Gravity Probe B (GPB) is a huge project of NASA and Standford university, in which a satellite carrying four ultra-sensitive gyroscopes were put into orbit around Earth. The idea was to test two of Einstein's General Theory of Relativity (GR) effects: the geodetic effect and inertial frame dragging.
The geodetic effect represents the effect that the curvature of spacetime have on a spinning, moving body, as predicted by GR. The geodetic effect is relatively large and should not have posed any problems for GPB to detect.
Inertial frame dragging is a GR prediction that the rotation of an object would alter space and time, dragging a nearby object out of position compared to the predictions of Newtonian physics. The predicted effect is incredibly small — about one part in a few trillion, according to Wikipedia.
Although the Wikipedia article on the geodetic effect states that it has been confirmed to the 1% level, there is evidence that the best value that they obtained are not in agreement with Einstein's GR! This NASA/Stanford slide: http://colloquia.physics.cornell.edu/11-12-2007/cornellpres_files/v3_sli...
is showing that to a 1 sigma error confidence level the results for the geodetic precession are inconsistent with GR.
There were two unexpected sources of error affecting the gyros that almost ruined the whole effort, but the project scientists are confident that they can filter out the errors and reveal the true data. They are still struggling with the geodetic effect, never mind the very much smaller frame dragging effect.
So what if this whole effort turns out one big waste of money, with no clear result?
SL: Your Aerospace Watchdog
Comments
Discoveries
November 14, 2008 by Anonymous, 33 weeks 1 day ago
Comment id: 32852
Will and usually not disclosed to the public until 40 years after the fact is very annoying, same with archeological finds, not disclosed to the public either I find that highly annoying. Most of the public doesn't even know or realize that NEW YORK had tons of giant skeletons and were over 10k years old. NEW YORK GIANTS! So funny how the most obvious thing is completely obscure to the many so busy with their lives....
NASA panel confirms: GPB has flopped!
May 29, 2008 by Burt, 1 year 5 weeks ago
Comment id: 30374
Now it's 'official'!
The science team may still prevail, though. If they 'only' need $3.8M to complete the analysis (while $800M has been spent on the mission), it seems silly to pull the plug now. Or is it a case of no good money after bad money?
Burt Jordaan (www.Relativity-4-Engineers.com)
Careful with your headline, Burt!
May 29, 2008 by Fred Bortz, 1 year 5 weeks ago
Comment id: 30376
People may miss the tongue in cheek tone here.
As you note, the decision was a budgetary one, not a scientific one. The scientists recommended further funding.
I'll pitch in ten bucks to complete the analysis if another 379,999 people join me. Or we could do it by spending 20 cents per taxpayer.
Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Re: Careful with your headline, Burt!
May 30, 2008 by Burt, 1 year 5 weeks ago
Comment id: 30405
The problem with GPB is that its reputation is now tarnished. Whatever the scientists may come up with as results will always be met with a certain degree of skepticism.
As an engineer, I feel sorry for the scientists - this has been an engineering failure to some degree, since the 'most perfect gyros in the world' did not work so perfectly!
However, I still think that NASA will allow the data to be processed to a conclusion, even if that means that failure is conceded by the scientists. After that, the 'tons' of data will be put into the public domain, where it will probably be utilized and perhaps abused for decades to come.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
It is me, Jin He
April 30, 2008 by Anonymous, 1 year 9 weeks ago
Comment id: 29498
It is me, Jin He, the anonymous software seller.
Please go to http://www.truthmost.com for details.
What is happiness? What is depression?
What is friendship? What is hatred?
What is conscience? What is evil?
What is life? What is death?
Over thousands of years, we human beings have not found the consensus answer.
We, the spoiled babies, have torn up the increasingly weak mother: the earth.
Ah, babies, it is time to lift up your heads, look at the wide and deep universe,
and trace down the blood lineage of your mother:
It is the bending hands of Milky Way -- the spiral arms - that hug Earth.
It is the broad chest of Milky Way -- the galactic disk - that shields the sun,
Are your hands and your chest related? Yes, there is your heart!
Are the Milky Way's hands and chest related? Yes, that is the meaning of the whole universe!
It provides the answer to all your questions.
Very luckily, here is a very simple ($3.8) computer software.
It says that galaxies' hands and chests are related. It provides nine real images of galaxies.
You can personally prove if the relation is true or false, solely based on the images and the software!!
The software toppling Einstein theory is for sale!
April 26, 2008 by Anonymous, 1 year 9 weeks ago
Comment id: 29402
The software toppling Einstein theory is for sale!
http://www.truthmost.com
Ignore the anonymous software seller
April 26, 2008 by Fred Bortz, 1 year 9 weeks ago
Comment id: 29404
Save your efforts, folks!
Clicking the link gets you to a bunch of hokum with the heading, "EXPLORING the Origin of Life and Conscience!"
When I read it, my plastic bust of Einstein toppled over and burst into flame :) Fortunately, my plastic Beethoven saved him.
Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Speaking for myself as a non-academic scientist
April 7, 2008 by Fred Bortz, 1 year 12 weeks ago
Comment id: 28650
Jin He,
First of all, there is no "Einstein camp." There are people who find his work compelling and interesting and spend a lot of time exploring its implications, but no serious scientist believes any theory to be beyond challenge.
Like David, I'm not an academic scientist, though I spent 20 years of my working life in an academic environment, much of it in liaison work between researchers and other professionals (sponsors, educators, etc.)
I suspect that the deletion you refer to was probably an error that needed to be corrected, but you are so upset about it that you can't see the error.
In any case, I have experience working with editors and publishers. If they own the copyright, there is little you can do. If you have the copyright, you should have been offered the chance to approve or disapprove before publication.
In this case, it sounds like the correction was necessary for the paper to be published.
But in any case, it is an issue between you and your editor. Ranting and spewing insults, as you did here, just makes you look like a jerk with a huge chip on his shoulder.
If that description fits, then you need to change the way you interact with others. If it doesn't fit, then you need to figure out why you acted like a jerk with a huge chip on his shoulder in this one case.
By the way, you might want to look at a recent book I wrote for high school and college libraries, Physics: Decade by Decade in the 20th-century science set from Facts on File (2007).
Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
How should I do?
April 7, 2008 by Anonymous, 1 year 12 weeks ago
Comment id: 28649
Re Halliday:
I do not want recall the bad exerience, e.g., a paper was published when the part against Einstein was deleted.
My urgent question is: how should I do?
I made a piece of software with real images. If it is right then Einstein is wrong. The point is that everyone can play the software and judge if it is right.
I would like to make the software to be free but I want to make profit of it for the reason you know.
But the critical problem is: will the Einstein camp be angry at me, and kill me if I make the software public?
Re: How should I do?
April 8, 2008 by Halliday, 1 year 12 weeks ago
Comment id: 28674
If you want to use some software to disprove Einstein then it will almost certainly need to be free and open source, so anyone can delve into the code to double and triple check the code to make sure it is doing what you claim it is (or else it would have to be so easy for anyone to replicate, from your description of what it does, that any reasonable implementation will reproduce what your version does).
This is necessary because one requirement of science is reproducibility!
So, other than some entertainment value, I'm hard pressed to see how you can fulfill the requirements of science, especially if you are trying to challenge a well established theory (regardless of authorship), and "make [a] profit". (I know, it tends to keep most of us scientists on the poor side.)
Now, it is good that you have expressed your "challenge" as "If it is right then Einstein is wrong." Of course I hope you recognize that the burden is on you to show whether the "software with real images" is "right". In science, the crux of any test of "right" is determined by comparison with actual experiments and/or observations of nature. No other test is meaningful—nature is the ultimate arbiter.
I certainly don't know what the nature of you software is, or what you mean by "real" images, nor do I know anything about this paper you say had what you felt was a key point "against" Einstein removed is about. I really don't even know, from what you've said, whether the two are very closely related (though I would guess that they may well be).
If you are trying to suggest that one or more of Einstein's theories suggests some unbelievable result, then the issue may simply boil down to opinion on what is "believable". If you are trying to suggest that one or more of Einstein's theories predicts something that conflicts with observations, then that's not a bad start, though you'll have to be prepared to have others show how additional considerations make a sufficient difference as to bring Einstein's predictions in line with observations. (His theories have withstood so many such challenges that it is difficult to believe that if this conflict were the case that this would not already be widely noised about.)
On the other hand, if you are trying to suggest some alternate theory, you have much more work to do. As I've said, any alternative theory must first show that it matches all previous experiments and observations. Fortunately, this is not quite as difficult as it may at first appear, so long as there are viable theories already in existence that do match such: This requirement then reduces to showing that in an appropriate limit (one appropriate for the regime for which such observations/experiments have been carried out), the new theory reduces to the alternate (this is how Special and General Relativity, and Quantum Mechanics/Field-Theory fulfilled this requirement).
Then you graduate to showing how the new theory predicts testable phenomena that differ from the former theory/theories. (You may even show how the new theory matches former observations/experiments without having to add additional assumptions, such as Dark Matter/Energy or some such.)
This is the way science progresses, this is how scientific revolutions are "fought" and "won".
David
P.S. While some "Einstein camp" may "be angry at" you, I don't see anyone other than some highly unstable type trying to kill you, in any literal sense. Now, can you expect to have your ideas criticized, receiving a great deal of critical scrutiny? Almost certainly. Extraordinary claims require extraordinary levels of "proof".
You should expect that your ideas will receive quite a "beating", being "bashed" from all possible sides against competing ideas. This is not intended to be any form of personal attach (unless you make it so, either by the way you take it and respond, or the tone you take when making your challenges—so be careful, and control your emotions). What it is intended to do is make sure that only the strongest ideas survive, and, even then, as many of the "rough" spots are smoothed out as possible. (Think of it as a testing and polishing process.)
So, admittedly, this is not for the faint of heart. This is only for those that truly believe (as objectively as they can possibly muster) that they have a better idea.
So good luck.
My addendum to Halliday
April 8, 2008 by Fred Bortz, 1 year 12 weeks ago
Comment id: 28675
Jin He,
David Halliday's advice is excellent.
You might also be able to benefit from Renaisauce's recent post, which was inspired by this discussion.
The "Galileo Complex," as Renaisauce calls it, is definitely a curable condition.
Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Re: How to vote??
April 7, 2008 by Halliday, 1 year 12 weeks ago
Comment id: 28647
I can't speak for Fred, but I'm no faculty scientist. I'm one of those non-faculty scientists you claim are the saviors of us all.
No, Fred is absolutely right, we, as scientists, are quite open to those theories that pass the test of matching experiments, both past and present, and will continue to consider such theories as potentially viable so long as they do pass said test. (Of course we'll tend to the most simple theory/explanation, all else being equal. Good ol' Occam's razor.)
There are a number of viable alternatives to General Relativity (GR) as contenders for a theory of gravity. All but one, that I know of (that have risen to the point of viability), have "tweak-able" parameters, and their parameters keep getting pushed closer and closer to being identical with General Relativity.
On the Quantum Mechanics (QM) side: I have often lamented that Quantum Mechanics is "too good for its own good", meaning that there are no viable alternatives (no alternatives have been able to be at least as good as Quantum Mechanics at matching experiments). If there exists a viable alternative (one that matches all experiments done so far), I'm more than willing to check it out!
Most serious physicists, I believe, recognize that while we have these two great theories (GR and QM), which are unsurpassed in their respective realms, there's a problem when venturing into realms that, logically, should require both or some combination thereof. GR and QM don't play well together! So there "must" be something missing, or something better.
The search for that "something better" has been going on for at least 50 years (maybe nearly 100 years, now, depending on when you "start the clock"). Unfortunately, I don't consider any of the alternatives I know of, at this time, to be quite there, yet. (Loop Quantum Gravity has some appeal to me, but I don't ascribe to it, yet. I have my own ideas, but they're not quite to the theory stage, yet. The problem would be far easier to solve if we had some viable experiments within this realm where both QM and GR should be used, but we don't have particle accelerators that are nearly powerful enough; and while some Cosmic Rays may be powerful enough it's very hard to get good statistics. If we could come by a nice microscopic "black hole" on which we could do experiments, that would really fit the bill!)
So, while we are open to viable new ideas, the hard hurdle that most seem unwilling or unable to pass is being able to match all known experiments. However, that is the critical point that must be satisfied by all theories that wish to be considered as viable. (Even GR and QM had to each satisfy this hurdle before they could be considered.)
So, if you know of something that satisfies this criteria, I'm all ears.
David
An important scientific innovation rarely
April 7, 2008 by Anonymous, 1 year 12 weeks ago
Comment id: 28646
An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out, and that the growing generation is familiarised with the ideas from the beginning
I Nominate Myself a Superdelegate
April 7, 2008 by Renaisauce, 1 year 12 weeks ago
Comment id: 28644
First, I think it's awesome that somebody responded to Fred's discussion on rants by ranting. Second, I think it's awesome that the dude thinks that he's unemployed because science isn't democratic. I suggest that going to a faculty board and calling their research a false bible isn't going to win you points with the committee. Third, is the Time Tunnel a man-made bible, or a 60's TV show?
However, if there are those of you who think that the democratization of scientific law is acceptable, I want you to know that I fully support you. I think its about time that we have a voice in simplifying the laws of physics a little. The tax code is easy by comparison. Therefore, I officially announce that I nominate myself a Superdelegate for the Election Board of Scientific Law.
I appreciate your support. I won't let you down.
How to vote??
April 7, 2008 by Anonymous, 1 year 12 weeks ago
Comment id: 28642
To Fred Bortz THE Science and technology books for young readers:
To David Halliday THE serious and careful scientist:
HOW TO VOTE????
Is there a democratic mechanism in scientific community?
No!! That is why there are millions of people who want to join faculty. No one can fire the members of faculty if they keep being compromized.
We non-faculty scientists do not have anything to lose, because we want to challenge the eternal theory of everything: BIG BANG, GENERAL RELATIVITY, TIME TUNNEL and other man-made bibles, which promise (?) to explain everything: life, conscience, man and women, how many atoms in human body, etc.
You respectable faculty SCIENTISTS have a burden: your man-made bibles are supposed and are controled to be eternal and ever-correct!!
Are you certain of your bibles? No!! Otherwise you would not visit this blog spot!!!!!!
What a great idea! Let's vote on the laws of nature.
April 7, 2008 by Fred Bortz, 1 year 12 weeks ago
Comment id: 28639
In a posting that demeans a serious and careful scientist, Jin He rants:
Like David Halliday and others here, I have seen too many posts (and received private e-mails) that say, essentially, "I've got this brilliant interpretation that overthrows relativity and/or quantum mechanics, but it is rejected by a cabal of stick-in-the-mud editors and establishment scientists who suppress it because it threatens them."
In the end such posts, and Jin He's rant, ignore that scientists are more open to new ideas and new evidence than almost anyone else.
As long as a growing body of evidence supports those theories and interpretations of natural phenomena, neither ranting nor democratic voting will discredit them. On the other hand credible evidence that is contrary to those theories and interpretations will force their reassessment.
Jin He wants to put the laws of nature to a vote. I would much prefer to discuss the evidence instead.
Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Re: ``I want to be famous?
April 7, 2008 by Anonymous, 1 year 12 weeks ago
Comment id: 28635
To Halliday:
If you visit those more democratic forums, you will see that there are large amounts of discussion on Relativity, Gravity, Cosmology. This means these area of science get big problems!!! You can not suppress the voices of the public!!
It is not the public who want fame, want Nobel, want status. It is those sitting on chairs, on offices, on editorial, on prestigious univs who dream of the fame, the Nobel.
I myself no longer consider Nobel prize a fame. It is a game like Chinese selection of SuperGirl!!
Copernicus, Bruno, Galileo were not courting such that "I want to be famous, so I invented a 'theory'".
They did not even have the most basic freedom. Today we are in the similar situation with modern guile!!!
You know some terminology of math does not mean you own truth!!
Jin He
An Important Scientific Innovation
April 6, 2008 by Anonymous, 1 year 12 weeks ago
Comment id: 28614
It has happened already. How many people are ignorant of the theory of Dipole Gravity?
Never heard of!!!
You have to read it to believe it. But then it is a theory proposed by a Korean physicist. He claims it is self evident and urges Dr. Kip Thorne or anyone considers him/her self an expert in the field to challenge it.
He has the fundamental physical anomaly in his theory to support the validity of it, that is, the anomalous shift of the center of mass of a rotating hemisphere.
He says there is a shift of center of mass for the rotating hemisphere but there is not for a rotating sphere and askes why ?
He came to the conclusion that this is the cause of the real, meaningful gravitational dipole moment, which is the true gravitomagentism thought to exist in general relativity.
The conventional gravitomagnetism described in Wikipedia was derived from the modified Maxwell's equation which is not the real gravitomagnetism.
The crooks in the field could not acknowledge dipole gravity. And they are looking for answers in the wrong place.
"An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out, and that the growing generation is familiarised with the ideas from the beginning."
This is happening right in front of your nose.
Re: An Important Scientific Innovation
April 7, 2008 by Halliday, 1 year 12 weeks ago
Comment id: 28633
Never heard of "Dipole Gravity". (Of course there are so many "I want to be famous, so I invented a 'theory'" type theories of gravity out there.)
Of course, if this "researcher" has to ask why there is no shift in the center of mass of a rotating sphere (as opposed to the rotating hemisphere) then I have to ask whether he has much in the way of understanding. Since I presume the rotating hemisphere is rotating about its axis of rotational symmetry, then the answer is simply the fact that the sphere has an additional mirror symmetry perpendicular to the axis of rotation, through the center of the sphere. This symmetry alone precludes any such shift! (See, so simple one doesn't even need any calculations, and the result is theory independent.)
David
P.S. Of course you'll probably claim I'm one of the "crooks in the field".
X-treme amounts of facts that GR, BigBang are majorly wrong!!
April 4, 2008 by Anonymous, 1 year 13 weeks ago
Comment id: 28553
X-ray man:
There two kinds of people in the world. One kind do not understand GR and even basic physics. The other who have business with GR are corrupted like people in the times of Galileo!
In fact, Newtonian theory is only applicable to the system of one or two bodies. For the system of three or more bodies which have similar masses like stars, Newtonian theory and all other theories have no answer for their patterns! But people insist on the application of these theories to the description of galaxies as well as the whole universe, in exactly the same way that people believed the sun as well as the whole universe had revolved around the Earth. Of course, this endeavor is unsuccessful and people resort to the assumption that the vast majority of the universe is some magical yet never-observable dark matter, dark energy and so on.
"An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out, and that the growing generation is familiarised with the ideas from the beginning.''
By the Father of Quantum Mechanics: Max Planck
Jin He
GP_B results
March 14, 2008 by Anonymous, 1 year 16 weeks ago
Comment id: 28128
To Scruffy:
are you serious? a 1 sigma observational discrepancy means that, given a large number of repeats of such an experiment, roughly 33% of such experiments would disagree at the 1 sigma level, even if they were perfectly consistent with Einstein's GR (given an observation with no experimental error)... so I would consider this excellent agreement with GR - only if there were something like a 3 sigma or greater discrepancy would I begin to get worried -
they do, of course, have a long way to go to verify the Lens-Thirring (frame-dragging) effect ... much more difficult analysis ..
X-ray man
An aside in Hilbert-Einstein discussion re causality
March 5, 2008 by Fred Bortz, 1 year 17 weeks ago
Comment id: 27946
For Hawking's view on the preservation of causality presented in accessible language, you might want to read his The Universe in a Nutshell. My review discusses that a bit, both in prose and in its opening limerick!
That's right, a limerick about wormholes, black holes, causality, and a smiling man with a synthetic voice tooling about in a motorized wheelchair.
Enjoy!
Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Re: An aside in Hilbert-Einstein discussion re causality
March 5, 2008 by Christopher Joh..., 1 year 17 weeks ago
Comment id: 27960
Fred Bortz, Thank you for this. Sincerely, Christopher
Re5: David, Whitehead, meaning of the Hilbert-Einstein
February 28, 2008 by Christopher Joh..., 1 year 18 weeks ago
Comment id: 27827
David.
Are you saying that you won't read Whitehead and Logunov and Hilbert because you rely on my comments instead?
Sincerely,
Christopher
Re: Re5: David, Whitehead, meaning of the Hilbert-Einstein
February 28, 2008 by Halliday, 1 year 18 weeks ago
Comment id: 27828
Christopher:
I'm not relying on your comments "instead". I'm only surmising from what you appear to be saying, since I haven't, yet, done the reading. (I'm not sure when I'll have the time to actually read their works, as opposed to some possible sources I have more readily available that may have touched upon some of this. I have work to do of a completely different nature that is becoming increasingly demanding, for the next month or so.)
My comments about "actual" vs. "effective" curvature and "interpretation" is simply a statement of a potential situation this issue may relate to. It's just a guess, based on the very limited, third hand information I have, right now. Nothing more or less.
I'm certainly not passing judgment based on such limited information. I'm sorry if I gave anyone any other impression.
David
Re6: David, Whitehead, meaning of the Hilbert-Einstein
February 28, 2008 by Christopher Joh..., 1 year 18 weeks ago
Comment id: 27833
David,
I think one way of putting it in a nutshell is whether there is just one underlying Minkowski space or whether there are uncountably many tangent spaces each with its private Minkowski geometry. I think the 'effective geometry' story says one, while the orthodoxy says many. I think this is a difference that matters.
Sincerely,
Christopher
Re: Re6: David, Whitehead, meaning of the Hilbert-Einstein
February 29, 2008 by Halliday, 1 year 18 weeks ago
Comment id: 27843
Christopher:
I have been able to read somewhat about Whiteheads idea(s) in Misner, Thorne, and Wheeler's Gravitation. (Admittedly, they are almost exclusively referring to his 1922 "theory", which you have pointed out, before, was more of an illustrative model.)
Would it be fair to say that the seminal difference between Einstein's interpretation and that of Whitehead is whether the "metric" within General Relativity is the "actual"/"true" (dynamic) metric (Einstein), or an "effective" metric or other "field" built upon an (unobservable) "background" metric (also referred to as a "prior geometry")? So the "one underlying Minkowski space" you refer to is this (unobservable) "prior geometry"?
If that's the case, then Whitehead is far from alone, right now. Within attempts to reconcile General Relativity and Quantum Mechanics (more specifically Quantum Field Theory), or, in other words, to create a Quantum theory of Gravity, it seems to me that the majority (nearly all) are "prior geometry" type theories. (Super-string theory is one such that you may be familiar with.) (Incidentally, many of these theories use a vierbein or tetrad formulation of the Hilbert-Einstein equation[s].)
Have I properly grasped at least a portion of the point of divergence between Einstein's (the "orthodoxy") and Whitehead's views?
David
P.S. I get the impression that Quantum Mechanics, at least as many of these practitioners envision and/or interpret it, has a very difficult time handling curved spacetimes. My dissertation pertained to a way of extending Dirac's equation(s), in addition to other aspects, such that, at least at the "first quantization" stage, one can, indeed, handle Quantum Mechanics (at least in the form of this generalized Dirac equation) with curved spacetime. One important aspect was to recognize that the "surface" (spatial) integral involved in a (Copenhagen-type) measurement does not have to be along a "plain" of simultaneity.
Re7: David, Whitehead, meaning of the Hilbert-Einstein
March 2, 2008 by Christopher Joh..., 1 year 17 weeks ago
Comment id: 27862
David,
Thank you for your reply that starts by referring to Whitehead’s illustrative model.
I am wary of talking at this stage of what is “true†or “observable†or “priorâ€.
Perhaps it may be useful to distinguish several viewpoints.
I am saying that as for how to read the equations, Whitehead is ceremoniously kicked down the front entrance steps by the palace guard of the orthodoxy, and then, because the lights go out and the stove goes cold and the clocks stop when he leaves, he is taken in again by the butler through the back door, so that the meals can be ready on time.
It is not common for a practical physical problem to be dealt with from first principles in full detail and with full rigour by the pure methods of strict orthodoxy. Mostly, I think people think and talk and calculate real physical problems in the heretical way, but when pressed on certain occasions, they report this as if they were doing it orthodoxly, and most readers are not too fussed by this.
I think the Whitehead position is that "Within General Relativity" one can accept nothing, not the "metric", not the "effective" metric. He thinks it is physically meaningless nonsense, because it abandons causality. He wants to refer to a single underlying Minkowski geometry (such as is not admitted by ‘the general theory of relativity’) and build effective geometries on that. Zeeman’s causality argument seems to support him.
I think Logunov also thinks that the ‘general theory of relativity’ is seriously deficient in physical meaning, but for slightly different reasons. He thinks that the ‘general theory of relativity’ is incomplete, so that it does not make definite predictions for empirical testing, and because it would leave physics crippled and incapacitated, lacking the conservations laws. (By way of correction of a previous remark of mine, Logunov seems to think that Hilbert is orthodox.)
Steven Weinberg at page 147 tells us that he is unfussed but in brackets he warns the reader that some others are not:
“ … the geometric interpretation of the theory of gravitation has dwindled to a mere analogy, which lingers in our heritage in terms like “metric†… … it simply doesn’t matter whether we ascribe these predictions to the physical effect of gravitational fields … or to a curvature of space and time. (The reader should be warned that these views are heterodox and would meet with objections from many general relativists.)â€
Feynman is also unfussed, on page 113:
“It is one of the peculiar aspects of the theory of gravitation, that it has both a field interpretation and a geometrical interpretation.â€
But Whitehead and Logunov are careful to argue that this should be fussed about: it is not a matter of two valid interpretations, but of one physically incapacitated or nonsensical and the other valid.
Perhaps I may unpack the nutshell a little.
In the Whitehead view, the speed constant that relates time and space for quasi-static geometry far from heavy things is the empirically apparently universally constant maximum speed of propagation of causal agency, and is the speed constant that appears in the Lorentz-Minkowski formulas. Experience tells us that far from heavy things, light travels very nearly that fast, but that is an empirical finding, not a definition. It is only since Shapiro that we have tried to directly measure the speed of light near a heavy thing, to compare it with the speed far from a heavy thing.
As I understand the orthodoxy, it is futile to speak of the speed of propagation of gravitational causal agency, because gravity is geometry, and the notions of its "propagation" and of its "causal agency" are both sheer nonsense, devoid of meaning.
According to the heresy, as I understand it, it makes sense to speak of the speed of propagation of gravitational causal agency. It has not proved easy to make empirical measurements of it (supposing it does have physical meaning). Far from a heavy thing, gravity is weak and hard to measure. Also we want to measure the speed of its propagation near heavy things, but there the climate can be uncomfortable. So far as I know, it is empirically an open question whether gravity travels perhaps at the speed of light, or perhaps at the (in principle not necessarily the same) universally constant maximum speed of propagation of causal agency, and whether it travels more slowly near heavy things.
I read Clifford Will, a redoubtable scholar, saying on the internet at http://physics.wustl.edu/cmw/SpeedofGravity.html
that the right way to measure the speed of gravity is by observations of gravity waves. Will there and also at http://arxiv.org/abs/astro-ph/0301145 comments on another proposed way to measure the speed of gravity. Will uses the post-Newtonian account for his analysis of the matter. I think the post-Newtonian account is a Whitehead way of doing things. Logunov also thinks that, like the speed of gravity, gravity waves have no meaning in the orthodoxy, but they have a meaning in the heretical view; Logunov thinks that Einstein adopts the heretical view when he talks about this, because, he says, of Einstein’s “formidable intuition†for physics. Caused by cyclical processes in far-off heavy things, gravity waves propagating to us have not yet been observed. We owe it largely to Will’s fine scholarship that we know and thoroughly understand that Whitehead’s illustrative model is empirically wrong.
Sincerely,
Christopher
Re: Re7: David, Whitehead, meaning of the Hilbert-Einstein
March 5, 2008 by Halliday, 1 year 17 weeks ago
Comment id: 27944
Christopher:
According to your comment:
You either don't understand "the orthodoxy", or "the orthodoxy" is not what you believe it to be (very nearly the same thing), or I have simply never experienced such an "orthodoxy" (which causes me to wonder whether such exists). (Of course this "causal agency" thing does appear to be a rather nebulous concept for geometry.)
(It might be of interest to note that Jim Arnold's "heretical" views of Gravitation fit into the category of "Gravitation as Geometry" precludes "energy bearing" gravitational waves. So if his views are "heresy", even though he appears to strongly adhere to the "orthodox" view that "Gravitation is Geometry" [including, it would appear, that "propagation" is not meaningful within such a context] then where is "the orthodoxy" here?)
I consider Feynman to be quite right in his observation: “It is one of the peculiar aspects of the theory of gravitation, that it has both a field interpretation and a geometrical interpretation.†(In fact, it can even be interpreted as a "dynamical aether" theory.)
You say:
Unfortunately, you either have misinterpreted Whitehead, or he has a far different view of "causality" than I, at least, do. (Unfortunately, I'm not sure what Zeeman's causality argument is, so I'm not sure what the disagreement is, here.)
Within General Relativity causality is fully preserved, at least locally. The only sense in which causality is even potentially violated is when the topology (non-local, an essentially global characteristic) is taken into account. However, this is way outside the purview of the Hilbert-Einstein equations, since they only apply locally. (Even Special Relativity, or even Newtonian Mechanics [Galilean Relativity], can succumb to this issue.)
Furthermore, on the matter of "conservation laws" you state:
I'm not sure what "conservation laws" he appears to think are "lacking". Going from Newtonian to Relativistic views did loose, or at least modify, some "conservation laws" (similarly going to the Quantum Mechanical view). And it is true that there are some "conservation laws" that are modified and/or combined into more general "conservation laws" within General Relativity.* However, this is far from "lacking conservation laws".
As for the assertion that General Relativity "does not make definite predictions for empirical testing", I'm not sure what is being referred to here, either. Surely he, and you, know of the myriad of tests General Relativity has inspired and passed. Is it simply the fact that there is no one-single answer for the "metric" when solving the equations? You do know there is a very physical reason for this, right?
I'll have to see when I can devote the time it appears I'll need to track down some of these issues/questions.
Personally, I prefer the "Gravity is Geometry" viewpoint. Within this viewpoint, I have no problem trying to trace the "propagation" of "disturbances" within this geometry (such as the propagation of waves). (In fact, I believe it may be instructive to take a look at the treatment of Gravitational Waves within Misner, Thorne, and Wheeler's Gravitation tome. They look at it both as a perturbation on an "underlying" geometry [the linear approximation, as in "perturbation", not to be confused with "prior geometry"], and at least one exact solution where all can be viewed as geometry. As they put it, it can aid the understanding to take a look at phenomena from a variety of perspectives.)
However, in order to view "propagation" of anything within a spacetime (a space that combines space and time) one has to shift one's perspective down to one of space plus time (the usual old "pre-relativistic" perspective), rather than the global spacetime perspective (that, frankly, most people appear to have a hard time actually achieving, or at least maintaining for long). After all, within the global spacetime perspective all of space and time is rolled into one single entity that is "static" in that it doesn't change (not in this global perspective), it just "is". It's really a matter of perspective.
David
NOTE: I have now edited this post. So, hopefully, it's improved. :-)
* For instance, the separate conservations of mass, energy, and momentum, within Newtonian Mechanics, are changed into a combined conservation of mass-energy-momentum (as a four-vector quantity) within Special Relativity. Furthermore, within General Relativity, this gets combined and generalized into a conservation of mass-energy-momentum-stress (as a tensor quantity). Even within Newtonian mechanics one has to add a new form of energy, gravitational "potential" energy, in order to preserve conservation of energy with gravity.**
** Incidentally, are you aware how distasteful Newton's own theory of gravity was to Newton? This whole "action at a distance" thing was just too much for him to accept. Of course, then "physics" invented the concept of "fields" to handle such issues. Is that the "reality", or simply "man's" own limited way of explaining what is not "fully understood"? (Is it too similar to invention of "gods" to explain things?)
Re8: David, Whitehead, meaning of the Hilbert-Einstein
March 5, 2008 by Christopher Joh..., 1 year 17 weeks ago
Comment id: 27958
David,
Thank you for this.
You write:
Personally, I prefer the "Gravity is geometry" viewpoint.
That is what I mean by the orthodoxy.
By 'Zeeman's argument' I refer to "Causality implies the Lorentz group" at http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMA...
It seems I am unwise to give my summary interpretations of Whitehead and Logunov. I look forward to your interpretations of them.
Sincerely,
Christopher
Re: Re8: David, Whitehead, meaning of the Hilbert-Einstein
March 6, 2008 by Halliday, 1 year 17 weeks ago
Comment id: 27981
Christopher:
I don't see that you are "unwise to give my summary interpretations of Whitehead and Logunov."
I have realized that you see the "Gravity is geometry" viewpoint as "the orthodoxy". However, your other characterizations of this "orthodoxy" appear to be inapplicable (as I've tried to point out). (Perhaps I was unwise to admit to this view, though I would expect it is reasonably apparent in my other messages. I also hope it is reasonably apparent that I see these things from multiple points of view. I, like most everyone, do, however, have a particular view I "prefer".)
On the "Causality implies the Lorentz group": First, the Lorentz group stems entirely from Minkowski space (nothing new, and nothing Zeeman is denying). Second, while Minkowski type metrics ("metrics", or pseudo-metrics, with only a single eigenvalue with opposite sign to all other eigenvalues) are the only non-singular metrics that provide for causality, the "metric" of Newtonian mechanics (Galilean Relativity) also preserves causality (as anyone steeped in classical physics can tell you). Third, the Minkowski-like metric is indeed the character of the metric of General Relativity. So, just as I, and Fred, said, General Relativity fully preserves Causality locally (in fact this is the only way the Lorentz group is typically applied in physics: Global gauge groups are a bygone concept, as far as I can see). And even globally causality is only "violated" under special topological cases that can just as well trip up Special Relativity, even with it's flat Minkowski spacetime. (So what's the argument here?)*
The only way I think you can think yourself "unwise to give my summary interpretations of Whitehead and Logunov" is if you think you need to hide information in order to get me, or others, to consider your position. (Unless, I suppose, you consider that you may have too narrow an understanding of their positions to do much more than mislead [unintentionally, of course] someone like myself as to their true/full positions.)
Don't fear, I'll still be looking into this when things settle down here, as I said in my previous messages.
David
* Interestingly, while searching for a copy of Zeeman's paper that I can read (without shelling out $30+) I found an intesting abstract to an article by A. J. Briginshaw, entitled Elementary proof of Zeeman's theorem, which claims "an elementary group-theoretic proof of the theorem that global causality implies the Lorentz group." So he, at least, appears to be pushing a global application of the Lorentz group. (Unfortunately, this paper also costs $30+.)
However, as I delve further, I find the Zeeman's theorem is not concerning causality in general, but causality preserving self-transformations of Minkowski space! So it already presumes Minkowski space.
(Incidentally, I also find the theorem referred to as the Alexandrov-Zeeman theorem, so I suppose Alexandrov either contributed to, refined, or extended it; or he independently came up with an equivalent theorem at about the same time, or even earlier. I wonder whether this is the A. D. Alexandrov I have seen references to.)
Re9: David, Whitehead, meaning of the Hilbert-Einstein
March 9, 2008 by Christopher Joh..., 1 year 16 weeks ago
Comment id: 28036
David,
Thank you for this.
According to Logunov, the Hilbert-Einstein equations mean that gravity does not form any black hole with a core of a singular accumulation of matter, and that causality is not violated, because they have to be read in terms of a single underlying Minkowski geometry. This is required by the conservation laws.
Sincerely,
Christopher
Re: David's reply to Re: meaning of the Hilbert-Einstein etc
February 25, 2008 by Christopher Joh..., 1 year 18 weeks ago
Comment id: 27768
David, Thank you for your very kind replies. I will read and consider the latest carefully and then reply. I note that you are not the textbook writer. That is no disappointment: what matters to me is your really serious and kind attention to my questions, and your perspicacity and perspective. Sincerely, Christopher
Scruffy's reply to RE: meaning of the Hilbert-Einstein equations
February 23, 2008 by Christopher Joh..., 1 year 18 weeks ago
Comment id: 27733
Hi Scruffy.
Thank you again for your reply, to which I have already replied, but now I need to add a small point. This present post is a near duplicate of one I tried to post, but that I cannot find as having made it into the blog.
I was mistaken to contradict you when I wrote that the Whitehead equations are not responsible for the Nordvedt effect. I then thought that their emprical failure was just due to the "Whitehead term". I have now learnt that the Whitehead equations do also predict the Nordvedt effect, and this is one of the now proven five ways in which they are now known to contradict empirical observations, thanks to the great scholarship of Clifford Will. As you say, Whitehead's equations are ruled out as a theory of gravity. But as I have written before, that does not impugn the point I was making.
Regards,
Christopher
Re: David's reply to Re: meaning of the Hilbert-Einstein etc
February 24, 2008 by Christopher Joh..., 1 year 18 weeks ago
Comment id: 27679
David,
Thank you for your very much appreciated reply. (I haven't mastered the navigation of this blog. I suppose I will learn.)
David, I greatly respect and admire your approach and history as you tell it in your reply ( I have not yet followed up your reference to "accounts elsewhere"). I am sorry that I have been unable to do the same as you have done. Yes, I really am sorry about that. I find it a serious handicap. I think it comes from a deep fear of learning something that seems to be very fundamental, and then having to unlearn it, a process that I fear, perhaps irrationally, is never really reliable for a simple mind.
I take the point that you were not brainwashed, though I said only that you were "in thrall to the orthodoxy". (I am glad to find that you were not brainwashed, and I did not wish that you were, though I confess I did fear it!) I trust you will accept my apology. Now that we have dealt with that, I am really hopeful of learning something from you if you have the patience. I trust you will forgive my previous initial rather pugilistic manner, intended to attract attention and to warn the reader that I really want a critical and creative answer.
Your next paragraph, about metrics and pseudo-metrics, is more or less intelligible to me, within my intellectual limitations.
It may perhaps clarify my viewpoint if I say that I think we are looking at something as simple as whether the metric is an alibi or an alias map. Likely that is not the right language for a many-to-one map, but the question that concerns me is indeed as simple as that, I think.
I mean that the textbooks of differential geometry refer the metric of the curved object back to the one and only underlying uniform host space.
But, in extreme contrast to this, indeed as I understand it, as a travesty of it, the 'metric' of orthodox 'general theory of relativity' refers to an infinity of local tangent spaces, each with its own private metric, one local tangent space for every point in the curved object. As I understand it, the local 'metric' refers to a local measurement in a the local tangent space. There is a generally non-uniform relation between the local tangent space and the underlying host space; even more, there is really no physical meaning for the underlying host space, and physical meaning holds only for the local tangent spaces. This is because the physical measurements are not referred to a single uniform underlying host Minkowski space but are referred to local physical atoms with their local electromagnetic radiations as examined in local atomic fountain clocks and local diffraction gratings.
Perhaps I am mistaken in this?
As I understand the situation, I believe that textbooks of differential geometry would refer the metric, of mixed sign and of non-uniform character when written in the exotic coordinate system, back to the underlying uniform host geometry. I take the point, now clear to me, that textbooks usually, initially at least, take the underlying uniform host geometry to be Euclidean, but quite validly departing from that, we have found empirically that space-time is Minkowskian, and so the textbooks would say the metric that interests us has mixed signature and refers back to our preferred underlying host Minkowski geometry (not some inappropriate Euclidean host structure). Minkowski geometry is, as I understand it, one of the possible hyperbolic geometries of R^4, Euclidean as to 3 dimensions and 1 dimension in each restricted frame, hyperbolic as to 4 dimensions in the full frame.
I use the " " around the word geometry to emphasise what I think is the case, that a geometry has a specific uniform kind of transformation that characterises it (Klein), as against the non-uniformity of the adventures of the 'general theory' picture of "curved space-time". As I see it, the non-uniform "geometries" can easily have non-physical conceptually compound coordinate systems that mix space and time in ways that can only be approached by carefully adapted calculations and not by any direct measurement, while only space and time are directly and immediately physically measurable. This means that I think light travels more slowly and in hyperbolic arcs near heavy objects, and this statement has direct immediate physical meaning, and is not some kind of naive approximation to the ""reality of curved space-time"". The latter is, in my understanding, a metaphor for descriptions in terms of fancy coordinate systems. Yes, very suitable and well chosen coordinate systems, but still fancy. Whitehead and Logunov regard them as belonging to "effective geometries", which have physical meaning as geometries only in terms of the Minkowski geometry of the underlying host space.
For candidates as geometries to describe our physical world, I see it as, not that they can be seen as vector spaces, but rather, that they are uniform, that matters here. By uniform I mean that all points have the same status, and so also for lines; no preferred point such as an origin. We believe for empirical reasons that quasi-static physical space (as distinct from quasi-static physical time) is three dimensional and orientable, admitting measuring rods, with all points having the same status. Not because of any match to vector spaces, hyperbolic and elliptic space geometries count as candidate geometries for quasi-static space because they give all quasi-static space points the same status, are oriented, and admit measuring rods, admittedly strange ones, that in the event disqualify them from accounting our physical world, as found by Gauss's mountain-top measurements of angles. But they and Euclidean geometry are candidates because all their points are equivalent, and so they are what I call uniform. Projective geometry, though uniform, does not count here as a candidate geometry because it is non-orientable (it goes further than giving the same status to all points, and the same status to all lines, in giving the same status to all conics, I think; I am not sure about measuring rods for it.)
What I mean by the terms of the Hilbert-Einstein equations is how to put the measurement numbers into the algebraic formulas. What I mean is that physical measurement numbers should go into the equations at points where the equations are written in physical coordinates, not in general potentially non-physical coordinates. The only way this can be done is to transform the equations into the underlying host Minkowski frame. As I understand the orthodox view of "the general theory of relativity" such a uniform host Minkowski frame is fairy-tale nonsense, or at best, with a very charitable reading, an approximation to a proper account. (So they condescendingly call the PPN system an "approximation", implying that it refers to a ""local tangent space"" of the ""real curved space-time"". I take it as the only physically real description, as far as I understand it, though I am not sure that I do.)
For me, physically for a particular problem, I would approximate a suitable proper Minkowski frame by setting up a laboratory far enough, but not too far, from the nearest seriously heavy object, and taking the centre of gravity of that object as an origin of a coordinate system, which I will call inertial, to the approximation of the problem. Then I will do geometry with radar, photographs, and refer to remote pulsars for time, and other remote objects for direction. I will take into account that light rays bend and are delayed as they go by heavy objects, of which I will keep an updated chart for constant use. I will take into account that radio reports from my remote locally stationed research associates are made in their local conditions and must be adjusted to read properly in the proper Minkowski frame. For some problems, the earth is near enough to an inertial reference centre. For more delicate problems, the solar sytem is needed as a reference. And so as problems are more delicate, we progress to heavier and heavier reference systems as necessary (the Milky Way, and so on). The reference system has to be so heavy that nothing of interest to our problem has a detectable effect on its centre of gravity motion. This is more tedious than sophisiticatedly leaping to what I view as fancy local coordinate systems; but I feel safer with it.
I think I am not alone in my view. As you are doubtless aware, A. A. Logunov has written extensively in what I understand as being along the lines of the previous paragraph. He is no dill. I have read some four books on this by him, and several articles. I think (with a slight reservation not worth stating here) that he is mistaken in his claim that it makes sense to "derive" Minkowski geometry from dynamical experimental data. I think the choice of Minkowski geometry is rationally derived only from experiments, starting with measuring rods (Euclid) and ordinary clocks (Alfred the Great), with slowly moving objects far from heavy objects, and progressing to radar and photography, with fast moving objects far from heavy objects, and I think this is what Whitehead is proposing. I think light speed needs to be measured, not dictated by the definitions of length and time.
Your P.S. is most welcome to me. It tells me that you will really help me here. May I repeat that I think Whitehead knew and said that his equations were quite likely empirically wrong; their purpose is to illustrate the Minkowski approach by showing how it can write testable equations, not to try to deny the correctness of the more likely Hilbert-Einstein equations. I would like very much also to have your opinion about how you think Hilbert viewed this problem. I think Hilbert agreed with Whitehead on the single underlying host Minkowski matter, though of course he did not believe the Whitehead gravity equations. I have just last night read Clifford Will's five point demolition (an understatement!!!) of the latter. But in that paper he doesn't at all consider or address the question that I am raising here.
Last night I learnt from the internet that there is a David Halliday who has written books about this kind of thing. I might indeed be hearing from a really top expert here. That would have to count as a big stroke of luck, indeed a mighty privilege, for me.
Sincerely,
Christopher
Re: David's reply to Re: meaning of the Hilbert-Einstein etc
February 25, 2008 by Halliday, 1 year 18 weeks ago
Comment id: 27766
Christopher:
While I said it will take me some additional time to properly address your post, I believe there are a few points I may be able to take care of right now.
I'm not sure what texts on "differential geometry" you are referring to. The only such texts I have ever seen that refer back to an "underlying uniform host geometry" would be those that are intended only for classical (Newtonian) mechanics (like the one I had for an advance [classical] mechanics course). In this case any "exotic metric" (which will always be positive definite, unless one is going beyond classical mechanics) is simply a transformation of the coordinates away from those usually employed for classical mechanics (Euclidean). (One can certainly do the same thing with regard to the mechanics of Special Relativity, in which case the metric has Minkowski character.)
The only way the metric (or pseudo-metric) and/or coordinates can be referred back to an "underlying uniform host geometry" that is not of a higher dimensionality is if there is no intrinsic curvature (which, as per Riemannian geometry, is directly related to the Riemann Curvature Tensor, the "trace" of which yields the Ricci tensor usually used in the expression of the Hilbert-Einstein equation[s]). Under such conditions the spacetime is flat, and the whole space and the tangent space(s) can be identified as one and the same (like the Minkowski spacetime of Special Relativity). (Think of trying to relate the "geometry" of the surface of a sphere [such as is doable using classical Riemannian geometry, using only two dimensions] to an "underlying uniform host geometry". You cannot "squash" the sphere to a two dimensional plane without loosing geometric information, like distances and/or angles. [Think of the various projections of the Earth's surface.])
So classical differential geometry has the special status that all spaces are flat. The more "complicated" mathematics can be viewed as simply dealing with the otherwise Euclidean (or even Minkowskian) space in a way that doesn't explicitly take advantage of the ability to identify the (whole, global) space with its tangent space(s).
On the other hand, the full differential geometry of Riemannian geometry is explicitly designed to handle cases of intrinsic curvature that prevent any global identification of the space with its tangent spaces. Certainly one may do such for a very localized portion of the space (like a plot of land on the surface of the Earth), but it can only be accomplished for the whole space if the Riemann Curvature Tensor is zero everywhere (flat space and/or spacetime).
As for the treatment of coordinate points as equals. Well, this is one of the things that has "enamored" me with the differential geometry as used by Riemann and extended within General Relativity and beyond. :-)
I have seen no other system that treats all points and all coordinates with such equality. Certainly not Galilean Relativity (the "relativity" of Newtonian mechanics) or Special Relativity, with their emphasis (or even reliance) upon "inertial reference frames or coordinate systems". Differential Geometry, within classical (Newtonian) mechanics does open up classical mechanics to the use of arbitrary coordinate systems, and alleviates the reliance on inertial coordinate systems, but it can be seen as somewhat artificial, since there are always such special systems lurking in the shadows.
On the other hand, Differential Geometry as used within the context of (pseudo-)Riemannian geometry allows for full coordinate freedom (there are even coordinate free expressions, in terms of Tensors, covariant derivatives, and such): All coordinate systems are equally good. Basically the philosophy can be expressed as: The "stuff" of the universe (particles, fields, etc.) care absolutely nothing about what labels we apply to the points in space and time; they will "do their thing" regardless of how we choose to describe what they are doing. So there are truly no special points, special "reference frames", etc. You may use whatever coordinates suits you. You may "synchronize" your clocks any way you choose (or use the light pulses from a single pulsar, or whatever), you may mark out positions in any manner you wish. It doesn't matter, so long as you have at least finite coordinate patches that are "good" (don't map multiple points to a single set of coordinates, or vise versa, and are at least sufficiently continuous for your desired computations).
Really, what are "physical coordinates"? Any set of "measurements" that can be used to determine "good" coordinate patches (as I expressed above) may be used. These may involve rods and synchronized clocks, they may be observations of multiple pulsars, or anything. True, there will likely be an infinite number of such possibilities, and, even more so, the number of possible coordinate systems that may be used to express any given problem and/or solution within General Relativity (for instance). Such is the freedom one obtains.
Can you set up a coordinate system that is sort of "Minkowski-like", as you propose? Certainly. Is it any "better" than any other coordinate system? Probably not (though there may be "better" coordinate systems if yours "breaks down" at certain places, which is quite likely when trying to apply a flat space like coordinate system to something that is inherently not flat [again think of maps of the Earth]).
So as long as one keeps in mind the possible limitations of applicability of any particular coordinate system (hence the possible need for coordinate patches, where one may use different coordinates for different patches, with mappings between patches where they meet or overlap [but this is really a more advanced application of differential geometry that is usually avoided by most practitioners and many textbooks]), one is free to use any coordinate system one may desire, regardless of construction.
So, does this help, or just muddy the waters? (I hope it helps, of course.)
David
Re: David's reply to Re: meaning of the Hilbert-Einstein etc
February 25, 2008 by Christopher Joh..., 1 year 18 weeks ago
Comment id: 27771
David,
It seems you intend to read some of Whitehead. Perhaps it may save you some time if you have not already focused on them, if I point to An Enquiry concerning the Principles of Natural Knowledge, Cambridge, 1919, second edition 1925, reprinted 1955; and The Principle of Relativity with applications to Physical Science, Cambridge, 1922. Much of the philosophy is re-considered and re-cast, with the last tentative exposition in Process and Reality, an essay in Cosmology, but I think you may not want to start with that, since the philosophy is not too much different and perhaps not entirely necessary. (Do not be put off by Whitehead’s talk of god; I think it is entirely removable and ignorable without any damage to his work on gravity; to be put off by it would be like saying Aristotle is not worth reading because … etc.)
My belief that this matter is worth serious pursuit is based not only on Whitehead’s persuasive reasoning, but also on the work of Anatoly Alexeyevitch Logunov. Logunov is not a Whitehead fan, but he agrees in the most important respect, apparently independently, with the key position that I think Whitehead takes. I think Logunov may be of more use to you than Whitehead, because Logunov is far more up-to-date and of course he is aware of the strength of the orthodox view and has a range of arguments to deal with it. You may need to buy on the internet copies of Logunov for yourself if they are not in your local library. I think Lectures in Relativity and Gravitation: a Modern Look, translated from Russian by Alexander Repyev, Nauka and Pergamon, 1990, ISBN 0 0803 7939 7, printed in the USSR, is the one to start with. It deals with fundamental questions. If you can no longer buy this, it is perhaps possible that I might be able to find a copy for you. The other books by Logunov mostly assume much of the basic material.
Besides Logunov, who is quite open about his heretical position, I have read, but cannot confirm for myself (because of my limited skills and because I have not spent too much time on it), that Feynman’s Lectures on Gravitation, and Weinberg’s Gravitation and Cosmology are also in the Whitehead camp, though they do not fly flags to that effect.
I have still to consider and reply to your latest post.
Sincerely,
Christopher
Re: David's reply to Re: meaning of the Hilbert-Einstein etc
February 25, 2008 by Halliday, 1 year 18 weeks ago
Comment id: 27773
Thanks, Christopher, for the pointers to some sources you consider helpful.
David
David, Whitehead, meaning of the Hilbert-Einstein
February 25, 2008 by Christopher Joh..., 1 year 18 weeks ago
Comment id: 27775
David,
Here are some comments on your recent post starting “While I said …â€
I am referring to E. Kreyszig, Differential Geometry, Dover 1991.
I do not think differential geometry books are intended solely for students of mechanics.
I think we are making progress; your remarks are not having the effects of muddying the waters; they are helping to clarify the matter.
Standard differential geometry books, as you say, start for beginners by taking Euclidean space as their uniform underlying space.
It is not necessary to their general program that they do so. Any of a wide variety of uniform underlying spaces would do (of course I am thinking of uniform manifolds over the reals). The results would differ in detail, but the principles would be the same. We are presently interested in the case of Minkowski geometry as the uniform underlying geometry. But from a physical viewpoint we may also consider other hyperbolic underlying geometries, such as the one with signature 2 , 2; it turns out that physical time in our world does not seem in our experience to be two dimensional, and so we quickly drop this one. But we do not quite so quickly drop the class that have elliptic three-dimensional spatial geometries, with one-dimensional time; it takes a few moments’ thought to see that they will not do for us, so far as our experience goes.
The underlying uniform space of interest here is not a Euclidean space with a “Minkowski metricâ€; my claim here is contrary to my reading of your sentence:
In this case any "exotic metric" (which will always be positive definite, unless one is going beyond classical mechanics) is simply a transformation of the coordinates away from those usually employed for classical mechanics (Euclidean). (One can certainly do the same thing with regard to the mechanics of Special Relativity, in which case the metric has Minkowski character.)
The underlying uniform space of interest here is Minkowski space.
As I understand you, you really mean that we are considering not Euclidean spaces but the abstract space R^4. R^4 is not a metric space until it is assigned a metric. The metric with signature 4, 0 is the Euclidean one. The Minkowski one is 3, 1. The orthodox position, as I read it, is that space-time is a manifold. A manifold, as you put it, “can be referred back to an ‘underlying uniform host geometry’ that is not of a higher dimensionality [only] if there is no intrinsic curvature.†The orthodox position is that experience tells us that our physical space has a generally non-zero intrinsic curvature and therefore cannot be referred back to a four dimensional uniform underlying host geometry.
Contrary to your sentence:
So classical differential geometry has the special status that all spaces are flat.
I think that it is not the case for the more general classical differential geometries that they must be flat (yes, of course for the beginners’ course we start work with truly flat, that is to say Euclidean, ones). I think it is valid for a general classical differential geometry to be hyperbolic or elliptic. Minkowksi geometry is hyperbolic as a whole, though it admits Euclidean flat spaces as subspaces. It is customary to say that Minkowski geometry is ‘flat’, but really it is only pseudo-flat; that is why Hilbert and Klein called it pseudo-Euclidean. One can think of trying an elliptic geometry, with a finite sized and more obviously curved universe; until now, experience has seemed to be against this, but we have open minds; there are empirical reasons to believe that the universe in the large as far as we can see is at least nearly pseudo-flat. A general classical differential geometry of interest for physics will be orientable, based on the reals, have an interval, have an interesting class of transforms that leave the interval invariant; it seems reasonable to require at least 4 dimensions, to accommodate Euclid and Alfred the Great.
Your sentence
On the other hand, the full differential geometry of Riemannian geometry is explicitly designed to handle cases of intrinsic curvature that prevent any global identification of the space with its tangent spaces.
is one I can find some common ground on, with a big proviso: the cases with intrinsic curvature that prevent any global identification of the space with its tangent spaces are, in my reading, cases of manifolds, not of Riemannian geometries, fully general or beginners’. My reading of the rest of your post seems to me to confirm this reading. This is the big divide, as I read it.
Please fasten and tighten your seatbelt around your hips, put on your hearing and eye protection, and activate your airbag; the captain has been silenced and here is the devil speaking: Experience tells us that the Riemann Curvature Tensor is zero everywhere in our physical space.
I am relying on the expertise of Logunov for this claim, as well as on the Whitehead arguments. It is anathema and the utmost heresy, of course. I am saying that whether you find the curvature tensor to be zero or not depends on how you put the numbers into the formulas, and that the orthodox way of doing it is not right. Logunov provides detailed expert arguments to this effect. I think his arguments are valid. I think the killer of reality is the doctrine that light speed is defined not measured. Casualties amongst the general staff include causality and the conservation of energy.
Some suggestions for guidance in exploring the territory of the devil: A reference frame is not a coordinate system. Each reference frame has indefinitely many physically admissible coordinate systems. An admissible coordinate system is not a scheme of measurement postings. A coordinate system is a mathematical construction, that can acquire physical meaning only by referring to physical measurements. Physical measurements are of space and time, not of general coordinate quantities. Inertial reference frames are not the only ones admissible in Minkowski geometry. A reference frame is a characterisation of the physical correlate of an abstract uniform underlying host geometry. (These suggestions sometimes apparently slip the mind of the translator of Logunov’s Lectures, and you need to keep alert for various mistakes like this, as well as for typos.)
Perhaps that is enough for this morning.
Sincerely,
Christopher
Re: David, Whitehead, meaning of the Hilbert-Einstein
February 26, 2008 by Halliday, 1 year 18 weeks ago
Comment id: 27782
Christopher:
While I shall keep your "suggestions for guidance" in mind I do have a few points to make, though there is apparently a terminology gap, at least.
I understand the potential distinction between a "coordinate system", "reference frame" (often via the association with "frame of reference"), and a "scheme of measurement postings". This is why I talked of "inertial reference frames" and pointed out that the number of possible "coordinate systems" is greater than the "coordinate systems" I alluded to via examples of "scheme[s] of measurement postings".
Now the greatest potential "terminology gap" appears to be with regard to your use of the term "geometry", especially highlighted by your comment:
Admittedly, I'm using the term "geometry" in what appears to be a more broad sense. So I would ask that you please enlighten me as to your apparently more particular usage. (I add the emphasis here only to try and make sure this request doesn't get lost in all the rest.)
As to whether the "Riemann Curvature Tensor is zero everywhere in our physical space." I expect this is more an issue "on the large". In other words, if one ignores the particulars of the distribution of matter-energy-etc. within our universe, and looks, instead, at the overall "shape" of the universe (at cosmological scales) there is some evidence, and tendency for physicists and astronomers (especially cosmologists) to "gravitate" toward the so called "flat" cosmologies. (At least some of which are truly "flat" in the sense I use the term; the "definition" of which I make more explicit hereafter.)
On the other hand, at least within the framework of General Relativity, the existence of tidal effects is extremely strong evidence for a locally non-zero Riemann Curvature Tensor, since the tidal "tensor" is a portion thereof. (It appears I'll have to read Logunov's account in order to be sure of what he is asserting.)
Incidentally, the "pseudo-flat"/"pseudo-Euclidean" monikers you claim are applied to Minkowski geometry is almost certainly stemming from the predilection of mathematicians to consider that all metrics, that can be called metrics, must be positive definite (elliptic, Euclidean). It's due to the fact that their definition of "metric" includes the "positive definite" requirement, nothing more nor less.*
The "flatness" to which I refer can be viewed as a kind of tautology: If a manifold (space, spacetime) is able to be identified with its tangent space(s) then it is "flat"; if not, then it is "not flat", or has "intrinsic curvature".** The differential geometry of Riemann manifolds (Riemannian geometry, according to Wikipedia*** and my previous usage of the term) shows that this distinction is entirely equivalent to whether the Riemann Curvature Tensor is zero or non-zero.
Does this help?
I look forward to better understanding your use of the term "geometry".
Sincerely,
David
* We physicists just see no reason why "positive definiteness" must be a requirement, especially since the universe in which we reside specifies an indefinite "metric". In a very real sense, the use of the term "metric" has a very different basis for mathematicians vs. physicists: For physicists it's about how actual measurements behave, and so is determined by nature (as the ultimate arbiter); while for mathematicians it is about "definitions", most of which are handed down though history. It's not that one is more correct than another, it's just a difference in emphasis that should be kept in mind when delving into both worlds.
** I assume you understand the difference between intrinsic and extrinsic curvature. For the sake of other readers I shall provide an example of a rolled up piece of paper in the form of a tube: It has extrinsic curvature, but no intrinsic curvature. It can be flattened out without any loss of geometry, except, possibly, for topology, which can actually be retained by a mapping at the edges.
*** The Wikipedia definition of Riemannian geometry is basically the definition I have been using implicitly in all my posts:
Re2: David, Whitehead, meaning of the Hilbert-Einstein
February 26, 2008 by Christopher Joh..., 1 year 18 weeks ago
Comment id: 27785
David,
Thank you for this reply.
The important thing here for me is what you think about the arguments of Whitehead and Logunov.
My inflammatory rhetorical games are only intended to light up the issues, not to settle them. Perhaps my rhetoric has put up more heat and smoke than light. Let's forget my rhetorical games.
The problem is that the 'general theory of relativity' admits endless singularities as I read it and you. Smooth manifolds don't have singularities in the relevant sense, I think. But of course I am claiming more wickedness than the mere absence of singularities in physical space-time.
I am pointing to the diabolical proposal that physical space-time has zero Riemann curvature tensor locally everywhere as a fundamental empirical finding (not just the overall approximate picture or tendency). This is the issue to be examined.
Sincerely,
Christopher
Re: Re2: David, Whitehead, meaning of the Hilbert-Einstein
February 27, 2008 by Halliday, 1 year 18 weeks ago
Comment id: 27792
Christopher:
Thank you for clarifying, to wit:
...
I am pointing to the diabolical proposal that physical space-time has zero Riemann curvature tensor locally everywhere as a fundamental empirical finding (not just the overall approximate picture or tendency). This is the issue to be examined.
I'll respond back once I have had a good opportunity to read, consider, digest, etc. the proposals/arguments of Whitehead and Logunov.
By the way, on the "'general theory of relativity' admits endless singularities" issue. I have noticed how much angst this issue causes among so many physicists. It may even be said to be a somewhat polarizing issue among many who study General Relativity. I have even seen physicists claim that the singularities of many of the solutions in General Relativity "violate physics"! :-)
Admittedly, the formulation of Riemannian geometry (both "normal" and "pseudo"), and the way such was originally (always?) applied by Einstein (and reiterated in nearly all texts on General Relativity), explicitly specifies smooth manifolds. In fact, the "smoothness" is often specified to be C∞ (continuous in all derivatives, without limit). So, yes, singularities "violate physics" in the sense that they violate the assumptions applied in the usual derivation of the theory.
However, within the variational formulation of the theory, using the Einstein-Hilbert "action" (ultimately with the "action" of the matter and other fields added), the admissible "space" of solutions is no longer restricted to C∞, but to some appropriate Sobolev space, where an appropriate number of derivatives exist "almost everywhere" (everywhere but a set of points of "order zero": see distribution theory).* This is in many respects very much like Dirac's delta "functions", that mathematicians criticized so heavily (as not being "functions" at all) until the development of distribution theory.
So, whether one believes that such singularities are "physical" or not (just as whether one believes that Dirac's delta "functions" are physical or not, even though they crop up in Quantum Mechanics practically "all the time"), physicists usually "put up with them" due to the great success of the theory from which they stem. (Or, in the case of Dirac's delta "functions", due to the utility of such devices.) However, in any case, there is a branch of mathematics (distribution theory) that makes all this quite rigorous and "acceptable", at least to a mathematician. :-)
Does this help open up any new avenues of thought for you, or help in any other ways?
Sincerely,
David
* I have yet to see a physics text on General Relativity that does much more than mention the variational approach (with a few exercises to show that it is "equivalent"). I have certainly not seen any that even mention how this admits Sobolev spaces, let alone the consequences of such.
I suppose there are mathematics texts that do admit this approach, along with the appropriate Sobolev spaces, but I haven't seen one myself. (I simply came to this realization myself when taking some advanced differential equations and abstract algebra courses in a Mathematics department.)
Re4: David, Whitehead, meaning of the Hilbert-Einstein
February 27, 2008 by Christopher Joh..., 1 year 18 weeks ago
Comment id: 27809
David,
Thank you for this.
I look forward to your thoughts as you read Whitehead and Logunov. Then to what you think Hilbert thought about this.
Whitehead's position is subtle ands simple. It rests on the ideas that causal action propagates with a finite maximum speed, and that the descriptive apparatus should not offer privileges. Zeeman in later years also showed that causality demands Minkowski geometry.
Logunov is different. He thinks that we rely on dynamics to discover Minkowski geometry. I think he is mistaken in this and that Whitehead is right about the path to the discovery of Minkowski geometry.
But they agree that Minkowski geometry is fundamental and that the curved space-times of dynamics are derived from it, as "effective spaces". The empirical discovery of 'effective singularities' would not hit the underlying Minkowski geometry. In these thoughts they are heretical.
Sincerely,
Christopher
Re: Re4: David, Whitehead, meaning of the Hilbert-Einstein
February 28, 2008 by Halliday, 1 year 18 weeks ago
Comment id: 27825
Christopher:
Years ago I asked the question: What types of "spacetime" admit/support causality (in a global sence of all observers being able to agree on a chronological order of events with a cause and effect relationship).
It turns out that the only types with this characteristic (with one possible third canidate) are either Minkowskian (non-singular with only a single eigenvalue of opposite sign to all others), and Galilean/Newtonian (singular, with only a single zero eigenvalue, while all other eigenvalues have the same sign). (Actually, I didn't have time to fully determine whether a mixed type, a single zero eigenvalue, and only one non-zero eigenvalue with a sign opposite to all others, would work. It's rather complex and difficult to handle. So it's somewhat possible that such a mixed case may work.)
However, the Minkowski character of our local spacetime (at least at the scales accessible to us) is empirically the only form that is consistent with all observations so far.
So, the apparent "argument", then, is only whether our spacetime manifold is truly curved, or only "effectively" curved. (Of course, if the "effective" curvature is such that all measurements will be the same as an "actually" curved spacetime, then it all boils down to an "interpretation", as I've defined such already. Then it all depend upon which one considers "simpler" or in some other way "more compelling".)
David
Re: David's reply to Re: meaning of the Hilbert-Einstein etc
February 25, 2008 by Halliday, 1 year 18 weeks ago
Comment id: 27763
Christopher:
Apologies accepted. :-)
It will take me some additional time to properly address your post. However, I would like to set you straight on which David Halliday I am.
While my name is David W. Halliday, just like the textbook writer, I believe the W. stands for something different. Furthermore, I am not nearly as old as the textbook writing David Halliday.
So, I'm sorry to disappoint you, but I am not he, and I certainly don't wish to mislead anyone into thinking otherwise. :-)
David
David's reply to Re: meaning of the Hilbert-Einstein equations
February 18, 2008 by Christopher Joh..., 1 year 19 weeks ago
Comment id: 27611
David, thank you for your kind and careful reply. I greatly value your thoughtful help.
I did not mention the general theory of relativity, just the Hilbert-Einstein equations. I did not talk about interpretations of theories, just interpretations of equations. My use of the word 'interpretation' does not intend concern with what you call 'what it "really means" and/or "what is really going on". Your posting, though kindly meant, is not a reply to what I wrote, nor to what I meant. Your posting reflects your obviously thorough training in and apparently complete acceptance of the authoritative orthodoxy, and is undoubted testimony to your great intellectual powers and attention to scholarship, but still I have to say in answer to your question "So, does this discussion help you?" that it helps only insofar as it may be the beginning of a valuable discussion if you have time for it. You ask and answer your own question 'Is there some "orthodoxy" that "prevents" us as researchers from considering such? I've never noticed such.' That's quite right, you haven't noticed yourself as in thrall to the orthodoxy. But I am in this correspondence claiming to bring it to your attention that you are so.
Let me clarify. The orthodoxy that I was trying to bring to attention is the idea that space-time is curved in a non-uniform way. This idea was espoused by Einstein and it seems you accept it. But you have the opinions of some more respectable minds than mine to contend with if you want to say that your view takes rational criticism into account. Alfred North Whitehead will be enough as an example for the present. Whitehead draws a distinction between geometrical space and active "space". We start with ideas of space and time for quasi-static far-from-gravity situations. For our basic understanding, we have to start like this. Books of differential geometry are quite unintelligible to students who have not studied Euclidean geometry for years. We go on to look at motion at relativistic speeds, and we find that inertial frames are very helpful, and we come up with Minkowksi geometry. But we don't abandon the basic facts of Euclidean geometry for quasi-static situations. Whitehead points out that there are other uniform geometries besides the Euclidean for a quasi-static space: namely hyperbolic and elliptic. Gauss had the same idea. Experience does not support the idea that we have either of those two uniform geometries in our world for quasi-static situations. But the idea of non-uniform "geometries", Riemannian "geometries" is something else. In my textbooks, Riemannian geometry is introduced in a frame of Euclidean geometry, and the metric refers back to that. In the Einstein curved space-time story, the "metric" does not refer back to a Minkowski frame, but instead it erects a new "locally inertial" frame for every moment of every observer's experience. This is a difference of interpretation of the meaning of 'metric'. The Einstein view is supported by authoritative orthodoxy in its declaration of local measurement as king, with time and space being measured by local atomic clocks. That it takes longer than expected for radar to travel in the Shapiro effect is attributed to "curvature of space-time" and not to slowing of light by gravity. This is a difference in interpretation. Perhaps we might agree that "a transformation can be interpreted as alibi or alias". This is the sense in which I am using the word interpretation.
I think I have said enough to suggest to you what I mean by interpretation. Your email starts with the view that I have 'a number of misunderstandings concerning both General Relativity*, and "interpretations" of theories.' My reading of the situation is that I do not accept the orthodox interpretation of the physical meaning of the terms of the Hilbert-Einstein equations, because I think they have physical meaning only in terms of the Whitehead interpretation. I simply do not write in terms of the orthodox interpretation, and that is what you call 'misunderstanding'. I am writing because I have read many orthodox texts on what they call "general relativity" and I find that they blithely assume the correctness of their position without bothering to confront its logical structure, and so I find them lacking in intellectual coherence. You are welcome to say that this is because I am some kind of dill (a kindly meant soft spoken Australianism for a fool or simpleton), but it will, I think, not be quite so easy for you to say that Whitehead was a dill. He was writing texts of differential geometry when Einstein was in nappies. I would be grateful to have from you an account of how you read Whitehead on these questions.
Christopher
Re: David's reply to Re: meaning of the Hilbert-Einstein equati
February 20, 2008 by Halliday, 1 year 19 weeks ago
Comment id: 27664
Christopher:
You are sadly mistaken about me and my approach to "the orthodoxy", as you put it. I will not go into my history here, you can find my accounts elsewhere. Suffice it to say that I went into Physics partly because I most certainly didn't believe in "the orthodoxy". However, it appears that unlike yourself, I was perhaps wise enough (you may say "foolish enough") to believe that the only way I was going to be able to "correct or fix" the situation was to learn all I could in order to have the tools and understanding to do so. (You may say that I was "brain washed". You may believe anything you wish, but that won't make it so.)
You are also mistaken if you believe that the Differential Geometry upon which General Relativity is based in anything besides Riemannian "geometry" where the metric is allowed to be indefinite (as opposed to the positive definite requirement of standard Riemannian "geometry"—which, as you point out, hails back to Euclidean geometry). Differential Geometry, in this form, can handle classical (Newtonian) mechanics (via a three dimensional positive definite metric), General Relativity (via an indefinite four dimensional metric with Minkowskian character/signature), and even well beyond (with general definite or indefinite [though invertible] metrics of arbitrary, though finite, dimension). (Though a Mathematician may insist upon calling indefinite "metrics" pseudo-metrics, and the resulting geometry pseudo-Riemannian, I very much doubt that you will be able to find any professional Mathematician that will contend, as you appear to, that the Differential Geometry used in General Relativity is anything other than Riemannian "geometry"* extended to such pseudo-metrics.)
While it is true that Einstein called upon various phenomenological aspects/characterizations/etc., since that was both his way of approaching physics (physical phenomena) and of persuading others, it is certainly not the only way of approaching the subject. (You will find that Mathematicians have and do approach it precisely as I have outlined—as Riemannian "geometry" extended to pseudo-metrics.)
So what more is there for me to say? (Incidentally, you keep referring to "the terms of the Hilbert-Einstein equations" [my emphasis added]. Are you aware that there are multiple formulations of the Hilbert-Einstein equations in terms of different "fundamental" "terms". Perhaps I should ask exactly what "terms" you are referring to, since, perhaps, your issue is with something other than what I perceive.)
David
P.S. You have intrigued me sufficiently to look into Whitehead's interpretation of the Hilbert-Einstein equations. So thanks.
* By the way, I'm using the quotation marks around "geometry", in the context of Riemannian "geometry", because that has been your usage. Unfortunately, I'm not at all clear as to why you are treating it thus, other than the fact that there is, indeed, a distinction between geometries that are also vector spaces (like Euclidean, Minkowsian, etc.) and those that are not (such as those of Riemann).
RE: meaning of the Hilbert-Einstein equations for gravity probe
January 25, 2008 by Scruffy, 1 year 23 weeks ago
Comment id: 27142
Christopher John Aylward Game wrote: "Whitehead also enunciated a hypothetical alternative theory of gravity different from Einstein's, in order to clarify the logical meaning of his different interpretation of the Hilbert-Einstein equations."
I believe Whitehead's "theory of gravity" has been found to predict the "Nordtvedt Effect"(1), which was ruled out by experiments, i.e., it cannot exists at the levels Whitehead predicted. That rules Whitehead's theory out for all practical purposes.
(1) A violation of the "strong equivalence principle" between inertial mass and gravitational mass. http://en.wikipedia.org/wiki/Nordtvedt_Effect
SL: Your Aerospace Watchdog
meaning of the Hilbert-Einstein equations for gravity probe B
February 15, 2008 by Anonymous, 1 year 19 weeks ago
Comment id: 27558
Second attempt to reply to Scruffy's of 25 Jan 2008. Thank you Scruffy for your helpful reply. Sorry to reply so late. Sorry that my initial reply appears anonymous. I didn't see an 'author' field to enter. I still don't see an 'author' field. This is Christopher John Aylward Game writing again.
The Whitehead theory of gravity is not responsible for the Nordvedt Effect. It is responsible for the 'Whitehead term'. Nevertheless it was found to be empirically wrong, which we agree about. Clifford Will was crowing about it because it was such a threat to orthodoxy. He was to thrilled to show that the Whitehead equations were wrong but he was missing the important physical point; that what matters is the Whitehead interpretation of the Hilbert-Einstein equations, not the empirical correctness or otherwise of the Whitehead equations in terms of the Whitehead interpretation. But your reply that the Whitehead equations are empirically wrong was already in my original comment, and you have not focused on the point of my original comment. That is to say, there is a distinction between Whitehead's theory of gravity, and the Whitehead interpretation of the Hilbert-Einstein equations. I think the latter was also the Hilbert interpretation of the Hilbert-Einstein equations. The interpretation is about how to assign physical meaning to the terms of the equations, not about whether the equations are empirically correct. To test their empirically correctness one needs a way to put physical meaning to their terms. A way of putting physical meaning to the terms makes it logically possible to propose other equations (which I am calling 'theories') which are to be tested empirically. Whitehead offeres such another set of equations to illustrate that his interpretation was physically meaningful. That his other set of equations was empirically tested is proof that they had physical meaning. One cannot make an empirical test of meaningless equations. That the test showed them not to describe nature is just confirmation that they have a physical meaning, empirically wrong though it is. Rejecting the Whitehead interpretation because his theory is wrong is throwing out the baby with the bathwater. It is the interpretation that is physically important, not the example to illustrate its logic. Whitehead was pointing out that the Einstein interpretation that is now authoritative orthodoxy is physically meaningless nonsense. That is why people don't try to test the Hilbert-Einstein equations in terms of the Einstein story of curved space. They use the post-Newtonian parameters that have physical meaning in terms of the Whitehead interpretation, but they don't recognise that that is what they are doing. Einstein's story is about 'curved space'. But that is just a metaphor. What matters is a uniform geometry. Minkowski geometry is the only known empirically valid uniform geometry. People think they are very clever in being able to 'think' in terms of Einstein's 'curved space', but they are too clever by half. It can have meaning only in terms of Minkowski geometry, and is not the geometry of space, but is, in metaphorical language, the "geometry" of light signals in the presence of gravity. This view is of course ridiculed by the authoritative orthodoxy; it is in the nature of authoritative orthodoxy to ignore its critics until forced to reply, when it ridicules their argument instead of understanding and replying to it.
Re: meaning of the Hilbert-Einstein equations for gravity probe
February 18, 2008 by Halliday, 1 year 19 weeks ago
Comment id: 27608
Christopher:
Unfortunately, you appear to have a number of misunderstandings concerning both General Relativity*, and "interpretations" of theories.
First, on the matter of "interpretations" of theories: Alternate interpretations of a theory provide alternate conceptualizations of the "physical meaning" of a theory—what it "really means" and/or what is "really going on"—but have no testable effects—can have no effect upon actual measurements that are predicted by the theory. (See, for instance, the various alternate interpretations of Quantum Mechanics.)
Additionally, it is reasonably well known, among "relativists", at least, that Einstein's Theory of General Relativity can be interpreted as a "dynamical aether" theory. One can also ask questions of "how many dimensions, and of what character, would a flat embedding space need to have in order to embed the curved spacetimes of General Relativity?" (After all, Riemannian geometry, the basis for General Relativity [though extended to "pseudo-metrics"], was invented, by Riemann, to handle curved "surfaces" without having to consider the embedding space.)
Second, on the misunderstanding of General Relativity itself: The "geometry" of General Relativity is not the "'geometry' of light signals in the presence of gravity". Not in "metaphorical language", or otherwise. Furthermore, when spacetime is curved there can be no identification of the "manifold" (the "surface" of spacetime) with its tangent (vector) space (which is Minkowski geometry). (Such an identification can only be accomplished if the spacetime is flat, in which case one can, indeed, say that the geometry of the spacetime is Minkowski geometry.)
Incidentally, the "dragging" aspect of "frame dragging" is simply a "metaphorical" way of referring to the asymmetrical angular character of the geometry that is the solution in question to the Hilbert-Einstein vacuum equations. (It can be seen to be a consequence of a non-zero angular momentum. After all, a non-zero angular momentum has the particular asymmetry seen in the solution.)
Furthermore, purely "local" measurements will only truly show the Minkowski geometry of the local tangent space. It takes somewhat less "local" measurements to elicit the "curved" character of spacetime (which is not just spatially curved, by the way, but curved in the combined space and time that is spacetime).
Now, as to whether it is appropriate to view General Relativity by way of multiple, alternate interpretations? I say it most certainly is. Is there some "orthodoxy" that "prevents" us as researchers from considering such? I've never noticed such. In fact, the best texts I've seen on General Relativity take a multi-pronged approach: It tends to aid understanding.
So, does this discussion help you?
David
* General Relativity consists of more than just the Hilbert-Einstein equations, though the Hilbert-Einstein "action" (think calculus of variations), along with the action(s) of the matter-energy-fields-stress-etc., is more fully complete.