Can barely follow even the outline of that first linked article in above thread enough to determine whether they are really proposing a non-geometric theory or not. Given mine and A.T.'s admittedly brief inputs are not helping, and given you have read above linked thread contents maybe it boils down to that the notion of curved spacetime is simply philosophically repugnant to you. Can't be denied it works extremely well wherever applied so far. Whether that continues to be the case when unambiguous data relating to black hole candidates finally arrives is still some time off. I happen to share dislike of the purely mathematical nature of GR and imho the single presumed 'fact' of gravitational radiation carrying off actual momentum and energy (binary pulsar data) strongly implies either spacetime having physically real properties of a 'substance/ether', or a bona fide field theory cast in flat spacetime background is called for. But that's a layman's viewpoint.
I don't know about "mass evolves to space" or even what it's supposed to mean, but gravity might be an entropic force. Which is to say that objects "moving under the influence of gravity" follow the most probable path through space. --http://en.wikipedia.org/wiki/Entropic_force See also: http://en.wikipedia.org/wiki/Entropic_gravity
What is (mildly) repugnant to me is the use of the ordinary word 'curve' to mean something completely different. Time curves ? Space curves ? This is conflation. I am not oblivious to these ideas. They are nothing new. But to call them actual curvature is a misnomer IMO. Incidently, Ouspensky had some highly developed ideas on similar lines a hundred (or so) years ago, particularly in his book TERTIUM ORGANUM. Really, in reading that and comparing it to what I read here, I can see nothing different in principal - only in mathematical complexity.
MD - I posted some replies to your earlier just now, but can't see 'em. Maybe they've gone into morderatorland. Will re-do them if they don't turn up.
I agree that to speak of a scalar entity clock-rate as curving is in the literal sense oxymoronic. But given you are aware of how in SR/GR space and time are mathematically combined to form spacetime, it's generally less clumsy to speak of the latter's curvature than to have to always separately refer to each component's distortion/dilation/compression or similar terms. Along with the compact terminology 'curvature' comes the interpretation of what that means for clocks vs rulers. Take for instance a plot of coordinate values (i.e. those remotely evaluated by an observer 'at infinity') of clock-rate (vertical axis) vs radial displacement (horizontal axis) in the case of exterior Schwarzschild geometry. The line is not straight horizontal as it would be in Newtonian theory but a curve, and in that kind of sense time curves. Regarding Ouspensky's outlook, did a quick read in Wikipedia and the only pertinent part seems to be in the last para here: http://en.wikipedia.org/wiki/P._D._Ouspensky#Career The dates linked to such (following, not preceding 1905 SR), his other, much different main interests, and being labelled an esotericist :m: in general, suggests there is not much to be gained by studying his notions on time and space. Just might be wrong though. Please Register or Log in to view the hidden image!
The term 'curved spacetime' indeed causes confusion for two reasons: - Most people think about ordinary extrinsic curvature, not the intrinsic curvature that is actually meant. This is further confused by non-inertial world-lines which are indeed extrinsically curved. - The intrinsic spacetime curvature is connected to tidal forces, while the gravitational pull is possible without intrinsic curvature: The cone shape in the animation doesn't have intrinsic curvature, and yet it results in gravity. And sometimes it is the other way around: In the center of a spherical mass the gravitational pull is zero, but the curvature isn't (unless you have a cavity).
Esoteric Confined to and understandable by only an enlightened inner circle (Wordweb) Lol .. Anyway, I don't want for a moment to seem to be promoting him or anyone else. I found the book enormously interesting - couldn't put it down. He deals with 3, 4, 5, and 6 dimensions in a manner I thought quite brilliant. You could download the book (free) and read it yourself. You may find it well worth the effort, even though it's not hard science.
Arghhh ! I am now more confused. By extrinsic curvature I understand you mean what I call normal curvature. Such as a wheel rim is curved. I don't understand the rest of what you said. About the diagram (the U tube you linked earlier) all I got from that was that someone bent the coordinate graph lines to straighten out a curved line. That's it. What is intrinsic curvature ? And what motivates an object to move along such curvature ? Are you able to reply to these two questions in a non - esoteric (see above), simple manner that I can understand ? PS - did you read or peruse the 'spacetime is a fairytale' link I posted earlier ?
Lol .. Oh, master of the skirt .. I did answer your question. MD: Do you see the mass moving away from the center or moving towards the center? Lakon: Away .. There are numerous queries in my previous posts directed to you however, which you skirted, the main one being; MD: This is why the universe works the way it works, because of geometry. Lakon:How can measurement (geometry) be the cause of the workings of the universe ?
Not sure of the tangent you're on there, but it's good to see that at least, your're not saying that the measurement (metry) of it, cuased it to flow. Yes, I agree that all things that people do start with an idea .. I think ..
The curvature of space-time is a mathematical construct; math cart leads the horse. The pressures generated by gravity, on the other hand, results in repeatable physical phases changes of matter. These can be observed even without a math construct; horse leads the cart. There is no brain washing need to observe phase changes, since they are real, tangible and repeatable. The space-time construct need prestige and repetition since this are more of a subjective state of mind which would not come from common sense observation. You need to tell people what to think like the pet rock has prestige. If we look at special relativity, velocity causes space-time reference changes. However, these changes in space-time references do not cause phase changes of matter. For example, say we start with the twin paradox in SR with one twin moving close to C. At that space-time he ages slower. Next, let us simulate the same space-time with gravity. We can place one of the twins inside a huge star. The pressure will end the experiment as he is squished into a tiny smudge. It is not space-time that did that. If you look at a phase change, such as water vapor existing as liquid water on the surface of the earth, what is happening is mass gravity is causing an actual change in the EM force interaction of the matter. Gravitational force connects to other forces when matter is present allowin phase changes like new atoms. The pressure affect of gravity is more unified than just GR, which leaves out the changes in EM and nuclear forces that result in phase changes due to gravitational pressure. This does not need a math cart to lead since the observations can be seem by any and all even without any cart leading the horse.
Right, and a definition applying well to the GR and QM crowd too. Was easy enough to find a pdf copy. May or may not get round to digesting much of it, though I see it gets rave reviews from some into philosophy more than science per se., which fits your description. [Edit: don't take that last bit the wrong way - I meant your description of the book.]
Esoteric is more difficult to understand, compared to logic and cause and effect, because esoteric attempts to explain 3-D concepts. Logic uses two intellectual dimensions where cause=X and effect=Y. Esoteric adds a third dimension or Z, connected to an intuitive understanding. Logic is more left brained, while esoteric makes more use of the right hemisphere, which more spatial. The left hemisphere is more differential, uses logic and is the side of the brain that process language. The right brain is more spatial or integral and it is intuitive; gut feeling. The limitations of language, since it is processed within the left hemisphere, is differential and/or cause and effect. The extra dimension of esoteric makes use of the intuitive aspect of the right brain to access 3-D and therefore cannot be fully processed with language since it is 2-D. You need that extra hunch for Z-axis. An esoteric schema can be helpful when one wants to access theory in terms of 3-D. Some theory is perfect for the left brain. It is logical, differential and can be explained with language so it is easy to communicate. But it may or may not be spatial enough for the right brain to be a good 3-D theory. The right brain is looking for 3-D connections, and not just cause and effect. Such a left brain theory may give a sour esoteric intuition. One may sense something is wrong is not perfect in 3-D. It may take time to put that gut feeling of the Z-axis into words, since one needs to express 3-D within the limits of 2-D language. You may need to find others would can think esoterically to transfer at least the gut feeling. If you keep working at translation, you may also be able to use differential observations, logic and language to show the limitations within a bigger 3-D picture; gravitational pressure connects all forces beyond the limitation of GR.
Yes, that's all there is to it. I explained the motivation for this already. Note that this particular distortion doesn't have intrinsic curvature. And the extrinsic curvature of the diagram has no physical relevance. Only the distances measured within the diagram matter. http://en.wikipedia.org/wiki/Curvature#Gaussian_curvature [video=youtube;8cOaagyEWVI]http://www.youtube.com/watch?v=8cOaagyEWVI[/video] The free falling object doesn't move "along curvature". It advances through space time along a geodesic, a locally straight path. Objects dont need "motivation" to do this. It is their default state, if no forces are acting on them. All of physics is a mathematical abstraction.
AT and wellwisher; thanks for the interesting, informative and understandable replies. Have downloaded them to think a lot about. Will reply soon. EDIT; OOPS ! And to Q-reeus too (just noticed his post).
Just words. You were looking for some other way to describe curved spacetime. It's not a motivation. It's the effect of projecting straight line motion onto the relativistic frame.
Lakon, I think we agree that spacetime is an ingenious explanation for what we observe, and the math works almost perfectly. We observe the motion of stars and planets and moons, and the inverse square law does a good job, but the influence on each other of objects in motion in space proves that the more complicated spacetime math is needed to better predict what we observe. It is the mechanism that makes those stars and planets and moons do what they do that we don't know. Further, those larger objects are aggregates of particles, atoms and molecules which are pretty well understood, at least down to the sub-atomic level. That is where the Standard Particle Model represents what we know and theorize about the quantum realm. But the quantum realm becomes a place where the questions we ask are not yet answered, at least not to the extent that there is a generally accepted theory of the mechanism of gravity. Would I be within the allowable area of discussion in this forum to bring up that some of the theories of quantum gravity from professionals at universities and private scientific projects might be called "wave based", meaning that they predict that there are no "solid through and through" particles at the quantum level; particles are wave phenomena? In professional circles a question like that surely seems ignorant and typical of a mere layman, but I'm not trying to say I know even a tiny bit of real science. I'm not saying waves of what, in what, or what new fields might serve those wave phenomena, and I'm not mentioning the "A" word (aether, oops, there it is, right here in the Physics and Math forum, sorry). (1934)
Orthogonal E and B (or H) fields. free space The electric and magnetic fields "serve" wave electromagnetic wave propagation. You mean A as in acoustic, the perceptually appealing mode of propagation. And cause for rejecting belief in aether as pseudoscience.
You're saying that the "waves of what" is orthogonal E and B (or H) which is theory specific; I do recall coming across those terms? What theory is that? Maxwell's? I've heard "free space" mentioned. What is it? Its not empty space I wouldn't think. Isn't there at least permitivity or permeability or something in any free space? Does that mean that gravity is electromagnetic? Yes, of course ... acoustic, lol. Are you saying that it is the consensus of the scientific community that aether is pseudoscience, and that is why I should not have mentioned the "A" word in this forum? Or is that your conclusion from some sampling of the community, or is it published fact? Can you give me a reference that puts the aether idea to rest once and for all? (1968)
The first of those youtube vids is interesting because it conveys the difference between Newtonian and Einsteinian views of gravity in a way that's easy to spot: the rolled-up versions of each spacetime diagram are different because time is the same regardless of gravitational potential (or height above the surface) in the Newtonian frame, but has a smaller 'radius of curvature' at higher potential (where clocks run more 'freely'), than lower potential (where clocks slow down), in Einstein's frame. So a 'newtonian' cylinder turns into a section of a cone: this deformation preserves the orientation and direction of the 'free-falling' object by making the curves the same shape in each case. So you get a picture of topological invariance along with this idea of 'time measured at different rates' being the same as the difference between the radii of two circles.
