In section 1.4 on page 8 there are multiple problems with the discussion of absolute time. It says
The English physicist Isaac Newton stated, "Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external.''
1) It's more-or-less true that he said that (Principia, book I, first scholium). However, an appeal to authority is not good practice. It is a very poor substitute for critical reasoning. When an authority says something, that doesn't make it true, and it certainly doesn't make it relevant or important.
In other words, the notion of past, present and future is universal -- "now" for you, wherever you are at this instant, is also "now" everywhere else in the universe.
2) No, that is not a restatement "in other words" of the original. Newton's meaning is clear if you read even one more sentence, or indeed the rest of the quoted sentence (continuing past the semicolon in the original Latin). Similarly the meaning is clear if you look at the preceding sentence. The words "absolute" and "true" carry equal weight, and are meant to be more-or-less synonymous. All Newton wanted was to distinguish the Platonic ideal prototypical time from some less-than-ideal operational definition or intuitive notion.
This demonstrates another of the many problems with appeal to authority. Very commonly, when I investigate quotations, I find they are being used to «prove» something wildly different from what the authority actually said.
Although this notion of the universality of time, which is given the name absolute time, is intuitive [....]
3) No, that is the opposite of what Newton was saying. The whole point of that passage was to _distinguish_ absolute time from "common" and intuitive notions of time.
4) Even if Newton had said that "true" time was the same everywhere, it would still be a bad idea from the physics point of view. It's wrong physics.
5) Even if it were true, it would be unwise to mention it, for pedagogical reasons. It would be an unnecessary complication. There is no reason whatsoever to mention "absolute time" in chapter 1, or anywhere else in the book for that matter. There is especially no reason to re-emphasize it in the chapter summary on page 27. (The summary is called a «glossary»; see item #171.) It is extra-especially weird that the summary on page 27 does not hint that there might be something wrong with the idea.
Every minute spent talking about this notion of «absolute time» is at least two minutes wasted, because it will have to be unlearned.
Suggestion:
I would say something like this
For thousands of years, people have been using physics to keep track of time. Water clocks were in use 2500 years ago. In the early 1600s, Galileo famously made good use of an oscillating pendulum. By the 1760s John Harrison was building portable chronometers accurate to a fraction of a second per day. Nowadays there are clocks that are accurate to better than 1 part in 10^15 ... or about 1 second in 300 million years.
You can keep time using mechanical processes, electronic processes, optical processes, chemical processes, biological processes, or whatever. Any real clock will have imperfections, but using your imagination you can abstract away the imperfections, and what you are left with is an ideal clock. In any reference frame, at any point, an ideal clock at that point gives us an operational definition of what we mean by time.
In section 1.4 on page 8 there are multiple problems with the discussion of
absolute time. It says1) It's more-or-less true that he said that (Principia, book I, first scholium). However, an appeal to authority is not good practice. It is a very poor substitute for critical reasoning. When an authority says something, that doesn't make it true, and it certainly doesn't make it relevant or important.
2) No, that is not a restatement "in other words" of the original. Newton's meaning is clear if you read even one more sentence, or indeed the rest of the quoted sentence (continuing past the semicolon in the original Latin). Similarly the meaning is clear if you look at the preceding sentence. The words "absolute" and "true" carry equal weight, and are meant to be more-or-less synonymous. All Newton wanted was to distinguish the Platonic ideal prototypical time from some less-than-ideal operational definition or intuitive notion.
This demonstrates another of the many problems with appeal to authority. Very commonly, when I investigate quotations, I find they are being used to «prove» something wildly different from what the authority actually said.
3) No, that is the opposite of what Newton was saying. The whole point of that passage was to _distinguish_ absolute time from "common" and intuitive notions of time.
4) Even if Newton had said that "true" time was the same everywhere, it would still be a bad idea from the physics point of view. It's wrong physics.
5) Even if it were true, it would be unwise to mention it, for pedagogical reasons. It would be an unnecessary complication. There is no reason whatsoever to mention "absolute time" in chapter 1, or anywhere else in the book for that matter. There is especially no reason to re-emphasize it in the chapter summary on page 27. (The summary is called a «glossary»; see item #171.) It is extra-especially weird that the summary on page 27 does not hint that there might be something wrong with the idea.
Every minute spent talking about this notion of «absolute time» is at least two minutes wasted, because it will have to be unlearned.
Suggestion:
I would say something like this