The rolling has no physical significance. It doesn't change the intrinsic curvature, which is zero in this example (tidal forces are negligible on small scale). It is true that an actual closed cone has intrinsic curvature, if you include the apex in the parallel transport loop. But you cannot do this here. The diagram is not a closed cone: The cone surface is not closed at the "seam", but continues on a new layer, so you cannot parallel transport around it in a closed loop.
There's nothing taboo about the discussion of aether nor is it too far afield of the subject matter of this thread especially since you've been alluding to it. And I wouldn't call this forum hard science, neither in the sense of being rigid or difficult. The idea about avoiding pseudoscience is to encourage intelligent discussion, which is the basic rule in play here. With that in mind, I think we can probably agree that neither EM fields nor gravity propagate on account of the 19th century belief that waves travel through space the way they travel through air or water. That is, there are no molecules in a vacuum to act in tandem collisions to send energy from one point to another. Hence the term free space. Keep in mind that in the 19th c. the idea of an electromagnetic wave was novel, that particle-wave duality had not yet been discovered, and the concept of fields was only beginning to emerge. This left the idea of free space propagation problematic and mysterious, so folks simply assumed there must be some kind of unknown medium in space. They simply believed it was probably true, and this was the origin of aether. It never achieved the status of a theory. The theory they were trying to develop was one that would explain propagation. Enter James Clerk Maxwell, Scottish child prodigy who lived in the Victorian era. He is considered the founder of electromagnetics, for demonstrating that four equations define just about everything you need to know to solve problems in electrodynamics in the classical context (i.e. prior to the discovery of quantum physics). One of Maxwell's equations is Coulomb's Law: Please Register or Log in to view the hidden image! Gravity operates under a dual law: Please Register or Log in to view the hidden image! And both are said to emanate a field. Note equivalence in the two equations: the product of two observable properties in the numerator, divided by the square of the distance between them (more precisely, the differential element of the surface of an ever expanding sphere). These "causes" then are joined at the hip. Note the similarity in calculating the force between two magnetic dipoles: Please Register or Log in to view the hidden image! Without leaving the 19th c. we can reconcile the futility of the belief in aether once we recognize that it has no meaning in problems of propagation of these static fields. The analogy for water would be something you might imagine in the movie depiction of Charleton Heston leading the Israelites across the floor of the Red Sea. If they were electrons, the static field would somewhat resemble the height of the water to an observer in a boat nearby*, as the crest stood there in defiance of gravity. This isn't the best analogy, since the propagation is actually spherical, but it gives you an idea of the problem with aether - it can't send a static field no many how many ways you try to justify it. That's where the pseudoscience comes in. (*this is in reference to nonlinear shape of the field as it sharply drops off as you egress from the source.) Where gravity comes from, then -- at least in the classical model -- is no different than asking how and why any static field propagates, and what causes fields at all. Without any knowledge or preconception of quantum electrodynamics, or the Lorentz law and special and general relativity, you can pretty well ascribe it to nature. That is, particles are attended by fields. To the extent they have mass, they have attendant gravitational fields. To the extent they have an electric or magnetic "charge", they have attendant electric or magnetic fields. These are intrinsic properties of matter, just as free space has the intrinsic properties of permittivity and permeability that define the propagation velocity of electromagnetic fields: c. Thus, without worrying about any of the more advanced concepts of 20th c. physics, and without even worrying about how waves relate to fields, you can arrive at a simple understanding of your initial question simply by contemplating the classical consequences of propagating static electric and magnetic fields in comparison to the propagation of gravity.
The properties of aether have been redefined many times to accommodate different issues. I also think your explanation was crisp, clear and covered a great deal.
You are definitely on target with your explanations and accounts of charge, EM, fields, and the concept of a luminiferous ether, as well as the practical idea that gravity certainly could be field related. My intention for the thread was to make sure that there was no generally accepted description of a mechanism for gravity yet, and I've already been challenged on if I know what the words "describe" and "mechanism" mean. So I am not going to get into an argument about word usage or what current theory says in a forum that is moderated to be hard science, even though I agree with you that this forum is not hard science. I know that moderation in the Physics and Math forum is not tuned to people who enjoy alternative thinking, even when there is no falsifiable mechanism that describes an observable phenomenon that is generally accepted, as is the case with gravity. My objective has been achieved in this thread. If your interest is to stay away from my hobby thread and supposed model because it is pseudoscience then I can only respect your decision and consider you to be a down-to-earth person who is well educated in generally accepted science, and who has no time or room for playing with hobbies and models that cannot be falsified. On the other hand, posting my ideas in a closely moderated forum ties my hands and keeps me from being able to defend the internal consistency of my model and to defend my claim that it is not inconsistent with scientific observations and data. I can only do that in the "Fringe" forums where I can label my ideas as non-science and use that as the explanation for why I am posting them in the "fringe".
Good to hear that you have achieved your objective, though I am quite confused as to what your objective actually was. Also I think that whatever you brought up in this thread is reasonable and is not pseudoscience.
You might have a better idea of the objective, as stated several times, if you had a compulsion to have a continually improving personal model of the universe that answers all of the "imponderables" about the universe to your own personal satisfaction. This forum, to the extent that it represents the established scientific community, is restrained by the scientific method. By that I mean, for example, when existing theory cannot achieve a consensus on the physical mechanics of a mathematical theory, if that theory makes quite accurate predictions and is the best model yet within the constraints of the scientific method, the theory can still be generally accepted. That does not satisfy my personal compulsion to have some description of the mechanics, even though my proposed mechanics violate the scientific method in that they cannot be tested or falsified. I'm sure no one wants my non-scientific simple-minded alternative ideas to be aired in this forum, and there is even discontent that I am allowed to air them in the pseudoscience and fringe forums. (2906)
The mechanism is described in various places on the internet. It's really simple, but is generally not accepted. Indeed it's utterly rejected by some, even though in his 1920 Leyden Address Einstein said this: "According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that ‘empty space’ in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν), has, I think, finally disposed of the view that space is physically empty. Even though in Opticks queries 20 and 21 Newton said this: "Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?" Newton got the density back to front, but you catch the drift. See modern papers like Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime. Also see the Einstein-de Haas effect which "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". Then see Albrecht Giese's website for an outline of the mechanism. He does says things like "relativity without Einstein" which I don't agree with, but such is life.
I agree. Mathematics is in fact, independent of physicality. Besides that, "physical significance", although it sounds intuitive is probably not easy to define. Yes, the spacetimes are obviously flat, rolling them up doesn't change this. "Parallel transport carries a direction along any curve in a plane so that an arrow points in the same direction everywhere on the curve. To extend the idea to parallel transport along a curve on a surface that is not planar, one can imagine that parallel directions in the plane are printed onto the surface as it rolls on the plane, without slipping or twisting about the vertical, so that the point of tangency always remains on the curve. To roll a sphere along one of its circles of latitude, it is convenient to draw a cone tangent to the sphere along the circle." --p 103, SciAm Jul 1981
Well, interesting post. I gotta luv Newton, but he didn't realize what Einstein acknowledged, and what you quoted from the Leyden Address, that there are influences on any given local environment from distant matter and energy. That realization was invoked as he closed in mathematically on the quantification of the overall surrounding influences, and the very good accuracy of the EFE's might be explained by his acknowledgement that space is not physically empty, but contains the directional influences of distant bodies. Warning, Pseudoscience in the Physics and Math forum; Please Ignore: My "thing", which I don't discuss in this forum, is that those directional influences are the result of wave energy traversing the foundational medium. That makes the mechanism of gravity the wave energy density emitted spherically from objects and "felt" directionally by distant objects, i.e. objects move in the direction of the highest net wave energy density arriving at their local space. (3055)
Would you be able to put it into your own words? I'm having a hard time believing you even know what you're quoting.
I think he did. Think about that denser by degrees, then note that in a letter to Dr Richard Bentley on 25 February 1692 he said this: “That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it” He also said this in Opticks query 30: "Are not gross bodies and light convertible into one another?" So if he knew that light bends because of local conditions and that light can be converted into matter, I imagine he had an outline idea about the mechanism. He was certainly very interested in light, he wrote Opticks after Mathematica. I think Einstein thought along these lines from 1911 when he said this: "If we call the velocity of light at the origin of co-ordinates c[sub]o[/sub], then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = c[sub]o[/sub](1 + Φ/c²)." He never backtracked on this, he reiterated it. Even in 1916 he said die Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert. IMHO you'd be better off thinking in terms of a static energy density gradient, because thing like electrons and protons have their electromagnetic fields, and the QED virtual photons are field quanta rather than actual photons moving back and forth - a hydrogen atom doesn't twinkle. So imagine a swimming pool. Every morning you swim from one end to the other in a straight line. But one day in the dead of night I truck in a load of gelatine powder and tip it all down the left hand side. This starts diffusing across the breadth of the pool, imparting a viscosity gradient from left to right. The next morning when you go for your swim, something's not right, and you find that you're veering to the left. If you could see your wake, you'd notice it was curved. That equates to curved spacetime, the pool equates to the space round a planet, the viscosity gradient equates to Einstein's non-constant gμν, and you equate to a photon. Then imagine you're swimming around a square path. Whenever you're swimming up or down the pool you're veering left, hence you find yourself working over to the left. Then imagine you're swimming round in circles, and you still work over to the left.
I stand corrected. My thinking had to do with his gravitational relationship and the inverse square law which did not prove to be accurate enough to predict proper planetary motion, at least not as accurately as the EFE's. He was The MAN, Please Register or Log in to view the hidden image!. I appreciate the suggestion, and at this point I am going to have to stop talking about my so called model in this forum because it is not my intention to antagonize the members who have been pretty tolerant so far. (3361)
I and others have been over this with you many times. Your view is rejected with good reason. In any case the quote you keep taking out of the Leyden address does not support your case: The bolded part just asserts that spacetime is inhomogenous. That is true (e.g. the curvature of spacetime varies throughout the solar system) and as stated here is not at all controversial. What is not supported is your view that inhomogeneity of either space or spacetime can be viewed as a mechanism behind general relativity. Every time you bring this up you never explain the most important thing from a scientific perspective: why we should believe the idea actually works. You never explain how this is compatible with general relativity as it was formulated by Einstein in 1916 (i.e. the only "version" of general relativity that has experimental support for it). In particular, you ignore that many of the quantities you like to refer to as supporting your position, such as the metric components (the \(g_{\mu\nu}\)s) and the speed of light (e.g. from your expression \(c' \,=\, (1 \,+\, \Phi/c^{2}) \, c\) are, according to GR, hopelessly coordinate-dependent. In fact, the fact that the latter (the speed of light formula) shows nothing special is obvious if you realise it can actually be derived in the context of special relativity. In SR, the metric in an accelerating coordinate system looks like this: \( \mathrm{d}s^{2} \,=\, -\, \bigl( 1 \,+\, \frac{ax}{c^{2}} \bigr)^{2} \, c^{2} \mathrm{d}t^{2} \,+\, \mathrm{d}x^{2} \,+\, \mathrm{d}y^{2} \,+\, \mathrm{d}z^{2} \,, \) so in particular the metric component \(g_{00} \,=\, \bigl( 1 \,+\, \frac{ax}{c^{2}} \bigr)^{2}\) is inhomogenous (it depends on x). You also get a coordinate speed of light of \(c' \,=\, \bigl( 1 \,+\, \frac{ax}{c^{2}} \bigr) \, c\) (compare \(\Phi = gh\) with \(ax\)). Yet obviously nothing really physical is going on: this is just taking special relativity (i.e. flat spacetime, no gravity) and choosing to work in an accelerating coordinate system. I don't know where it went, but originally you had a post saying something along the lines that, if Lakon was asking about why spacetime curves (in response to the presence of matter), you couldn't answer that. That was a far better and more honest reply. (And in any case, even if you could "explain" GR in terms of "inhomogeneity of space", it wouldn't be an improvement in that regard since it wouldn't explain why space becomes inhomogeneous in response to the presence of matter either.)
If you mean the acoustic model, keep in mind that this was the idea that was abandoned in the 4th quarter of the 19th century. It might be useful to discuss why that model ever was conceived of in the first place and why it was overtaken by modern physics. The acoustical model ceased to be a model when it no longer represented the observations and data from Maxwell, Michelson, Lorentz, Poincare, Einstein and a whole horde of their peers and successors. Their work alone leaves nothing to defend. As I understand your rationale, it stems from a disbelief that fields propagate in free space. This speaks to a difference in belief about what constitutes science. In my experience the folks who survive the first year of coursework are usually quick to converge at a generally consistent definition. Working through the logic, the history of discovery, and the exacting standards of the field are common experiences which lead to reasonable discernment between science fact and fable. Without leaving the 19th century we can even see that the acoustic idea won't survive the static field test. That was my reason for mentioning it. But it also helps to understand that it was just a conjecture to begin with, based on a relatively primitive state of science. Considering we live in an era where this is all hindsight, we have the advantage of looking back at it with 20/20 vision.
Well said, and I agree with your recap of the events. After all, Michelson falsified the luminiferous ether, and Einstein's EFEs superseded any so called fixed particulate ether in absolute space. Still, we have no mechanism for gravity and the foundational medium and wave energy density are just my personal mind games, not presented as science because the so called medium cannot be detected and the concept of particles being composed of standing wave patterns is far afield. However, my model is not the falsified ether of our great granddaddy's day. (3448)
The idea of a mechanism is what was abandoned and replaced by propagation. That was why I compared the propagation of the gravitational field to that of the electric an magnetic fields. A field is similar to your notion of an energy density, but it doesn't rely on a medium. The static field is more generalized than the case of wave propagation, and more typical of cases involving gravity. Once you come to the understanding that particles are attended by fields, and put this together with the notion that fields naturally propagate in free space at c, then you arrive at the more recent explanation that superseded the mechanical or acoustical "mechanism". As soon as you say "mechanism" and "medium" you allude to the earlier belief that was replaced with an understanding of (among other things) electostatic and magnetostatic fields. Note, it does not appear that folks of that era were looking for a medium to explain gravity as an acoustical phenomenon since it doesn't usually rely on wave propagation. Nevertheless, electromagnetics offered definitions for them that pretty well cements the notion of free space propagation. It wasn't so much a question of falsification, but just a corroborating fact, that Michelson disproved the medium. It would have presented serious issues contradicting electromagnetics and especially it would have required that all static fields ride on some kind of invisible current. Eventually the gravity of the earth would have been detectable using an interferometer, or something like that. Physics would have been turned upside down and relativity would have died in gestation. On the flip side, we'd have a device that draws free energy from this current flowing through the medium, and poverty and hunger would be long ago have been wiped out. No wars or starvation would have followed, as we'd all have been living like kings on free energy. Unfortunately for humanity this turned out impossible, but it does hold physics together as a coherent set of principles. I think your stumbling block is that static field propagation in free space is somewhat counter-intuitive, in that it goes against common experience. (I recall one person here once posted something like "You expect me to believe in magic"?) Other than the lack of common experience I can't think of any motivation for wanting to insert a medium. But you'd be hard pressed to explain how any medium can support a constant flow of "force-current" for the static electric, magnetic and gravitational cases. They do simply propagate, as mysterious as that may seem.
When you move a copper wire loop through a magnetic field you get an electric current through the wire, which is a simple example of electromagnetism. The magnetic field is a complex of flux lines in free space that charged particles respond to. Magnetic fields bend the path of charged particles but have no effect on uncharged particles, which is why certain neutrino types are so difficult to detect, and why the energy of particles detected in particle colliders can be quantified. If we are to equate gravity to electromagnetism, and the gravitational field to the magnetic and electric fields, would there be some characteristic of matter that is influenced by the gravitational field? If you wave off the concept of gravity's mechanism, don't you need some particular characteristic of particles to make them respond to the gravitational field you are predicting, similar to how the charge of various particles makes them respond to electric and magnetic fields? What is that characteristic?
Try to avoid being a "my theory" guy. Instead play close attention to what the likes of Einstein said. Then you can talk about "my understanding" rather than "my theory", which will be better received. For example Einstein referred to inhomogeneous space rather than curved spacetime. And in section 22 of his 1916 book Relativity: The Special and General Theory he said this: "In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position". The word velocity in the 1920 English translation is the common usage, as in "high velocity bullet". This was a popular science book, and the original word in German was geschwindigkeit, which means speed. It was translated into velocity because it sounds better, but it isn't the vector-quantity velocity. See this bit of this Baez article for corroboration: "Einstein went on to discover a more general theory of relativity which explained gravity in terms of curved spacetime, and he talked about the speed of light changing in this new theory. In the 1920 book "Relativity: the special and general theory" he wrote: . . . according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [. . .] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so." He did mean so. So when he said a curvature of rays of light can only take place when the speed of light varies with position, he was telling you that light curves just like a car veers when it encounters mud at the side of the road. He never said anything about why an electron falls down, you have to look elsewhere for that. Like at the Einstein-de Haas effect. But there's your mechanism, like low-hanging fruit.
