How should I continue learning?

[Jonnjonzz]

Hello, I want to know how I should continue learning physics, but first i will give some of my background.

I'm 17 years old and I like physics. I decided that in order to learn physics I need to read books on physics. So far I read over a dozen books, few of which are The Great Physicists From Galileo To Einstein and Mr. Tompkins, both by George Gamow, Hyperspace and Parallel Worlds, both by Michio Kaku, The Dancing Wu Li Masters by Gary Zukav, and In Search of Srchodinger's Cat by J. Gibben. Some time ago I came across The Feynman Lectures on Physics and noticed that I could not understand any of the math, which I think is calculus, so I started learning calculus by reading Calculus Made Easy by Silvanus P. Thompson. I am almost done with the book, but still need practice on integrating, and my question is whether I have enough knowledge to understand or at least read through The Feynman Lectures and if not what books should I continue reading to understand the math needed for physics.

 

[Defennder]

If I'm not mistaken the Feynman lecture series themselves contain the math needed to understand the book, but of course it's always better to pick up the skills you need from external sources. Try Stewart's Calculus for a good calc intro. If you want something condensed but still readable, a good number of people would recommend Mary L Boas' Mathematical Methods in the Physical Sciences.

 

[snipez90]

Moreover, you might want to consider reading an introductory calculus based physics textbook before delving into Feynman Lectures. Halliday-Resnick seems to be the standard.

Solving lots of problems will improve your physics intuition greatly. Then you could go to the Feynman Lectures for a deeper understanding. Defennder is more or less right. The feynman lectures attempt to explain the math in a straightforward and intuitive way but they are by no means self-contained.

 

[Jonnjonzz]

Thank you I will check those books out

 

[codelieb]

When Feynman started teaching the course that would later become The Feynman Lectures on Physics, most of his freshman students did not know any calculus. So, the first several lectures he delivered were a kind of a "mini-course" in calculus. Unfortunately those lectures were not preserved.

To understand The Feynman Lectures on Physics, Vol I, you will need to know differential calculus and a (very) little integral calculus. (Basically you just have to understand what an integral means, and know how to "differentiate in reverse.") You will also need to know some things about vectors, complex numbers and simple differential equations, but Feynman lectures on these subjects in Vol I, so you do not necessarily need to go to other sources.

The book Feynman learned calculus from (when he was 14), is "Calculus for the Practical Man," by J. E. Thompson, https://www.amazon.com/dp/1406756725/?tag=pfamazon01-20 .

For Vols II and III, you should know the differential calculus thoroughly, and be fairly proficient at integral calculus - however, you don't have to be expert (so don't waste time learning how to integrate complex expressions, unless you really want to). In Vol II Feynman makes much use of the differential and integral calculus of vector fields - but again, he lectures on these subjects, so you should not need to go to other sources.

Finally, I recommend "Feynman's Tips on Physics, a problem solving supplement to The Feynman Lectures on Physics," which was published with the most recent ("Definitive") edition of The Feynman Lectures. 'Tips' includes 3 lectures Feynman gave to his freshman students just before their first term exam; he talks about the math required to follow his lectures - vectors, differential and integral calculus, etc. - and about problem-solving in physics, giving many instructive examples. 'Tips' includes 80 exercises (with answers) that were assigned as homework to students in Feynman's class, which you can use to test and reinforce your understanding of The Lectures. It is very important that you do such exercises, because only reading The Lectures, will not really teach you very much. Feynman was such a brilliant and entertaining lecturer that you might feel "enlightened" after reading one of his lectures (at Caltech this was humorously known as "The Feynman Field Effect"). However, if you can not make use of what you read to figure out what happens in a given physical situation, you have not learned anything useful. So - do not forget to do exercises! [Recommendation: Do each exercise without looking at the answer. See if you can find different methods to solve each exercise (for example, you might solve the same problem by resolving forces or by conservation of energy, by using calculus or by geometry - there is usually more than one way "to skin a cat"); check yourself by seeing that the different methods you use produce the same result. Do not look at the answer in the back of the book until you are thoroughly convinced, in this way, that you have solved the exercise correctly.]

Good luck to you in your pedagogical adventure! If you run into problems you may write to me at the Feynman Lectures website, www.feynmanlectures.info .

Michael A. Gottlieb
mg@feynmanlectures.info

 

[Doc Al]

Good luck to you in your pedagogical adventure! If you run into problems you may write to me at the Feynman Lectures website, www.feynmanlectures.info .

Michael A. Gottlieb
mg@feynmanlectures.info

Welcome to PF, Michael! As a life-long Feynman fan I'd like to take a moment to acknowledge and thank you for the work you did in ferreting out all those errors/typos in the Lectures and for maintaining that website. Cheers to you!

Anyone interested in the Feynman lectures--and that should be just about everyone!--must visit Michael's website.

 

[codelieb]

Thanks for the welcome, Doc Al.

With regard to the errata for The Feynman Lectures on Physics: we are still receiving error reports. To date, 280 errors have been corrected in print, another 260 have been approved for correction by Caltech, and about 300 more await approval.

At this time we are in the process of preparing a new electronic source for The Feynman Lectures, which will include corrections for all errors to date, as well as new typography and accurately drawn/plotted figures. We plan, initially, to use the new source to produce a paperback version of The Definitive Edition - perhaps sometime next year (or the year after - these things take time!). It is also hoped that the new source will eventually be published in an eBook edition that will include tape recordings of the original lectures, photos of Feynman's blackboards and of Feynman demonstrating in class, all the original handouts given to Feynman's students (before the books were written), including lecture summaries and outlines, homework, tests, lab guidelines, and descriptions of experiments, plus other ancillary material.

We are also working on a comprehensive set of exercises for The Feynman Lectures, which will include all the exercises in the (out-of-print) Caltech exercise books for The Feynman Lectures (Vols I - III) and "Exercises for Introductory Physics" by Leighton & Vogt, with answers for all exercises. This will be a first, as the Caltech exercise books for Vols II and III have never been published with answers.

I would like to remind readers of this forum that we are still "debugging" The Feynman Lectures, and welcome error reports. Reports should be sent to the email address given below. Newly reported errors (verified by our staff) are added to the lists of errata posted on the FLP Errata page at feynmanlectures.info, and the names of contributors are also listed there.


Michael A. Gottlieb
mg@feynmanlectures.info

 

[mal4mac]

Is Maths the main problem when reading Feynman? I have a physics degree, but have forgotten most of it, so I'm reading Feynman's lectures again. Of course, it goes without saying, they are wonderful, but I fear they demand a certain "maturity" to get the most out of them without help -- fortunately there is help..

For instance, look how he defines "field" in I 2-4 -- "the existence of the positive charge, in some sense, distorts, or creates a "condition" in space, so that when we put the negative charge in, it feels a force. This potentially for producing a force is called an electric field..."

Compare this to Gribbin's definition in his (excellent) popular physics dictionary "Q is for Quantum" - "The simplest way to think of a field is as a set of numbers that label every point in spacetime with the strength of the appropriate force at that point."

Feynman is not wrong, of course, but the allusive ("distorts"), hesitant ("in some sense", poetic ("condition") language might cause people problems. Note, in no way am I suggesting that these difficulties should stop people from attempting to read Feynman.

Just be prepared to get stuck now and again.

In summary, I'd recommend having "Q is for Quantum" to hand when reading Feynman. Hit a difficult sentence, read it twice, think and visualise hard, check Gribbin's definition, read sentence again, move on...

P.S. I notice that Aitchison, Oxford's gauge theory guru, sets readings from Feynman's mathematical chapters in his post-calculus Mathematical Methods course (along with Boas).

 

[Defennder]

Compare this to Gribbin's definition in his (excellent) popular physics dictionary "Q is for Quantum" - "The simplest way to think of a field is as a set of numbers that label every point in spacetime with the strength of the appropriate force at that point."

Are you sure it really says that? It's not even correct to begin with since E-field is a vector and not scalar. Personally I don't find such a definition helpful at all, Feynman's definition is more exact and understandable.

EDIT: Yeah I noticed he said "set of numbers" instead of just "a number", but his definition about assigning a set of numbers doesn't say anything about the motivation for the definition of an E-field.

 

[mal4mac]

Are you sure it really says that? ... E-field is a vector and not scalar. Personally I don't find such a definition helpful at all, Feynman's definition is more exact and understandable... Yeah I noticed he said "set of numbers" instead of just "a number", but his definition about assigning a set of numbers doesn't say anything about the motivation for the definition of an E-field.

The Gribbin quote comes from a mini-article on "field" stretching over three pages. Pertinent to your point he goes on to say, "in order to describe the value of the electromagnetic field at any point in three dimensional space, you need a set of eight numbers - one to describe the intensity of the electric component and three to specify its direction, plus a similar set to to describe the intensity and direction of the magnetic component."

He precedes this with a long discussion of the history of field theory, bringing out the original thought experiment of Faraday. In this Faraday asked an audience to imagine the sun alone in space and the Earth suddenly appearing at an appropriate distance... (and so on, read Gribbin!)

I liked the section I quoted most because it seems to combine exactness with the simplest possible example, but I agree with you about motivation being important.

And, again, I came not to bury Feynman, but to praise him. I'm just trying to see why faculty stayed with the original lectures, hanging on every word, while average undergraduates crashed and burned. I'm suggesting it might have been the twisting subtlety of his thought, rather than the mathematics. Therefore, don't stop reading Feynman but find a way to deal with the twists -- like supplementing with a good dictionary.

 

[codelieb]

FLP does not "define field" in Vol I:2-4; fields are merely mentioned there in the course of an introductory discussion on basic physics. The concept of a field is not defined (or used) until much later, in section 12-4, where it is discussed in detail and at length. Fields - in particular, vector fields, scalar fields, and the electromagnetic field - are further discussed in the introductory chapters of Vol. II. [mal4mac: You can not judge the whole of FLP by what is written in the first two chapters. I encourage you to read on!]

I agree with Defender that Gribbin's definition of a field is not informative with regard to physical fields, nor is it correct for vector fields, and furthermore it is incomplete, because all (physical) fields have properties (such as continuity and linearity) that are not satisfied by just any "set of numbers that label every point in spacetime."

Finally, I would like to mention in passing that anyone who quotes FLP and says "Feynman said this or that," is forgetting that FLP has two other authors, Leighton and Sands, who contributed _a great deal_ to the book. If you ever listen to Feynman's lectures on tape or CD while reading along in the book at the same time, you will see/hear what I mean. [In his oral history at the Caltech Archives, Leighton describes his work on FLP as "translating Feynmanese into English," but in fact Leighton and Sands did a whole lot more than that.]

Michael A. Gottlieb
www.feynmanlectures.info

 

[codelieb]

Mal4mac, if is absolutely false that "average undergraduates crashed and burned" in the Feynman lecture course. First of all, there are no "average undergraduates," at Caltech, where only the best of the best are admitted. Secondly, the performance of Feynman's class and subsequent classes that used FLP were not markedly different from the performance of other introductory physics classes at Caltech using other textbooks. I don't know where you are getting your information from, but with regard to this particular issue, I suggest you read Matt Sands Memoir about the Feynman Lectures, in "Feynman's Tips on Physics."

Michael A. Gottlieb
Physics Department
California Institute of Technology

 

[codelieb]

The Gribbin quote comes from a mini-article on "field" stretching over three pages. Pertinent to your point he goes on to say, "in order to describe the value of the electromagnetic field at any point in three dimensional space, you need a set of eight numbers - one to describe the intensity of the electric component and three to specify its direction, plus a similar set to to describe the intensity and direction of the magnetic component."

This is also incorrect, and leads me to wonder what qualifications John Gribben has to write a book about physics: Six, not eight, numbers are needed to describe (the intensity and direction of) the electric and magnetic fields at a point.

 

[mal4mac]

FLP does not "define field" in Vol I:2-4; fields are merely mentioned there in the course of an introductory discussion on basic physics. The concept of a field is not defined (or used) until much later, in section 12-4, where it is discussed in detail and at length. Fields - in particular, vector fields, scalar fields, and the electromagnetic field - are further discussed in the introductory chapters of Vol. II. [mal4mac: You can not judge the whole of FLP by what is written in the first two chapters...]

I'm just judging the first two chapters :-)

I was involved with developing the UK's largest initial (BCS award winning) computer science course, so I'm reading Feynman with a highly critical course developer's eye (as well as re-learning physics!)

I question Feynman's decision to even mention "field" at this point. If you introduce a concept then you should define it properly. Not use elusive language that is only liable to confuse freshers.

I agree with Defender that Gribbin's definition of a field is not informative with regard to physical fields, nor is it correct for vector fields, and furthermore it is incomplete, because all (physical) fields have properties (such as continuity and linearity) that are not satisfied by just any "set of numbers that label every point in spacetime."

I accept that my extract from Gribbin was incomplete, and you make a very good point about continuity and linearity. In his defence, Gribbin has a page of diagrams and text discussing lines of force, with diagrams, that show continuity. He doesn't mention continuity, I guess, because he doesn't want to frighten the layman!

Have you ever considered publishing a Feynman dictionary? I recently read through Kant's first critique (Pluhar's lucid translation) and found Caygill's "A Kant Dictionary" by far the most useful piece of secondary literature. Being able to look up (say) "cognition" the first time Kant used it to know *exactly* what he meant by the term was very useful. I'm sure you could, for instance, pull together quotes from Feynman about various concepts (like "field"), add supporting text, and produce a better (slightly higher level?) dictionary that Gribbin's. Other physics dictionaries are very lack lustre. "A Feynman Dictionary" might help people struggling with Feynman's lectures (and other physics texts!)

 

[mal4mac]

This is also incorrect, and leads me to wonder what qualifications John Gribbn has to write a book about physics: Six, not eight, numbers are needed to describe (the intensity and direction of) the electric and magnetic fields at a point.

John Gribbin graduated with a degree in physics from the University of Sussex in 1966. He later completed an MSc in astronomy, also from Sussex (1967) and a PhD in astrophysics from the University of Cambridge (1971). He's one of the UK's most prolific & respected writers on popular physics. He's written hundreds of books, including a biography of Feynman that garnered respectable reviews.

How do you get six numbers? Don't you need the (x,y,z) co-ordinates of the end points of the force vector for both fields at a point? Plus, of course, the magnitude of each force. That makes eight.

 

[mal4mac]

Mal4mac, it is absolutely false that "average undergraduates crashed and burned" in the Feynman lecture course... I don't know where you are getting your information from...

"Genius" by James Gleick is my source, generally regarded as the best biography of Feynman. Quote:

"The course ... was not for freshmen. As the months went on, the examination results left Feynman shocked and discouraged... As the course wore on, attendance by the kids at the lectures started dropping alarmingly, but at the same time, more and more faculty and graduate students started attending, so the room stayed full, and Feynman may never have known he was losing his intended audience."(p.363)

He adds that Leighton and Sands did some intensive editing to try and make the published lectures understandable to the "kids". But he adds the truth available from looking at lists of recommended textbooks from University sites:

"Colleges and universities worldwide tried to adopt them as textbooks and then, inevitably, gave them up for more manageable and less radical alternatives."

I've looked at many such lists, recently. None recommends Feynman's lectures as course texts, but many highly recommend them as supplementary reading. That's how I used them (many mooons ago) when studying UG physics. I read the course text, then, in the odd sections where it confused me, I read Feynman. Feynman often helped. But I didn't read cover-to-cover because Feynman also, quite often, confused me.

 

[codelieb]

> ["Genius" by James Gleick is my source, generally regarded as
> the best biography of Feynman.
>
> Quote:
>
> "The course ... was not for freshmen. As the months went on,
> the examination results left Feynman shocked and discouraged...
> As the course wore on, attendance by the kids at the lectures
> started dropping alarmingly, but at the same time, more and
> more faculty and graduate students started attending, so the
> room stayed full, and Feynman may never have known he was
> losing his intended audience."(p.363)

I wonder what Gleick's sources are. Mine are Matthew Sands and other people that attended Feynman's Phys 1 & 2 lectures at Caltech, as well as other Phys 1 & 2 courses - these are required of _all_ Caltech students, not just physics majors. The attendance rate of such "big" courses at Caltech typically drop radically after a short time, as many students prefer to study by reading and practicing exercises - either alone or in "study groups." I would therefore be very surprised if Feynman was "shocked" that attendance dropped in his Phys 1 & 2. I also find it hard to believe (having sat in that cozy lecture hall - E Bridge 201 - many times) that Feynman could have been so unobservant to mistake faculty and grad students for freshmen and sophomores. I do not remember reading any statement of Feynman's in which he mentioned attendance in his undergraduate course (but perhaps you know of some source I am unaware of - I do not consider Gleick authoritative, unless he quotes an authoritative source).

> He adds that Leighton and Sands did some intensive editing to try and
> make the published lectures understandable to the "kids". But he adds
> the truth available from looking at lists of recommended textbooks from
> University sites:
>
> "Colleges and universities worldwide tried to adopt them as textbooks and
> then, inevitably, gave them up for more manageable and less radical
> alternatives."

FLP was never intended to be a textbook, but only a book of lectures (which does not include common textbook elements, such as exercises), and it was never intended to be used outside Caltech, where the standard of admission (particularly with regard to math and science) is unusually high (so the material could be aimed a bit higher than usual for freshmen and sophomores). The idea of turning FLP into a book came from publishers, and was snatched up by the Caltech administration, as a way to generate revenue for the physics department (which it continues to do to this day).

"Leighton and Sands" did more than 'make the published lectures understandable to the "kids".' Sands was in the first place responsible for FLP, because his was the idea of revising the undergraduate physics course to include more advanced and interesting material; Sands was also responsible for the idea of asking Feynman to give the lectures (and for talking Feynman into it!). Leighton was responsible for the program as a whole, which included not only his involvement in the editing and illustration of Feynman's lectures, but also in the creation of new labs and experiments, recitation sections (creation of homework, quizzes and tests), etc.

> I've looked at many such lists, recently. None recommends
> Feynman's lectures as course texts, but many highly recommend
> them as supplementary reading.

The Feynman Lectures on Physics is published in over a dozen languages. Did you check the lists in Russian, Chinese (simplified, and traditional), Korean, Czech, Polish, Italian, German, ... ? (More copies have been printed in Russian, alone, than in English.) FLP is getting close to 50 years old, and it is not a textbook, so it is not very surprising that it is not recommended, today, as a textbook. Nevertheless, it was used at Caltech as the primary text for Phys 1 and Phys 2 for almost 20 years, and it continues to be used at Caltech even today (piecemeal, in the form of chapters that are copied and passed out to the students).

> That's how I used them (many mooons ago) when studying UG physics.
> I read the course text, then, in the odd sections where it confused me,
> I read Feynman. Feynman often helped. But I didn't read cover-to-cover
> because Feynman also, quite often, confused me.

I read FLP (the first time) in 1999-2000, and found, on the points that confused me, that it was often because of some typo or other kind of mistake in the book. I found about 200 errors like that, which (after several years of campaigning) were corrected in the first printing of the most recent (so called "Definitive") edition. Since then another 80 errors have been corrected in print, while 260 more that have been checked by Caltech await correction; in addition, we have about 500 newly reported errors that have not yet been "officially" checked, and we continue to receive reports. The lists of errata can be found at The Feynman Lectures website,

http://www.feynmanlectures.info.

If you find yourself confused on some point in FLP, you might want to check the lists of errata to see if there are any errors that might be involved. If you find an error (which could include, for example, an unambiguously confusing statement) that is not reported in our lists, please write to

Michael Gottlieb
mg@feynmanlectures.info

 

[codelieb]

>> ["Genius" by James Gleick ...
>>
>> Quote:
>>
>> "The course ... was not for freshmen. As the months went on,
>> the examination results left Feynman shocked and discouraged...
>> As the course wore on, attendance by the kids at the lectures
>> started dropping alarmingly, but at the same time, more and
>> more faculty and graduate students started attending, so the
>> room stayed full, and Feynman may never have known he was
>> losing his intended audience."(p.363)

> I wonder what Gleick's sources are.

I know what Gleick's source is now. It is the Special Preface to the 1989 Commemorative Issue of the Feynman Lectures on Physics, by David Goodstein and Gerry Neugebauer, which I quote, below:

"Many of the students dreaded the class, and as the course wore on, attendance by the registered students started dropping alarmingly. But at the same time more and more faculty and graduate students started attending. The room stayed full, and Feynman may never have known he was losing some of his intended audience." (Goodstein & Neugebauer, 1989)

Here is what Matt Sands says about this in his memoir:

"In a Special Preface to the Commemorative Issue of the Feynman Lectures on Physics, David Goodstein and Gerry Neugebauer have written that "… as the course wore on, attendance by the registered students started dropping alarmingly." I don't know where they got this information. And I wonder what evidence they have that: "Many of the students dreaded the class..." Goodstein was not at Caltech at that time. Neugebauer was part of the crew working on the course, and would sometimes jokingly say that there were no undergraduate students left in the lecture hall—only grad students. That may have colored his memory. I was sitting at the back of the hall at most of the lectures, and my memory—of course, dimmed by the years—is that perhaps twenty percent or so of the students were not bothering to attend. Such a number would not be unusual for a large lecture class, and I do not remember that anyone was "alarmed". And although there may have been some students in my recitation section who dreaded the class, most were involved and excited by the lectures—although some of them, very likely, would have dreaded the homework assignments." ('On the Origins of The Feynman Lectures on Physics, A memoir by Matthew Sands,' Feynman's Tips on Physics (2006), pp.1)

 

[mal4mac]

I've joined two sources in my (highly condensed!) quote. Yes, Goodstein is quoted by Gleick as the main source on "attendance". But, note, Feynman was not "shocked and discouraged" by the attendance, but by the examination results. Charles Weiner was the source of that comment, from an AIP interview with Feynman in 1966 or 1973 (I can't trace the orginal on the net). Maybe you have contacts at CalTech who can dig out the actual results?!

 

[codelieb]

> Feynman was not "shocked and discouraged" by the attendance, but by
> the examination results. Charles Weiner was the source of that comment,
> from an AIP interview with Feynman in 1966.

I have listened to the AIP interview at the Caltech Archives. Feynman was basically reiterating his self-deprecating preface in FLP. In the same interview (which spanned several days) Feynman told Weiner that "People who were directly in contact [with the students] would tell me that I was underestimating them, and that it wasn't as bad as I thought.", and that he had "better feelings" about The Feynman Lectures since writing his preface. (Years later, in interviews with Mehra, Feynman said that The Feynman Lectures on Physics was one of the best things he did. So, his feelings about FLP seem to have improved with age.)

About Feynman's FLP preface, Sands writes the following:

"After the completion of the second year of lectures—near the beginning of June, 1963—I was in my office assigning the grades for the final examinations, when Feynman dropped into say goodbye before leaving town (perhaps to go to Brazil). He asked how the students had performed on the exam. I said I thought pretty well. He asked what was the average grade, and I told him—something like 65 percent as I recall. His response was, "Oh, that’s terrible, they should have done better than that. I am a failure." I tried to dissuade him of this idea, pointing out that the average grade was very arbitrary, depending on many factors such as the difficulty of the problems given, the grading method used, and such—and that we usually tried to make the average sufficiently low that there would be some spread in grades to provide a reasonable "curve" for the assignment of letter grades. (This is an attitude, incidentally, that I wouldn't approve of today.) I said that I thought that many of the students had clearly got a great deal out of the class. He was not persuaded.

I then told him that the publication of the lectures was proceeding apace and wondered whether he would like to provide some kind of preface. The idea was interesting to him, but he was short of time. I suggested that I could turn on the dictating machine I had on my desk, and that he could dictate his preface. So, still thinking about his depression over the average grade on the final exam of the second year students, he dictated the first draft of "Feynman's Preface", which you will find in front of each volume of the Lectures. In it he says: "I don’t think I did very well by the students." I have often regretted that I had arranged for him to make a preface in this way, because I do not think that this was a very considered judgment. And I fear that it has been used by many teachers as an excuse for not trying out the Lectures with their students."

from 'On the Origins of The Feynman Lectures
on Physics, A memoir by Matthew Sands,'
Feynman's Tips on Physics (2006)


And, finally, here's what Feynman said to Mehra in a January 1988 interview (only about a month before Feynman died, so these, I believe, are Feynman's last words on this subject):

"At the end of the two years [1961-63] I felt that I had wasted two years, that I had done no research during this entire period and I was muttering to this effect. I remember Robert Walker saying to me: "Someday you will realize that what you did for physics in those two years is far more important than any research you could have done during the same period." I said,"You're crazy!" I don't think he's crazy now. I think he was right. The books [Feynman Lectures on Physics] are popular, they are read by a lot of people, and when I read them over [I find] they're good, they're all right. I am satisfied; rather, I am not dissatisfied with them. I am am just dissatisfied with the system - whether it would transmit. But when you have a book and somebody from far away writes that he is learning from it... then I feel that I may have done something to a large number of other people, to people everywhere.


They have the books on the shelves. They are used all the time. They are twenty-five years old, and they are still on the shelves. Undergraduate and graduate students use them. They look them up for fundamental ideas behind advanced subjects. There is all kinds of stuff there, more basic physical points of view, and so apparently they are useful. I must admit now that I cannot deny that they are really a contribution to the physics world."

from The Beat of a Different Drum,
by Jagdish Mehra, 1994
(by far my favorite Feynman biography)

 

[codelieb]

How do you get six numbers? Don't you need the (x,y,z) co-ordinates of the end points of the force vector for both fields at a point? Plus, of course, the magnitude of each force. That makes eight.

The reason you need only 6 numbers (and not 8) to describe the EM field at a point is because if you have, as you put it, "the (x,y,z) co-ordinates of the end points of [a] force vector" then you also know it's magnitude = sqrt(x^2 + y^2 + z^2) - there is no need to specify a fourth number for it's magnitude, as you seem to think. At a given point to describe the EM field you need three components for the Electric field, (Ex,Ey,Ez) and three components for the Magnetic (Bx, By, Bz), and that's it - that determines the directions and magnitudes of the fields.

Excuse me for not replying sooner - I don't check this forum often. If you wish to continue this discussion please email me: codelieb@caltech.edu.

Michael A. Gottlieb
Physics Department
California Institute of Technology

 

[NinjaHelper]

My piece of advice to actively learn would be to be involved with the local college or universities physics clubs. Attend them, and have a notebook and pen handy.

At the University of Washington (where I go to college); there's many clubs involving physics, mathematics, engineering etc. Many work with local high schools, and are glad to have high school kids come in.

Though, books are good =). I'd rather go look up Notes for Physics from .edu websites. Many Univerisites put their notes online, and those can be more easy to follow. MIT has an open-courseware which occasionally has lecture videos all for free =). So, the internet is your resource. Use it well