Elysium and Interior Solutions

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Benish</i>
<br />it is not yet obvious to me what that new order will be.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If you read "Pushing Gravity", I think it will become obvious. But there may yet be room for improvements, especially with the gravitational heating model.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I've kept pretty close tabs on such tests of the inverse square law, G-measurements, etc. Unfortunately, these are all (to my knowledge) essentially <i>static</i> experiments. Any motion of the test object is restricted to a very small range. Whereas, there may indeed be reason to refrain from concluding that this means observation of a test mass free to move through the whole interior would obey Newton.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The gravitational force inside a uniform spherical shell is everywhere zero. So any new motion would be a deviation from Newton. Artificial satellites have been used to test this. (Gravity Probe B is the most recent.) A satellite is placed inside a shell to shield it from all non-gravitational forces (such as air drag), so that it becomes an excellent probe of Earth's gravity field irregularities.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">First, perhaps, I should point out that observations of the kinematics of stars within Globular Clusters are beginning to yield unexpected results.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">"Unexpected" only by the standard model. Both Milgrom's MOND (MOdified Newtonian Dynamics) and Meta's GGR (graviton GR) predicted this kind of effect. The reason for the latter's prediction is the finite range of gravity. It is the same effect that causes galaxy velocities to remain higher than expected far from the nucleus. And verifying that expectation, the effect is greatest in globulars that are farthest from the Milky Way's center.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">"/Users/rizzle/Desktop/Gravity-Experiment-Stuff-2007/Cluster-Dist-Vel-Graph/Cluster-Data-Chart-LR.jpg"<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Your image used a path on your own hard drive. You must use a web path for an image to be visible here. Put the image on your own web site, or send it to a commercial or free web site that provides space for such images. Then use that URL here.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">This model also predicts that, given a uniformly dense sphere with a diameter hole through it, a test object dropped into the hole will not harmonically oscillate.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That is an extrmely non-Newtonian effect. A sphere of uniform density is made up of numerous uniform spherical shells. Each shell causes an inverse square attraction outside itself, and no force inside itself, as experiments confirm. That would cause an object in a tunnel through the center to bob back and forth. Why should a concentric collection of such shells behave so differently in your model?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">the model is radical. It assumes that accelerometer readings and the rates of stationary clocks are utterly reliable indicators of the acceleration and velocity of these instruments (motion detectors).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">What is radical about that?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">To make sense of this interpretation, another (fourth) space dimension is invoked, and I know you've had occasion to state your dislike of extra dimensions.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Besides all the other objections, it is an untestable hypothesis because extra dimensions are unobservable. To be scientific, it must be testable. -|Tom|-

Bernoulli set a competition for the solution of this problem: What shape is the curve on which a body subjected only to the force of gravity will slide (without friction) between two points in the least possible time?

He, Leibniz, Newton and Huygens found the curve to be part of an inverted cycloid. A trochodal curve.

I would expect the the swinging weights to bob back and forth but to damp down if they are running in a radius curve. They want to run in a cycloidal curve.

Tom:

My model agrees with the inverse square law and that the field is zero inside a spherical shell. So it also predicts an absence of accelerated motion throughout the interior. My apologies for not being clear about this in my previous post.

Thanks for the tip about posting images. Here's the link to the one I tried posting last time:

[url] www.gravitationlab.com/ClusterDist-VelChart.html [/url]

The chart reveals a pattern different from the one predicted by MOND, as it shows up primarily within the inner few parsecs or tens of parsecs of Globular Clusters (and one open cluster for which data were compared in a similar way).

If my model is correct the pattern would also show up in a laboratory experiment. Although the model expects an inverse square law, it predicts a strongly non-Newtonian effect when there is substantial matter both beyond and within a given radius (as a uniformly dense sphere with a hole through its center) because what I said about accelerometers and clocks is not as "innocent" as it may at first appear.

To clarify this, the best analogy is a body undergoing uniform rotation. Accelerometers and clocks attached at various distances from the rotation axis reveal a range of centripetal accelerations and tangential velocities. Since the system as a whole maintains its integrity even while undergoing this range of accelerations and velocities, we may describe the system as being in an overall state of <i>stationary motion</i>. I think you'd agree that this motion is absolute and not relative.

Knowing that the physical facts are quite similar to what is found in a gravitational field, Einstein characteristically argued that observers in the rotating system have the right to regard themselves as being at rest. Although most relativists do not take the analogy to such absurd extremes, they nevertheless agree with Einstein that, at least the gravitating body and its surrounding field are at rest, i.e., static.

The interpretation I propose is the exact opposite. Since accelerometers and clocks reveal the rotating system to be undergoing absolute acceleration and absolute velocity, while at the same time remaining stationary, the similarity in instrument readings suggests that the same may be true of massive bodies in general. In the latter case the accelerations and velocities are both radially outward. At first this seems crazy because it would seem to require that everything is expanding in a most absurd and disorderly way. I admit that the model can't be easily modeled or visualized -- but I suggest this may only be true if we limit ourselves to three space dimensions.

I know it sounds kooky, but all I've done is to suppose that accelerometer readings and clock rates are really and truly and always telling us the truth about their state of motion. The instruments appear to be telling us that there is no such thing as a static chunk of matter or a static gravitational field.

If this interpretation is correct it means the rate of a clock at the center of a spherical mass will be the same as a clock at infinity – which means objects dropped into a hole through the mass will not oscillate.

It means line of sight velocities of stars in clusters will be, on average, slower than proper motion velocities (as observed) and that the model can be very conclusively tested in an Earthbased laboratory.

At the top of the left column in GravitationLab.com are three PDF files. The first describes in more detail the laboratory experiment and the astrophysical observations. The second goes into the cosmological implications (infinitely old Universe with suggestive "large numbers coincidences"). And the third explains how the model agrees with the results of the Shapiro-Reasenberg and Vessot-Levine experiments.

RBenish

Stoat:

I think I see now what you mean. A marble dropped at the inner upper edge of a spherical bowl "wants" to follow a cycloid path instead of the circular path it would be constrained to. Assuming that gravity works according to Newton, I suppose this might be of some relevance. It's not obvious, however, because in the case of the bowl (or the swing mentioned earlier) the situation involves an essentially uniform field (constant g); whereas in the case of the tunneled sphere the force varies directly with radial distance.

What is obvious though, is that any such effect would involve only a small correction to the oscillation predicted by Newton. By my reply to Tom, above, it should now be quite clear that my model predicts an entirely different behavior. The apparatus I've built may yet suffice to reveal the gross differences between Newton's prediction and my own. But a rather more delicate instrument would be needed to reveal the smaller effect that you've pointed out.

RBenish

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Benish</i>
<br />Although the model expects an inverse square law, it predicts a strongly non-Newtonian effect when there is substantial matter both beyond and within a given radius (as a uniformly dense sphere with a hole through its center)<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">You gave me no clue why everything is Newtonian for one uniform spherical shell, but becomes non-Newtonian if we have two such shells, concentric but with different radii. The case you describe as strongly non-Newtonian is just a many-shell case.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">... a body undergoing uniform rotation ... we may describe the system as being in an overall state of <i>stationary motion</i>.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Stationary motion is an oxymoron with the standard definitions of the words. Is a flying swarm of bees, each keeping its relative place, in "stationary motion"? What are your definitions of these words?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Since accelerometers and clocks reveal the rotating system to be undergoing absolute acceleration and absolute velocity, while at the same time remaining stationary, the similarity in instrument readings suggests that the same may be true of massive bodies in general. In the latter case the accelerations and velocities are both radially outward. At first this seems crazy because it would seem to require that everything is expanding in a most absurd and disorderly way. I admit that the model can't be easily modeled or visualized -- but I suggest this may only be true if we limit ourselves to three space dimensions.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Accelerometers respond to both accelerations and forces. If someone had chosen to name to instrument a "forceometer" instead, would you have developed a model with forces but no motions?

Likewise, you suggest not limiting ourselves to three space domensions. Normal space is defined with three and only three dimensions because matter has that many dimensions, and space is where matter resides. Okay, now define your fourth space dimension, and include how you propose to detect or sense or test it. Without rigorous definitions, we will be talking and thinking nonsense; or at the very least, we will be unable to communicate the abstract "feelings" in our minds to other minds.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I know it sounds kooky, but all I've done is to suppose that accelerometer readings and clock rates are really and truly and always telling us the truth about their state of motion.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Trying to reason without rigorous definitions -- something all of us do from time to time when we don't have enough facts at our disposal -- is what I sometimes call "fuzzy-think". It's not kooky, but it's also not science. It's more akin to wishful thinking.

Contrast your model with the clear, crisp, rigorous "pushing gravity" model, in which the apple falls from thr tree because a graviton wind forces in toward the Earth (because the counterpart wind from below is partly blocked by the Earth). Even your grandmother gets a sense she now understands what gravity is and why all bodies appear to have gravity. It's easy to understand, passes all experimental tests, and makes more testable predictions.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">If this interpretation is correct it means the rate of a clock at the center of a spherical mass will be the same as a clock at infinity – which means objects dropped into a hole through the mass will not oscillate.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Because gravitational force or acceleration per se does not affect clocks, even at accelerations of 10^19 g, the logic of this statement escapes me.

I recommend you start from the best model we now have, PG, and if you see any deficiencies in it, see if you can think of ways to improve it or replace it with something better. But the first step is rigorous definitions. Without those, you will not only confuse others; but much worse, you will confuse yourself. -|Tom|-

Tom:

A swarm of bees may indeed be described as a stationary system of motion. But there is a more relevant sense of the word, "stationary," as distinct from the word, "static," that has often been discussed in textbooks on Relativity. In each instance the authors use uniform rotation as an example of a stationary system and a non-rotating massive body and its gravitational field as an example of a static system: [C. Moller, <i>Relativity</i> (1972) p. 284; Landau and Lifschitz, <i>Classical Theory of Fields</i> (1971) p. 247; and W. Rindler, <i>Essential Relativity</i> (1969) p. 152.] The latter reference provides this definition:

"Let us more carefully define a static field. By definition it shall be time-independent and also have the property that to every possible 'forward' motion of a particle or photon there corresponds an identical 'backward' motion; or, in other words, all motions are time reversible. The 'gravitational field' on a turntable, for example, is not static: it is merely stationary, which means it is the same today as tomorrow. Stationariness corresponds to the existence of a coordinate system in terms of which the metric coefficients are time-independent. Staticness, we assert, corresponds to the existence of a coordinate system in terms of which the metric is not only time-independent but also without time-space cross terms."

The second sentence is especially applicable to my model, as its prediction for particle motion through the center of gravitating bodies is grossly asymmetrical. Upward motion is not the same as time-reversed downward motion.

The reason my model strongly disagrees with Newton for the tunneled sphere problem is that it does not regard gravity as a force of attraction. I agree that non-zero accelerometer readings indicate the presence of a force, but it's not a centripetal force; I don't think gravitons are either pulling or pushing things towards the center. Without appealing to such hypothetical entities, I defer to the motion sensing instruments; I trust that the direction of the force is the same as the direction of the acceleration, as revealed by accelerometers. On a rotating body accelerometers indicate that the acceleration (force) is inward. On a non-rotating massive body accelerometers indicate that the acceleration (force) is outward. This interpretation may be wrong, but at least it's consistent.

Imagine an extremely tall vertical pole planted on the surface of a large uniformly dense body. Suppose at the base of the pole a tunnel is dug through the center and to the other side. Accelerometers attached at various locations on the pole and in the tunnel reveal the inverse square law: For accelerometers on the pole the mass is constant so the acceleration varies as 1/r^2. In the tunnel the mass varies as the cube of the distance, so the acceleration varies directly as the distance. If we naively trust what these accelerometers are telling us, we arrive at the idea of a "field" of stationary outward motion.

Since this seemingly rigid system possesses a wide range of acceleration along a given non-rotating radial line, it cannot hold together if there are only three dimensions of space. Space dimensions are often conceived as a hierarchy. A point has zero dimensions. But as soon as the point moves we have not only a one-dimensional line, we also have time. The line is an extension or a projection of the point. A two-dimensional surface comes into existence (or anyhow, may be conceived as) an extension or projection of the line into a new direction. A three-dimensional volume is similarly generated by projecting the plane into a new direction. This is standard geometry. After building up the hierarchy to this point, in his book, <i>Conceptions of Space</i>, Max Jammer concludes that this kind of

"…deduction comes to an end apparently because the conception of a motion of a three-dimensional space as a whole lacks all intuition based on experience."

As most readers of this forum probably know, extra dimensions are in vogue these days in mainstream physics' String Theory. In this theory, as with its early 20th century precursors (Kaluza-Klein) space dimensions in excess of the third are conceived as being "compactified," which means they are rolled up so small that they have no testable effect. I don't have much appreciation for that kind of theory.

By contrast, in the literature one often finds attempts to visualize a fourth space dimension as a "hypercube" or "tesseract," that looks like a small cube nested inside a larger one -- the larger cube being a projection of the smaller cube. Perhaps it makes sense to conceive of a higher dimension being not "compactified," but "expandifiied."

(See graphic: [url] www.gravitationlab.com/DimsnHier-StatnryMot.html [/url])

With this image in mind I juxtapose it with the image of the array of accelerometers attached to the massive body and I come back to where Jammer put up the roadblock. Does the "conception of a motion of a three-dimensional space as a whole lack all intuition based on experience?" Or are these accelerometers telling us otherwise?

Although details are surely missing, the broad outline of the idea suggested here (gravity is a process of outward movement) is not fuzzy. But even if it were, that doesn't mean it couldn't turn into something concrete and valuable. Many important discoveries begin fuzzy.

I can understand why one might reject or resist my suggestions. They conflict very deeply with our long-held conceptions of matter, space and time. Fortunately, the truth or falseness of my suggestions can be tested relatively easily by experiment. If somebody would only prove that a test object oscillates in the tunnel, then, perhaps, I could begin to accept gravitons as something concrete. I am seriously working on this in my laboratory. I'd like nothing more than to resolve the matter, to kill my model if I can, or to find out for certain that I can't.

Thanks for your patience.

RBenish