Paul you are quibbling over small points as far as a pop program like NOVA is concerned. It's not a graduate seminar in the history of physics where your distinctions would be perhaps appropriate.
On the substantial point. Modern picture (e.g. Rovelli's Quantum Gravity):
You can picture curved spacetime as a geometrodynamical set of four tetrad Cartan 1-forms e^I that live on a fictitious Minkowksi spacetime in which e^I is a 4-vector.
Mach's Principle is then a kind of Green's theorem in which the interior BULK e^I fields in 3D+1 are determined from anyonic fields that live on the past and future fractal horizons that are pixelated hologram screen non-bounding surrounding surfaces..jpeg)
So you get Mach's Principle as the Hologram Principle.
On Nov 8, 2011, at 2:48 PM, Paul Zielinski wrote:
I like your review of Greene's book, which I found at
http://www.google.com/url?sa=t&rct=j&q=woodward%20greene%20fabric%20of%20the%20cosmos&source=web&cd=6&ved=0CEEQFjAF&url=http%3A%2F%2Fforum.nasaspaceflight.com%2Findex.php%3Faction%3Ddlattach%3Btopic%3D13020.0%3Battach%3D257690&ei=j6m5Ts6-Ao3YiQK53Y3BBA&usg=AFQjCNF71xW6Sg-IYdz7XAWZG3R_TmkYCg&cad=rja
but there are a couple of points that don't seem to add up here.
From the first Nova program:
"Space. It separates you from me, one galaxy from the next, and atoms from one another. It is everywhere in the universe. But to most of us, space is nothing, an empty void. Well, it turns out space is not what it seems. From the passenger seat of a New York cab driving near the speed of light, to a pool hall where billiard tables do fantastical things, Brian Greene reveals space as a dynamic fabric that can stretch, twist, warp, and ripple under the influence of gravity. Stranger still is a newly discovered ingredient of space that actually makes up 70 percent of the universe. Physicists call it dark energy, because while they know it's out there, driving space to expand ever more quickly, they have no idea what it is."
So, so-called "empty space" is not what it seems, it is not physically empty; it is an objective physical system, exactly as Einstein said in 1920.
I can't see how Greene could argue that this fits in with the "relationalist" paradigm that you allude to below. So I can only conclude that far from *adopting* the original relationalist version of Mach's principle, he is merely *considering* Mach's original relationalist version of what Einstein later called "Mach's principle", and is rejecting it as inconsistent with GR. Is that what you meant?
Of course I understand that you are proposing a *physical* version of "Mach's principle" which doesn't imply a relationalist view of spacetime, and which you argue is fully consistent with GR.
Interestingly, in his book Greene attributes an abstract conception of spacetime to Einstein, whereas in the 1920 Leyden address he says the exact opposite. Will the real Einstein please stand up?
Also I note that in the first Nova program the discovery of the objective physical unity of space and time (in "spacetime") is erroneously attributed to Einstein, instead of Minkowski. This is a very
common misrepresentation. In fact there was no invariant spacetime metric in Einstein's 1905 theory of relativity, and Einstein even rejected the concept as physically redundant when it was
first proposed by Minkowski.
On 11/8/2011 12:30 AM,
Gentlefolk,
I've decided to collect a little data on a new device of slightly different design before sending anything out with more results. In a few days.
Wes Kelly has noted that Brian Greene is doing a new series on Nova. It is titled "Fabric of the Cosmos", the title of a book by him published back in 2004. A choice I find a bit odd as his latest book, "The Hidden Reality", was published this past year. The Fabric of the Cosmos is also a bit odd -- because one of its central themes is Mach's principle. Something one finds almost nowhere in the popular scientific literature. [So odd, I wrote a review of the book back in 2004: Found. Phys. vol. 34, pp 1267-1273 (2004). The only other popular book I can think of that deals extensively with Mach's principle is John Gribbin's Schrodinger's Kittens and the Search for Reality published in the mid-'90s.] If you find the Mach's principle stuff unfamiliar, Greene's book does an excellent job on it -- though he opts finally for the "relationalist" version of the principle (which is physically uninteresting).
The first episode aired last week. It was promising. So, if you've got nothing better to do when Nova airs in your neck of the woods. . . .
Best,
Jim