Physics has all but surrendered to mathematics in the last hundred years. I believe this has been detrimental, and nowhere more than in gravitation theory. The general theory of relativity was conceptual in origin, mathematical in its corroboration. The theory has represented gravitation as a product of the “curvature” or deformation of spacetime in the presence of mass, and both the evidence and the supportive mathematics have been entirely adequate to justify its acceptance. Gravitation is nevertheless described in terms of the mathematics of quantum theory as a force and associated with a hypothetical particle, without either an explicit dissension from the geometric conception or empirical evidence of the particle.
Conceptual physics, which I take to be roughly coextensive with pre-quantum physics, involved the initial development of coherent hypotheses and secondarily the employment of mathematics (and/or experiments) to support their plausibility. A mathematical formalism without conceptual coherence would be regarded as irremediably provisional, if not unsatisfactory, in the former methodology. With respect to the former physics, two thought-experiments will be employed here, without resort to mathematics, to demonstrate that the quantum interpretation of gravitation is conceptually flawed and without empirical support.
A description of the first experiment may be unnecessary, but the pre-relativistic association of gravitation with inertia and of inertia with universal mass is still maintained on occasion, if only tacitly, and may be the ultimate basis of the continued identification of gravitation with force. The identification may also be a residue of one of our most familiar experiences on the earth’s surface: The pressure we feel between ourselves and the surface is fundamental to our original concept of gravitation; we tend to regard the pressure as a force (“the force of gravity”) and our surface station as being at rest. The following experiment may therefore be helpful toward more clearly dispelling the identification of gravitation with force and inertia, and also in prefacing the second experiment (actually a thought-investigation) of the force-free continuity between astronomical gravitation and gravitation at the surface of a massive body:
Imagine a spacecraft traveling a uniform path relative to the “fixed stars” which comes under the influence of a stellar object nearby and
begins to deviate toward it, while continuing in uniform motion by the evidence of free-floating objects inside. In order to maintain the
original course a thruster is fired and inertial effects are experienced onboard as the craft accelerates just enough to counter the influence
of the local gravitational field.
Note that in this experiment inertial effects are associated with uniform motion relative to the distant stars, contrary to the pre-relativistic Machian expectation. Aside from the discrimination of inertia from any influence of the overall mass of the universe (an association that is seldom explicitly defended now anyway), the experiment demonstrates what I hold to be most significant, that at least in the situation just described, force becomes evident in conjunction with gravitation only when gravitation is being resisted.*
Now consider an experiment that comprehends the transition from astronomical gravitation along a geodesic to an involvement with force and inertia at the surface of a massive body:
Imagine two test bodies gravitating toward the earth from some considerable distance. For the sake of simplicity, consider the earth to be at
rest and the test bodies to be gravitating directly toward its center of mass. (They appear to be simply “falling” from a perspective on the
earth’s surface.) One body is an immense hollow sphere of negligible mass, the other is relatively small in size — an extra-vehicular scientist,
let’s say — and also of negligible mass. Notice that while the test bodies are falling toward the earth (or more accurately, while the three
bodies are converging) there is among them a purely relative transformation of potential energy to kinetic energy as each moves uniformly in
its own frame of reference — there is, at least as yet, no occasion for an exchange of mass-energy in the form of the supposed gravitational
energy. Let the sphere and the scientist be placed initially close together so that as they approach the earth their geodesics converge enough
to bring their surfaces in contact some time before the larger impact. (It is the fantastic size of the hollow sphere that allows the surfaces of
the two bodies to meet somewhere above the earth’s surface). From the moment the sphere and the scientist come in contact until they reach
the surface of the earth an inertial acceleration between them will intensify as each tries to conform to its own geodesic at an ever greater
angle to the normal. The situation will, if viewed in isolation, come to resemble the gravitation of a small body pressing against a planetary
surface (although the gravitation between them is actually insignificant due to their negligible masses) and the scientist will even be able to
stand upon the sphere. This development of an increasing inertial acceleration between the test bodies is the only aspect of the situation
which changes from the moment they meet; the earthward component of their motion continues as before, a relative gravitation. In a way
similar to the first experiment, force has developed in the resistance to what is in this case a convergent gravitation of two bodies toward
another. And once the two reach the earth the situation remains essentially the same: Each one, now in conjunction with the entire
conglomerate of the earth, presses toward the center of mass with the same sort of conflict of geodesics as was observed between them
when they were gravitating from a distance. Along with the other components of the earth at and below the surface, they are resisted, and
thereby accelerated, by those further below, due to the coincidence of the common inclination toward the center of mass and the
subordinate obstructions.
This second experiment demonstrates that it is only in the inertial conflict of geodesics (or as in the first experiment, in a singular inertial acceleration) that force can be observed in association with gravitational phenomena. The intersection of geodesics and the consequent inertial effects constitute the interruption of gravitation, and what is commonly conceived as “the force of gravity” at a surface would be more accurately described as anti-gravitation.
Gravity has to be considered absolute in the aspect that a geometric vertex exists at a center of mass that cannot be transformed, either conceptually or mathematically. But unless the geodesic of a body brings it to a massive obstruction, such as the surface of a planetary body, gravitation involves uniform motion with only relative accelerations — no force can be attributed.
There remains a most significant aspect of the situation disclosed in the second experiment to be comprehended, although its full implications must be left outside the scope of this discussion. The energy expressed in the continuous static acceleration of bodies at or below a surface toward a center of mass is rendered inexplicable in purely geometric terms when gravitation is finally discriminated from force. If there is no “force of gravity”, what accounts for the persistent energy of the inertial acceleration at a surface after a body has come to a relative state of rest? Recall that in the initial appearance of force in the second experiment only a conflict of geodesics is present and resistant against the otherwise uniform motion of the test bodies. No extrinsic source of energy can be identified, yet there is a static acceleration between the two, while the gravitation with the earth remains relative. I believe the only available explanation is that motion as-such, the motion of matter in general, must be regarded as absolute, although relative in the various incidental trajectories between individual bodies. I wish to maintain that the source of the energy usually identified as gravitational energy must be attributed to an intrinsic and ceaseless dynamic of mass-energy, independent of gravitation but uniquely revealed by its coincidence.
Having briefly acknowledged the implications of a consistent geometric theory of gravitation, that gravitation and motion in general are each in their own way both relative and absolute, that mass-energy is somehow intrinsically dynamic and the source of the energy disclosed in the opposition of gravitation and its occasional resistance, I will consolidate the findings with regard to quantum theory in the following summation:
Gravitation is evidently a deformation of spacetime in the presence of mass, its effects the product of the concentration of spacetime at vertices, at centers of mass. As such, gravitation cannot be a force, and cannot therefore be mediated by a particle. The assimilation of gravitation by quantum theory and its derivatives (e.g., string theory) as a field of force, and the positing of a gravitational quantum of action where none is apparent, theoretically necessary, or conceptually coherent is entirely without justification.
This is admittedly an unsettling proposition, but in consolation its acceptance would make one of the principal projects of quantum theory less complicated, as gravitation with all its peculiarities could be disregarded in the pursuit of a unified field theory. I hope that it might also signal the need to rely more upon conceptualization, and not so heavily on mathematical formalisms, in the development of physical hypotheses.
Endnote
* Incidentally, there may also be evidence of force if the gradient of a gravitational field is severe enough to produce tidal stresses to a body’s molecular binding energies.
Fred,
You may not be aware of it, but you tend to write derisively when dealing with someone who disagrees with you. Don’s theory of black holes was easily refuted without degrading him.
You’ve misquoted one of my “silly things.†I wrote “a body moving freely in a gravitational field is always moving uniformly from its own frame of reference†– not “a body moves with respect to its own frame of reference.†A body, a conscious body, can regard himself as either moving or at rest, with equal validity, can he not?
Regarding the task you set for me: “Since Einstein’s work is broadly accepted and your views are a challenge to them, your task is to propose a set of observations or an experiment to distinguish between them. If your analysis holds up, those measurements should support your prediction rather than Einstein’s.â€
I’ve challenged only one aspect of Einstein’s work, his tendency to associate gravitation with inertial acceleration and force, and to posit, consequently, a prediction that gravitational waves will carry energy. How many years, how many hundreds of millions have been spent trying to detect gravitational energy? So far, my position carries the day, does it not?
I’ve offered numerous thought experiments here and on the “Black Hole†blog to support my contention that gravitation is never involved with force or inertia except when it is interrupted – i.e., when a geodesic is obstructed. I’ve pointed out that in Einstein’s original thought experiment, where he sought to demonstrate an equivalence of gravitation and inertial acceleration, the two situations are not in fact equivalent – as is proven if the observer drops two objects, and determines that they converge when gravitation is involved. You asked for one experiment in support of my position, i’ve given you two. May I give you a task, or would that be impudent? If I may, I ask that you please provide a simple thought experiment that refutes my contention that gravitation is exclusively a geometric distortion of spacetime in the presence of mass – not a force.
David,
Here’s the link to my previous discussion. You have to put up with a lot of nonsense before Jim jumps in. He’s clearly not as far off-base as Don, the poster of the Black Hole Myth, but he does say some silly things, such as that a body moves with respect to its own frame of reference.
Now that we’re “talking,” if you’re interested in reviewing my recently published history of physics in the 20th century, contact me by e-mail through my website or watch the “books received” listing in Physics Today. The target market is library reference collections, high school and up.
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Fred:
Actually, part of my patience may have to do with my not having had a prior “run in” with Jim before. Besides, at least so far, I’m actually still uncertain whether Jim is actually challenging Einstein’s theory of General Relativity, or simply some interpretation thereof, or maybe something else altogether (like a misunderstanding).
I prefer not to jump to the conclusion that he is challenging this well established theory until I have some proof (like a direct statement on his part), since if I judge incorrectly (or even jump to the defense of this theory too strongly) the whole discussion degrades rapidly.
I still have hope for our exchange. (Perhaps I’m being naïve.)
David
Jim:
It does appear we may actually be converging, at least to some extent.
By the way, when I stated that I “agree that these four cases are not transformable into one another†the “four cases†I mentioned were not your four points, per se, but the four conditions of geodesic (g) vs. non-geodesic (~g) motion, along with the separate zero (R=0) or non-zero (R0) Riemann curvature tensor. It appears we can both agree that non-geodesic motion implies a force besides gravity is acting on a body. It also appears that you would agree that geodesic motion with a non-zero Riemann curvature tensor implies that the body is moving under the influence of gravity. (Am I right?)
So the crux of this matter, then, is whether you would consider that geodesic motion when the Riemann curvature tensor is zero implies that the body is moving under the influence of gravity, or whether this implies the absence of gravity (even though there may be geodesic trajectories that don’t appear to be “uniform motion” by any stretch of the imagination, such as trajectories that cross themselves [at least within just the three-space, but there are more possibilities]). (This is not a big deal, but is does have its implications.)
Note: Since I most certainly agree that appearances can be deceiving, my concept of tests for geodesic motion (g or ~g) and the Riemann curvature tensor (R=0 or R0, in the vicinity of the body in question, or the region of the experiment) does indeed rely upon “instrumentality,” or, at least, a set of highly controlled, associated “experiments” (tracking trajectories of a number of free, neutral test bodies in the vicinity, for instance). I point this out in case you might, otherwise, assume I’m merely appealing to a “mathematical” formulation. (The analysis of such tests, though, will certainly have a “mathematical” form, even if it’s accomplished via a digital computer.)
On another matter (of not especially great import, but has an affect on people’s perception of whether you have a full understanding)… You say that “it wasn’t until GR was developed that a space-time geodesic was conceived.”
In a sense you are right, in that before the concept of curved space(-time) manifolds (“surfaces,” but not “spaces” in any sort of vector sense) was developed (by Riemann, or maybe before—certainly before GR) there was no need to generalize the concept of the “straight line” (think Euclidian geometry, Galilean relativity, or SR). However, with the advent of curved manifolds, it is recognized that the old “straight lines” of flat manifolds (that can be identified with their tangent space) are nothing more or less than geodesics (within their manifolds).
On to somewhat more important issues…
You said, in response to my pointing out that the convergence referred to in your fourth point will occur if and only if there is a non-zero Riemann curvature tensor:
The crux of this problem/issue is that one should have a consistent description regardless of the complexities of a given situation. One should not be dependent upon a simple subset of circumstances (like an isolated, compact gravitating mass). This is why I refer to more general concepts, like geodesic motion and whether the Riemann curvature tensor is non-zero in the vicinity of the test body or experiment (determined by “instrumentality,” as noted above).
To move on to another (perhaps somewhat minor) issue… You state:
While it appears that you are (here) saying that you see the lunar (and solar) tides to be evidence of gravitational waves, and (essentially?) a proof(?) that energy can be “provoke[d]” thereby. The question, I suggest, still remains as to whether gravity wave “travel” through space(-time), and whether they can carry or convey energy.
In addition, may I suggest that the lunar (and solar) tides are to gravity what near field effects are to electromagnetism? So we do have this large “near field” effect. What of long range “transmission” or propagation? Is this not worthy of testing?
Unfortunately, I have to go, so I’ll continue this later.
David
David,
I don’t feel that you are attacking me. Your willingness to dialog with me has been generous, and extraordinary. I hope my counterpoints don’t seem obstinate.
You wrote: “The coordinate system may be chosen such that an object that is experiencing “uniform” motion is not actually experiencing geodesic motion, and vise versa.â€
I think this is really the crux of the issue, where we might finally come to a state of dialectical repose (not to say rest)!
I believe what you’re saying is that from an arbitrary coordinate system a body might APPEAR to be following a geodesic when it is not, or might APPEAR not to be following a geodesic when it is… or that it may/may not be mathematically described as such. But this only holds if the appearance is limited to a remote visual or mathematical description of the body’s trajectory. If instrumentation is employed to determine whether the body is undergoing inertial effects (I’ll respond below to your comments on the four general criteria I listed by which inertial, non-inertial, and gravitational effects can be discriminated), then gravitation and inertial acceleration will be fully distinguishable and agreed upon from any coordinate system. In effect, the exclusive focus on the relative trajectory of an object is an abstraction from its characteristics, precisely the abstraction that has led to the association of apparent, relative accelerations to force, and hence to a mistaken association of gravitation with force.
I believe the alternatives you mentioned can be characterized in two simple situations: 1) You and I are orbiting a massive body at different elevations, I am closer to the massive body than you; although each of us is following our geodesic in spacetime, I appear to be accelerating (non-geodesic-ly) toward it. 2) The situation is the same, but I am accelerating by means of a thruster, just enough to parallel your geodesic; I appear to be following a geodesic (yours), but I’m not. The situations are incongruous, and subject to any number of interpretations from various coordinate systems, only if we limit our powers of discrimination to the observation of relative trajectories. This is, I think, the main point of our disagreement, which puts my four previous points of discrimination into perspective.
Although you “agree that these four cases are not transformable into one anotherâ€, you raise several objections:
In response to my earlier point (1) you wrote: “Actually, within SR ‘relative uniform motion’ is identical with ‘geodesic motion’ (motion along a geodesic).â€
You’re right – instead of saying “geodesic motion remains unresolved in SR†I should have used the past tense, as it wasn’t until GR was developed that a spacetime geodesic was conceived.
In response to my earlier point (2) that “an inertial acceleration is distinguishable from a state of rest and/or uniform motion (or geodesic motion)â€, you wrote: “How do we place a spring between the electromagnetic force and an electron, for instance?â€
Well, of course, it was an example. Your question is problematic, but we could satisfactorily demonstrate that electromagnetism is a true force, capable of producing an inertial acceleration, by another example: Let a naked observer (without prostheses or appliances) stand in an empty and stationary elevator. Introduce a powerful electromagnet above the elevator so that it accelerates toward the magnet. The acceleration will be inertial, and the observer will be unable to distinguish it from a mechanical acceleration. If the observer is given a towel, and shares the elevator with a magnetic object, he’ll be able to identify the acceleration as due to electromagnetic force, but the effect will still be recognized as inertial, and can be determined as such from any coordinate system according to my earlier point (3) revisited below.
In response to my point (3), that gravitational acceleration, or geodesic motion, is distinguishable from an inertial acceleration, you wrote: “This is only true if whatever forces that are leading one to think that there is an ‘inertial acceleration’ are acting upon the container, rather than allowing the container to be just as free as the neutral test body….†That’s true, allowing the container to be just as free as the test body would ruin the experiment, as an inertial acceleration on the container is essential. So let’s make sure the experiment is constructed to properly convey the principle.
And in response to my earlier point (4), that an exclusively inertial acceleration is distinguishable from an interrupted gravitational acceleration by “dropping†two objects (if gravitation is involved they will, if the measuring apparatus is sensitive enough, be observed to converge) you wrote: “This is true if and only if there is a locally non-zero Riemann curvature tensor (detectable tidal effects, since the convergence you are trying to observe is precisely that).â€
That’s true, but it’s only to say that the proximity and mass of the body to which we are attributing a gravitational field must be suitable for the experiment. The convergence, the non-zero Riemann curvature tensor, is due to the concentric nature of the local gravitational field, by which each object is drawn toward a center of mass – so let’s be sure a discrimination is possible before testing the principle.
To return to what I’ve identified as the “crux†of the issue here, although I agree with you that a door shouldn’t be closed on mathematics, and I would agree that the field equations have unmatched utility in describing relative geodesics, I don’t believe there are legitimate “alternate perspectives†that justify the association of gravitation with inertial acceleration, or gravitation with force. I believe it’s an important principle to insist upon – it makes the search for a unified field theory vastly more simple if gravitation is considered a by-product of mass-energy. And it clarifies many of the current objectives occupying gravitation theory. For instance:
You asked “what, then, of distortions that may be conveyed upon (the Riemann curvature) tensor? These very distortions (and the energy that can be transferred thereby [think frictional heating, for instance]) are behind the search for gravity waves, not some concept of gravity as ‘force.’ Yet you presume to direct researchers to not search for such merely from a single perspective of ‘not force’ implies ‘no energy’ implies ‘no detectable ‘whatever’. (Am I wrong? Is this not one of your conclusions?)â€
I think I mentioned elsewhere that once gravitation is distinguished from inertial acceleration it becomes evident that the moon provides us with a big, slow gravity wave to study, and with very little effort. The search for virtually imperceptible gravity-waves becomes pointless. The distinction also introduces some provocative but previously not-so salient questions about the tremendous energy a moving wave/curvature can provoke (not exert), as with the ocean tides.
Mathematics is good. But… it should be restrained, like a hormonal teenager heedless of right and wrong!
Jim,
I’ve stayed out of this discussion between you and David Halliday, and I agree that he is more patient with you than I have been regarding the discussion of the principle of equivalence (see our conversation Don Hamilton’s blog entry on the Black Hole Myth, where I eventually gave up).
Still, there is a simple way to resolve whether your challenge to Einstein’s theory has any validity.
Since Einstein’s work is broadly accepted and your views are a challenge to them, your task is to propose a set of observations or an experiment to distinguish between them. If your analysis holds up, those measurements should support your prediction rather than Einstein’s.
If you can’t propose a way to test your ideas, then existing theory will prevail — at least until the next challenge comes along.
Fair enough?
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Jim:
Just so you’ll know that I wasn’t ignoring your thought-experiment: I didn’t comment on it since, from my perspective of curved space-time and general invariance, it doesn’t appear to be particularly relevant (the shape of space-time is different in the two cases—they don’t occur in the same space-time). This is true even if viewed as an answer to Mach-like equivalence of gravity and inertia, since it is one of a number of thought-experiments that lead one to recognize that any such Mach-like principle must take into account proximity to local mass (etc.) distributions (so it’s not simply a fixed universal reference frame solution).
Personally, I’m quite glad that such a universally unique reference frame doesn’t exist, or, even if it does, there is no requirement that it be recognized in order to practice physics. (One of the main issues I do still positively loath about Superstring theories is the dependence on a special, flat, base space upon which the space-time we observe is built. Even the usual Copenhagen approach to Quantum Mechanics appears to require flat space-time in order to “properly” define the collapse of the wave function. However, this is all beside the point.)
Anyway, please don’t think I either ignored your thought experiment, or that I’m belittling it. I simply felt that effort was better spent on other, more direct, issues (like your four points that I addressed directly).
Take care, and I do still look forward to your reply to my earlier reply.
David
Jim:
Let’s skip down to the “points.”
Actually, within SR “relative uniform motion” is identical with “geodesic motion” (motion along a geodesic): Uniform motion in SR is geodesic motion in the flat space-time of SR (Minkowski space-time). Furthermore, if we don’t have flat space-time, then the closest thing to “uniform” motion is geodesic motion. Additionally, even for flat space-time, one is able to choose any arbitrary labeling of points/events (a coordinate system, and the way we take measurements) within the space-time, so the only reliable way to determine “uniform” motion is to determine whether it is geodesic motion. (The coordinate system may be chosen such that an object that is experiencing “uniform” motion is not actually experiencing geodesic motion, and vise versa. This is one of the potential “sources” of inertial force that violates your third point.)
How do we place a spring between the electromagnetic force and an electron, for instance? I’m assuming from the rest of the point that what you are calling “inertial acceleration” is motion of a body that deviates from geodesic motion. (If your definition of “inertial acceleration” is what I’ve stated, then the only reliable test is that of deviation from geodesic motion, in which case it is a tautology.)
This is only true if whatever forces that are leading one to think that there is an “inertial acceleration” are acting upon the container, rather than allowing the container to be just as free as the neutral test body (especially with the stipulation you provide in you parenthetical statement). This is an analogous problem to attaching a spring between a body and the force that (would) act upon it (see your second point).
This is true if and only if there is a locally non-zero Riemann curvature tensor (detectable tidal effects, since the convergence you are trying to observe is precisely that).
I agree that there are four possible cases for a body in motion: The motion is geodesic or it is not, and, independently, the Riemann curvature tensor is either zero or not in the vicinity of the body. These two tests can be accomplished via neutral test particles (the geodesic test only requires a single test particle, while the Riemann curvature tensor test requires multiple test particles, especially if one want’s to make sure about all its components, since simple convergence/divergence of two test particles only tests a subset of components). Furthermore, I agree that these four cases are not transformable into one another. (While transformations can change the appearance of the motions, and even cause various components of the Riemann curvature tensor to go to zero, the tensorial nature of the Riemann curvature tensor and geodesic motion means that one can never transform them completely away or create them when they are absent.)
The remaining question is “what is gravity?” If it is simply the shape of space-time, so all “gravitational” motion is geodesic motion, and vise versa, then gravity is the same as any “inertial force” (meaning a “pseudo” force that’s only considered a force due the observer’s choice of coordinate system and definition of “force” in terms of deviation from some expectation of “uniform” motion). If, on the other hand, it is the curvature of space-time (identification with the Riemann curvature tensor), then it is associated with a tensorial quantity that is (at least mathematically) distinguishable from other force fields only by the nature of the vector space upon which it acts (it acts on the tangent space, the vector space of directional vectors at a point).
If it is the latter case, then what is to be thought of those cases where there is no locally detectable Riemann curvature tensor (tidal effects) even though there are geodesic motions that don’t appear to be “uniform” by any stretch of the imagination (like geodesic paths that cross themselves)? Furthermore, how does one distinguish gravitation from other force fields if there exist formulations for said other fields such that they, too, are merely curvatures on a higher dimensional space-time manifold, where the additional dimensions are somehow outside our experience (like compact dimensions)?
What if space-time is not a continuum? How is the tangent space then distinguishable from the other directions of the fiber space?
It is well and good to have a finite set of thought experiments and/or other test cases (like your four points, above). It is quite another to be able to handle the broader picture: Especially if one has difficulty seeing alternate perspectives.
I agree with your criticism that “physics has all but surrendered to mathematics in the last hundred years.†In fact I stated some time ago that Einstein himself can be accused of this self same affliction, and, in fact, it may well have been a major contributor to his lack of success with “unification.” This, however, is not quite the same thing as saying that one cannot ask the question of whether some mathematical similarity may be pointing toward some additional insight.
I agree that simply because there is a mathematical similarity does not, in and of itself, justify an attribution of all, or even a significant portion, of other characteristics. On the other hand, one must not simply close the door merely because some particular perspective precludes such.
Furthermore, if gravity is to be distinguished from mere geodesic motion by the presence (or absence) of the Riemann curvature tensor (tidal effects), then, even if one refuses the “force” label (since its motions are geodesic), what, then, of distortions that may be conveyed upon this tensor? These very distortions (and the energy that can be transferred thereby [think frictional heating, for instance]) are behind the search for gravity waves, not some concept of gravity as “force.” Yet you presume to direct researchers to not search for such merely from a single perspective of “not force” implies “no energy” implies “no detectable ‘whatever’”. (Am I wrong? Is this not one of your conclusions?)
What of the possibility that we may not have a true handle on the nature of gravity, space-time, mass/matter/energy, or whatever? You have stated that you view the equivalence of inertial mass and gravitational mass as a tautology. What is your basis, besides some finite experience and some theories (Newtonian gravity and GR, for instance)? Is it possible that there may be some subtle difference? Is it of no worth to devise experiments to test such?
I could say much more, but I’m sure I have said so much that you may perceive me as attacking you. I’m most certainly not feeling like I’m in any attack like stance, nor am I feeling like I need to defend some “status quo” from your attacks. I simply think that not being able to see the variety of possible perspectives actually weakens your arguments.
(By the way, I do look forward to your response. There is much more I can share with you on so much of this, if you are willing and have the desire. Having the ability to come at a question or issue from multiple directions and perspectives is quite possibly the only way we may ever hope to unify that which is so well explained by General Relativity with that which is so well explained by Quantum Mechanics—regardless of one’s personal feelings about either.)
David
David,
I’m willing to stipulate that except for one issue I’ll respond to below, and a few issues that aren’t central to my fundamental point, your remarks are welcome clarifications of my contentions.
The one substantive issue I have goes back to the first line of my original “blog,†where I wrote “physics has all but surrendered to mathematics in the last hundred years.†You infer from the similarity between the mathematics of the Riemann curvature and the electromagnetic field to an arbitrary equivalence or non-equivalence of gravity and other “forcesâ€, to the viability of the description of gravitation as a force.
I contend that analogous mathematical models are not in themselves compelling, and if they conflict with observation, they are without value. To use a loose and homely allegory, the flight of a rock and the flight of a baseball might be mathematically analogous or identical, but that doesn’t make a rock into a baseball.
More to the point, I’ll employ a thought-experiment I’ve used elsewhere:
Let a spacecraft in a region far from significant mass simulate an orbit around an imaginary star with some specified mass and location. Navigation of the simulated orbit is plotted by means of the “fixed stars” and accomplished by the continuous firing of a thruster. Let the inertial effects on the craft due to the simulation be detectable. (A “static gravitational field” of some intensity will be observed at the inside surface of the craft that is farthest from the imaginary star as it rotates around the imaginary position — unsecured objects will press against that surface.) Now introduce an actual star of the specified mass at the location posited in the simulation, and let the engine of the craft be simultaneously switched off. The craft will continue on the accelerated path, but now without inertial effects — the “static field” immediately disappears and the occupants of the craft float weightlessly as the craft follows an actual geodesic around the star. Thus, without altering the mathematics of the craft’s trajectory, and (for those who assert some variation of Mach’s equivalence of gravitation and inertia) without altering its trajectory relative to the universe or “fixed stars”, its inertial effects (and the supposed influence of the universe) have been entirely canceled by the introduction of an arbitrary local mass. A fundamentally different sort of acceleration has replaced the earlier acceleration, even though its trajectory as described by some distant observer remains analogous, even identical. The former “gravitation†that is supposed to be equivalent to force or inertial acceleration has been replaced by an actual gravitation, with manifestly different characteristics, and without a trace of force or inertial involvement.
I’ll repeat my earlier points, modified to comply with your clarifications as I understand them:
1) A state of rest is indistinguishable from a state of relative uniform motion, as is stated in Special Relativity (although geodesic motion remains unresolved in SR). They are relative, mathematically transformable and equivalent. 2) A state of inertial acceleration is distinguishable from a state of rest and/or uniform motion (or geodesic motion) by the introduction of a spring between a body and a force. 3) A gravitational acceleration, or geodesic motion, is distinguishable from an inertial acceleration by, for example, observing a neutral test body in a container; it will distinctly express a situation as exclusively gravitational/geodesic or inertial by either floating freely or tending toward one wall of the container (ignoring any detectible tidal effects due to the steepness of the gravitational gradient within the container, which in any case is consistent with the purely geometric description of gravitation). And 4) an exclusively inertial acceleration is distinguishable from an interrupted gravitational acceleration (interrupted by whatever force or forces) by “dropping†two objects; if gravitation is involved they will, if the measuring apparatus is sensitive enough, be observed to converge. All these latter cases are manifestly, self-evidently NOT relativistic, because unlike rest, uniform motion or geodesic motion, they are distinguishable and non-transformable (except by superficial analogy) from the perspective of any frame of reference. Consequently, any association of gravitation with force, or energy, depends upon its more or less implicit identification with an inertial acceleration, in violation of the above-mentioned observations of absolute, non-transformable characteristics of geodesic motion.
Jim:
First, let me respond to why I made the comment on “interruption” of gravitational acceleration. I made the comment because of your referring to this as the “only” force associated with gravity. I was merely pointing out, for clarification, that this force is not really “associated” with gravity, it is some other force (usually of electromagnetic origin, in our everyday experience, though we refer to it by other names, such as contact force, or tension, or such).
Actually, I really should have added some more to what I was saying about forces (including inertial forces, that you assert can in no way be called forces [which is usually the way Newtonian physics is taught]). Within four dimensional General Relativity there is one primary distinction between inertial forces (including gravity, by the way) and what may be called “true” forces: It is the test of whether the motion of a test particle (that one is trying to determine whether it is being acted upon by “true” forces, or only inertial forces) is following a geodesic or not. As I hope you know, a geodesic is the closest thing to “uniform motion” that is available within Differential Geometry (and, hence, GR).
The motion of “an electrically neutral test body” (actually it should be more than just electrically neutral, due to forces besides E&M) is precisely that of a geodesic (the extremum path between two points, just as a straight line is the shortest distance between two points in Euclidian geometry, and an inertial reference frame follows the longest path between two points in special relativity). This is independent of whether there is gravity (distortion of space-time from the Minkowski space-time of special relativity), or any other inertial force.
There are, however, often times when there is a way to determine that there is gravity present, but it doesn’t work in all possible cases. In the weak field case it is equivalent to detecting tidal effects (the convergence of spatially separated neutral test particles—the point of departure between Einstein’s “equivalence” principle embodied in the elevator comparison and oft-time reality for sufficiently large containers). In general it is the detection of the Riemann curvature tensor (this leads to the Geodesic Deviation of two neutral test particles relative to each other). However, as I said, this cannot work, even in theory (let alone practicality) in all cases, because there are cases where space-time is distorted but where the Riemann tensor is zero anywhere near the test apparatus (there are cases where it is zero everywhere except at a single point).
However, if one wishes to use the presence of a non-zero Riemann curvature tensor as a definition of the presence of gravity, even though there is no deviation from geodesic motion (only a relative Geodesic Deviation), then one finds oneself using a field-like quantity (the Riemann curvature tensor) that is quite analogous to that of the Electromagnetic field (the Electromagnetic field tensor) and all other Yang-Mills type fields (Electroweak, Quantum Chromo-Dynamic, etc.). You see, the Riemann curvature tensor determines the deviation of a (tangent) vector quantity when taken over a closed infinitesimal loop, while the other field tensors determine the deviation of other fiber bundle quantities (like Dirac fields) when taken over the same closed infinitesimal loop. (Oops, we appear to have crossed the line into equating gravity with other “forces”.)
Interestingly, mathematical models have been constructed whereby these other field tensors that act upon non-tangent vector fiber bundle quantities can be equated with purely geometric Riemann curvature tensors on higher dimensional manifolds, where the extra dimensions are somehow kept from our experience (such as having them be very compact).
Does this last part sound familiar? It should, it is taken advantage of in Superstring theories. (Not that I like Superstring theories, but that’s beside the point.)
So, while I agree with the stated premise of your initial post (that gravity has been misappropriated, in terms of being treated as a force that should have an associated force particle) I am trying to point out that there are alternative points of view that are available.
Basically, as Einstein recognized (his “epistemological defectâ€), gravity holds a sort of in-between position: The motions it imposes on point-like, neutral test particles is purely geodesic motion (the closest thing to “uniform” motion available), yet it is (at least potentially) distinguishable by the presence of a non-zero Riemann curvature tensor, that is quite analogous to any of a number of other (force) field tensors. Furthermore, it has been shown that at least under some circumstances, these other force fields can be formulated in a manner analogous to gravity (in fact, they simply become aspects of gravity, just in additional dimensions that are somehow hidden from our experience, so the geodesic motion thereof just doesn’t appear to be such).
I hope this has helped broaden your perspective. I have enjoyed our discussion. (Unfortunately, as I’ve had to think somewhat more deeply in these other perspectives I’ve gained additional respect for Superstring theory. Something I haven’t wanted! :-) )
David
David,
You are most gracious, and it’s been a pleasure to engage in this discussion. And it seems we have progressed toward isolating the point where we diverge.
But the following is not that point, where you wrote: “I would certainly not say that ‘The generalization of relativity to include accelerating reference frames was never achieved.’ … it can certainly be argued that the generally invariant language of Differential Geometry (generalized as it is in GR to allow for indefinite metrics, rather than only the positive definite metrics Riemann envisioned) does fully generalize relativity, since any and all choices of coordinate system, no matter how bizarre (as long as it is differentiable), are seen as equally good for expressing, describing, and explaining dynamical systems.â€
I don’t disagree with you here, but I think the point where we are in disagreement is on the implicit association, or tolerance for an association of gravitation with force. In your point I just quoted, gravitation as an unobstructed geometric dynamic is, I agree, fully relativized, but not, I would argue, when it is involved with inertial acceleration.
You wrote: “However, this is not the same as trying to claim that gravitation is the ‘same’ as inertia. (This is not a claim I or, I believe, Einstein have ever made. However, there is sometimes the specter of ‘Mach’s principle’ that is sometimes brought up in connection with Einstein’s GR. I would tend to agree that Mach’s principle is not realized in GR.)â€
Here’s a quote from Einstein in 1916, where he is discussing an “inherent epistemological defect” in mechanics where acceleration seemed to retain an absolute status. He saw a need for “an extension of the postulate of relativity” to include acceleration, because “the laws of physics must be of such a nature that they apply to systems of reference in any kind of motion” (“The Foundation of the General Theory of Relativity”, in The Principle of Relativity, Lorentz, et al, pp 112-113). So at this point he was clearly seeking a way of extending relativity to any kind of motion, and this led to the thought experiments associating the accelerating elevator and the “stationary†elevator in a “static gravitation field.†The original principle as formulated by Einstein referred to the equivalence “of a gravitational field and the corresponding [inertial] acceleration of [a] reference frame” (“ueber das Relativitatsprinzip und die aus demselben gezogenen Folgerungen”, Jahrb. Radioakt. Elektr. 4:411-462, (1907) trans, pp134-5, Relativity and Geometry, Torretti, R., New York: Pergamon Press, 1983).
You continued: “I would also not say that ‘gravitation is only involved with force when gravitation is resisted.’ …. (A similar inertial force that is not simply manifest when ‘resisted’ is that of the centrifugal ‘force’ on an object on a frictionless surface in a vehicle involved in a turn, or on a spinning platform. In fact, just as with gravity around a planet, this inertial force has converging/diverging vectors.)â€
Well, but, we can agree that the term “centrifugal force†is a misnomer, there is no such particular “forceâ€, as the acceleration of an object connected with a radial acceleration is just undergoing an inertial acceleration with radial characteristics. A gravitational orbit may have the same converging/diverging vectors, but unlike centrifugal acceleration, there are no inertial effects.
You continue: “The ‘equivalence’ principle most strongly associated with GR (as opposed to the weaker one between an accelerating elevator in deep space and a stationary one on the Earth’s surface) is the equivalence of inertial and gravitational mass….â€
This is no doubt the version most defensible today, I would argue that it’s only defensible because it’s a tautology, but I think it’s best to proceed to our main point of contention:
“What I take exception to is the presumption that there is one and only one interpretation of what is and what is not ‘force-like’…. I have been trying to point out that there are multiple perspectives that can be brought to bear upon them….â€
Here is why I believe there is one an only one valid interpretation, drawing on a comment I recently made in response to another blog:
1) A state of rest is indistinguishable from a state of relative uniform motion, as is stated in Special Relativity. 2) A state of inertial acceleration is distinguishable from a state of rest and/or uniform motion by the introduction of a spring between a body and a force. This is the “epistemological defect†Einstein wanted to resolve with General Relativity. But this remains unresolved and (I contend) is un-resolvable, because: 3) A gravitational acceleration is distinguishable from an inertial acceleration by, for example, observing an electrically neutral test body in a container; it will distinctly express a situation as exclusively gravitational or inertial by either floating freely or tending toward one wall of the container. And 4) an exclusively inertial acceleration is distinguishable from an interrupted gravitational acceleration by “dropping†two objects; if gravitation is involved they will, if the measuring apparatus is sensitive enough, be observed to converge. All these latter cases are manifestly, self-evidently NOT relativistic, because unlike rest and uniform motion, they are distinguishable from any frame of reference. (A purely gravitational acceleration and an inertial acceleration may appear identical, but only if their trajectories are considered exclusive of inertial effects.) Consequently, any association of gravitation with force, or energy, depends upon its more or less implicit identification with inertial acceleration, in violation of the above-mentioned observations of absolute, non-transformable characteristics of non-uniform motion.
Finally, the following comment seems to be a misunderstanding. I’m not sure why you’re making the point – it’s precisely the sort of “interruption†I’m referring to: “(Incidentally, the ” interruption of a gravitational acceleration toward the earth’s center of mass” is also accomplished via the application of a force: The force of the surface of the Earth on the elevator, either by direct contact, if it’s resting on the ground, or indirectly through the structures of the building and the mechanisms used to move it [be they pistons, cables and pulleys, or whatever].)â€
Apologies for the length of this “commentâ€!
Jim:
I finally have some time to respond, once again. :-)
I don’t disagree with the desirability of “overall coherence and consistency.” In fact, this is the raison d’être for the pursuit of Grand Unification. :-)
It is true that Einstein started his attempt at “relativising†gravity (Newton gravity is quite incompatible with special relativity) with his elevator thought experiment (and the like). (Not unlike your thought experiments.) While his thought experiments probably did lead him to consider equating gravitation and inertial “forces” (accelerations due to the use of non-inertial frames of reference), I believe it unfair to characterize this as the initial reason for his pursuit. (I am, however, not a historian, nor do I have personal knowledge of Einstein’s thinking.) However, I would certainly agree that the use of Riemann’s Differential Geometry as the mathematical language of General Relativity is highly significant. (This leads to the consequences of non-flat pace-time geometry, and how matter, energy, and stresses form the “source” for this dynamic geometry. In fact, I would say that the fact that space-time is dynamic is the greatest fundamental revolution of RG.) :-)
I would certainly not say that “The generalization of relativity to include accelerating reference frames was never achieved.” In fact, even if one were not to allow for space-time to be dynamic (as GR demands), it can certainly be argued that the generally invariant language of Differential Geometry (generalized as it is in GR to allow for indefinite metrics, rather than only the positive definite metrics Riemann envisioned) does fully generalize relativity, since any and all choices of coordinate system, no matter how bizarre (as long as it is differentiable), are seen as equally good for expressing, describing, and explaining dynamical systems. However, this is not the same as trying to claim that gravitation is the “same” as inertia. (This is not a claim I or, I believe, Einstein have ever made. However, there is sometimes the specter of “Mach’s principle” that is sometimes brought up in connection with Einstein’s GR. I would tend to agree that Mach’s principle is not realized in GR.)
I would also not say that “gravitation is only involved with force when gravitation is resisted.” While it is true that the force that most people “on the street” equate with gravity (the force they feel on their feet as they stand, for instance) is a force that is only involved when gravitation is “resisted.” The concept of force, as created by Newton, is that which, in total (vectorially), is proportional to acceleration. The constant of this proportionality is “inertial mass.” (A similar inertial force that is not simply manifest when “resisted” is that of the centrifugal “force†on an object on a frictionless surface in a vehicle involved in a turn, or on a spinning platform. In fact, just as with gravity around a planet, this inertial force has converging/diverging vectors.)
The “equivalence” principle most strongly associated with GR (as opposed to the weaker one between an accelerating elevator in deep space and a stationary one on the Earth’s surface) is the equivalence of inertial and gravitational mass. (The same equivalence used by Newton in his law of gravitation, but which he never attempted to explain.) This is a rather fundamental equivalence of GR, though it has undergone a number of experimental tests—just in case it isn’t true.
What I take exception to is the presumption that there is one and only one interpretation of what is and what is not “force-like.” While I have stated that I have no problem with your thought experiments, I have been trying to point out that there are multiple perspectives that can be brought to bear upon them which quite fully muddy these distinctions. This, however, is not to say that I am trying to argue that a quantum description of gravity is free to treat it like any other “force”, complete with “force” particles. In fact, I do actually prefer the perspective where gravity is simply a dynamical geometric phenomenon (as embodied in the usual perspective on GR). I simply wish to point out that there is a much broader field of perspectives.
(Incidentally, the ” interruption of a gravitational acceleration toward the earth’s center of mass” is also accomplished via the application of a force: The force of the surface of the Earth on the elevator, either by direct contact, if it’s resting on the ground, or indirectly through the structures of the building and the mechanisms used to move it [be they pistons, cables and pulleys, or whatever].)
I’ll continue this in another post sometime later (maybe tomorrow).
Take care, and please don’t think of me as an adversary, because that’s not at all what I’m trying to do here. (In fact, I read your post in order to learn something new, or gain a new perspective. I certainly didn’t come here to “squash” your “dissent†or anything like that.)
David
David,
I suppose I could say I’m coming from a perspective with a primary concern for overall coherence and consistency. I believe this is increasingly important as science becomes increasingly compartmented. The need may be nowhere so significant as with gravitation theory.
As you know, the original project of GR was to generalize the relativity of uniform reference frames to include accelerating frames. This seemed to require that gravitation and inertial acceleration be comprehended as two aspects of one principle, transformable just like uniform motion and the state of rest. It was only later that Einstein conceived what may be the most remarkable, unprecedented achievement of human thought, the idea that gravitation is a function of spacetime geometry. The latter achievement has never been fully distinguished from the original project, and that’s the point of my issue with GR.
My point is: The generalization of relativity to include accelerating reference frames was never achieved, gravitation is fundamentally distinct from inertia, and most importantly, gravitation is only involved with force when gravitation is resisted. If that sounds preposterous, or “junky”, I invite anyone to posit a situation where un-interrupted gravitation is force-like. (Citing a formalization that presumes gravitation is a force or can be treated as a force doesn’t qualify, because of course the presumption is what’s in question.)
The difficulty of the challenge may be better appreciated by reconsidering Einstein’s own original illustration of the equivalence of gravitation and inertia, or inertial force: The common experience of standing in a motionless elevator and the experience of standing in an elevator somewhere out in space while being towed with an acceleration equal to “g”, were considered to be equivalent. The problem with this illustration was revealed with the subsequent recognition of gravitation as a geometric principle, but it was never revisited: The reason the two experiences appear similar is that both involve inertial accelerations – the one due to the application of force, the other to the interruption of a (non-inertial) gravitational acceleration toward the earth’s center of mass. Inertial acceleration had thus only been shown to be equivalent to inertial acceleration.
So where I’m coming from is a recommendation that a fundamental theoretical flaw be recognized for what it is, and the construction of theoretical superstructures based upon the flaw (quantum gravity, gravity strings) be abandoned in favor of justifiable, productive endeavors.
Jim
Jim:
Sometimes it appears that you agree with General Relativity, other times you deviate as if you are advocating for a replacement, or at least a refinement of General Relativity. Which is it?
This is why I asked about your background. I have not asked as some form of “put-down” or to cast any sort of “bad light” upon your arguments. I simply ask in order to understand where you come from and what you already know, so I can better understand where to go from here.
David
Dr. Halliday,
I value your engagement on this issue, and I appreciate your balanced, critical defense of the conventions.
You write “gravitation, from the standpoint of General Relativity, is just as much a force, or not, as are all other ‘inertial forces’.”
But this only holds if one associates gravitation with the inertial acceleration occasioned by its resistance. Gravitation can only be classified with “centrifugal force†if gravitation is identified with its coincident inertial interference. If my thought experiments are valid, gravitation and its inertial resistance are absolutely non-equivalent. Granted, the General Theory was originally conceived as a pursuit of a comprehension of their equivalence, deriving from Mach’s contemporary association of the two. It was the “relative†in “general relativity†as initially conceived. As you know, the original principle as formulated by Einstein referred to the equivalence “of a gravitational field and the corresponding [inertial] acceleration of [a] reference frame.” Among various subsequent moderations of the principle, Dicke’s “weak principle of equivalence” stipulated only that gravitational effects in most laboratory experiments can be transformed away by regarding the lab as falling freely. But if it is only claimed that in a sufficiently small region of spacetime gravitational distortions can be ignored for practical purposes, “equivalence” is thereby reduced from a principle to a prescription or license for experimental expedience. It would, after all, be a curious principle that could only be invoked if we agreed to ignore the distinction between a dynamic and its resistance, or to limit the scope of our observations and the precision of our instruments just sufficiently to render an undesired aspect of our object undetectable. A comparable “principle†of animal husbandry might state that all cows are black if the night is sufficiently dark.
In a similar way, the Quantum approach is based on the implicit and uncritical association of gravitation with accelerations occasioned by force. You point out that “almost as soon as one tries to go to loop level Quantum Field theory… the problem “blows up,” leaving us with nonsensical answers like “the universe never existed.” With all due respect, as they say, I’d have to describe quantum gravity as an up-blowing formalization of a non-principle. I don’t want to sound quarrelsome, but at least in this aspect, Quantum Theory is a field lacking in analytical rigor.
Regarding “gravity wavesâ€, you write “while the curvature of space-time causes matter and energy to ‘move’ in ways that differ from flat space-time, there will, of necessity, be ripples and waves in space-time, caused by matter and energy, and influencing such…. One finds that these ripples carry energy away from the source… astronomers have actually detected many instances where the motions of binary and other star systems… are slowing down in just the way predicted by General Relativity….â€
I don’t question the idea of wavelike fluctuations in the geometry of spacetime, but like the immense gravitational wave caused by the moon’s orbit, such fluctuations don’t “carry energyâ€, but rather upset the gravitational trajectories of masses that come under their influence. And the observed slowing orbits of star systems can be just as well (and more consistently) interpreted as transformations of potential and kinetic energy, entirely internal to the systems, without requiring or justifying a hypothetical radiation of energy.
I don’t want to be a gadfly or trouble-maker. There is simplicity in regarding gravitation as a purely geometric phenomenon, and there’s potential for a significant simplification in the effort to unify the various forces, if gravitation is excepted as a bi-product of mass-energy
Jim:
You stated:
The problem is that even if one accepts that gravity is not a force, this does not, necessarily, imply that there is no gravitational “energy” wave.
Fully within the framework of General Relativity, without any Quantum Mechanics, one finds that the fact that matter and energy distort/curve (the fabric of) space-time, while the curvature of space-time causes matter and energy to “move” in ways that differ from flat space-time, there will, of necessity, be ripples and waves in space-time, caused by matter and energy, and influencing such. One of the reasons for this is that space-time cannot instantaneously, at all points in space, accommodate the motions of matter and energy: Such instantaneous accommodation would violate relativity.
In addition, at least in the weak field (linear) limit, one finds that these ripples carry energy away from the source, in a manner not entirely unlike electromagnetic waves (except that the quadrupole moment is the lowest order allowed). Furthermore, astronomers have actually detected many instances where the motions of binary and other star systems (usually including one or more neutron stars) are slowing down in just the way predicted by General Relativity, when one uses the space-time wave propagation predicted thereby.
So, unfortunately, this appears to be one area where your thought experiments fail you. You appear to have prematurely jumped to a conclusion that’s not supported either by the predictions of General Relativity or the observational evidence.
On the other hand, I recognize that there are at least some writers I’ve seen that equate the detection of gravitational waves with detection of the “graviton” (the Quantum Mechanical “force” particle of gravity). Perhaps this has “distracted” you? For after all, the detection of such waves need not suggest that there is some Quantum Mechanical “force” particle associated with such waves. (However, traditionally, waves, in Quantum Mechanics, come coupled with particle like behaviors, ever since Max Planck found that he could only correctly fit Black Body Radiation by assuming finite packets of radiation, giving rise to the Planck constant [which he had assumed would take the limiting value of zero].)
This issue was the main point where I was “criticizing” your post. If you take issue with gravitational waves (whether or not one accepts that they carry “energy”, at least in some sense) then you take issue with General Relativity itself, not just with it having being “misappropriated” by quantum theory.
In fact, the detection of gravitational waves is one of the few (the only? [other than singularities]) predictions of General Relativity that has yet to be verified. Some suggest that if gravitational waves are not detected by some of the newest proposed detectors that General Relativity itself will be in trouble.
So I am, and was, simply trying to help you understand where predictions of things like gravitational waves come from so you can avoid a potential trap—unless, of course, you really do want to go down that particular road.
David
Jim:
There is basically nothing wrong with your thought-experiments. As I stated, they are quite similar to ones created by Einstein.
The only possible “argument” one can have with them is that one can interpret them in other “reference frames” (general coordinate systems) wherein one will “see” accelerations that one can interpret (admittedly from a standpoint instilled from Newtonian mechanics) as coming from “forces”. However, as I tried to point out in my original post, such an interpretation will cause one to accept that other “inertial forces,” like the “centrifugal force,” are just as much “forces” as is gravity: These are the only two interpretations possible because gravitation, from the standpoint of General Relativity, is just as much a force, or not, as are all other “inertial forces.”
This last point, which I was trying to make in my original post, is, and was, not intended to be any form of refutation of your thought experiments. On the one hand it is a confirmation of your claim that gravity is not a force (from the viewpoint that all “inertial forces” are not forces). However, on the other hand, it is, and was, intended to add some breadth to your perspective in letting you know that there is another perspective from which this can be seen, in which all “inertial forces” may be seen as equally real forces as that of gravity.
However, just because one can interpret “inertial forces” as forces, just like gravity, does not imply that one should, necessarily, try to incorporate them into Quantum Mechanics by way of “force (gauge) particles.” On the other hand, we do get somewhat reasonable results when we use the minimal coupling approach to incorporating the curved space-time of General Relativity into (classical) Quantum Field Theory, in the weak field (linear) limit, at least so long as we don’t try to go beyond the branching level. However, almost as soon as one tries to go to loop level Quantum Field theory, al least if one doesn’t force space-time to be rigid (so the curvature of space-time does not depend on the fields, which goes completely against General Relativity), the problem “blows up,” leaving us with nonsensical answers like “the universe never existed.” :-)
Unfortunately, this post is getting long, so I’ll address your second paragraph separately.
David
Dr. Halliday,
My background can’t compare with yours. But surely, that’s not relevant to the question of whether my thought-experiments demonstrate that gravitation cannot be considered a force. I’m unable to imagine how a putative gravitational force can be introduced into the transition I’ve described, from relative acceleration to surface acceleration. If the mathematics of quantum theory, if the convention of treating gravitation as a force, can’t be applied to such a simple description, of what use, of what relevence and significance are the mathematics and the convention?
If gravitation is not a force, the good people presently devoting their careers to the detection of a gravitational energy wave should be alerted, and rescued from profound futility. If it is a force, there must be something I’m misrepresenting in my descriptions. Please advise, in concrete terms.
I’m sorry it has taken me so long to get back to this. (I suppose you are a bit impatient. :-) )
I’m also sorry you appear to have almost completely misunderstood my message. Other than a few points, I was agreeing with you far more than disagreeing.
I suppose I was insufficiently clear. I’m sorry. :-(
Unfortunately, I have to be going, so I’ll have to get back to this another time.
Until later…
David Halliday
It may be that Dr. Halliday is not going to respond to my reply to his comments on my article, or it may be that I’m being impatient. In any case, in the following remarks I’ll treat responses such as his as belonging to a common class. I don’t wish to single him out, but unfortunately, he has been my single critic here. It is to his credit that he even responded.
Physics today rests solidly in the quantum-theory paradigm. And unlike all prior scientific paradigms, quantum theory is, by its nature, irrefutable even in principle. Regardless of its validity, it can never be overturned – because once the irrational became accepted, once physics was based on (rather than corroborated by) abstract formalisms, once the expectation of comprehensive consistency was discarded, rational argument became irrelevant, a telltale of “junk science.â€
In my article I tried to reason by means of a step-by-step thought experiment that gravitation cannot be regarded as a force, that mathematical formalisms based on gravitational force are invalid in principle. As a review of Dr. Halliday’s response will confirm, my reasoning was considered irrelevant, and needless of a direct response or refutation. Instead (and I have found this to be typical), Dr. Halliday chose to counter in terms of the conventional formalisms in question, arguing, in essence, that only “junk science†would attempt a rational analysis. (To paraphrase, “perhaps nothing can be considered a force, perhaps everything can be considered a force, perhaps particles don’t exist at all.â€)
“Junk scienceâ€, or rather, uninformed thinking about science, is certainly a common annoyance. I’ve found such theories and ideas to be based on unsupported premises, or developed with erroneous arguments, and easy to refute. It continues to amaze and frustrate me, after years and countless attempts, that no one has been willing, no one has considered it worthwhile, to attempt a direct, physical refutation to my contention that gravitation cannot be considered a force, or identified with a particle, or with a wave of energy.
I wouldn’t use the term “junk†to describe a science based on mathematics that remains incomplete, on a particle that remains undetected, and a paradigm that is unassailable in principle. But I question whether it should be called a science.