# Questions about the definition of a metre (A. P. French's book)

• I
In summary, the author discusses the standard unit for length, the meter, and its precision in terms of light waves. They mention the disadvantage of not being able to directly measure a meter with ordinary light sources due to optical interference effects. However, the development of lasers has allowed for interference effects to be observed up to 100 m. The author suggests that the meter may be defined in terms of an optical wavelength from a laser source in the future. The conversation also touches upon the attitude one should have towards such material as an autodidact and strategies for dealing with the drawbacks of thoroughness in understanding concepts. The author also notes that the information may be outdated as the meter is now defined based on the speed of light.
In his book, Newtonian Mechanics, while describing the standard unit for length, A. P. French writes (being American, he uses meter and not metre):
Although the use of extremely small units of length represented by light waves means that the meter can be defined with immense precision -- to 1 part in ##10^8## or better -- there is the disadvantage that an object as long as a meter cannot be directly measured, in a one-step process, in terms of light waves from ordinary sources. The reason is that the measurements depend on observing optical interference effects that begin to wash out if the distance in question becomes more than about 1 ft. The development of lasers has completely transformed this situation, and interference effects have been observed up to path lengths of over 100 m. It thus seems quite probable that the meter will, at some future date, be defined in terms of an optical wavelength obtainable from a laser source, perhaps one of the characteristic spectral lines of neon in a helium-neon laser.
My questions are twofold:
1. The first one is about the physics. What does the text in orange really mean? There is no sidebar about "optical interference". How did he arrive the limit of 1 ft.?

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The first one is about the physics. What does the text in orange really mean? There is no sidebar about "optical interference". How did he arrive the limit of 1 ft.?
This refers to the optical coherence length of a source. In order to get an interference pattern the interfering waves must be coherent, meaning that they must have a well-defined phase relationship. Different sources and arrangements of optical elements have different coherence lengths. I actually was surprised to read that "ordinary sources" could have a coherence length as long as 30 cm, so I suspect that the source he is thinking of is not what I would consider an "ordinary source".

By the way, this seems horribly out of date. The light-wavelength based definition of the meter has come and gone. Now, and for the foreseeable future, the meter is defined based on the speed of light.

Since there are several experienced mentors, advisors are there on this revered forum, the second question is about what kind of attitude one should have toward such material? The audience of this text is an undergrad student, the content is Newtonian Mechanics. Should you be insistent on not reading further till you understand what this means?
If you are an autodidact then you have the luxury of deciding for yourself how you should treat such material. As you have noted, it is a digression from the core concepts. You are not in a class and are not pressed for time to master a concept in a fixed amount of time. So you should decide for yourself how much of the yak you wish to shave.

Thanks! Got it (somewhat).
By the way, this seems horribly out of date. The light-wavelength based definition of the meter has come and gone. Now, and for the foreseeable future, the meter is defined based on the speed of light.
I agree. I check Wikipedia from time to time. I am aware of the fact that it is a 1971 edition.
You are not in a class and are not pressed for time to master a concept in a fixed amount of time.
Aren't we all out of class at some point? I was more interested about some helpful techniques for people who are out of a formal class (perhaps by the people who have been out of the class, but everyone is welcome to suggest). I realize that this is a broad question, but I am hoping that it is not unanswerable. Something like "Here's what I do ... and here's why I think it works:" will go a long way.

Thanks! Got it (somewhat).

I agree. I check Wikipedia from time to time. I am aware of the fact that it is a 1971 edition.
I'd get an up-to-date book.

vanhees71 and Dale
I was more interested about some helpful techniques for people who are out of a formal class (perhaps by the people who have been out of the class, but everyone is welcome to suggest).
Helpful techniques for not shaving the yak? Don’t shave the yak.

Helpful techniques for choosing how much of the yak to shave? Shave as much as you feel like shaving and then stop.

It’s your yak. If you want to leave him hairy then do that. If you want him shaved bald then shave him.

The only actual “helpful tip” I can think of is to recognize that most textbooks are intended to be self contained. So if you are looking at material outside of the textbook then you are shaving. That said, if that is what you want to do then go for it.

anorlunda
I don't think there's any way to know a priori whether you need to understand any side topic.

I have often found reading conversations here (or listening into physicists more generally, but here is accessible) to be useful in determining where there's a hole in my knowledge that I need to fill. I sometimes find that I understand a question and the start of an answer, but then it all suddenly becomes incomprehensible because it relies on something I've forgotten or never knew. Then it's time to hit the textbooks and/or start a thread.

So I'd advise setting Classical Physics to send you alerts and skim every thread that looks interesting.

PeroK said:
I'd get an up-to-date book.
Thanks! But then, after some research and referring to PF I picked up this book in the hope that at least some of the fundamentals of physics I might (re) learn would not have changed (of course, I understand that physics is not math). French's style resonated with me, it was recommended by PF, but the book hasn't been published in a while. And now that Anthony French is no more, there's little possibility that there will be a more recent edition. Yeah, I could pick up a new, more recent book (either by starting a yet another "Book Recommendation" thread here or by referring to an existing one) for the reintroduction of a relatively slowly changing and familiar-sounding branch of physics like Newtonian Mechanics, but that book could have some issues of its own like a style that does not resonate with me or typo's etc. I am also not physically in the US or Europe or Australia. The cheaper books we get here are often reprints of popular international titles by a local publisher. According to Donald Knuth and also from some personal review of such reprints I have come to a conclusion that there are way too many stylistic (e.g. fonts, diagrams) issues and typo's in them. I cringe picking up them.

Given this background, would you consider expanding your terse (and perhaps pithy) advice of simply procuring a newer book?

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Ibix said:
I don't think there's any way to know a priori whether you need to understand any side topic.

I have often found reading conversations here (or listening into physicists more generally, but here is accessible) to be useful in determining where there's a hole in my knowledge that I need to fill. I sometimes find that I understand a question and the start of an answer, but then it all suddenly becomes incomprehensible because it relies on something I've forgotten or never knew. Then it's time to hit the textbooks and/or start a thread.

So I'd advise setting Classical Physics to send you alerts and skim every thread that looks interesting.

Thanks! I of course do that (not only here, but elsewhere too). But I do feel the need of a "backbone" like a book or a video lecture series in order to stay on course.

The tacit question I was really asking (I apologize if it did not quite come out the way I wanted) was "How do you approach a new topic of extraordinary interest (you don't just want to know the names of things, sound scholarly, but want to grok the material) if you are an autodidact?" Suppose you are 40 years old, out of formal schooling, and completely unfamiliar with Group Theory in mathematics and you are curious about it. How would you learn it? Would you start with a concrete goal (e.g. solve all the problems from some book)? Would you apply your tried and tested techniques that helped you learn, say, Real Analysis, back when you were 30 and autodidact? Or would you be looking for improved ways of learning? What tools would you use (for example, I use the spaced repetition software like Anki, refer to various resources, interpretations etc.)? It's through understanding your learning principles that I want to enhance my own. If someone asked you to write down the essence of how you learn or relearn a topic of interest, what would you say?

How do you approach a new topic of extraordinary interest (you don't just want to know the names of things, sound scholarly, but want to grok the material) if you are an autodidact?

I get a project. Not just something that I want to learn, but something that I want to do and the learning is necessary in order to accomplish. That helps me focus and also gives me a way to gauge my progress, plus at the end I get the result of the project.

I have used that approach for self studying programming languages, statistics, physics, farming, and building.

KedarMhaswade, vanhees71, jbriggs444 and 1 other person
Given this background, would you consider expanding your terse (and perhaps pithy) advice of simply procuring a newer book?
Physics and science move on. With French you are expicitly having to ask someone like @Dale with up-to-date knowledge to set you straight where French is out of date.

There are those on here who recommend books like French (that's personal opinion) but I believe they are leading you astray. I've fielded a few homework questions from French over the years and my first thought is often "what book is this from?" It feels like something from before my time.

My feeling is that French might have been old-fashioned even when it was published. If you look at the Feynman lectures from that era, they still feel quite modern.

It's your choice, but if people keep repeating that French is an out-of-date text, then I think you should take issue with whoever recommended it; not with those who tell you honestly that it hasn't aged well.

French's style resonated with me,
I would say that a book that resonates with you will make it easier to learn from it. It you can understand and solve the problems in French, you will have a freshman's understanding of Newtonian physics comparable to what you would learn in most universities today.

That being said, it is from 1971 and will have some anachronisms in it. You need to learn to recognize the things you need to understand in depth. If you had read a little bit further, you would have come across the second highlighted paragraph. So in this case you were Yak Shaving.

I don't know this specific book, but one should not dismiss a book only because it's old. A subject like classical mechanics was finished in its foundations centuries ago and you can learn a lot from old books. In fact many old books seem to be written with somewhat more care than more modern books, which look just more colorful.

E.g., my favorite introductory theoretical-physics textbook is the 6-volume set "Lectures on theoretical physics" by Arnold Sommerfeld, written 70-80 years ago. Of course, it's "outdated" in many points. E.g., it uses the ##\mathrm{i} c t## convention and the concept of "relativistic mass" in special relativity. Nevertheless content and didactics wise the chapter on the relativistic formulation of electrodynamics in vol. III is a gem. Admittedly it is somewhat outdated in methodology but the physics content is very well explained. I think, it's of course good, to find a good modern textbook on a subject, but it's always also worth looking at older textbooks.

In the concrete example in the OP it's pretty obvious, that this is a (in my opinion quite confusingly written) side remark on the definition of units. Since the author doesn't bother to explain

I would say that a book that resonates with you will make it easier to learn from it. It you can understand and solve the problems in French, you will have a freshman's understanding of Newtonian physics comparable to what you would learn in most universities today.
Great; thank you! And that is my modest expectation too. Of course, I would like to ask you, @caz , what you would suggest to follow up this book with. And believe me, I want to learn from better resources available, all the time. But so that I don't spend an inordinate time just choosing a book, I ended up with this one.

That being said, it is from 1971 and will have some anachronisms in it. You need to learn to recognize the things you need to understand in depth. If you had read a little bit further, you would have come across the second highlighted paragraph. So in this case you were Yak Shaving.
I realize that. And I read it further as well. I also referred to many resources given in the book. I wonder how one can not not refer to at least some of the cited resources (especially when they are available freely) and still feel confident about the material presented. There is no substitute for hard work and pure reflection, but different interpretations are clearly useful. For example, in this book, Fig 2.1 is taken from a PSSC (Physical Science Study Committee) book that I found on archive.org for borrowing. And I was so happy to see that beautifully written material which is perhaps timeless (I know, nothing is quite timeless in science, but it is so, at least to some extent). And my intuition, which could be quite faulty, tells me that that material has got to be better than dozens of the most "up-to-date" books around.

With respect to this particular definition of 1 metre however, I do think French could have been more expository. That first paragraph comes across as more intimidating than helpful and that last paragraph fortunately puts things in perspective.

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what you would suggest to follow up this book with.
Typically mechanics is followed up by EM. There are multiple threads at PF where people provide recommendations.

The only dedicated text I know is Purcell Electricity and magnetism, but be warned it is an advanced freshman text. You would probably be best served by getting one of the standard freshman physics texts like
Halliday Resnick
Young Freedman
Serway
There are others.
There is no reason to own the most recent edition unless you are in a class with a prof assigning problems.
Be aware that there are calculus and noncalculus text versions. You want the calculus version.

As a supplement (not your primary text) you should consult
Feynman Lectures (they are online)

Be aware that there is also a math component to physics. In their first couple of years of schooling, physicists typically learn (with more following)
differential and integral calculus
differential equations
vector calculus
linear algebra
Likewise there are threads with recommendations. Be aware that there are theoretical and applied math versions of these topics. I would stick with the applied versions. If you have a mathematical bent, then you could do both.

My favorite PSSC film is
https://archive.org/details/magnet_laboratory_1959

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My favorite PSSC film (at least for Newtonian mechanics) is "Frames of Reference"

Motore, KedarMhaswade, etotheipi and 1 other person
vanhees71 said:
My favorite PSSC film (at least for Newtonian mechanics) is "Frames of Reference"

Absolutely!

vanhees71
vanhees71 said:
E.g., my favorite introductory theoretical-physics textbook is the 6-volume set "Lectures on theoretical physics" by Arnold Sommerfeld, written 70-80 years ago. Of course, it's "outdated" in many points. E.g., it uses the ##\mathrm{i} c t## convention and the concept of "relativistic mass" in special relativity. Nevertheless content and didactics wise the chapter on the relativistic formulation of electrodynamics in vol. III is a gem. Admittedly it is somewhat outdated in methodology but the physics content is very well explained. I think, it's of course good, to find a good modern textbook on a subject, but it's always also worth looking at older textbooks.
If you don't mind @vanhees71 , would you explain your journey? (No problem if you don't want to). e.g. When did you pick up Sommerfeld's books? What kind of preparation did you do? Did you do it in a class setting? What do you believe worked for you and what could have been better? Thanks!

etotheipi
Well, I got interested in theoretical physics in the last three years on high school, getting inclined to study physics after high school.

Before that I had pretty severe problems with the subject that is called "math" at school. I couldn't understand it and had not too good marks and wanted to improve. So I went to the public library and looked through many math books to find help. Fortunately I found some textbooks "Mathematik für Ingenieure" (Mathematics for Engineers), which was like an enlightenment. These books strated with geometry and trigonometry at high school level but with proofs and explanations I could understand. This also made my grades much better pretty soon, and I liked it so much that I read on and learned some calculus (differentiation and integration), which was not yet covered at school. So I had an advantage later, because I knew this stuff already when it became subject in class.

Then of course, in these math books, a lot of examples were taken from physics and engineering applications. So I started to get more interested in this stuff too, though already at school the science classes were much better than "math". Again in the library I found Sommerfeld's textbooks on theoretical physics. I could follow the introductory part of the first volume on point-particle mechanics, though even that was of course pretty hard. So it took a while until I could understand also the other volumes, for which you needed also vector calculus, but one could learn it from Sommerfeld's volume 2, though it took quite a time to really get the idea and being able to apply it to the physics covered in these books. I also needed other less advanced books like Gerthsen Physik (a intro university experimental physics book, which I think has not been translated to English, but comparable to a book like Halliday&Resnick) to understand the physics and, last but not least, help from my really brillant physics teacher, who was willing to help with questions also going beyond what was covered in class.

I think, Sommerfeld's books are just a class for themselves concerning classical theoretical textbooks. I think the quality of these books explains why the "Sommerfeld School" is among the most successful theoretical-physics programs ever developed. Just have a look at the list of "pupils" of and "postdocs" working with Sommerfeld or in his institute at the time (among them Pauli and Heisenberg) and how many Nobel Prizes it "produced"!

KedarMhaswade, Frabjous, etotheipi and 1 other person

## 1. What is the definition of a metre?

The metre is defined as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second.

## 2. Who came up with the definition of a metre?

The definition of a metre was first proposed by the French Academy of Sciences in 1791 and was later refined by the International Bureau of Weights and Measures in 1983.

## 3. How accurate is the definition of a metre?

The current definition of a metre is considered to be extremely accurate, with a margin of error of only 0.00000005 metres.

## 4. Why was the definition of a metre changed?

The definition of a metre was changed in order to create a more precise and universal standard of measurement that was not based on any physical object, as previous definitions had been.

## 5. How is the definition of a metre used in everyday life?

The definition of a metre is used in a wide range of scientific and technological fields, such as physics, engineering, and telecommunications. It is also used in everyday life for measuring length and distance in metric units.

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