Is this GR Explanation Accurate for Teaching 9th Graders?

[mishima]

From an online book where the author tries to discredit GR, there's a part where he talks about forgetting about the rubber sheet analogy and just remembering:

"A body moves along the path that makes time dilation a minimum."

Then he presents a diagram and a little argument that is really clear. I'm wondering if at least that part is ok or if the whole book is garbage.

Link: [...link deleted by bcrowell...]

I'm curious because I've been struggling for a way to conduct a lesson on GR for 9th graders and this is the simplest explanation I've come across so far (if correct at all). Thanks and sorry if this is taboo to post. I just don't honestly know enough about GR to criticize this properly.

 

[bcrowell]

Hi, mishima,

Actually it is a no-no to link to crackpot sites, and Burchell's Alternative Physics site is definitely crackpot. I've edited the link out of your post.

But yes, the quote is more or less right.

The one important mistake in the quote is that it's not time dilation that is minimized, it's simply the time measured on a clock that moves along with the body from the initial event E1 to the final event E2. This clock time is usually referred to as the proper time ("proper" meaning "its own").

More minor quibbles: (1) The body has to have a small mass. (2) The proper time doesn't actually have to be minimized, just extremized. That is, it could be a local maximum rather than a local minimum. (3) The extremum is local, not global. That is, the time is only at an extreme compared to other paths that differ from it infinitesimally.

A book that presents a significant amount of GR without any math is Geroch, General relativity from A to B. Gardner's Relativity simply explained is lots of fun, although it's pretty cartoonish. A book that uses a little more math, but that I like better than Geroch, is Taylor and Wheeler, Exploring black holes.

 

[mishima]

Thanks, and again sorry. I had never seen an explanation like that and figured he probably just framed his argument in a way to help him further on or something. But good to know there's some truth to it.

And yes, I've got the A to B book coming through our interlibrary loan, its just taking a long time. I've been reading Max Jammer's "Concepts of Space", Einsteins "Relativity", and Akhundov's "Conceptions of Space and Time". The nice thing about a conceptual physics class is we can spend more time on the philosophy and history of things. I just wish I had a killer lab activity for it, but everything seems way "too big". We can't really reproduce any of the verification experiments, for example.

That's why I was desperate for this to not be pure garbage, hopefully I can retool this into a discovery activity of some sort. And why your response is most appreciated.

 

[Nabeshin]

It's also important to note that this is only for freely falling objects! Certainly not true of objects under an acceleration.

I think the simplest way to explain it is just to give up the notion of time and say that it takes the shortest path between two points. This is really the crux of the idea, it's just that the points happen to be in (t,x,y,z) space rather than normal (x,y,z). :)

 

[pervect]

The principle of maximal (or, if you're being extra cautious, extremal) aging is a common way to describe it. There's some good references on Taylor's website. "Shortest distance" is close, but really not-quite right.