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Elysium and Interior Solutions
- Larry Burford
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17 years 3 months ago #19646
by Benish
Replied by Benish on topic Reply from Richard Benish
Larry and Nemesis
Thanks for your thoughtful comments and questions.
Unfortunately, both a vacuum and full magnetic suspension are beyond my means. A vacuum would not be likely to improve the results by any large degree because the motions involved are very slow; drag by air is virtually negligible. Nevertheless, I agree entirely that such modifications are desirable, especially the full magnetic suspension.
I should also say, however, that I sometimes get promising results even with my air-filled enclosure and magnet-plus-jewel pivot system. With the large spheres not yet installed, I have sometimes achieved very slow arm movements with long oscillation periods (1-2 hours). Typically the movement is more rapid with shorter periods (about 20 minutes). Most of this unwanted movement traces back to asymmetries in the magnetic field. I have devised some strategies for reducing this problem (e.g., rotating the upper magnet). If I could get the problem just a little better under control, the plan would be to first demonstrate with a number of preliminary runs that drag (pivot friction) is sufficiently minimal, so that when the large spheres were installed one could be reasonably assured that the loudest signal is caused by gravity. I have not yet convinced myself that this is impossible for me to achieve with the means at my disposal.
Concerning the idea of "expanding matter," you have asked some excellent questions. A lucid critique that expounds on these and other questions may be found at [url] www.mathpages.com/home/kmath077/kmath077.htm [/url]
I have read the works of, and in some cases have corresponded with, authors who similarly think gravity's mechanism involves some kind of matter expansion. I have asked the same questions but have never been satisfied with the answers. The problems you have posed may also be stated with reference to the accelerometers attached to one body. E.g., if a seemingly rigid pole extends from the surface to twice the radius of the surface, an accelerometer at the top reads 0.25 of what an accelerometer reads at the surface. How is the appearance of rigidity (or constant relative size) maintained if the system possesses these different accelerations?
My short answer is: I don't know exactly how to explain it.
One thing that seems quite clear is that, if there are only three dimensions of space, it's impossible. A simplistic view of matter expanding into a background of three-dimensional Euclidean space is not at all tenable. One might therefore say "game over" and move on. But, as I have mentioned earlier, one of the well-known consequences of movement into (or out from) a four-dimensional space is that we would not be able to directly see it. In other words, it is <i>expected</i> of a space of four dimensions that motion therein may not be directly perceivable as such to sentient beings who are embedded in this space. Such conclusions have been reached by various authors who have discussed the dimensionality of space, either as a purely mathematical question or as a question presumed to be answerable independent of matter.
Before continuing, I had better make two points up front:
1) The question of the dimensionality of space has been a lively (even if "backwater") topic of debate among physicists for many decades. To my mind the most scholarly and convincing of these arguments always include statements as to their tentativeness. The question is widely regarded as being open. And
2) As I have stated earlier, I would not be interested in this question if it involved extra dimensions whose existence is impossible to detect (or at least convincingly deduce) by experiment. What motivates my research into the relationship between space dimensionality and gravity is both negative and positive: A) Dissatisfaction with existing explanations of gravity based on static spacetime curvature, pulling gravitons and pushing gravitons. And
<i>Analogies</i> that strike me as being very suggestive clues that this may be a fruitful direction to pursue.
Now let's approach the crux of your questions, the seemingly discordant acceleration problem, from two different perspectives, first local, then cosmological.
The rotation analogy, which readers of this thread will recall, actually has a double purpose. The first purpose is as follows. An array of clocks and accelerometers attached to a rotating body indicate the magnitude of the motion as a range of non-zero readings (accelerometers) and a range of different rates (clocks). Having justified use of the term, "stationary" in an earlier post (August 2, 2007) we can refer to the range of accelerometer readings as being due to their "stationary centripetal acceleration," and refer to the range of clock rates as being due to their "stationary tangential velocity." This is analogous to what we find on a gravitating body. In the latter case the accelerometer readings are all positive. Could this possibly mean that each accelerometer is undergoing "stationary outward acceleration"? Could the range of clock rates similarly represent a range of "stationary outward velocities"? Why not allow ourselves to play with this idea?
If one insists on trying to visualize all these accelerations and velocities in terms of three-dimensional space, it obviously won't work. But if we bend our minds enough (in the spirit of Michael Faraday) to allow that this conception of motion can be accommodated and described mathematically in terms of four space dimensions, we can at least see where it leads.
The second purpose of the rotation analogy concerns the relationship between one space dimension to the next in the hierarchy which begins with a zero-dimensional point. As noted earlier (and as depicted at: [url] www.gravitationlab.com/DimsnHier-StatnryMot.html [/url]) both time and the "first" dimension are generated as soon as the point moves. The most common progression from here is to move the line linearly, perpendicular to itself, and so on, to generate a square (plane) and a cube (volume). Movement of the cube "perpendicular to itself" produces the common nested cube ("tesseract") image, which clearly suggests that four-dimensional motion involves or may involve some kind of expansion; the smaller cube generates the larger one.
An alternative progression presents itself as soon as the first dimension has been generated. Instead of moving perpendicular to itself in only one direction to generate a square, the line may <i>rotate</i> to generate a circle (plane). And the circle may then <i>rotate</i> to generate a sphere (volume). Along this line of thought we come to the interesting idea that a three-dimensional object generates a fourth space dimension by "rotating" along every possible three-dimensional axis at once. Generating the latter part of the dimensional hierarchy by rotation suggests the properties of matter.
Material bodies are the focal points of this four-dimensional motion. The existence of focal points implies the existence of the less concentrated, less well resolved regions of "empty space." In this picture both matter and space are participants. Matter generates space (according to the inverse-square law) not as a discontinuous void which increases disproportionately to matter, but as a continuum whose overall density remains constant. If this is true, it implies that, on a cosmological scale, the cumulative effect of the locally inhomogeneous inverse-square expansion of planets, stars, etc., will be smoothed out into a homogeneous exponential expansion. On this scale, due to the small overall density of matter, the rate of expansion from one brief moment to the next is quite slow.
Since this perspective is just as valid as the local perspective, I would hesitate to say that the Earth's surface is accelerating radially outward at 9.8 m s^-2, unless such a statement is immediately qualified by acknowledging its impossibility in three dimensions.
The idea that the rates of clocks attached to a large gravitating body vary because of their varying stationary outward velocities, leads to some definite predictions for the behavior of light and the rates of clocks falling near such bodies. (See: [url] www.gravitationlab.com/Grav%20Lab%20Link...-Clocks-SGM-2007.pdf [/url])
The idea that the cumulative effect of many gravitating bodies adds up to a Universe with constant density undergoing exponential expansion, leads to some definite predictions for various cosmological constants and some definite relationships between these constants and atomic physics. (See [url] www.gravitationlab.com/Grav%20Lab%20Link...nd-LNC-July-2007.pdf [/url])
Not being an especially accomplished mathematician, I regret that I cannot satisfy those who would like to see exactly how this fourth space dimension I envisage "accommodates" what I call "stationary outward motion." It is perhaps somewhat ameliorating, however, to consider the words of R. H. Oppenheimer: "The notion of analogy is deeper than the notion of formulae."
Even if it were possible to develop a rigorous mathematical theory corresponding to the concepts I have tried to piece together (as I suspect it is) it would hardly be of any use if it does not as a whole correspond to physical reality. Perhaps in the end we'll find that the test object does indeed oscillate in the tunnel. Whether it does or not, I am grateful for those who have ventured along, curious to get a glimpse of a new way to conceive gravity.
RBenish
Thanks for your thoughtful comments and questions.
Unfortunately, both a vacuum and full magnetic suspension are beyond my means. A vacuum would not be likely to improve the results by any large degree because the motions involved are very slow; drag by air is virtually negligible. Nevertheless, I agree entirely that such modifications are desirable, especially the full magnetic suspension.
I should also say, however, that I sometimes get promising results even with my air-filled enclosure and magnet-plus-jewel pivot system. With the large spheres not yet installed, I have sometimes achieved very slow arm movements with long oscillation periods (1-2 hours). Typically the movement is more rapid with shorter periods (about 20 minutes). Most of this unwanted movement traces back to asymmetries in the magnetic field. I have devised some strategies for reducing this problem (e.g., rotating the upper magnet). If I could get the problem just a little better under control, the plan would be to first demonstrate with a number of preliminary runs that drag (pivot friction) is sufficiently minimal, so that when the large spheres were installed one could be reasonably assured that the loudest signal is caused by gravity. I have not yet convinced myself that this is impossible for me to achieve with the means at my disposal.
Concerning the idea of "expanding matter," you have asked some excellent questions. A lucid critique that expounds on these and other questions may be found at [url] www.mathpages.com/home/kmath077/kmath077.htm [/url]
I have read the works of, and in some cases have corresponded with, authors who similarly think gravity's mechanism involves some kind of matter expansion. I have asked the same questions but have never been satisfied with the answers. The problems you have posed may also be stated with reference to the accelerometers attached to one body. E.g., if a seemingly rigid pole extends from the surface to twice the radius of the surface, an accelerometer at the top reads 0.25 of what an accelerometer reads at the surface. How is the appearance of rigidity (or constant relative size) maintained if the system possesses these different accelerations?
My short answer is: I don't know exactly how to explain it.
One thing that seems quite clear is that, if there are only three dimensions of space, it's impossible. A simplistic view of matter expanding into a background of three-dimensional Euclidean space is not at all tenable. One might therefore say "game over" and move on. But, as I have mentioned earlier, one of the well-known consequences of movement into (or out from) a four-dimensional space is that we would not be able to directly see it. In other words, it is <i>expected</i> of a space of four dimensions that motion therein may not be directly perceivable as such to sentient beings who are embedded in this space. Such conclusions have been reached by various authors who have discussed the dimensionality of space, either as a purely mathematical question or as a question presumed to be answerable independent of matter.
Before continuing, I had better make two points up front:
1) The question of the dimensionality of space has been a lively (even if "backwater") topic of debate among physicists for many decades. To my mind the most scholarly and convincing of these arguments always include statements as to their tentativeness. The question is widely regarded as being open. And
2) As I have stated earlier, I would not be interested in this question if it involved extra dimensions whose existence is impossible to detect (or at least convincingly deduce) by experiment. What motivates my research into the relationship between space dimensionality and gravity is both negative and positive: A) Dissatisfaction with existing explanations of gravity based on static spacetime curvature, pulling gravitons and pushing gravitons. And
<i>Analogies</i> that strike me as being very suggestive clues that this may be a fruitful direction to pursue.Now let's approach the crux of your questions, the seemingly discordant acceleration problem, from two different perspectives, first local, then cosmological.
The rotation analogy, which readers of this thread will recall, actually has a double purpose. The first purpose is as follows. An array of clocks and accelerometers attached to a rotating body indicate the magnitude of the motion as a range of non-zero readings (accelerometers) and a range of different rates (clocks). Having justified use of the term, "stationary" in an earlier post (August 2, 2007) we can refer to the range of accelerometer readings as being due to their "stationary centripetal acceleration," and refer to the range of clock rates as being due to their "stationary tangential velocity." This is analogous to what we find on a gravitating body. In the latter case the accelerometer readings are all positive. Could this possibly mean that each accelerometer is undergoing "stationary outward acceleration"? Could the range of clock rates similarly represent a range of "stationary outward velocities"? Why not allow ourselves to play with this idea?
If one insists on trying to visualize all these accelerations and velocities in terms of three-dimensional space, it obviously won't work. But if we bend our minds enough (in the spirit of Michael Faraday) to allow that this conception of motion can be accommodated and described mathematically in terms of four space dimensions, we can at least see where it leads.
The second purpose of the rotation analogy concerns the relationship between one space dimension to the next in the hierarchy which begins with a zero-dimensional point. As noted earlier (and as depicted at: [url] www.gravitationlab.com/DimsnHier-StatnryMot.html [/url]) both time and the "first" dimension are generated as soon as the point moves. The most common progression from here is to move the line linearly, perpendicular to itself, and so on, to generate a square (plane) and a cube (volume). Movement of the cube "perpendicular to itself" produces the common nested cube ("tesseract") image, which clearly suggests that four-dimensional motion involves or may involve some kind of expansion; the smaller cube generates the larger one.
An alternative progression presents itself as soon as the first dimension has been generated. Instead of moving perpendicular to itself in only one direction to generate a square, the line may <i>rotate</i> to generate a circle (plane). And the circle may then <i>rotate</i> to generate a sphere (volume). Along this line of thought we come to the interesting idea that a three-dimensional object generates a fourth space dimension by "rotating" along every possible three-dimensional axis at once. Generating the latter part of the dimensional hierarchy by rotation suggests the properties of matter.
Material bodies are the focal points of this four-dimensional motion. The existence of focal points implies the existence of the less concentrated, less well resolved regions of "empty space." In this picture both matter and space are participants. Matter generates space (according to the inverse-square law) not as a discontinuous void which increases disproportionately to matter, but as a continuum whose overall density remains constant. If this is true, it implies that, on a cosmological scale, the cumulative effect of the locally inhomogeneous inverse-square expansion of planets, stars, etc., will be smoothed out into a homogeneous exponential expansion. On this scale, due to the small overall density of matter, the rate of expansion from one brief moment to the next is quite slow.
Since this perspective is just as valid as the local perspective, I would hesitate to say that the Earth's surface is accelerating radially outward at 9.8 m s^-2, unless such a statement is immediately qualified by acknowledging its impossibility in three dimensions.
The idea that the rates of clocks attached to a large gravitating body vary because of their varying stationary outward velocities, leads to some definite predictions for the behavior of light and the rates of clocks falling near such bodies. (See: [url] www.gravitationlab.com/Grav%20Lab%20Link...-Clocks-SGM-2007.pdf [/url])
The idea that the cumulative effect of many gravitating bodies adds up to a Universe with constant density undergoing exponential expansion, leads to some definite predictions for various cosmological constants and some definite relationships between these constants and atomic physics. (See [url] www.gravitationlab.com/Grav%20Lab%20Link...nd-LNC-July-2007.pdf [/url])
Not being an especially accomplished mathematician, I regret that I cannot satisfy those who would like to see exactly how this fourth space dimension I envisage "accommodates" what I call "stationary outward motion." It is perhaps somewhat ameliorating, however, to consider the words of R. H. Oppenheimer: "The notion of analogy is deeper than the notion of formulae."
Even if it were possible to develop a rigorous mathematical theory corresponding to the concepts I have tried to piece together (as I suspect it is) it would hardly be of any use if it does not as a whole correspond to physical reality. Perhaps in the end we'll find that the test object does indeed oscillate in the tunnel. Whether it does or not, I am grateful for those who have ventured along, curious to get a glimpse of a new way to conceive gravity.
RBenish
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- Larry Burford
-
- Offline
- Platinum Member
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- Larry Burford
-
- Offline
- Platinum Member
-
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