and making them appear to be going slower. They are still traveling at the speed of light while moving between electrons, but it takes time and causes a pause when being absorbed and reemitted.

In laser materials the electrons in the lasers atoms are held in a higher energy state by an external electric field (or heat). When they absorb a photon of the correct frequency (the energy equal to the difference in energy between the energy level the electron is in and the higher energy state), this photon and another identical photon are then emitted. Each collision of a photon results in an additional identical photon being emitted and traveling in exactly the same direction. After a numerous collisions there are a large number of identical photons traveling together in exactly the same direction. These beams of photons bounce back and forth between two parallel mirrors. One mirror is a perfect reflector, while the other only partially reflective. The beam, after bouncing back and forth between the mirrors, eventually exits through the partially reflective mirror as a laser beam.

There are four types of polarization of light and it is sometimes ignored in general discussions. An important point is made that if two electrons have the same polarization they exhibit destructive interference if they try to occupy the same position. This is the basis of the Pauli Exclusion Principle. It is also the reason we have so many elements in the universe. As protons and neutrons combine to make heavier atoms, electrons are added to keep the atom neutral and stable. Since electrons can’t all have the same energy they have to populate other higher energy levels within atoms, This produces all of the known elements which have different properties. The chemical and physical properties of a given element are mostly due to the number of the outermost electrons. Feynman sees the principle of least action at work in the interaction of electrons and photons with external electric and magnetic fields. This interaction is responsible for all the effects we see around us in our everyday world, and are predicted and explained very accurately by QED.

The renormalization technique that allows calculations with QED is tricky and is based on the odd fact that if you use m and e, the mass and charge on the electron, to determine n and j, the coupling constants in QED, then use these n and j to solve another problem your answer is accurate. If you do it again with another n and j that are close then the answer to the other problem is again close.

In the fourth lecture he mentions chromodynamics which is used to explain the large number of subatomic particles. Unlike QED its ability to predict accurately is very limited - only 2.7 plus or minus 0.3 (2 significant figures) for the magnetic moment, instead of 12 significant figures using QED. It does provide a framework to discuss three of the four main interactions in Nature. The “strong interactions” of quarks and gluons (strong force that holds the paste okaynucleus together), “weak interactions” of W’s (weak force that causes most radiation), and the “electrical interactions” of photons (electromagnetic forces). The fourth interaction, gravity, is so weak at the subatomic particle level that it can be ignored unless you need about 40 significant figures. At the moment we are not capable of experiments to this type accuracy.

The interaction between theoreticians and experimentalists is constantly changing. Sometimes the theoreticians suggest an experiment, such as Dirac predicting the positron. Other times experimentalists find values that force theories to be updated and improved. At the moment the very smallest particles, quarks, cannot be measured. At the very largest objects, the cosmology of universe, no one has been able to think of experiments to test some of the theories. We could use another Feynman.

The lectures on QED, that the book is based on, are available on the internet and Wikipedia has an article on QED that includes good explanations and animations that improve understanding.

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