David,

The site I referred you to (http://math.ucr.edu/home/baez/einstein/node2.html), which you didn’t want to consider, was a treatment of the Field Equations by John C. Baez, a mathematical physicist and author at UC Riverside and Emory F. Bunn, a physicist at U of Richmond. I don’t think their discussion can be considered “half-baked.” My point in referring you there was to show that the mathematics of the field equations is ambiguous as to geometry or force. If math can be ambiguous, if in the case of gravitation it can model the phenomena as either the manifestation of geometry or force, then the dilemma you pose for me – “You cannot hold to the field equations of General Relativity, while also holding that Gravitational Waves do not have the characteristics predicted thereby” – excludes my position, and it remains for you, or someone, to explain (non-mathematically) how grav waves can result from a consistent geometric model.

Jim:

First, you appear to have, once again, mischaracterized/misrepresented my positions, assertions, and/or "requirements".

I simply wish to know where you stand in order to determine how to proceed in any possible attempt at answering your question: "to show how uniform motion/geodesic motion (choose whatever term you wish, it’s the state in the physical world revealed by a gravitiometer) transforms into energy, other than by an interpretive mathematical formalism."

Either you accept Einstein's Field Equation(s) of General Relativity (at least for the sake of further progress), or you call into question even the field equations of General Relativity as not properly having embodied the curved spacetime nature of gravitation.

Either choice is acceptable. You just have to make your choice as to where you stand.

It's quickly nearing time for me to make good on what I said I would do if you refused to make your choice.

So your next post will determine my next step. If you continue to refuse to make your stand clear, so we may proceed, then I will follow though as promised.

You make statements like:

I’m questioning your interpretation, the standard interpretation, of the field equations.

Which appears to suggest that you accept Einstein's field equation(s) of General Relativity, but then at other times you appear to be calling these field equations into question.

I simply want to know which is your actual position, so I may know what I have to work with, so I can know how to proceed (if at all).

On the other hand, if your last statement ("So yes, farewell.") is intended to ask me to "leave", then so be it.

I await your answer, so I will know how to proceed, if at all.

Fare well.

David

Jim, Jim, Jim!

You have turned to insulting a most patient teacher who asks a simple yes/no question.

Do you accept the mathematics of GR as a valid description of the universe or not?

David has pointed out that the mathematics of GR, not a mere interpretation thereof, predicts the existence of gravitational waves just as the mathematics of Maxwell's equations predict the existence of electromagnetic waves.

Answer his question yes or no, or expect a perturbed gadfly to bite your pompous posterior.

This bite of realism brought to you by "Gadfly."

David,

You insist that I “accept the field equations of General Relativity, in which case [you] can show [me] how one finds that these ‘ripples’ in spacetime do indeed have ‘energy’-like characteristics…”, otherwise you “don't believe it's worth [your] time,” and it would “would involve the entire derivation of General Relativity, and, then from there the derivation of models of Gravitational Waves.” The burden of the showing would be the same regardless of my initial position, of course, so it seems clear you’re demanding my acceptance before you’ll endeavor to show me why I should accept.

You “haven't bothered to read the reference [I] link to” as you’ve decided it’s irrelevant to your challenge. My challenge precedes yours, and you’ve continued to avoid it - to show how uniform motion/geodesic motion (choose whatever term you wish, it’s the state in the physical world revealed by a gravitiometer) transforms into energy, other than by an interpretive mathematical formalism. You not only ignore my challenge, you insist I make one of two choices that presume my challenge doesn’t exist, or that it isn’t more fundamental, or that it has already been addressed.

The mathematics of gravitational phenomena can follow from an implicit interpretation of gravity’s association with some sort of energy, or it can follow the physical evidence of the geometric distortion of spacetime in the presence of mass. An excessive absorption in mathematics can obscure the dilemma you refuse to acknowledge, that the mathematics of physics should depend upon an explicit physical interpretation. (There is no problem with a mathematical characterization of free-fall as an acceleration presumed to be due to a gravitational force, for example.) The mathematics of gravitation is uniquely ambiguous with respect to the basis of gravitation. The physical evidence of gravitation as a geometric phenomenon is however not ambiguous – provided, of course, there is an interest in isolating the evidence. And on the other hand there’s no unambiguous physical evidence of “gravitational energy.”

We live in different worlds. Yours and your colleagues’ is abstract mathematics, with occasional reference to the observable physical world. I’m reminded of a discussion by Hawking, where he concludes from the fact that the equation for entropy is indifferent to sign that entropy may arbitrarily go backwards somewhere, sometime. In my world, such leaps of abstraction are unpersuasive, and literally nonsensical. It suggests an implicit neo-Pythagorean philosophy that exceeds the bounds of science while claiming the special standing of science.

Despite your framing of my “two-choice dilemma” I’m questioning your interpretation, the standard interpretation, of the field equations. That’s my choice, and it makes your framing irrelevant. Your refusal to recognize the issue as such is what makes our conversation circular and fruitless.

Huff and puff all you like, I don’t believe you can form an explicit, coherent explanation of how force-free gravitation can produce radiant energy. To me, that’s a problem, a critical problem, no matter how many physicists say it isn’t.

So yes, farewell.

Jim:

Just a few "corrections", mostly for the sake of other readers (if there are any, by now).

There is no "basic premise of GR" stating "that geodesic motion is uniform motion." It is correct to say that geodesic motion ("free fall") is the closest thing to "uniform motion" one may find within General Relativity. But that's not the same as saying they are the same thing.

Also, within GR one really cannot talk about "kinetic energy" as if it was isolable. In fact, even the Special Relativistic concept of mass-energy has trouble being isolated. It's really all a part of the mass-energy-momentum-stress tensor (though one can look at various components in appropriately chosen coordinate systems, or by way of various assumed forms of matter and/or energy, to see that such contains all that has previously been designated via various separate treatments).

David

P.S. I haven't bothered to read the reference you link to, since it is not relevant to your "two-choice dilemma". However, it is quite possible (though I cannot be certain without reading it) that the "positive pressure" and "flow of energy" you deride actually pertains to the mass-energy-momentum-stress tensor, that is the source term in Einstein's field equation(s), rather than some supposed aspects of gravity itself. But as I say, that's not relevant to the core discussion.

Jim:

My reference to "being a man" was not in any regard questioning your "manhood", but regarding whether or not you would face your dilemma, or, like most people, simply try to avoid such by trying to manufacture some "third choice", as you appear to be trying to do.

Half baked "conceptual" discussions are irrelevant to the "two-choice dilemma" I have shown you are faced with. Such are unfortunate, but what one can expect when trying to discuss GR with novices (just as the very unfortunate "rubber sheet" is so often used). It is not relevant that such can lead one down unfortunate conceptual paths. Such is often the case when analogies and sub-models are used (rather than the full mathematical model that is General Relativity).

I don't believe it's worth my time to attempt to try and take you "step-by-step, from a geometric principle to a radiation of energy." This would involve the entire derivation of General Relativity, and, then from there the derivation of models of Gravitational Waves, and showing how they lead to the exhibition of "energy"-like characteristics, whether one wishes to ascribe to them, or any aspect of "gravity", any "energy" designation/moniker.

It is because I know that from the field equations of General Relativity one can, via multiple methods, determine such "energy"-like characteristics, I have pointed out that you cannot claim to consider the field equations of General Relativity to be "correct" while disputing the "energy" that is effectively "transmitted" via Gravitational Waves (hence the term Gravitational Radiation). Either you accept the field equations of General Relativity, in which case I can show you how one finds that these "ripples" in spacetime do indeed have "energy"-like characteristics (even bending spacetime).* Or you must admit that you call into question the field equations of General Relativity (the "step-by-step, from a geometric principle to" the field equations of General Relativity). (You are most certainly free to choose the latter case, as I have tried to make clear in previous posts. Just don't continue denying that this is your contention.)

This is simply your "two-choice dilemma", again. So either you face it, and make your choice, or I leave you in your dilemma (as you continue in denial).

So, until you make your choice, fare well.

David

* Be warned, however, that what I will be showing you is highly mathematical, and directly from Misner Thorne and Wheeler's Gravitation. (Their's is the only text I have seen that doesn't stop at the linear approximations and/or analogies. However, this makes it much more difficult for those not fluent in Differential Geometry. Which is almost certainly the reason why most authors stop at the linear approximations and/or analogies.)

David,

I don’t think my motive or manhood need to be questioned. And I don’t “hate” mathematics. I do believe it should be treated as a tool, not an oracle.

The problem with mathematics as applied to gravitation is that it’s ambiguous with regard to the basis of gravitational acceleration.

Look at the conceptual discussion of the field equations at http://math.ucr.edu/home/baez/einstein/node3.html

Already there’s an interpretation, based on the mathematics, of “positive pressure” and an ambiguous treatment of the “flow of energy” that obscures the basic premise of GR, that geodesic motion is uniform motion. There is no “pressure” with geodesic motion, and the only energy involved with the "collapsing ball" is kinetic. Although the mathematics succeeds in characterizing the dynamics of gravitation, the seeds are already sown here for derivations based on misinterpretation, on a confounding of the basis of gravitation (the geometric distortion of spacetime) with an analog of force-like “attraction.”

So your “two-choice dilemma” leaves out my choice, which is that the mathematics of the field equations is fine up to the point where it is wrongly interpreted, and over-extended. If I’m wrong, my motives and manhood are irrelevant. I would hope that you will choose to point out how “pressure” and “energy flow” apply to gravitation as a geometric principle, and how we can legitimately move, step-by-step, from a geometric principle to a radiation of energy.

Jim:

Once again you either misunderstand my position, or you have (intentionally?) misconstrued it.

I most certainly do not hold that simply because something is predicted by General Relativity then it must be. (Regardless of how successful the theory has been, thus far, anything that has not yet been measured is a potential test. Furthermore, even if a theory passes all tests with flying colors, this still does not imply that its description is the Truth or Reality.)

You certainly have a right to take a stand against General Relativity. Just be a man and state that such is your position! That is one of your two choices, as I have pointed out. (Then you can have the integrity, and our respect, in being honest about your position concerning the curvature and geodesic aspects of GR vs. the Gravitational Wave etc. aspects. Of course, then the onus is upon you, and any cohorts you can convince to join you, to come up with a viable alternative to General Relativity that has your desired characteristics while simultaneously explaining all presently measured results at least as well as GR.)

Your only other choice, as I've explained, is to continue to hold that you believe that the field equations of General Relativity are "correct" (as per your assertion that you do not dispute such), recognizing that predictions like Gravitational Waves are inextricably tied to such.* While you may still be free to dispute "force"-like interpretations appended thereto.

The problem, as I pointed out, is that you cannot have it both ways: You cannot hold to the field equations of General Relativity, while also holding that Gravitational Waves do not have the characteristics predicted thereby. It's as simple as that.

Be a man, make you choice, within your "two-choice dilemma".

I await your decision.

David

* If you wish to see "proof" of this inextricable connection, we may be able to help. However, so far, I have seen no evidence that you have taken advantage of the references you have been presented. So do try those references first, and if they are still unsatisfactory (as I expect they may well be) simply come and ask for some more specific "proof" you desire.

(I'm afraid that some "hand waving", conceptual level will almost certainly not satisfy you, since all such I have seen rely upon "energy" like concepts. So, if you can really stand by your prior assertion that you do not dispute the field equations of GR, any such "proof" will be quite mathematical, I'm afraid. So I suspect you won't like it in any case. But please do let us know what you desire.)

Jim:

Short of going through a mathematical derivation of Gravitational waves (deeper than the level given in previous references, which you don't appear to have taken advantage of), and I know how you hate the mathematical approach, you are left with the two choices I outlined. For there is no way Gravitational Waves, as predicted by the field equations of General Relativity can be "excised" while maintaining the substance of the theory (the field equations).*

As I, and others have pointed out, the Gravitational Wave predictions are inextricably tied to the field equations of General Relativity, without any reference to "gravity as a force" or "gravity having energy". (Except to the extent that the nonlinearities of the field equations may imply some form of "energy" like characteristic, and/or the predictions of decaying orbits imply such a transformation. It's only secondary, not primary or necessary for the derivation of said prediction.)

I will give you one last chance... If you make your choice in your "two-choice dilemma", rather than avoiding the dilemma (as most tend to avoid such, until they pluck up the courage to undergo the anxiety and pain of growth, thereby), I will help you with the next stage.

Otherwise, I will delete your blog from my bookmarks and never visit again.

Until then, fare well.

David

* The best one could accomplish would be to start over from the "Arnold" hypotheses, and derive a new theory.

It way, I emphasize MAY, be possible to modify the field equations such that no such waves are produced while maintaining the other measured predictions, but no one has accomplished anything like this. Furthermore, unless one modifies the theory such as to rid it of the indefinite metric (like that of Special Relativity) it is almost certain that any dynamical character of spacetime will lead to waves.

Keep in mind, when Einstein created this theory I'm sure he had no intention of creating anything like Gravitational Waves, just as he had no intention to create a theory that predicted an expanding (or contracting) universe. It simply came as a part-and-parcel consequence. (A controversial one at that, as I and others have already pointed out.)

I apologize for any part I had in the duplications. I don't know how it happened.

David,

We do seem to be at an impasse. You’ve been generous with your time, but your focus seems never to have gone beyond defending and imparting the convention.

To say “I don’t get it” (one of the nicer things I’ve heard from contributors here) when it’s presumed that the only issue is whether I’m being consistent with GR is simply dogmatism. To object that my position is inconsistent with GR isn’t to refute my position. And I’ve stated repeatedly that GR can be clarified as simply a description of the distortion of the geometry of spacetime without invalidating GR in its entirety. To object that discarding any part of GR would be catastrophic to GR is a theoretical fundamentalism.

“since General Relativity does not allow gravitational effects to travel at infinite velocity (unlike Newton), there are waves that are set up and propagate away from the system at the speed of light. It is these wave that are referred to as Gravitational Waves, not the near field tidal effects. (You also appear to have totally ignored, or not recognized, my discussion on the difference in how such effects diminish with distance, such that the waves will always dominate at sufficiently large distances.)”

Ripples in spacetime due to changes in the distribution of mass, whether tidal or somehow energetic, would in any case propagate at the speed of light. Given that I’ve questioned the reality of non-tidal gravitational waves, it's unavailing to argue that “Gravitational Waves” exist because “Gravitational Waves” exist.

“(I'll ignore your perpetual confusion concerning orbital mechanics and the energies involved.)”

I suppose I’ll have to ignore it too.

“you are correct that if there is a decaying orbit there must be something that is causing or facilitating the reduction of total energy of the system: Energy is ‘going away’ (somewhere). Since all of science has found that energy can neither be created nor destroyed, but can only change form, one will certainly expect that the orbital energy has been transformed into some other form and is, in some way, leaving the system. (Unless we find that the system is heating up, in which case it will eventually leave through electromagnetic radiation in the infrared, etc.)”

If there’s a net loss of kinetic energy to the system, there’s a net gain of kinetic or potential energy (unless maybe the intensity of the magnetic field is somehow being dissipated) outside the system. You’ve yet to explain where “Gravitational Energy” comes in, except to say that it’s predicted by GR. It is because it is because GR says it is.

“the prediction of gravitational waves, from the General Theory of Relativity, is derived from first principles within said theory, without any electromagnetic fields being involved. Hence, if the observations could be completely explained via electromagnetic effects, this could actually be viewed as a refutation of the General Theory of Relativity!”

Ripples in spacetime due to changes in the distribution of mass can be interpreted as only tidal fluctuations without a complete rejection of GR. My point is that any loss of energy to a system (given that I don’t see how geometry can produce energy) could be attributed to either potential/kinetic energy, or to the radiation of some other established (presumably electromagnetic) form.

“face it, this ‘exotic form of (gravitational) radiation’ is inextricably tied to the field equations of General Relativity…. you cannot hold that you don't dispute the field equations of General Relativity, while only disputing interpretations that use ‘force’-like concepts (and, by extension, and your own assumptions, ‘energy’-like concepts), if you assert that the predicted nature of gravitational waves are not as predicted by General Relativity. You can't have it both ways! ….You may accept that the General Theory of Relativity predicts Gravitational waves, with their predicted characteristics of causing orbits to decay (thus maintaining that you believe in the field equations of General Relativity, while disputing interpretational issues). Or, you must admit that there is more to your dispute with the General Theory of Relativity than the interpretational disputes you have admitted to thus far.”

Your challenge sounds strangely doctrinal. I’m not trying to conceal the depths of some awful heresy. And again, there’s no reason why any aspect of GR that associates geometry with force or energy can’t be excised without abandoning GR's basis as a geometric interpretation of gravitation, and of its confirmed, unambiguous predictions. You’ve given me to choose between orthodoxy and heresy. Can’t I be just somehow “reformed”?

David, who is clearly one of the world's most patient physicists, writes:

"Jim:

Once again you don't get it."

Like Jim, David appears to have two choices:

(1) To continue trying to teach the unteachable Mr. Arnold
(2) To recognize that Mr. Arnold is unteachable and perhaps use his talents to enlighten other Science Blog threads, such as those begun recently by aerospace watchdog Scruffy

This bite of realism brought to you by "Gadfly."

Jim:

Once again you don't get it.

You say:

Gravitational ripples in spacetime due to changes in the distribution of mass are tidal changes. Two bodies in a stable binary star system are each moving uniformly along their geodesics, and their orbits will produce tidal ripples, but that in itself shouldn’t cause the orbital system to decay. If there is a decaying orbit there is some factor that is slowing the relative kinetic energy (producing a lower orbit), while increasing their relative kinetic energy in the lower orbit. Parenthetically, I’d be very interested in your interpretation of what could be producing the orbital decay. Pulsars are highly magnetic - could the interaction of their magnetic fields be producing a radiation of magnetic energy, and hence, a decay of their orbits? That seems to me to be the most likely explanation. And it would give substance to the prediction of the General Theory without introducing an exotic form of (gravitational) radiation.

First, in the near field (close to the orbiting bodies*), you are correct to talk about tidal effects. The difference is that since General Relativity does not allow gravitational effects to travel at infinite velocity (unlike Newton), there are waves that are set up and propagate away from the system at the speed of light. It is these wave that are referred to as Gravitational Waves, not the near field tidal effects. (You also appear to have totally ignored, or not recognized, my discussion on the difference in how such effects diminish with distance, such that the waves will always dominate at sufficiently large distances.)

(I'll ignore your perpetual confusion concerning orbital mechanics and the energies involved.)

Second, you are correct that if there is a decaying orbit there must be something that is causing or facilitating the reduction of total energy of the system: Energy is "going away" (somewhere). Since all of science has found that energy can neither be created nor destroyed, but can only change form, one will certainly expect that the orbital energy has been transformed into some other form and is, in some way, leaving the system. (Unless we find that the system is heating up, in which case it will eventually leave through electromagnetic radiation in the infrared, etc.)

You are correct that pulsars are "highly magnetic". However, to suggest that the energy is leaving in some form of "magnetic energy" (don't you mean electromagnetic energy?) would "give substance to the prediction of the General Theory without introducing an exotic form of (gravitational) radiation" is to show a complete misunderstanding of the "substance" of the "prediction(s)" of the "General Theory (of Relativity)".

First off, the prediction of gravitational waves, from the General Theory of Relativity, is derived from first principles within said theory, without any electromagnetic fields being involved. Hence, if the observations could be completely explained via electromagnetic effects, this could actually be viewed as a refutation of the General Theory of Relativity!

Secondly, you act almost as if someone concocted these gravitational waves in order to try and explain the decay of such orbits. Yet it's quite the opposite! The prediction of gravitational waves came directly from General Relativity, before any evidence for such had been observed. In fact, it was a prediction that was so far beyond anything one would expect, from our experience with Newtonian mechanics and observational astronomical mechanics, that it was quite controversial. (What?! You mean that "stable" orbits are only an approximation?!)

Jim, face it, this "exotic form of (gravitational) radiation" is inextricably tied to the field equations of General Relativity, and, just as with any dynamics within any form of spacetime that has an indefinite metric (like that of Special Relativity), these waves have a finite speed of propagation (which is really one of the reasons they are "waves", and not just "undulations"). This is why I have asserted that you cannot hold that you don't dispute the field equations of General Relativity, while only disputing interpretations that use "force"-like concepts (and, by extension, and your own assumptions, "energy"-like concepts), if you assert that the predicted nature of gravitational waves are not as predicted by General Relativity. You can't have it both ways!

So, you have but two choices (a "two-choice dilemma", if you will), if you wish to retain any semblance of integrity. You may accept that the General Theory of Relativity predicts Gravitational waves, with their predicted characteristics of causing orbits to decay (thus maintaining that you believe in the field equations of General Relativity, while disputing interpretational issues). Or, you must admit that there is more to your dispute with the General Theory of Relativity than the interpretational disputes you have admitted to thus far.

That's the choices you are left with. That's your dilemma.

Fare well.

David

* "Close" in this case meaning less than about one wavelength of the associated gravitational wave, or any other hypothetical wave that travels at about the speed of light and has a period like that of the objects' motion (their orbital period, in this case).

David,

You wrote: “I won't dignify any of your comment that's in line with ‘in general it’s too dark to tell red from blue’. Your going way too far off the mark with such comments.”

I’m sorry you feel that way. I resorted to an “undignified” simile because my more direct and “dignified” point was unavailing. So forget my example of obscuring the difference between colors when light is removed – it’s essentially the same to argue that gravitation and force, or geodesic motion and force-induced accelerations, can’t be distinguished when conditions necessary for their discrimination are made problematic.

“Again, just as on Scruffy's blog, you appear to have a problem recognizing that there is a distinction between gravitational waves and tidal effects. While they have some relations, there are significant differences.”

I recognize that you’re hypothesizing something that’s supposed to be distinct from tidal effects. But let’s be clear: You’re referring to a hypothetical principle (the energy-bearing gravitational wave) that has not been observed, in contrast to a principle (the tidal effect) that is manifest and unquestioned.

“I pointed out, in my post, that the gravitational waves do not rely upon any concept of ‘gravitational energy.’ They come about simply as ‘ripples’ in spacetime itself—from General Relativity itself!”

Gravitational ripples in spacetime due to changes in the distribution of mass are tidal changes. Two bodies in a stable binary star system are each moving uniformly along their geodesics, and their orbits will produce tidal ripples, but that in itself shouldn’t cause the orbital system to decay. If there is a decaying orbit there is some factor that is slowing the relative kinetic energy (producing a lower orbit), while increasing their relative kinetic energy in the lower orbit. Parenthetically, I’d be very interested in your interpretation of what could be producing the orbital decay. Pulsars are highly magnetic - could the interaction of their magnetic fields be producing a radiation of magnetic energy, and hence, a decay of their orbits? That seems to me to be the most likely explanation. And it would give substance to the prediction of the General Theory without introducing an exotic form of (gravitational) radiation.

Jim:

I won't dignify any of your comment that's in line with “in general it’s too dark to tell red from blue”. Your going way too far off the mark with such comments.

Again, just as on Scruffy's blog, you appear to have a problem recognizing that there is a distinction between gravitational waves and tidal effects. While they have some relations, there are significant differences.

Burt did a rather good job of pointing out that "In a way, tidal gravity, with its short range, sets up a 'near field antenna' that radiates away long range gravitational waves." Tidal effects decrease as the inverse third power of the distance (in terms of "potentials"), while the waves propagate (at least in the weak field, small amplitude, perturbation approximation, where we can treat them as linear waves) with amplitudes that decrease as 1/r. So when talking about gravitational waves we are taking about effects that are far from the "near field" tidal effects. (Generally more than one wavelength away from the source, so for the Earth-Sun system we're talking more than about a light-year, while for the Earth-Moon system we are talking 1/13 th of that, which is still far outside our solar system.)

You say that

I don’t deny that gravitational waves can produce variations in the distribution of kinetic and potential energy between, e.g., a binary star system and the rest of the universe. But I believe such variations are entirely relative between the system and the universe. It’s no different than the relationship between the earth and moon, where the moon’s orbit produces immense tidal dislocations without an exchange of “gravitational energy.” If you can explain how a gravitational model based on curvature and geodesic motion can do otherwise, I’d love to learn.

I'm not quite sure what you mean by "such variations are entirely relative between the system and the universe." Are you calling upon Mach? But once again you rely upon aspersions on any concept that uses anything like “gravitational energy.”

I pointed out, in my post, that the gravitational waves do not rely upon any concept of “gravitational energy.” They come about simply as "ripples" in spacetime itself—from General Relativity itself! That's "how a gravitational model based on curvature and geodesic motion can" give rise to gravitational waves. Of course, an important feature of this particular "gravitational model based on curvature and geodesic motion" is that curvature is dynamic, it depends upon the locations and motions of the particles/fields/etc. within the universe. It's not static and immovable. (If spacetime were static and immovable, you would be correct that there would be no way for such to "cause or allow a source system to lose or decrease in energy, while causing or facilitating a receiving system to gain or increase in energy.")

Admittedly, since gravitational waves do "cause or allow a source system to lose or decrease in energy, while causing or facilitating a receiving system to gain or increase in energy" it does beg the question of where is the energy that "went from" the source system until it "reaches" the receiving system? It's this question, really, that I believe lead to the desire to obtain some kind of "localizable" "gravitational" energy-momentum-stress (tensor-like) "something" that can be used in such an accounting, not some "gravity as force" concept held over from Newtonian mechanics. (Unfortunately, as I pointed out so many times before, such attempts have failed. However, we are able to obtain something reasonably satisfactory in the weak field, small amplitude, perturbation approximation, where we can treat gravitational waves as linear.)

There is no need for "gravitational energy" or "gravity as a force like electromagnetism" or anything besides curvature and geodesics (and a metric, so we can actually make measurements like distances) that dynamically depends upon the distribution and motion of particles/fields/etc. within the universe.

One place you may wish to look for a potentially accessible explanation is in Wikipedia's "Gravitational wave" or the reference Burt gave in Scruffy's blog. If you wish to delve into greater detain, feel free to follow the references these references provide. (Burt's reference refers directly to Misner, Thorn, and Wheeler's Gravitation, which can be quite difficult for the layman. However, I may be able to help you, if you are willing.)

You do end with "I'd love to learn", but I have to question whether you mean actually learning what General Relativity has to say on this matter, or whether you are referring to something else. If you are willing to learn what General Relativity has to say on this issue, I may be able to help you.

'Til then.

David

David,

I apologize. I’ve just discovered your commentary from long ago:

“What you appear not to be able to grasp is that the ‘absolutes’ of ‘mathematical statements that are absolute’ such as the ‘tenets of special and general relativity’ or the ‘fundamental tenets of quantum physics’ are all model dependent. Hence, they are never absolutes unless one "absolutely" adheres to their respective models. So long as one is trying to understand what is ‘actually’ the nature of this universe in which we reside one must recognize that any model is tentative, and, hence, not absolute.”

Well, sure. But how is a statement that gravitational waves can carry energy any less absolute, or any more tentative, than a statement that they can’t? Could it be you find my statements objectionable because you disagree with them, or disagree with their worth?

“there are multiple choices available for defining what is meant by the ‘existence’ of a ‘gravitational field’. Unfortunately, you have yet to make your choice.”

I’ve expressed my preference for assuming a gravitational field exists everywhere, but it makes no difference to my distinction between gravitation and force whether it exists in any particular region. For my purpose, it suffices to say if there is a detectible curvature, the effects of the curvature (gravitation) can be distinguished from force. If there is no detectible field, the distinction is, of course, problematic, and in such a region, irrelevant.

“there is the matter of distinguishing the effects of gravity from those of other inertial (pseudo,’false’) ‘forces’ (those that result from observing particle motions from any sort of non-inertial "reference frame"). With regard to this issue there is the little ‘problem’ that if spacetime is curved there are no inertial reference frames definable.”

In demonstrating the difference between gravitation and force I have sought to construct experiments that allow for their distinction to be made. It is certainly possible to construct an experiment that makes it impossible to make the distinction. But 1) why would we want to do so and 2) how would that refute the distinction, or make it problematic in any meaningful way? An inertial reference frame is definable within an enclosure where neutral test particles indicate an inertial reference frame. It’s impossible to distinguish red from blue if we turn out the light, but darkness doesn’t render the distinction insoluble. Let’s turn on the light.

“This is why I've maintained that, in general, there is no theoretical way (let alone any practical way) one can uniquely distinguish between geodesics that are gravitational vs. ‘other’ geodesics caused by non-inertial motion.”

Are you saying something more than an analog of “in general it’s too dark to tell red from blue”? Inertial or non-inertial motion from my planet may look inertial or non-inertial from yours, or from your free-moving spacecraft. Let’s work together and find away around the problem, and see if gravitation and force are equivalent. Then it’ll be no problem.

“You have expressed incredulity at the idea of geodesics due to inertial "forces". You appear to have the supposition that all inertial ‘forces’ are actually manifestations of an application of "true" forces upon something. May I suggest you simply consider rotations: No more an imposition of external ‘true’ forces as non-rotation.”

What sort of rotation are you thinking of? The rotation of a planetary body? Any body that is bound to a planet by gravity (actually by the resistance to its gravitation) will be forced to participate in the planet’s rotation by its consolidation with the planetary mass, which rotates due to the curvature of the geodesics that originally formed the planet, making for a rotation of inertially accelerating bodies. Do you mean a small-scale rotation, where gravitation is not a factor in the rotation? A body that is part of a rotation will be affected by a centrifugal “force” attributable to the actual force producing the rotation. Do you mean the rotation of a container in an experiment with test particles? A test particle inside a box or sphere will be unaffected by the rotation of the box or sphere unless it comes in contact with the box or sphere.

“your assertion that even if there are gravitational waves predicted by General Relativity, that such can, in no way, be ‘a carrier of energy’… is what is most untenable of all your assertions. You admit that gravitational waves (as predicted by the fundamental equations of General Relativity) may exist and travel, but you appear to refuse to allow that they may, in any way, cause or allow a source system to lose or decrease in energy, while causing or facilitating a receiving system to gain or increase in energy. (I hope you do recognize that General Relativity conserves energy… within the universe, in an absolute way, just as with all prior classical theories.”

I don’t deny that gravitational waves can produce variations in the distribution of kinetic and potential energy between, e.g., a binary star system and the rest of the universe. But I believe such variations are entirely relative between the system and the universe. It’s no different than the relationship between the earth and moon, where the moon’s orbit produces immense tidal dislocations without an exchange of “gravitational energy.” If you can explain how a gravitational model based on curvature and geodesic motion can do otherwise, I’d love to learn.

Jim:

What you appear not to be able to grasp is that the "absolutes" of "mathematical statements that are absolute" such as the "tenets of special and general relativity" or the "fundamental tenets of quantum physics" are all model dependent.  Hence, they are never absolutes unless one "absolutely" adheres to their respective models.  So long as one is trying to understand what is "actually" the nature of this universe in which we reside one must recognize that any model is tentative, and, hence, not absolute.

As I alluded to in my previous response, there are ways in which your "tenets" can be made defensible.  Perhaps now is as good as any to present such to you.

First, there is the matter of distinguishing the effects of gravity from those of "true" forces (like electromagnetism).  If one restricts oneself to the apparent four dimensional spacetime (manifold) (assuming that there are no additional, even compact, dimensions; that spacetime is a continuum; etc.) then one can certainly distinguish between the motion of free neutral test particles (at least to the extent that any actual particles can be said to actually approximate such), which one can "define" as geodesic motion, vs. non-geodesic motions.  This distinction is independent of any assumed or actual motions of whatever "box" such experiments may be contained within.

Second, there is the issue of distinguishing when a "gravitational field" exists.  As I pointed out several posts ago, there are multiple choices available for defining what is meant by the "existence" of a "gravitational field".  Unfortunately, you have yet to make your choice.  (I would hope it's reasonably apparent how one would go about determining said "existence" once one has chosen what such means.)  However, at this point, let's just assume a choice has been made, and, since all of the definitions I presented would agree that a region with nonzero spacetime curvature (in its most general form, meaning a nonzero Riemann curvature tensor) is a region where a "gravitational field" exists, let's assume that all the remaining discussion refers to such a region of spacetime.

Third, there is the matter of distinguishing the effects of gravity from those of other inertial (pseudo,"false") "forces" (those that result from observing particle motions from any sort of non-inertial "reference frame").  With regard to this issue there is the little "problem" that if spacetime is curved there are no inertial reference frames definable.  In fact, within Differential Geometry (the language of General Relativity), so long as spacetime has nonzero curvature, at least somewhere within it (as we observe everywhere near us), then all observers must cope with the realities of making observations from a non-inertial standpoint.  Furthermore, all non-inertial "reference frames" are "equivalent" (just as good as any other, at least up to some measure of mathematical ease), from this point of view.  (This is the "relativism" of "acceleration", or, rather, the "relativism" of non-inertial "reference frames" that is embodied within General Relativity.)

This is why I've maintained that, in general, there is no theoretical way (let alone any practical way) one can uniquely distinguish between geodesics that are gravitational vs. "other" geodesics caused by non-inertial motion.  (You have expressed incredulity at the idea of geodesics due to inertial "forces".  You appear to have the supposition that all inertial "forces" are actually manifestations of an application of "true" forces upon something.  May I suggest you simply consider rotations:  No more an imposition of external "true" forces as non-rotation.)

However, for the sake of this discussion (hopefully not an "argument"), let's assume that there exists some method for separating "purely" gravitational geodesic motions from "other" geodesic "motions" cause by other non-inertial aspects of one's observations.  (Supposing that somewhere buried within Differential Geometry, at least within General Relativity, there is some mechanism that can be used to disentangle these contributions to geodesic motions.)

Then there remains your assertion that because gravitational motions (geodesics) are distinguishable from those of (at least "true") forces, and based upon an apparent assumption that the only way "energy" can come into play is via "forces", then gravity can have nothing (directly, at least) to do with "energy".  Hence, your assertion that even if there are gravitational waves predicted by General Relativity, that such can, in no way, be "a carrier of energy".

This is what is most untenable of all your assertions.  You admit that gravitational waves (as predicted by the fundamental equations of General Relativity) may exist and travel, but you appear to refuse to allow that they may, in any way, cause or allow a source system to lose or decrease in energy, while causing or facilitating a receiving system to gain or increase in energy.  (I hope you do recognize that General Relativity conserves energy, actually the mass-energy-momentum-stress tensor of all objects/things/energies/substances/etc. within the universe, in an absolute way, just as with all prior classical theories.*)

If this statement is not a correct characterization of your position, please let me know.  Otherwise, I will consider addressing this issue from within the General Theory of Relativity.  (Fortunately, I went to my office today and retrieved my General Relativity texts.)

David

*    Please don't confuse the mass-energy-momentum-stress tensor with my comments about the failed attempts to determine some form of energy-momentum-stress of the gravitational field itself.  I'm sorry I ever mentioned such, since I have seen it divert your thinking more than once.

David,

I think if I’ve been “absolute” you’ve been “relativistic” (in the philosophical sense). You write that “‘quantum theory' is far from a singular. In fact it's something more like a theory of theories…. So it's rather difficult, if not impossible, to characterize 'quantum theory' as treating gravity as or not as a 'force', of some kind.”

If there’s some school of quantum physics which holds that it’s unjustifiable to consider gravitation a force, or to believe a gravitational wave can carry energy, I’m not aware of it. Are you? Or do you raise this as a hypothetical of the kind that would render any definite (absolute) position untenable in principle?

You wonder if I believe “if we were to cease and desist in any attempt that even smells of treating gravity as ‘force’ or related to ‘energy’, then all would be far better.” Yes.

“I'm not sure it would be proper to characterize the way [string theory] tries to incorporate gravity as ‘force’-like, except that it is a fair example of a theory/model that tries to use the success of General Relativity as a guide by trying to treat all ‘forces’ (interactions, really) as curvature (in a higher dimensional spacetime).”

My understanding of the concept of “strings” is that they are identifiable entities which embody or transmit force (choose any definition you like), which in terms of gravitational geometry I find to be wildly speculative and absolutely incoherent. (More on absolute statements below.)

“So, Jim, at this point it appears that your greatest enemy is your own predilection for "absolute" statements. Have you not learned that, especially in matters of science, such are seldom, if ever, fully valid?”

Physics is built upon mathematical statements that are absolute. The tenets of special and general relativity are expressed as absolutes. The fundamental tenets of quantum physics are absolutes. I suggest to you that we tend to find absolute statements objectionable when we are loathe to abandon the beliefs the absolutes are threatening, and we’re unable to effectively defend our beliefs directly (or absolutely), without abstract relativism or obscurantism.

I've tried to show as methodically as I can that there is no empirical or even coherent transition from the concept of gravitation as a curvature of spacetime to gravitation as a force or a carrier of energy. You've raised speculative hypotheses that presume a transition. A hypothetical presumption doesn't undermine an absolute, and it doesn't render absoluteness objectionable. I illustrated in the beginning, in a specific narrative of a thought experiment, how force enters into combination with gravitation-as-curvature. Unless a specific counter example can be offered, where gravitation itself is shown to be force-like, the distinction between gravitation and force seems absolutely clear.

Jim:

You quote me with

You wrote: “I wouldn't say that any ‘identification of gravitation with 'true' force’ is ‘ubiquitous’ (except possibly in your mind).”

After which you respond with

You are of course familiar with quantum theory, and with string theory, just the most prominent examples. I’m trying to imagine what you’re thinking here. I specified “true” force because you’ve frequently invoked the “pseudo” forces, and I hoped to avoid that digression. It seems I’ve stepped on a mine while trying to avoid a trip-wire. Maybe we could be a little less crafty and interpret each other in the interest of productive communication. Gravitation is treated as a force in quantum theory. Let’s just go with that.

I'll get to the reference to "quantum theory" and "string theory" a little later.

First, the only "mine" field I see has been lain by you.  Most specifically with your use of absolute statements like "ubiquitous", "routinely, implicitly, and illegitimately treated as givens", "absolute distinction between gravitation and force".  So what I was commenting on, above, was your use of "ubiquitous", not your reference to "true" forces.  (I'm sorry you appear to have misunderstood this.)

Then you go on to rail about so much else you have misunderstood (or intentionally misconstrued).  I'll skip all that, at least for now.

Now, let's return to the "quantum theory" and "string theory" references.

First and foremost, "quantum theory" is far from a singular.  In fact it's something more like a theory of theories, at least in its present form.  Or, perhaps, it would be more reasonable to characterize it as an approach or methodology toward the creation of theories that are "quantum" in nature.  So it's rather difficult, if not impossible, to characterize "quantum theory" as treating gravity as or not as a "force", of some kind.

Early, non-relativistic "quantum theories", if they even looked at gravity, did treat it as a force in the same manner as Newtonian mechanics (after all, early "quantum theory" stemmed from a reassignment of differential operators for classical quantities like energy and momentum).  Then, after the advent of relativistic "quantum theory" it was quite natural to try and incorporate gravity via General Relativity's curved spacetime (an approach you appear to endorse in some of your posts where you declare there to be an "absolute" distinction between gravity and "forces" of any kind or nature—suggesting that if we were to cease and desist in any attempt that even smells of treating gravity as "force" or related to "energy", then all would be far better).

Unfortunately, as I tried to point out in my first post, all such attempts that have tried to incorporate General Relativity's curved spacetime in any dynamic form (so the "quantum particles/fields", and their associated mass-energy-momentum-etc., "properly" give rise to the source term for the spacetime curvature) have ended in predictions that are violently inconsistent with observed reality.  (Talk about "non-empirical".)

So, at this point, there are multiple "quantum theories" that try to incorporate gravity, in various ways.  "String theory" is only one of many such.

Now, I certainly cannot claim to be an expert in "string theory", but I'm not sure it would be proper to characterize the way in tries to incorporate gravity as "force"-like, except that it is a fair example of a theory/model that tries to use the success of General Relativity as a guide by trying to treat all "forces" (interactions, really) as curvature (in a higher dimensional spacetime).  (Admittedly, it also does a great many other things, like treat particles as "strings" or higher dimensional "brains", and incorporating "super symmetry".)

So, Jim, at this point it appears that your greatest enemy is your own predilection for "absolute" statements.  Have you not learned that, especially in matters of science, such are seldom, if ever, fully valid?

I hope you understand now.

David

P.S.  My first attempt at a response was primarily focused on what statements you could make that would be at least defensible.  With the final emphasis on what you have been asserting that can in no wise be construed as defensible, unless you wish to challenge the field equations of General Relativity, as opposed to your assertion that you only challenge certain interpretations thereof.

I'll attempt this process again, later.

David,

You wrote: “I wouldn't say that any ‘identification of gravitation with 'true' force’ is ‘ubiquitous’ (except possibly in your mind).”

You are of course familiar with quantum theory, and with string theory, just the most prominent examples. I’m trying to imagine what you’re thinking here. I specified “true” force because you’ve frequently invoked the “pseudo” forces, and I hoped to avoid that digression. It seems I’ve stepped on a mine while trying to avoid a trip-wire. Maybe we could be a little less crafty and interpret each other in the interest of productive communication. Gravitation is treated as a force in quantum theory. Let’s just go with that.

“I have never seen… ‘non-empirical, non-four dimensional models’ ‘routinely, implicitly, and illegitimately treated as givens.’ They are only given/proposed/used/etc. as theories and/or models.”

You’ve done it yourself, and repeatedly. I’ve described empirical tests that demonstrate the absolute distinction between gravitation and force (substitute any term you prefer to describe non-gravitational phenomena I’ve described) in our empirical, four-dimensional universe, and you’ve invoked non-empirical, non-four dimensional or super-galactic models to suggest that they undermine the distinction. If they aren’t “givens” then their relevant effects need to be confirmed before they in any way diminish empirical “givens” like the behavior of test particles in a box.

“I would not say that any such [model] is any less legitimate than any four dimensional model.”

The four-dimensional spacetime continuum has been (I don’t think it’s too strong a word) legitimized by various experimental confirmations. Models in excess of four dimensions have less scientific legitimacy, to say the least. You’ve accused me elsewhere of “crankdom.” I don’t know how I would categorize your statement, except to say it’s astounding.

“what is the nature of the motion of a free neutral test particle undergoing any of your listed inertial (pseudo, "false") "forces" (free of any "true" forces)? Are not such motions geodesics? If so, then how are these geodesics to be distinguished from any other geodesics?”

No. I’ve already described the behavior of test particles in a box under centrifugal acceleration - not "free of any 'true' force", I don't know what empirical "pseudo' force that would be. it would be astounding if you would want to describe the effects of centrifugal acceleration (due to the application of force) as geodesic. Are you referring to some hypothetical "pseudo" force no one has ever seen?

“Often times you have suggested that the geodesics of such inertial (pseudo, ‘false’) ‘forces’ will be divergent while gravitational geodesics will be convergent (apparently relying upon an unspoken ansatz [one that appears to rely upon an assumption of a central concentration of mass]). This is why I brought up the observed ring/torus of ‘dark’ matter.”

First, gravitational geodesics can be divergent if, for example, motion of a box is perpendicular to a gravitational field. Second, as you know, the nature and the effects of “dark” matter are still in question, and in any case, the effects are galactic. If there is any reason to think “dark” matter might indicate an equivalence of gravitation with force when controlled empirical tests in our vicinity show no equivalence, when controlled empirical tests leave nothing paradoxical such that recourse to an influence by a ring/torus might promise some plausible avenue of resolution, I can’t imagine what it would be. Can you? Frankly, you seem to be throwing the idea out like nails in the road during a car chase.

“If your ‘box’ was placed within a similar ring/torus, especially if the ring/torus was spinning/rotating (and practically everything we observe in this universe spins/rotates, besides, in order not to have such collapse under its own gravity one would almost certainly need it to spin/rotate) you would observe motions of free neutral test particles, within the box, that would be quite indistinguishable from having the box spin/rotate in a region of space devoid of such a massive ring/torus.”

First, such an effect would be no different from tidal effects, except centrifugal instead of centripetal. And inasmuch as the influence of such a ring/torus has not been observed to have noticeable effects in our vicinity, or in any sub-galactic vicinity, inasmuch as it would presumably be of such dimensions that its complete rotation would take millions if not billions of years, its effects would be flat in the extreme… so why don’t we just pretend it’s not an issue here.

“This is only one of an innumerable set of such possible examples.”

No doubt, and each one evidently credible enough to make “lyin’ eyes” of the effects you observe in a box.

“Basically, given any example of motions of free neutral test particles within a ‘box’ under the influence of whatever inertial (pseudo, ‘false’) ‘forces’ one wishes to conjure up, one may find a distribution of mass-energy-momentum-stress such that those same motions may be attributed to gravity. (Geodesics are geodesics, after all.)”

I’d still like to hear a specific description of the effects one could actually observe in a box. Please conjure one that would render the distinction between gravitation and force invalid.

“This is also why I brought up the ‘box’ in orbit around the Earth…. did you notice that the few test particles you used undergo divergent geodesics, similar to your assertions for non-gravitational inertial ‘forces’?)”

Similar, but not identical. Therefore, “different.”

Yes, I’m frustrated. Let’s not throw nails in the road anymore.

Jim:

You said:

Then you’ll agree that the ubiquitous identification of gravitation with “true” force is based on non-empirical, non-four dimensional models which are routinely, implicitly, and illegitimately treated as givens.

First, I wouldn't say that any "identification of gravitation with 'true' force" is "ubiquitous" (except possibly in your mind). Secondly, for those who do "identif[y] gravitation with 'true' force", I cannot speak for why they may think this way or what their basis for such thinking may be. Thirdly, I have never seen any such "non-empirical, non-four dimensional models" "routinely, implicitly, and illegitimately treated as givens." They are only given/proposed/used/etc. as theories and/or models.

I can only point out that there is at least one approach that makes such an identification legitimate by way of making all motions geodesic motions. Furthermore, I would not say that any such is any less legitimate than any four dimensional model. Only careful predictions and experiment may tell the difference. (In fact, at the classical level, the level of General Relativity, there may, indeed, be no detectable difference. For such a case, the decidable criteria will be suitability for handling Quantum-type phenomena, or other cases beyond the classical.)

You then go on to say:

I’ve tried to get you to describe one of these pseudo forces, assuming you’re referring to something other than the Coriolis, or centrifugal or centripetal “forces”, which can most definitely be directly attributed to true forces and distinguished from gravitation. ...

First, centripetal force refers to the central pointing force that leads to the non-inertial nature of the reference frame in which one supposes there is such a thing as a centrifugal "force".

Second, what is the nature of the motion of a free neutral test particle undergoing any of your listed inertial (pseudo, "false") "forces" (free of any "true" forces)? Are not such motions geodesics? If so, then how are these geodesics to be distinguished from any other geodesics?

Often times you have suggested that the geodesics of such inertial (pseudo, "false") "forces" will be divergent while gravitational geodesics will be convergent (apparently relying upon an unspoken ansatz [one that appears to rely upon an assumption of a central concentration of mass]). This is why I brought up the observed ring/torus of "dark" matter.*

If your "box" was placed within a similar ring/torus, especially if the ring/torus was spinning/rotating (and practically everything we observe in this universe spins/rotates, besides, in order not to have such collapse under its own gravity one would almost certainly need it to spin/rotate) you would observe motions of free neutral test particles, within the box, that would be quite indistinguishable from having the box spin/rotate in a region of space devoid of such a massive ring/torus.

This is only one of an innumerable set of such possible examples. Basically, given any example of motions of free neutral test particles within a "box" under the influence of whatever inertial (pseudo, "false") "forces" one wishes to conjure up, one may find a distribution of mass-energy-momentum-stress** such that those same motions may be attributed to gravity. (Geodesics are geodesics, after all.)

This is also why I brought up the "box" in orbit around the Earth. (By the way, I'm glad to see you made some attempt at the exercise. I'll get back to your work on it another time. However, did you notice that the few test particles you used undergo divergent geodesics, similar to your assertions for non-gravitational inertial "forces"?)

See, no need to appeal to "hypothetical, dependent on non-empirical, non-four dimensional or multiple-universe models".

David

* The ring/torus of "dark" matter is not some otherworldly hypothetical construct. It was observed based upon gravitational lensing (another highly successful prediction of Einstein's General Theory of Relativity). The matter is called "dark" matter because there appears to be no way to observe it besides its gravitational effects (gravitational lensing, orbits of other objects, etc.)

** When I refer to "mass-energy-momentum-stress" or an "energy-momentum-stress tensor" I'm referring to the source of spacetime curvature (the distribution of mass, and such, in the universe). Please don't confuse such with my mentioning of attempts to illicit something similar from the gravitational field itself.

As I pointed out in my first post, such attempts at identifying some "energy-momentum-stress" in the gravitational field does not have a tensorial character, and, hence, is not well defined (or local).

Perhaps I should have never mentioned such attempts. Perhaps it has served nothing but to cloud your understanding of what I havbe been trying to help you understand.

David,

You wrote: “I say it again. Other than to point out that there are theories/models wherein all forces are handled via curvature (so all motions are geodesic), I have never tried to suggest that within a purely four dimensional framework (such as General Relativity) one would not be able to distinguish between the purely geodesic motions of pure gravitation (independent of whether the curvature is non-zero) and the non-geodesic motions caused by non-zero net ‘true’ forces.”

Then you’ll agree that the ubiquitous identification of gravitation with “true” force is based on non-empirical, non-four dimensional models which are routinely, implicitly, and illegitimately treated as givens.

“I recognize that you appear to think that [pseudo, or false forces] [are] distinguishable [from gravitation]. However, such distinguishability is illusory…”

I’ve tried to get you to describe one of these pseudo forces, assuming you’re referring to something other than the Coriolis, or centrifugal or centripetal “forces”, which can most definitely be directly attributed to true forces and distinguished from gravitation. If they are hypothetical, dependent on non-empirical, non-four dimensional or multiple-universe models, they don’t undermine or refute the empirical distinction between gravitation and force (and pseudo-force).

Jim:

I hope you've had a good Merry Christmas. :-)

I'm amalgamating some of my responses to three of your latest posts* here, since you have an issue in common in all three.

The issue is that you continue to act as if you haven't recognized that (other than theories/models that use curvature to explain all forces**) I have never argued that one cannot distinguish between purely gravitational effects (geodesic motion), at least when the local curvature is non-zero, and the effects of non-zero net "true" forces (deviations from geodesic motion, what you appear to want to label as "inertial acceleration").

Even though I do point out that there is no operational or theoretically available distinction between gravitational effects and the effects of any of an innumerable set of inertial (pseudo, "false") "forces"*** (at least so long as the spacetime is not completely flat, since all produce geodesic motion, in the absence of "true" forces), I have never suggested (other than the "everything is curvature" theories) that any such could not be distinguished from "true" forces (that cause a deviation from geodesic motion).

The problem is that you continue as if I had argued otherwise. This is why I have stated, before, that you treat me as if I was your enemy/nemesis/whatever.

If we are to have any sort of productive exchange you must recognize what I'm actually saying.

I say it again. Other than to point out that there are theories/models wherein all forces are handled via curvature (so all motions are geodesic), I have never tried to suggest that within a purely four dimensional framework (such as General Relativity) one would not be able to distinguish between the purely geodesic motions of pure gravitation (independent of whether the curvature is non-zero) and the non-geodesic motions caused by non-zero net "true" forces.****

David

* The three posts are Re: The phenomenology of Shinola and other stuff, part 2, Shinola exercises, and Re: Re: The phenomenology of Shinola and other stuff.

** Basically, such "everything is curvature" theories/models take the approach that if it worked for gravitation, why not the other forces? One may certainly argue as to whether such theories have, thus far, been successful, or not, and whether such is "the right approach". However, they exists, and have been at least somewhat successful, at least at the same classical level as General Relativity.

I would hope that you recognize that different free neutral test particles released with different initial velocities (from the same spacetime point) will follow different geodesics. Well, the same is true in these "everything is curvature" theories: The reason different types of particles (non-neutral particles with various "charges") follow different geodesics, even if their initial four-velocities are the same (at least proportionately), is that their various "charges" give rise to various additional components of their full (higher dimensional) velocity. So they follow different geodesics because in the full set of dimensions their initial velocities are different.

*** I recognize that you appear to think that such is distinguishable. However, such distinguishability is illusory, unless, possibly, one knows, a priori, what the local spacetime curvature is (basically via an ansatz, as you yourself have engaged at various times). All inertial (pseudo, "false") "forces" enter into the motions in precisely the same way as gravity. The only time one has any ability to transform these away is when the entire spacetime is flat. (If the local spacetime is flat, then one may transform them all away locally, including gravity, but this still leaves its mark on the surrounding spacetime in such a way that questions of what is gravity and what are "other" inertial "forces" is still undecidable, without some ansatz.)

(Actually, even when the local spacetime is not flat one is always able to transform all inertial "forces", including gravity, away "locally". Its just that "locally" becomes far more restricted. Under this condition, exact cancellation can only occur at a single point, while for any finite level of precision there is a neighborhood of this point that exhibits no inertial "forces", including gravity, up to said level of precision.)

**** What I believe is the most general and true statement is that since the success of General Relativity one can no longer hold to the Newtonian concept that gravity is just as much a "true" force as electromagnetism and the nuclear forces (strong and weak), while asserting that all inertial (pseudo, "false") "forces" are most definitely not forces.

David,

I’ve had a little time to return to your earlier point about evaluating hypotheses and grandness of vision.

You wrote: “If we are to be able to unify that which is described by our, arguably, two greatest theories (General Relativity and Quantum Mechanics); or if we are to ever hope to create methods of traveling (effectively) faster than the speed of light (or, in other words, if we are to ever hope to visit any of the wondrous places in our vast universe, outside out very restricted, parochial experience in and near this rock upon which we reside), then we need thinkers that can handle a far greater range of circumstances than what we have locally.... Unfortunately, Jim, you are showing yourself to be insufficient to the task. Your "real world" is far too restricted. (I, and others, have no problem explaining all that lies within your "real world". So I most certainly don't mean that your "real world" is too "restrictive". The difference is I, and others, have a viewpoint [or viewpoints], and theories, that can extend far beyond your "real world" to encompass much more that is possible, to say nothing of that which has been, and will yet be observed within our universe.)”

Regarding the unification of General Relativity and Quantum Mechanics, if gravity is recognized as nothing more than a property of mass, rather than a force, there’s no need for unification, the task of QM becomes much simpler, and therefore more promising.

You believe you and others “have no problem explaining all that lies within [my] ‘real world’”, yet you haven’t explained how -- if in controlled, local experiments, gravity (the noun) is nothing more than a geometric distortion of spacetime, and gravitation (the verb) is nothing more than geodesic motion in a gravitational field -- larger-scale or hypothetical gravitational phenomena become (presto) manifestations of force and energy.

Your aspirations are commendable, but sometimes one has to choose between aspiration and devotion. Am I limiting myself by insisting on building upon elementary empirical principles, or are you restraining yourself by your devotion to a flawed paradigm that could only spin fictional hypotheses? That seems to be the ultimate question between us.

David,

Being a good professor, you’ve given me exercises to perform. As you say, they “are far from being as trivial as [my] other thought experiments.” The most important point remains, though, that the behavior of the test particles in both exercises are distinguishable from test particles in a box being accelerated by a force. That, after all, remains the issue between us.

In the first exercise, I (we) are asked to “consider a box in orbit around the Earth. Let's start by considering the box to be orbiting in such a way as to maintain one side always facing the Earth, so we have the "floor" being the side facing the Earth, the "ceiling" facing away from the Earth, the "front" facing the direction of "travel" of the orbiting box, in opposition we have the "back", with the "left" side being on the left and the "right" side on the right of an astronaut facing the "front". The question, then, is what will be the motions of free neutral test particles within this box? Especially, what will be the motions of the subset of such particles that don't hit any of the sides of the box?”

Test particles that are placed in the box with relative motion will of course bounce around the box. Test particles that are placed in the box without relative motion will begin to separate slightly toward the walls, depending on their placement. Those that are closer to the “floor” will tend more toward the “floor” and the “front”, as their geodesics have greater curvature than the box as a whole, and their velocity is greater than is required for a stable orbit at their relative elevation from the earth. The influence on particles closer to the “ceiling” will be opposite. The behavior of particles in the spherical container will have a similar separation, and the characteristics of their separation can indicate the direction of the earth.

In all cases, the tendency to separation will be different from particles in a box or sphere being accelerated by a force – the latter will have the same apparent acceleration toward the walls no matter where they are placed (although they may separate or converge if the force is centrifugal or centripetal). Can we return to that point?

Jim

David,

[I wrote the following before I noticed your more recent, most interesting post. I’ll have to address it later.]

You may be disappointed. I wonder if you’re more disappointed than I am. You’re asking me to consider multiple universes and giant rings of dark matter that may undermine my position in some unspecified way (who could say?), before you’ll consider the behavior of two test particles in a box to be persuasive. Forgive my frivolity, but time may run backwards in Universe D11, gravity may be Newtonian on the Planet of the Apes, but I’m absolutely convinced that scientists in those places are primarily concerned with their own physical laws. I just wish they would jump in here at ScienceBlog with some learned advice on methodology – or ygolodohtem no ecivda, as the case may be.

You mentioned Occam's razor. I’d like to say to everyone, among whom you are just the most patient and articulate representative: Why don’t we proceed with just our one empirical world, with one set of empirically-established physical laws, before imagining how they might be effected if it turns out we’re just, say, the lint in some higher being’s navel (pierced with a safety pin of dark matter). I think I’m right about this: It’s the way good scientific methodology is supposed to be practiced.

I’ve argued that there is no controlled experiment in this world of accepted science where test bodies moving in geodesics in a gravitational field (with non-zero curvature) can be observed to behave like test bodies being accelerated (directly or indirectly) by a force. It’s a testable claim. By scientific standards, it prevails against un-testable models or hypotheses. But no one, it seems, wants to confront the issue, no one wants to give up a cherished doctrine.

Moving on to your earlier post, I think everyone’s concern, and aversion to “looking through Galileo’s telescope”, is expressed in your question: “Are you aware that if we can never detect gravitational waves that the theory of General Relativity may be in real trouble?”

I think you mean energy-bearing waves, because I’m not claiming that changes in curvature aren’t propagated as waves of changing curvature. I’m not an expert on the field equations, but I believe the stress-energy tensor can be simply dropped, leaving the rest of the structure intact, leaving the association of gravitation with force and energy behind. If not, some modification of the remainder should be possible. My belief in this stems from the coherence of the concept of gravitation as a curvature or distortion of spacetime, and of its affects on geodesic motion. So yes, I am taking issue with an aspect of GR, but no, I don’t think it’s life-threatening.

You wrote: “You appear to accept that ‘as the tides make clear’ that a moving mass can, indeed, cause motions that can be quite energetic (when integrated over the very significant volumes affected, at least in the case of the tides). Whether one wishes to use the term ‘energy’ in this regard is semantics. The reality is that energetic processes ‘happen’, and are well associated with the movement of at least a nearby object.”

This isn’t semantics. The orbit of the moon would require a great deal of energy if it weren’t for a geometric effect that makes it a curved geodesic path. No one seems to be attributing the moon’s orbit to force anymore. The changes in the local geodesics on earth produced by the changes in the relative position of the moon are no different, except they stress molecular binding energies, and in aggregation, produce massive dislocations of large fluid bodies. The effect is wave-like. Given a clear distinction between gravitation and force, by the application of Occam’s razor there is no need (and certainly no evidence) to support an additional wave-like, energy-bearing effect from cosmological sources. Is it justifiable to continue to look for such an effect? I suppose it depends on the budget.

“I could certainly understand a ‘layman’ like explanation using an ‘energy’ (and maybe even a ‘force’) like argument in order to try and convey the concept of gravitational waves, but I have yet to see a truly General Relativistic argument made in such terms. I don't know, I'm just trying to make sense of where you actually stand.”

Given the seminal concept of gravitation in GR, of the geometric effects of mass, in view of the inability to demonstrate an equivalence of gravitation with force and energy when they are considered in isolation, the aspect of GR that presumes an association of gravitation with force and energy can be seen as a legacy of the previous paradigm. To drop that aspect of GR is a simplification of physical theory, it brings theory back in line with empirical evidence. It could re-direct theoretical energies in productive directions. It could be good.

Jim:

I've thought of a few more things. (Sorry, I've been on vacation, so I have plenty of time. It has been nice to be away from the office. :-) )

First, you state:

I’m inclined to believe there’s no place in the universe where curvature is actually zero, although it’s no doubt a legitimate construct for the purpose of illustrating a principle. I’ve used it myself to illustrate the nature of a “pure” inertial acceleration, “unadulterated” by gravitational curvature. But that relates to an issue you’ve brought into focus about the difference between empirical hypotheses or principles and mathematical models. I think it’s a mark of real progress that we’ve arrived at this point.

Unfortunately, I can think of at least two* interpretations of your statement concerning "an issue you’ve brought into focus about the difference between empirical hypotheses or principles and mathematical models." So I'm not quite sure whether this is a positive development. I'm hopeful, though.

You then go on with (starting with a quote of me):

You wrote “depending on other circumstances, like the distribution of mass-energy-momentum-stress surrounding [a uniform gravitational field], there may, indeed, be a definable magnitude” of the field.

While there may be a workable mathematical model of such a region, I don’t believe we can point to a place in the “real world” where it’s been found to exist. It may be worthwhile to hold the model in stock to help explain some new discovery, or to apply in a novel way to some existing unexplained phenomenon, but it has no standing against any empirical hypothesis that is otherwise coherent and useful.

To your last assertion ("it has no standing against any empirical hypothesis that is otherwise coherent and useful") I'll say that in the sense that such cannot be used as an experimental verification or refutation of such an "empirical hypothesis", you are correct. However, as a hypothetical situation (like any thought experiment) that may be used to distinguish between one "empirical hypothesis" that "refuses" to work with such and another (more complete) theory that naturally includes such within its framework (without any special accommodation), I would have to say that it may be quite relevant.

Secondly, I'm beginning to believe that your concept of the “real world” would have trouble with even nearby, actually realizable experiences.

For instance, consider a box in orbit around the Earth. Let's start by considering the box to be orbiting in such a way as to maintain one side always facing the Earth, so we have the "floor" being the side facing the Earth, the "ceiling" facing away from the Earth, the "front" facing the direction of "travel" of the orbiting box, in opposition we have the "back", with the "left" side being on the left and the "right" side on the right of an astronaut facing the "front". The question, then, is what will be the motions of free neutral test particles within this box? Especially, what will be the motions of the subset of such particles that don't hit any of the sides of the box?

Another instructive way of looking at essentially the same scenario may be to consider letting the "box" be a spherical shell, so symmetry allows us to ignore any issue of whether the "box" is "rotating" or not. (So any question of inertial "forces" may be avoided.) Then one may simply ask: What subset of geodesics (orbits) will always remain within the confines of the "box" without ever touching any of the walls?** Then one only needs to consider what such orbits will look like to an astronaut within the "box"? (This is to be considered because such is the nature of your other thought experiments.)

In both of the above scenarios (or two ways of looking at a single scenario, depending on how one looks at it) it is permissible to do it all within the framework of Newtonian mechanics and gravitation, since relativistic corrections are sufficiently small that the major features are all captured via the Newtonian approach.

If you attempt these exorcises at all I will think far greater of you for the effort. I expect you will find that these “real world” scenarios are far from being as trivial as your other thought experiments.

I wish you well.

David

* Perhaps this is a problem with my flexibility in being able to see multiple perspectives. :-)

** One may use the cylindrical symmetry of the system to reduce all the orbits to a class of orbits having their major axis and apogee all in the same direction, as seen from a vantage point along the axis of rotation. In addition, one has reflection symmetry above and below the plane of the "box's" orbit.

Jim:

I'll reserve complete judgment until you've been able to respond to all I've posted (I know I posted a couple of very long messages). However, so far, I'm very disappointed.

Yes, it is true that our experience is sufficient to rule the scenario of “when the whole spacetime manifold is flat” as inconsistent with this universe. But what of other universes? Just because a scenario is inconsistent with our universe, should that preclude us from being able to develop a framework that can encompass such? (Especially when it costs us nothing, as is the case withing General Relativity.)

Far beyond this, none of your other scenarios can be dismissed out of hand, simply due to the very narrow range of our experience. Besides, what would you expect of free neutral test particles within a box surrounded by a massive ring? (Say the extremely massive, and huge, dark matter ring that has been observed within our universe.) Or what about positioning your box in orbit about a spinning black hole? (I say "in orbit" so as to have it in "free fall", or as close as possible.) What would be the motion of free neutral test particles within the box if the box is set to orbit in such a way that (at least for a period of time) it maintains a constant orientation with respect to the distant stars. What if it had a different rotation?

If we are to be able to unify that which is described by our, arguably, two greatest theories (General Relativity and Quantum Mechanics); or if we are to ever hope to create methods of traveling (effectively) faster than the speed of light (or, in other words, if we are to ever hope to visit any of the wondrous places in our vast universe, outside out very restricted, parochial experience in and near this rock upon which we reside), then we need thinkers that can handle a far greater range of circumstances than what we have locally.

Unfortunately, Jim, you are showing yourself to be insufficient to the task. Your "real world" is far too restricted. (I, and others, have no problem explaining all that lies within your "real world". So I most certainly don't mean that your "real world" is too "restrictive". The difference is I, and others, have a viewpoint [or viewpoints], and theories, that can extend far beyond your "real world" to encompass much more that is possible, to say nothing of that which has been, and will yet be observed within our universe.)

As I said, I'll reserve complete judgment until you've been able to respond to all I've posted. But at this point, I'm very disappointed.

Take care.

David

David,

Thank you for responding. No problem about the “weasel” thing. I’m probably more like a domesticated marmot than a weasel anyway.

I may not have time to respond to your second post right now…

I’m inclined to believe there’s no place in the universe where curvature is actually zero, although it’s no doubt a legitimate construct for the purpose of illustrating a principle. I’ve used it myself to illustrate the nature of a “pure” inertial acceleration, “unadulterated” by gravitational curvature. But that relates to an issue you’ve brought into focus about the difference between empirical hypotheses or principles and mathematical models. I think it’s a mark of real progress that we’ve arrived at this