Relativity and Empiricism

[Qfwfq]

However, most of my colleagues choose do their science the standard way, and I am not so stupid as to deny the possibility—probability even—that somewhere my chosen path is producing the wrong answers.

As an astrophysicist, you should be able to judge when one or the other is suitable.

 

I suppose an argument could be made for most globes having bumps and ridges for mountain ranges and therefore being 3-D.

Actually, even the surface of these is a 2-D manifold. Now the projection of it onto a flat surface is basically the essence of what a choice of chart does. Hmmm, could that not be why the words chart and atlas are used in differential geometry? Now, for each chosen chart, the is a metric; what is the purpose of it at all? Perhaps its very purpose is to avoid being taken in by how huge Greenland appears! :confused:

 

Coordinates are nobbut numbers, it's the metric that gives you the length!

[modest]

A 2-D map of the earth isn’t wrong, it is just sometimes more convenient than a globe.

 

Er... the globe's surface is also a 2-D manifold; not a flat one, but nonetheless a 2-D manifold. To a farmer in Holland, the fields are quite flat. To anyone that can see a larger extent at a time, it becomes obvious that it isn't perfectly flat.

 

Actually, even the surface of these is a 2-D manifold. Now the projection of it onto a flat surface is basically the essence of what a choice of chart does. Hmmm, could that not be why the words chart and atlas are used in differential geometry? Now, for each chosen chart, the is a metric; what is the purpose of it at all? Perhaps its very purpose is to avoid being taken in by how huge Greenland appears! :)

 

Coordinates are nobbut numbers, it's the metric that gives you the length!

 

Quite right, I never should have said a "map is more convienient than a globe" I should have said a set of 2 or more charts representing the surface of the earth contained in an atlas are more convienient than two or more two-manifolds representing the earth projected on a Euclidean 2-sphere containing a ball in 3d metric space.

 

What was I thinking :doh:

 

-modest

[Turtle]

...

Given the phenomenal success of theories special relativity based theories (such as QED,QCD,electroweak), how can we doubt that special relativity wasn't on to something?

 

In other words, you wish to work with a euclidean 3 dimensional universe with an absolute time parameterizing trajectories. However, the best tested theories we have are not mappable to this model (i.e. quantum field theories). How can we hold to Euclid in light of this? How can we ignore Minkowski?

-Will

 

Hi Will, et al. :) Please forgive a novice's intrusion, but I mentioned Buckminster Fuller earlier in regard to projections and I'd like to know what you think of his tetrahedral metric for space. I don't know how his work in Synergetics falls on the time-line with Minkowski, but Einstein was Fullers' contemporary and apparently thought well of him.

 

In reading a bit on Fuller's Dymaxion projection, they mentioned how that projection has no "up" or "down" and that Fuller acknowledged that by saying such parameters were arbitrary and that "things" really have an "inside" and "outside."

 

If you are familiar with Fuller's tetrahedral divison of space metrics, how does it jibe with Mikowski et al? If you are not familiar with Fuller's Synergetics, why is that? Takk. :doh:

[Buffy]

Buffy, I think you may here have made a promising suggestion why I am wrong to ignore Relativity.

"Promising!" Wow! Cool!

 

But why dismiss it so readily with such a flimsy and misleading excuse? To wit:

Unfortunately GR has not been tested at those extremes (has it?) and in attempting what Coldcreation suggested elsewhere, viz setting boundaries of applicability for NM and GR, we may run into a logical obstacle: GR and SR apply to the exclusion of NM in a very remote place, but have only been tested locally.

Setting boundaries of applicability is conjecture that requires some sort of theory as to *why* such boundaries might exist, and at least some evidence to support it.

 

I fully appreciate "errors of extrapolation" as a methodological problem, but until there is some evidence that such extrapolations do indeed obey exceptions, and in the face of at least some evidence that *supports* such extrapolations, it would be foolish to *assume* that the extrapolations are wrong.

 

Now I'll accuse you of misrepresenting a great scientist to your own benefit:

Dr Subrahmanyan Chandrasekhar responded as follows to a lecture by Paul Dirac in which he (Dirac) claimed that Einstein’s theory of gravitation was eminently successful:

“It does not seem to me that the successes of Einstein’s theory are either long or impressive…[]…all these relate to departures from Newtonian theory by a few parts in a million; and of no more than three or four parameters in a post-Newtonian expansion of Einstein’s field equations. And so far, no predictions of general relativity in the limit of strong gravitational fields have received any confirmation; nor are they likely in the foreseeable future.”

Indeed this is his statement, but to say that he believes that this "lack of evidence" disproves GR is something that he would strongly disagree with. Dr Chandrashekhar's theories depend quite significantly upon GR, and misusing this quote--which is focussed solely on whether or not there is "a great deal of evidence supporting" some very *specific* predictions of GR which you conveniently left out in your ellipses to mask the limited scope of his objections--is both unfair to him and taking credit to your alternative theory when none is due.

 

To be very clear, it is certainly true that experiments for time dilation in Earth orbit are in the range of more than -6 orders of magnitude, but gravitational lensing using the sun and galaxies is -2 orders, and is exactly the kind of "error" I point out as being significant enough to warrant caution. I don't think you'd find Dr Chandrashekhar would disagree with me on this!

 

Can you point to any experiments that show that such extrapolations are *not* valid?

 

I don't mind your questioning these assumptions, but until there's some evidence to the contrary, I'll continue to insist that your use of Euclidean Geometry in dealing with computations of cosmological scope are likely to be horridly in error, and hardly justifiable especially if you are attempting to show "errors" in GR because by doing so you "discover" a discrepancy.

 

Dick Cheney says that homosexuals should have all the same rights as heterosexuals, *

Buffy

 

* in the states that vote to allow them to have those rights.

[Hilton Ratcliffe]

Hi Buffy,

 

Buffy said:

"Promising!" Wow! Cool!

 

Buffy, facetious sarcasm has no place in civil discussion, especially one that ostensibly seeks to reconcile diverging views in science. This remark and parts of the rest of your post constitute a slur on my integrity, and verge on insult. I am an invited guest on this thread, so please don't think I am here merely to be the face for your custard pies. You are a forum moderator - shame on you!

 

I did not say, or even imply, that Dr Chandrasekhar believed that the lack of evidence referred to disproved GR. Once again you are guilty of putting words into my mouth. The sole purpose of the quote given in my post was to illustrate my long-held opinion that GR may have applicability at extremes of measurement and that in more local environments produces no advantage over NM.

 

The significance of your reference to Dick Cheney and sexual orientation is quite lost on me.

 

Best

Hilton

[Qfwfq]

Buffy is very lively and imaginative, don't be upset by her wit. We're used to her and we all just adore her. ;)

 

...and that in more local environments produces no advantage over NM.

Maybe that's why astronomers were getting such excellently accurate predictions before GR and it took a substantial effort for Mercury's perihelion precession to be noticed. It was however noticed.

 

The significance of your reference to Dick Cheney and sexual orientation is quite lost on me.

The nexus is the fact that a rather fundamental part was added as a footote. They say: Before signing, always read the small print. And get good advice about its legal implications. :D

[Buffy]

Hi Hilton!

 

I deeply apologize for the fact that you were offended my response. I'll disagree though that,

...facetious sarcasm has no place in civil discussion, especially one that ostensibly seeks to reconcile diverging views in science...

Its sometimes quite useful rhetorically in jarring the participants into seeing other points of view.

 

I realize that you may not be familiar with this style, but to me it has proven useful especially in highly contentious discussions where partisans maintain strongly held positions, sometimes based on selective use of evidence.

 

You might also want to think about the fact that your use of the word "promising" immediately followed by the dismissal of one of the points presented is also a rhetorical technique known as "damning with faint praise" and can be taken as offensive as well. A lot of people tell me "not to worry my little head" about complex topics while pretending I did not pose a valid objection. That gets tiring. I'm sorry you got blasted for it.

 

Normally I do not resort to this technique until the object of the comment has shown strong resistance to considering the data presented. Unfortunately my technique backfired in this case because it gave you the opportunity to express consternation and offense instead of actually responding to my comment that there are indeed at least some measurable effects of GR that do not fall into the "insignificant" category.

 

Now the thing is that when you say:

I did not say, or even imply, that Dr Chandrasekhar believed that the lack of evidence referred to disproved GR. Once again you are guilty of putting words into my mouth. The sole purpose of the quote given in my post was to illustrate my long-held opinion that GR may have applicability at extremes of measurement and that in more local environments produces no advantage over NM.

You seem to be ignoring the fact that you originally prefaced the quote by saying:

Unfortunately GR has not been tested at those extremes (has it?) and in attempting what Coldcreation suggested elsewhere, viz setting boundaries of applicability for NM and GR, we may run into a logical obstacle: GR and SR apply to the exclusion of NM in a very remote place, but have only been tested locally.

How am I supposed to interpret the use of Dr. Chandrasekhar's quote except as evidence supporting these "boundaries of applicability?" It may only be a plausibly deniable implication, and indeed you seem to have admitted that he's only saying there's "not a lot" of evidence, which is quite different than saying there's "no evidence," let alone "evidence that there are boundaries of applicability." So, if your intent in this thread is to justify ignoring GR, then I feel quite justified in saying that the use of this quote does not help your argument much, and it can be interpreted as trying to be misleading, even if that is not your motivation.

 

And thus we come to the reference to Dick Cheney. Q explained it succinctly, but I'll try to be a bit more clear. The quote contained ellipses where you had excised some significant circumscriptions that were a key qualification in its full exposition. Mr. Cheney is a quite conservative fellow, and he's on the record as supporting the decidedly unconservative notion of gay marriage, but if you leave out his key qualification--that it should be left up to the states (where states rights are a foundation of conservative thought in the US)--you can make him sound like some wacko liberal.

 

I draw the parallel not to offend you but to shake you into understanding that many others may find the support you give for your arguments more than a little bit shaky, and many of us would love to see you respond to the objections we've posed rather than ignoring them.

 

It can certainly be difficult to defend theories that are out of the mainstream, but one must be wary of the pitfalls of using "unjustified persecution" as a defense of those theories, because no matter how sound the theories might be, this defense causes many to suspect that there is no evidence to support them.

 

Well, we did do the nose,

Buffy

[coldcreation]

 

 

But why dismiss it so readily with such a flimsy and misleading excuse? To wit:

 

 

Unfortunately GR has not been tested at those extremes (has it?) and in attempting what Coldcreation suggested elsewhere, viz setting boundaries of applicability for NM and GR, we may run into a logical obstacle: GR and SR apply to the exclusion of NM in a very remote place, but have only been tested locally.

 

 

Setting boundaries of applicability is conjecture that requires some sort of theory as to *why* such boundaries might exist, and at least some evidence to support it....snip...

 

 

 

Conjecture, certainly not. The theory exists. The question is not "why" a boundary condition might exist. The question is when, where and how does the boundary condition of GR manifest itself, and ultimately, what can be done to identify it.

 

 

You could ask; "why" has it not yet been physically identified, or "why" has the mechanism responsible for the boundary condition been overlooked. That would make sense and it would be a good question at the same time (unlike what you wrote above).

 

 

Not only is there compelling evidence to support the theory but the boundary condition can easily be tested empirically, i.e., there exists a simple cost effective test designed to falsify or corroborate the boundary condition principle, if astronomical observations prove insufficient to determine the extent to which GR is applicable to, and represents, the real world..

 

 

 

Wow! cool!

 

 

 

 

CC

[Buffy]

Conjecture, certainly not. The theory exists. The question is not "why" a boundary condition might exist.

Oh but that's still the most interesting question!

 

Physical laws tend *not* to have artificial boundaries--that is "kinks in the curve"--where all of a sudden a new set of laws applies. If it does, then its quite often a fundamentally different model (e.g. difference between quantum and macroscopic matter is due to the fact that the individual elements operate on completely different models).

 

Now the other questions:

The question is when, where and how does the boundary condition of GR manifest itself, and ultimately, what can be done to identify it.

...are certainly fairer, and indeed the scientific method would *only* require these questions, with no obligation on your part to say "why," although its important to note that when comparing theories, those that do answer the "why" question can be far more compelling! :eek:

 

Telling me that its "not a good question" avoids that very issue!

Not only is there compelling evidence to support the theory but the boundary condition can easily be tested empirically, i.e., there exists a simple cost effective test designed to falsify or corroborate the boundary condition principle, if astronomical observations prove insufficient to determine the extent to which GR is applicable to, and represents, the real world...

What's so amusing about this is its exactly the same argument that's being dismissed on the GR side: Easily "testable" experiments can be conceived, but can't be carried out to the satisfaction of certain parties due to "non-locality" or "extrapolation" or "unjustified assumptions."

 

I think its in the scope of this thread to discuss what that competing theory is and the empirical approaches that could be used to evaluate that vs. GR.

 

Please proceed! It would be way cool! :evil:

 

The sun is the same in a relative way, but you're older, :hyper:

Buffy

[coldcreation]

Physical laws tend *not* to have artificial boundaries--that is "kinks in the curve"--where all of a sudden a new set of laws applies. If it does, then its quite often a fundamentally different model ...

 

 

As far as I know, every physical law has a natural boundary condition, e.g., the second law of thermodynamics has a boundary at zero entropy, the third law of thermodynamics has a boundary condition at absolute zero, etc. These are not artificial boundaries created by a woman. :eek:

 

 

 

I think its in the scope of this thread to discuss what that competing theory is and the empirical approaches that could be used to evaluate that vs. GR.

 

Pehaps you've misunderstood. The boundary condition is not a theory in competition with GR.

 

It is inherent in GR, implicitely and explicitely.

 

 

 

Please proceed! It would be way cool! :evil:

 

I wouldn't want to high-jack this thread.

 

 

The sun is the same in a relative way, but you're older, :hyper:

Buffy

 

Great tune...

[Buffy]

As far as I know, every physical law has a natural boundary condition, e.g., the second law of thermodynamics has a boundary at zero entropy, the third law of thermodynamics has a boundary condition at absolute zero, etc. These are not artificial boundaries created by a woman. :eek:

We would *never* create one! :)

 

Now the thing is you're avoiding the question: the examples you cite here are exactly the kinds of "boundaries" that make sense *because* they're predicted by the theory. However there's nothing *in* GR, that says "this theory is only applicable at great distances and at distances less than X, there is a different set of equations that apply."

Pehaps you've misunderstood. The boundary condition is not a theory in competition with GR....It is inherent in GR, implicitely and explicitely.

Really? Where?

 

And if its already a part of the theory, then how can it be used to disprove it if the empirical measurements support a boundary (which if they do exist, as far as I can tell you're not willing to disclose them)?

I wouldn't want to high-jack this thread.

Fair enough. You've established then that it can provide no empirical results that would affect the support for or against GR...now is there anything else?

 

When we grew up and went to school, :hihi:

Buffy

[Erasmus00]

As far as I know, every physical law has a natural boundary condition, e.g., the second law of thermodynamics has a boundary at zero entropy, the third law of thermodynamics has a boundary condition at absolute zero, etc. These are not artificial boundaries created by a woman. :hihi:

 

I think this is a stretch. The third law, maybe. Certainly not the second (which itself doesn't mention anything about entropy potentially being negative).

 

Certainly, the principle of least action has no natural "boundary condition." Conservation of energy, conservation of momentum, etc. Force laws, etc.

-Will

[Hilton Ratcliffe]

Hi Buffy,

 

Buffy said:

I deeply apologize for the fact that you were offended my response.

 

You apologise for being offensive, then go off into a lengthy and contrived justification of that very offensiveness. Do you expect me to accept that you are being sincere?

 

Buffy said:

It’s sometimes quite useful rhetorically in jarring the participants into seeing other points of view. I realize that you may not be familiar with this style, but to me it has proven useful especially in highly contentious discussions where partisans maintain strongly held positions, sometimes based on selective use of evidence.

 

You are being arrogant and patronising.

 

Buffy said:

You might also want to think about the fact that your use of the word "promising" immediately followed by the dismissal of one of the points presented is also a rhetorical technique known as "damning with faint praise" and can be taken as offensive as well. A lot of people tell me "not to worry my little head" about complex topics while pretending I did not pose a valid objection. That gets tiring. I'm sorry you got blasted for it.

 

The word “promising” was a cordial indication to you that I accept that your opinion, although counter to my own, has potential worth investigating. Did you notice the “(has it?)” in my post? There was nothing insincere about it. Does sincerity offend you?

 

Buffy said:

Normally I do not resort to this technique until the object of the comment has shown strong resistance to considering the data presented. Unfortunately my technique backfired in this case because it gave you the opportunity to express consternation and offense instead of actually responding to my comment that there are indeed at least some measurable effects of GR that do not fall into the "insignificant" category.

 

Are you insinuating that my response to your post was given in lieu of answering your questions? It was not. The decision I will be making shortly is whether I want to discuss anything at all with you. We are all here voluntarily, but, it appears, for significantly different reasons. I’m not avoiding the issue under discussion; I am simply trying to establish whether you are genuinely and openly exploring scientific issues here, or practising some kind of privileged cynical overview in an attempt to put down people with whom you may not agree. Your tone is in marked contrast to the much more affable styles of other Hypography contributors.

 

Buffy said:

How am I supposed to interpret the use of Dr. Chandrasekhar's quote except as evidence supporting these "boundaries of applicability?" It may only be a plausibly deniable implication, and indeed you seem to have admitted that he's only saying there's "not a lot" of evidence, which is quite different than saying there's "no evidence," let alone "evidence that there are boundaries of applicability." So, if your intent in this thread is to justify ignoring GR, then I feel quite justified in saying that the use of this quote does not help your argument much, and it can be interpreted as trying to be misleading, even if that is not your motivation.

 

In the quote given, however you may wish to twist it around, Dr Chandrasekhar is perfectly clear. Read it literally, with or without the piece omitted between ellipses. There are areas of investigation where the use of either NM or GR produces only trivially different results. This is precisely my point, and I would say that Dr Chandrasekhar was in his utterances completely in agreement with it. The questions I ask, and which you seem to be avoiding, are 1. Is there some limit to the piece universe to which this applies? And 2. Can I practice astrophysics (excluding cosmology) to the limits of observation without necessarily using GR?

 

Best

Hilton

[Buffy]

...There are areas of investigation where the use of either NM or GR produces only trivially different results. This is precisely my point, and I would say that Dr Chandrasekhar was in his utterances completely in agreement with it.

I agree with this completely. The only point I have tried to make is that the statement "There are areas of investigation where the use of either NM or GR produces only trivially different results" does not establish that "*all* local phenomena produce only trivially different results." The gravitation of the sun produces translations of location of what most people would call local objects with differences from NM that are easily measurable.

 

So specifically, your questions are indeed what I am asking you to discuss:

The questions I ask, and which you seem to be avoiding, are 1. Is there some limit to the piece universe to which this applies?

Where is this limit? What empirical evidence of any kind shows that one exists?

 

This is my same query to CC, and I'd love to hear about this and have you describe the data that supports this concept.

 

As I am holding the position that GR does not postulate such a boundary, and the scientific method does not support proof of non-existence--indeed, in the absence of even a definition of what this boundary is, I have no place to even start to refute its existence--I'm asking you for evidence of the existence of such a boundary or even its defining qualities in more detail.

 

Is it unfair of me to ask for that?

 

It would be useful to hear why the statement that we all agree to--that "there exist some measures of GR vs. NM that are very small"--provides any support for the existence of boundaries.

2. Can I practice astrophysics (excluding cosmology) to the limits of observation without necessarily using GR?

I am not going to stop you, but it will be the first question out of many people's mouths if they are familiar with what you are doing. Given that GR is demonstrably more accurate than NM, albeit trivially in many cases--and to reiterate, I am not denying that--you will find that you will need to state somewhere within your justification for taking the shortcuts provided by NM and qualify the conclusions with an expected error.

 

You're certainly free to leave it to others to do the leg work, and there's nothing wrong with that at all, in fact I'll actually strongly support your methodology: I'm just pointing out the fact that using conveniences up front to speed up your work has back-end costs that will have to be paid eventually in order to answer natural and justifiable objections to the shortcuts.

 

Quartz often contains gold but it takes a lot more work to get earrings,

Buffy

[Hilton Ratcliffe]

Hi Buffy,

 

Buffy said:

Where is this limit? What empirical evidence of any kind shows that one exists?

 

You are answering a question with a question. Let me try to make my position clear. I do not as a standard method ask what I consider to be rhetorical questions. I ask the question because I don't know the answer and am turning to my peers for guidance. I came to be in the position I'm in as a result of intense discussion with one of my professors (an enthusiastic General Relativist), who made the very practical suggestion that I test my ideas on NM and GR by dropping GR and monitoring the consequences. That is what I have done. I have not detected any ill effects from doing this, but I am still open to the suggestion that I may be overlooking something. My philosophical stance is passive. The onus is therefore on you to show, if you will, exactly how it is that I critically need GR to practice astrophysics. You can start by properly answering my questions. As a guideline, my work is focussed on the Sun, especially chemical composition and energy production (I was co-discoverer of the CNO nuclear fusion cycle at the footpoints of coronal arches at the surface of the Sun). Of course, your critique does not need to be confined to my own work specifically, I am just as interested to learn of the appropriateness of GR in any field of astrophysics excluding cosmology.

 

Asking whether there is a limit, or even stating that the idea is intriguing, does not mean that there is such a limit, or that there are physical boundaries separating theories. It seems to me that it is difficult to define in real terms just where it is that my method fails, and by how much.

 

 

Buffy said:

As I am holding the position that GR does not postulate such a boundary, and the scientific method does not support proof of non-existence--indeed, in the absence of even a definition of what this boundary is, I have no place to even start to refute its existence--I'm asking you for evidence of the existence of such a boundary or even its defining qualities in more detail.

Is it unfair of me to ask for that?

 

Yes it is. You are the one holding the position. Provide evidence that the boundary does not exist - although it seems to me that your emphasis on a boundary per se deflects from the real issue. What I would really like to know from you is, given that NM and GR both apply to a reasonable approximation in some cases, whether there are other aspects of astrophysics where GR applies to the exclusion of NM.

 

Best

Hilton

[Buffy]

1. Is there some limit to the piece universe to which this applies?

Where is this limit? What empirical evidence of any kind shows that one exists?

You are answering a question with a question.

Sorry I made the assumption that I was saying was clear.

 

My answer to your question 1 is "No."

 

My argument in support of this is that GR consists of a number of equations which are basically monotonically increasing in their effect as gravitational fields increase. That is, from a mathematical point of view, there are no discontinuities or kinks in their curves.

 

This implies that there are no boundaries.

 

The data to support this is extensive, albeit that for *some* measurements in relatively low gravitational regimes--as Dr. Chandrashekar notes--the effects are small, and they seem to increase over increases in the inputs.

 

Thus the extant data normally used to support the validity of GR supports the notion that there are no boundaries to its applicability.

 

Typically most people interpret the Scientific Method as not being applicable for "proving the absence" of anything, so at best, what this does is say that the notion that there is no boundary is consistent with current observations, although it cannot "prove there is no boundary" especially in absence of a theory of what that boundary might be.

 

I came to be in the position I'm in as a result of intense discussion with one of my professors (an enthusiastic General Relativist), who made the very practical suggestion that I test my ideas on NM and GR by dropping GR and monitoring the consequences. That is what I have done. I have not detected any ill effects from doing this, but I am still open to the suggestion that I may be overlooking something.

I would absolutely agree with the suggestion that your professor gave you, and to help you out, I've been trying to point out one of the most obvious ones.

 

Newtonian Mechanics does not predict that light bends around objects with gravitational fields, and indeed the measurement of such gravitational lensing that is predicted by GR is significant to arcseconds even in the case of the Sun, which means it is significant to only 2-3 decimal places, which is hardly insignificant. You might want to consider this one.

 

Earlier Q pointed out the precession of Mercury, which is not as significant, but which became quite evident to even 17th century astronomers with archaic instruments. This issue is getting in to the range where you could argue that it is a "noise factor" but it is not something that can be ignored over the long term: those errors add up.

 

The exercise that is interesting is to look at how such additive error does create a big enough difference to start to see erroneous results.

 

I think it is important to consider that the "Mercury perihelion" problem drove astronomers batty, and unless one wants to consider them strangely obsessive-compulsive, I think there is an argument that says that even small differences cannot be ignored without consequences.

 

It may well be the case that within your specific areas of interest--coronal projections is an excellent example--that the difference between NM and GR is so insignificant that running the numbers will show error levels so low that you can easily ignore them.

 

However I believe that even with the few examples I and others have cited that it should be obvious that generalizing this "NM is good enough for everything non-cosmological" is clearly false.

 

So to answer your second question as clearly as I possibly can:

2. Can I practice astrophysics (excluding cosmology) to the limits of observation without necessarily using GR?

The answer is "yes, but" you need to be aware that there are indeed areas where the monotonically increasing differences between NM and GR can become significant, especially as you add error to error. Because NM is at best an "approximation" of a always accurate GR computation, the biggest part of the "but" here is that in order to justify your conclusions you will probably always at the end need to do the GR computation to show the actual error and conclusively show its insignificance in that particular case.

 

To clarify: this is not establishing a "boundary" between significance and insignificance. That is an issue of the *application* of the particular measurements in drawing your conclusions.

 

I hope this helps clarify what I have been trying to say.

 

A billion here, a billion there and pretty soon you're talking about real money, :)

Buffy

[Erasmus00]

What I would really like to know from you is, given that NM and GR both apply to a reasonable approximation in some cases, whether there are other aspects of astrophysics where GR applies to the exclusion of NM.

 

Gravity waves don't exist in a Newtonian setting, though they have yet to be detected directly, my understanding is that observations of binary stars shows strong indirect evidence for their existence. The decay of the binary star orbit doesn't make sense in Newtonian physics, but gravitational waves explain it nicely and match the GR prediction.

 

Similarly, you must be aware of the classic, weak field tests of GR (mercury, shapiro time delay, etc). These measure certain "post-newtonian parameters" and are clear indications that Newton's simply inverse square is NOT the end of the story. Hence, even in our solar system GR (or some other post-Newtonian theory) has some relevance.

 

Also, while there hasn't been a strong field test of GR, some groups claim to have indirect evidence of an innermost stable circular orbit, an effect with no Newtonian analog.

 

So, to wrap up, GR predicts accurately in both weak field (post newtonian parameters) and linearized gravity (gravitational waves). These have no analog (as far as I know) in standard newtonian gravity.

-Will