md65536

Nothing must lie beyond the closure. Nothing that can be considered part of this universe. Otherwise, the closure doesn't enclose the universe, which means it's not a closure. Owl, you're the only one talking about space being an entity, as far as I can see. You're arguing against imaginary foes who, apparent only to you, are arguing that it is. Think of it only as a measure. If it is curving or being stretched etc, it is the measure that we're talking about. If matter and energy is in that space, the measure affects their shape and size, but that doesn't mean that the space itself is an entity. You can measure the distance (and the curvature) of the space between earth and moon but that doesn't imply there's an "entity" attaching one to the other. Disclaimer: I'm not a physicist. If the following doesn't make sense, it's not you, it's me. Imagine taking some infinitesimal distance, and stretching it to infinity. I think this is what you'd have beyond the "closure" of the universe. This would mean that there is no distance at all beyond the edge of the universe. The distance beyond it is ZERO. Also there should be no abrupt change between an "inside" and "outside", as in a membrane on one side of which there is distance and on the other side there is no distance. It would probably have to be a "soft" or continuous, gradual closure, which you could not possibly travel to. I think that this "no distance" or "infinitesimal distance stretching to infinity" describes infinitely open curved space, and if you approached a potential "edge of the universe" beyond which there is infinite open curvature, local space would still (as always) be flat, meaning that it would have to appear that space continues on for additional distance (smoothly going between your flat space and the infinitely open space beyond). By approaching the edge of space, you would necessarily move the edge of space. It only makes sense (to me at least!) because we're not talking about an "entity" here.

Count me out of all this agreement. I don't think you need to add dimensions to figure any of this out. If we have a spherical shell in 3 dimensions, and we remove all distance, we get a degenerate sphere which is a single point in 3 dimensions. Isn't it also a 2D surface? Doesn't this still describe topologically a 2D manifold that reconnects to itself in 2 dimensions? You don't need a 3rd dimension to describe this. I might be wrong. ... Similarly, we can describe a closed infinite space without the need for a 4th dimension. How? Using spacetime curvature. Imagine we were able to arbitrarily curve spacetime, so that we could arbitrarily map distances in one view of the universe, to different distances in another view. Then suppose you have an infinite ruler in your view of space that counts distance from you in intervals of 1 meter (starting with 0, 1, 2... say). Suppose I map interval number n on that ruler, with a length of 1m in your view, to a length of 1/2^n in my view. The infinite ruler in your view will map to a length of 2 m in my view. I could fit your infinite universe into a bounded sphere and keep it in my garage. Then, you could travel indefinitely along this ruler, while I see you slowing and approaching 0 velocity as you approach the boundary of the sphere in my garage. If you think this "arbitrary mapping" has no connection to reality, let's toss something into a black hole and see what happens. (Empty space should curve in the opposite way so it may be a bad example.) ... But the thing is, you're not going to have a model of the universe that's completely flat, while I have one that is closed. We're all going to have equivalent models of the universe, but we're also all going to have different views of the universe, that appear differently curved depending on our location, velocity, gravity field, and whatever else. So as you travel along an imaginary ruler, distant space will not appear to stay flat while allowing an actual infinite ruler to remain infinitely long. I have a to get a bit vague cuz I've passed the limits of my knowledge, but I imagine that a part of space that appears to stretch to infinity (ie to the horizon) from one location, might appear arbitrarily small from another location. This means that instead of you having an infinite universe that can be curved to fit in my garage, rather you have an infinite universe that can fit in your own finite universe. As you move through this seemingly infinite space, it keeps changing its appearance, so that it can always appear infinite, and yet always fit within a finite 3 dimensional space. Another way to think about it is this: Take an infinite cosmological horizon, and imagine squeezing that into an arbitrarily small length. You have just imagined connecting space that is infinitely far away in one direction with space infinitely far away in an opposite direction, into a closed manifold, without resorting to adding extra dimensions. Instead of "curling" it into extra dimensions, just stretch across 3 dimensions. If this is too vague, it's because I don't really know what I'm talking about! But I hope that I sound like I do , enough that you can imagine and contemplate. ... I don't mean to derail this thread with black holes or unnecessary complications, but my opinion is this: You don't need extra dimensions to curve an unbounded space and connect it to itself. You can do that by curving space in whatever dimensions you're already working with. ??? Edit: And now that I've said all that, I'm wondering... doesn't spacetime curvature not mean just stretching, but actually curving into the 4th dimension so that the reason a 3D distance looks stretched or compressed is that the distance includes an unseen time component? Which makes me kinda a little bit totally wrong?

I don't think so. If we assumed all the above was true, I don't see how a big freeze follows and allows no other alternatives. I don't see anything that concludes that energy, once slowed, can never speed up. Speeding up, by the way, appears to be happening with cosmic expansion. "Heat death" seems the most plausible end of the universe (Big Crunch would require at the very least a slowing of the rate of expansion of the universe and the evidence is against that and I don't expect that to change). Heat death might be called a "Big Freeze", but I don't think your assumptions or logic apply to it. Nuclear fusion would be an example of your "slowed energy" being made fast again. Problems with assuming your "all the above" is true: Information at hand 2: The states of matter are not only dependent on the speed of molecules, but also pressure, and maybe other things. I think you're suggesting that the Big Bang implies a one-way strict slowing of energy (seems false), and that all very slow energy/matter is a solid, and that a Big Freeze would be a solidification of the universe. Heat death on the other hand would have (much or all?) matter spread so thin that I don't think it could be called a solid. Are individual particles in deep space considered a gas? Or is that not even considered a state of matter? Conclusions 1 to 3: Energy doesn't really slow. It is always moving and it is always moving at a fixed relative speed of c. Lower levels of thermal energy means less vibration or something, but the energy doesn't slow down. Disclaimer: I'm fairly clueless about this. It's not, so it's not... Logically, if "the above" is not true, then the statement "if the above is true, then The Big Freeze is the only possible end result of the big bang" is true. But I'm being a bit pedantic. Klaynos is right that your conclusion is false, but your false assumptions don't logically prove that it's false.

Nope, I change my mind again. If energy is oscillating in one dimension I assume it will be along a geodesic?, in which case it will never leave that geodesic. Then if you could "polarize" energy so that it's oscillating in only one direction, it wouldn't be accelerated due to gravity in a direction perpendicular to its oscillation, yet it could still be accelerated back or forth along the geodesic. That means 2 equal masses might accelerate you differently depending on your orientation relative to them. This does not match reality. 1D oscillation might produce specific acceleration. Universality of gravity would require that the oscillation happens in all directions (including all spatial dimensions) with a uniform probability distribution, at least on average.

I've made a mistake and want to correct it. If space is continuous, the travel distance from A to B should be the same as from B to A. You should be able to keep splitting up that distance into smaller steps until you're only moving a distance of epsilon each step, where epsilon is small enough such that it is completely within local "flat" space, such that the forward distance from X to X+epsilon is the same as the backward distance. Therefore continuous movement from A to B, through continuously changing space, would be the same distance as traveling through continuously changing space in the opposite direction. One way to fix it is to assume continuous movement is impossible, ie. that there is a quantum distance across which energy "leaps" rather than travels through. This quantum distance would place a minimum bound on epsilon, and if it's large enough so that the spacial curvature across that distance is not absolutely negligible, then the theory might still have hope. Version 3 of the conjecture: - Assume energy leaps across some distance of epsilon. Let point B be separated from A by a distance of epsilon, in a direction toward a gravitational mass. Again, the distance from A to B (viewed from A) will be smaller than the distance from B to A (viewed from B), and so it is slightly easier to leap toward a gravitational mass than away from it. - Assume energy continuously oscillates at some fixed rate, and in doing so physically moves toward and away from a gravitational mass, then it will move toward it more easily. This slight bias will build momentum and produce a noticeable acceleration after millions or trillions of oscillations. - Therefore: Spacetime curvature, plus constant motion evenly distributed in all directions, plus energy leaping across a quantum distance, implies gravitation. When a distant observer sees a particle traveling along a curved geodesic, they will see the particle rotate to follow the curve, while the particle itself does not experience any rotation (it is following a straight geodesic). Therefore, if the particle is moving in all directions with equal probability from the particle's perspective, it will not be moving in all directions with equal probability according to a distant observer. It will appear to favor moving toward the gravitational mass, as the distribution of directions seems "pinched" into higher density in that direction. This requires moving along a curving geodesic, which means not just moving toward and away from the mass, but also perpendicular to that, which seems to restore the requirement that the oscillations must be in 2 or more dimensions. But then again... you wouldn't need to see the particle rotate at all. If the particle is leaping back and forth across a fixed distance (from the particle's perspective), then from the distant perspective the particle is leaping a different distance toward gravitational masses than away from it, on each oscillation. So again only 1 dimensional oscillation may suffice. I don't know how the changing mass of the particle would come into the picture, and whether or not it would only affect the distant observer's take on it. Perhaps the mass times leap distance remains invariant, so each leap seems to take a fixed amount of energy, regardless of observer location. I think that the 2 different explanations for a distant observer (1 for traveling toward and away from the mass, and one for traveling perpendicular to that) might mean that there will be a gravitational effect regardless of the direction of oscillation. We might drop the requirement that oscillation is evenly distributed in all directions, and instead only require that for any given direction, forward and backward motion occurs on average with equal probability or rate.

I agree and I think that's the problem. It's not a problem with GR, but a problem people have with understanding it. We naturally want to describe things from the perspective of a distant observer, because that is the way we have always understood our world. But describing what is happening from this perspective is not always intuitive. I think the view from the perspective of affected particles better illustrates "how gravity works". Since both views are valid, what a particle might "see" corresponds to what a distant observer sees, and SR and GR fully explain that correspondence. Perhaps a different way to sum up my thoughts in this thread (while removing all of the incorrect stuff) is as such: - If a test particle moves from point A to point B toward a gravitational mass, it moves into relatively more-closed space which flattens. The space it came from opens. The distance from A to B according to an observer at A, is less than the distance from point B to point A according to an observer at point B. Therefore, the trip toward a gravitational mass is easier than the trip away from the mass, in terms of effort required, from the viewpoint of the traveler. (From a distant viewpoint, the equivalent might be that the trip from A to B is easier than the converse, due to the greater mass a particle has at B vs A.) - If energy oscillates, and in doing so physically moves toward and away from a gravitational mass, then it will move toward it more easily. This slight bias will build momentum and produce a noticeable effect after millions or trillions of oscillations. - Therefore, oscillatory movement and spacial curvature directly imply acceleration. What I don't know is: Is this even correct? Does this account for gravity, or is there a lot more to it, that would make this effect negligible? With this modified version, it seems like 1d oscillation is enough (as long as the movement is properly aligned). I'm not sure if this modification is essentially the same, or (if not) whether either version is correct. Note: There is still contention I think on the first point about which distance would appear greater??? I do concede that this might be a negligible effect. For example, in my original gas pressure example, I might have tried to claim that the pressure in the center of a sun is somehow only "an illusion of spacetime curvature", which is false. If you take a balloon filled with air to the bottom of a pool, it will compress, and the balloon's size may change slightly (maybe immeasurably so) due to a change in spacetime curvature between the top and bottom of the pool, but that doesn't explain at all why the balloon compresses. I'm not trying to account for the bending of light paths. I think spacetime curvature intuitively explains that. Light travels in a straight line in one direction. I don't think it's valid to describe energy actually traveling along the oscillating path one draws when illustrating light as a wave. ??? Even if it is, it does not apply here. When we speak of distances, we're talking about the straight line distances that light travels, not the length of a wavy line. Light of a higher frequency (thus more oscillations per unit of straight-line distance) does not travel a greater distance than light of a lower frequency. The oscillations I'm talking about with massive particles involve actually physically moving back and forth across a distance, which photons do not do. Thus, my conjecture would not explain any acceleration of photons, but that is good, because GR predicts no acceleration.

That's a good thread. I think that I've got some of it right, and some of it -- still/again -- backwards. Okay I propose a new law of relativity: The Law of Inverse Reasonability: If anything seems to make sense with relativity, then the opposite is true. Outline of proof: Relativity implies that different observers see different things. Since the universe is consistent, that requires that for any observed effect of relativity, a converse effect must be observable from somewhere else. Therefore anything that makes sense from one perspective, will be completely wrong when misapplied to another frame or perspective. Due to the statistical certainty of mixing up some detail of different viewpoints or frames or clocks or measuring sticks or light paths or etc etc etc, the law holds. This allows us to iteratively build an explanation for any aspect of relativity. The "Convergent Oscillating Explanation Algorithm": 1. Explain something any way you want so that it makes sense to you. 2. By the law of inverse reasonability, the opposite will be true. 3. Discuss the opposite until that too makes sense. Again by the law of inverse reasonability, the opposite of what you made sense of is true. 4. Repeat until the explanations become convergent. This of course requires that the explanations get a little bit closer to the truth when discussed. I think this may be the method I always use in these forums, to explain things with relativity... I just don't know how many iterations it takes to acquire convergence! Okay that was a bit of a digression. Back to the example: As a distant observer nears a bar that is "submerged" in a gravity field, she will see the curvature of the bar straighten, and see the length of the bar shorten (opposite of what I'd been suggesting). I'm still not sure what will happen to the end points of the bar (I don't think they will converge; they may stay the same distance apart?; I still think they will diverge, so that the space between the ends of the bar increases as you move into it and it flattens -- but they certainly wouldn't diverge as much as I'd originally assumed). Another digression: Suppose you had a closed loop of spacetime inside a blackhole horizon, by which I mean a geodesic in a loop: If light leaves a point in a certain direction, it will return to that point via another direction. I don't know if this is possible. If you moved into the black hole, the loop would flatten into a straight line and appear infinitely long. That seems to describe closed space inside a strong gravitational field, rather than open space as I was originally calling it. The effect would have to be on the order of 1 part in 3x10^7, if that statement makes sense. If a particle accelerates from rest to 10m/s after 1 s in Earth's gravity, it will travel about 5 m. But if the particle is made up of oscillating energy traveling at c, that energy will "travel" 3x10^8 m in the same time. The "smallness" of the effect I'm predicting is similar to the smallness of gravity, like say we were to compare the difference in freefall speed over 1 second compared to c. It makes sense that it would be small, because it would predict small changes in speed.

I think this is confusing. What does it mean for time to tick slower for an observer according to another observer? Local time ticks at a normal rate, according to all observers. I would restate it as such: As the bar gets closer to Earth it gets deeper down into the gravity well and therefore a clock in the locale of the bar ticks slower according to the observer at the spacecraft. This is a tricky puzzle! Your logic seems okay but I think the trick to this is that for a distant observer, the path of light will be curved. If the path of light appears to follow the length of the bar, then the bar will also be curved. Then, since the bar (or at least the path of light) is curved, it appears to us that there is a "short-cut" from end to end, which is a line from bar end to bar end that appears straight to us. The length of the straight line would necessarily be shorter than the (curved) length of the bar. Could it be that we're both right? According to the distant observer, the bar curves but does it also stretch in length, while at the same time the ends get closer together? Let's say space is warped in a way that the local observer on the bar sees the entire thing in flat space, and it remains 1 lightsecond long. According to the distant observer, the bar's clock ticks slower. So I agree with your logic, the bar must appear longer to the distant observer. I think the bar would curve for the distant observer, which means that the distance between bar ends is less than the length of the bar. But what does that mean??? Do we say the distant observer sees length expansion, because the bar length expands? Do we say the distant observer sees length contraction, because the distance between bar ends is shorter than the length of the bar, even if the distance between ends remains at 1 lightsecond long? Or do we say the distant observer sees length contraction, because the distance between the bar ends actually becomes shorter than 1 lightsecond? I should have split this thread into 2. If it remains a puzzle I'll post this in the relativity forum. But... I think that no matter how curved space is, you can find a small enough volume around yourself in which space is flat, to any degree of flatness you need. If we have a 1m bar and our equipment can detect a warping, then we can use a 1 micron bar, and it will be flatter. Certainly the limit of spacial curvature is flat, as distance from the observer approaches 0. I don't know if there's more to it than that. Is that alone enough to say that local space is flat, or does the way it approaches flatness matter? Yes... I can't call it an explanation of gravity without the math to show that it matches Newtonian gravity. One problem with this is that it seems as if the "oscillation distance" would affect rate of acceleration; if a random walk with small steps moves you in a certain direction, a random walk with large steps should move you there quicker? So wouldn't an electron moving around a nucleus have greater mass??? And wouldn't that also imply that greater masses would accelerate faster than smaller masses??? Or would the constant speed of light fix everything, implying that all "random or oscillatory steps" are done at the same speed, regardless of the size of the steps? Too many unanswered questions to say it explains gravity. HOWEVER, I still think it is possible to use this reasoning to show that spatial curvature and 2d oscillatory motion will cause acceleration, and that's a start. It is a leap to think it would account fully for gravity, but it is an imaginable leap. Needs work. No, this only affects energy that is oscillating in 2 or more dimensions. This idea assumes that everything (light or objects) consist of energy that is always moving (at c). In order for something to remain stationary, it would vibrate, so there must be an ability to "move backward" (otherwise it would shoot off in one direction at c). Light would never be accelerated this way, because it never moves back. Also, if something was moving in 1 dimension along a single geodesic, that uhh... that thing about closed space being "harder or less likely" to move into does not apply. If you squish a line, it is still a line. So a one-dimensional oscillation is not enough. What I mean is that space appears different for different observational viewpoints, so if you move from one viewpoint to another, you will see space "morph" from how it looks at one place, to how it looks at another. You won't just see this: Space and distances actually change as you move. I suppose one clarification might be that it is only distant objects and space that appear to change shape and/or size... however you can make distant space into local space by moving into it, so somewhere along the line that space has to warp.

Off topic: Another topic I was speculating on seems to imply that mass is related to particle size, and that particles that make up mass would have to behave in curved spacetime differently from other particles (including particles that are made up of any such "mass particles"). This might work if all mass could be divided up into particles with some identical properties (mass and size). I suppose my question is, does the Higgs mechanism/boson mean that it makes sense to think of all mass existing in identical "mass particles" that are somehow contained in all other particles that have mass? Relating to this topic, isn't the Higgs boson (division of mass into identical constituent parts) equally simple as OP's suggestion, as far as mass is concerned?

Doesn't the standard model currently predict that all mass is in the form of Higgs bosons? I don't know much about it, but wouldn't the Higgs boson have a particular mass? Then if (say) the proton is 2001 times the mass of an electron, it would need to have 2001 times the constituent Higgs bosons?

Please tell me you have that backwards! If I get this wrong yet again that will make it just about every time that I got it backwards, and I'd have to conclude that I have some kind of neurological disorder. Local time ticks at a "normal" rate for all observers. Time ticks slower in a gravity well according to distant observers. If I got that wrong it wouldn't be the first, hundredth, or last time. I think that's backwards??? Consider geodesics to show this. Light appears to follow a curved path around a strong gravitational mass, because that is the shortest path through curved space. If you moved onto the geodesic, space would flatten, and the geodesic would appear straight. If you imagine straightening a curve, you do it by expanding space on the "inside" of the curve. If you moved from a distant location to a geodesic near a large mass, space would appear to expand more on side of the mass, until the geodesic is straight. It is length-contracted for distant observers... lengths are shorter according to distant observers. -- Suddenly I have this feeling that I've said this before only to find out I was wrong. It is not moving the cylinder that makes it expand; it is moving the observer. I see... so my original example, described from the "inside" perspective, is not right and not very useful. However... with a long enough cylinder and enough curvature, the farther end of the cylinder can't be considered to be in "local spacetime". So the local area of the cylinder can always be the same size, no matter where you go in the cylinder, but the farther parts of it can still be warped. I think you had it right the first time, and only I was backwards! Yes... I'm suggesting that a hypothetical side effect of space warping can completely account for gravitational acceleration (would require math to show this). I want to abandon the "cylinder and gas pressure" example because it is complicated and misleading... or really just wrong. Yes, I agree. And I think that gravity can be completely explained by the differing curvature of geodesics, as a test particle shifts from one geodesic to another as it moves in multiple directions (due to random motion or due to oscillatory motion in 2 or more dimensions). As a demonstration of this, we could draw a bunch of curved geodesics around an imaginary massive object, then repeatedly trace distances of some fixed unit, along the current geodesic, in random directions*, and we would end up moving toward the gravitational mass. Granted I haven't done this... * moving along a curved geodesic would change your direction relative to an external perspective such as that of the person who is tracing these paths. That would have to be accounted for when choosing random directions. The random directions would have to be evenly distributed according to the test particle, not according to the person tracing. This would better be simulated with a computer. Space curvature is very slight, and the distances particles move when oscillating is very small (so the different geodesics they travel on are only VERY slightly different). However, gravity is very weak, and if you oscillate a few billion times in a short period of time, the effect would add up. SO, this is all a way that FOR ME satisfactorily explains gravity from the perspective of a distant observer. I think that the same thing can be explained, from the perspective of a test particle, in terms of the way that space appears to warp as you move in multiple directions onto different geodesics. The idea is a hypothetical explanation of how GR works. I would say that if it predicts a difference from GR then it is wrong. Exactly! Far away parts of the cylinder will appear a different size, but when you move to them, they appear to be the "normal" size. That means that these parts of the cylinder (and the space they occupy) are distorting as you move through it. Local space appears flat; distant space appears distorted; moving into that distant space makes it local which makes it flat which can only be done if it changes from distorted to flat.

I dunno how to get it moved. Either place is good for me. It seems to be half trying to understand GR, and half speculating based on that. I think the cylinder example is bad or misleading for several reasons. I don't think the shape of the volume actually matters, only the relative volumes of specific spaces, and how they change when viewed from different perspectives (most important of which are the changing viewpoints of a gravitationally accelerated test particle). I'll have to check out those links and try to understand them. From an external perspective, my example doesn't show anything, because we don't see space curvature significantly changing as a test particle (with low enough mass) moves through it. From the perspective of the moving particle, space changes a lot as it moves through highly curved space. From an external perspective, geodesics are good for describing what's going on, because they show the differing curvature of space that the test particle moves through. From an internal perspective, geodesics that I'm moving on are not so good for describing anything, because all geodesics that I'm on appear straight. The changing curvature of perpendicular geodesics that I approach and leave behind, might demonstrate it.

I see. I'd misunderstood. But then why don't you record time using the specific observer's clock? It doesn't matter what rate other clocks are ticking at. If the observer has a working clock -- whether or not it is physically quantized -- it should provide a fixed rate at which to record location data for everything else. Why would timing and position data be "according to an arbitrary observer" and yet "position data is being generated" according to another object's modified clock? It seems to me that if you're talking about data that is specific to an observer, the position data of other objects is specific to and valid for that observer, according to the observer's timing.

I suspect that I got it all backwards so I'll try restating it... backwards... - Curvature means that space will be more closed towards a gravitational mass, however it appears flat locally. - Local flatness means that random or oscillatory motion in any direction is equally probable as any other direction. - When moving toward a gravitational mass, the closed space flattens as you move into it (ie. closed space seems to open up as you move into it). Again this means that space warps around you and changes the probability or "ease" of moving back to the location you just came from. -- I can't describe this easily. I might have to draw a diagram. - Continually flattening space in one direction makes random movement in that direction more likely, which continually adds momentum in that direction.

I think you might be caught up in some cyclical reasoning. Yes, if space is quantized, you probably can't divide an arbitrarily small length into an infinite number of parts, which implies that space is quantized. But if space is continuous, you can divide it so, which doesn't imply that space is quantized. I think you're taking aspects of your conclusion, putting it into your assumption. Also... (not sure if I got this right but...) does your Turing machine require that you can record the state of the entire universe at a single time? I don't think this makes sense or is possible, because there is no universal instants of time (due to relativity of simultaneity). If GR says the machine is impossible, then explaining its working function won't disprove GR; proving that the machine is possible would.

Yes, that was a mistake I realized long after posting. The ideas are speculative but all my questions are about GR. Discussing implications of GR is really what I'm interested in. Now we're getting somewhere! On point 1: One of my assumptions is that "curved space" must always appear to be a different shape from some different perspectives, because locally it appears flat (which is the same as saying that all geodesics that pass through a point appear straight when viewed from that point???). If curved space looked the same (ie flat) from everywhere, then it couldn't be called curved. So I tend to talk about curved space looking different from "inside" (flat?) and "outside". HOWEVER, I think that if the space in the cylinder has significant curvature from one end to the other, then a viewpoint that moves around inside the cylinder would see the cylinder change shape as the viewpoint moved. So... would the cylinder always appear uniform, but as you move from one side to the other it appears to change size? (It still seems intuitive that one side would always be bigger than the other.) On point 2: Yes, I think that this is a better way to put it. Okay so if we instead say the cylinder IS uniform, and appears uniform in flat space, then from outside it appears narrower on the side closer to a gravitational mass. From inside, particles look uniformly distributed in a uniform(ish) volume, and from outside they appear slightly more dense in the narrower part. It seems certain that with significant enough curvature, the cylinder would look distorted from any perspective. On point 3: Yes, there's something I'm missing there. I think I'm failing to consider the effect of acceleration. Curvature causes acceleration -- I think I'm showing that in a hand-wavy way -- but the equilibrium state of gas in a volume depends on its acceleration, not just on the shape (as affected by curvature) of the volume. The particles would *accelerate* due to a random drift through changing space, but the momentum they gain would cause a non-random motion. In equilibrium, it is only gas pressure that counteracts gravitational force and allows the particle's motion to appear to be a "random drift". Perhaps using a single particle in an essentially endless tube would be a better example, and then only its inertial motion would be considered, but accelerated relative motion would have to be accounted for. So I'm wrong that the particles would appear uniformly distributed from inside the volume. They would still "feel" that the cylinder is accelerating around them, and would still experience the pressure difference within the cylinder. That all makes sense but I can't figure out how all the details work together. I think I have to simplify my example, and cut out the effects of gas pressure. I think I'm trying to speculate about "why" gravity happens as observed: - Curvature causes space in one direction to appear be more open or "roomy" in one direction vs the opposite direction. - Random motion, or oscillation, would favor the open direction over the more closed direction. - When you move in the open direction, space warps around you, so that it continues to open more in the direction toward the gravitational mass. What this means is that once you move in the direction of open space, that space closes up a bit around you so that it is not as easy to move back as it was to move forward. So I speculate that it is not static spacial curvature that explains gravitational acceleration, but it is that the geometry of curved space appears to CHANGE as you move through it, that explains it. - Random movement or oscillation would continue in all directions, but the slight favoring of one direction would continually add momentum in that direction. Yes... I think that's the way to fix this. It's not the difference between inside and outside the cylinder that is important, but the changing shape of space from one location to the next that's important. The cylinder might only be useful to illustrate the meaning of "open space being more roomy". Note: I don't know if I'm getting "open" and "closed" right here. I'm assuming that space opens toward a gravitational mass, because an object falling into that mass will see space appear to "open up and get roomier". Am I backwards?

Yeah, I don't know what's going on here either. Swansont: Is this an equivalent example? "if you need to count using a subset of rational numbers, you need to list the subset sequentially, but there are an infinite number of rational numbers between any distinct 2, so it is impossible to count using a subset of rational numbers". The fault here is only with the final conclusion. Using rational numbers as an analogy for moving along a line with an infinite number of similarly distributed points, I'd say the following are true: - Any non-zero movement will require moving through an infinite number of points. Therefore, any movement from one point to any other point will require passing through (infinitely many) other points. - The points are well-ordered and will be passed through in-order (ie. you'll never pass 2 points in the wrong order). Obviously then, there is no need to "count" the points you pass through, in order to pass through them. To count "1, 2, 3" or to draw a line with a ruler, I don't need to be aware of all the infinitely many points in-between, to be able to pass over them. It would be impossible to sequentially list all of the rational numbers between any other 2, I think. Thus it would be impossible to sequentially list all the non-discrete points anything moves through. But that doesn't mean that all the infinite points in-between don't exist, or similarly that "physical space must consist of discrete units". I think the main confusion is with the ideas of sequential vs in proper order, which aren't the same.

There's a video that reminds me of this thread: http://www.seventeengallery.com/index.php?p=2&id=80&iid=1 The video is made as a work of art, and it has a moving effect in my opinion (though it's better with a soundtrack... I like playing this song quietly at the same time: )... and yet, it is more rational and more "science" than this thread. Both the video and this thread seem to be about "interpretations." Your work is not valueless. Perhaps it is art. The images are certainly interesting and thought-provoking. Perhaps it can be developed into something involving psychology (interpretation of imagery or maybe even neurotic pattern matching). Perhaps philosophy, and the nature of reality vs the perception of reality. But I repeat: In its current form, I simply see no useful conclusions.

Imagine a volume with flat spacetime, inside of which is several particles whose movement is described as a random walk. We would expect that the particles would approach even distribution, just as gas pressure approaches equilibrium in a container. Now imagine that the same volume consists of highly curved spacetime. For this thought experiment, let us suppose that the volume looks to us, as outside observers, as a long uniform cylinder, but from an inside perspective, the volume looks more like a cone, where one end of the cylinder is wide and the other narrow. From an inside perspective, we would expect that the particles would tend to evenly distribute, so that more would be found in the wider larger side. From an inside perspective, we see nothing weird... no "force"... just particles drifting randomly. From outside, we see more particles migrating toward the side that looks wider from an inside perspective. From here, we see a weird force: Something is drawing the particles to one side of the cylinder, where they remain with greater density than on the other side. Is this exactly what would happen with a cylinder in a gravitational field? Say on earth, with an upright cylinder. The spacetime curvature is very very slight, but then so is the pressure difference between the 2 ends of a small container. The force on these particles would be very slight in slightly curved space. The force on an apple would only be apparent due to the many many particles comprising the apple. With this interpretation, the particles do not see a "gravitational pull" as we see from an external perspective. They "see themselves" drifting forcelessly through a space that happens to open up on one side (with more room to randomly wander into) more than on the other side. One problem with this is that the spacial curvature caused by the Earth, say, is very small, yet the density of matter in the Earth's core vs upper atmosphere is very different. So the gas pressure example would only be an example, and not an analogy for all particles. This part requires some more thought... Basically, it seems intuitive that if space was "completely open" in one direction and "completely closed" in the opposite direction, then particles would move at c in the direction of open space (there would be no room for the matter to move in the opposite direction, even if that movement just involved subatomic mass energy oscillation). So, I would think that there is some relationship between the ratios of our Earthly "fairly flat" spacial curvature vs. a "maximum curvature", and of the "fairly slow" acceleration due to gravity vs. some instantaneous acceleration to a speed of c. Questions: - Is this a fair interpretation of "how gravity works" according to GR? Is there even an accepted answer to "how" according to GR, as it relates to this discussion? - Any problems with the assumptions or inferences herein?

What then is the meaning of the name "So Undo Flight"? undo: 2. To untie, disassemble, or loosen: undo a shoelace. 4. a. To cause the ruin or downfall of; destroy. b. To throw into confusion; unsettle. flight: 8. An exuberant or transcendent effort or display: a flight of the imagination; flights of oratory. Does this mean that your theory is unraveling? Doesn't your theory hold that this interpretation is true due to some "law" or holographic truth of the universe? Just as a duck and an elephant can be found in any muscular arm, your very name spells out your theory's downfall.

I think this post speaks volumes in this thread. You've misinterpreted what Klaynos meant by "causal links". What I think he meant is that you must show how your theory links causes to observable effects in the real world, not how other work is linked to yours. You have misinterpreted the word "link", expanded it to include other meanings, and then associated all possible meanings together. This is what you're doing with your theory. You are misinterpreting connections between things and looking for meaning where there probably is none. The "causal link" that you probably need, would be to show that these connections actually DO have meaning, perhaps with some physical predictions your theory might make, or something like that. I don't know how you could possibly do that, and I agree with Klaynos that what's presented here isn't science. Synecdoche ( /sɪˈnɛkdəkiː/; from Greek synekdoche (συνεκδοχή), meaning "simultaneous understanding") is a figure of speech in which a term is used in one of the following ways: Part of something is used to refer to the whole thing (pars pro toto), or A thing (a "whole") is used to refer to part of it (totum pro parte), or A specific class of thing is used to refer to a larger, more general class, or A general class of thing is used to refer to a smaller, more specific class, or A material is used to refer to an object composed of that material, or A container is used to refer to its contents. Check out this "link": http://en.wikipedia.org/wiki/Faulty_generalization Some of the "links" at the bottom of that page may also be applicable to this thread.

I've seen your previous posts about similar things, and I am interested but skeptical, and remain confused about what it is exactly you're describing. Can you provide some more specifics about some aspect of this? For example, falling asleep by will... Do you simply have to decide to fall asleep, and it happens? How long does it take to fall asleep? How do you know that you've fallen asleep (do you retain consciousness, or do you awake after some time has passed)? How long do you sleep for? Is it controllable? Is the sleep, or the process of falling asleep, different from "normal" sleep (by that I guess I would mean intentional but not willfully induced periods of sleep)? What thoughts or senses are noticeably "different" from what you would expect everyone else to experience when falling asleep? etc...

The aspect of causality that I keep referring to is that no information can travel faster than light in a vacuum, which means that nothing can affect anything else over a very long distance and very short time interval (the limit is the distance light can travel in a given time), which implies that if we can observe an effect of something (including gravitation), then that something is (or was) within an observable distance (horizon). A "common sense definition" is not really a good thing, because it is imprecise and can vary. For me common sense is that the horizon is the limit at which any observation is theoretically possible. Your definition seems to exclude things that may be theoretically observable but are not currently practically observable. So I may be wrong and causality is not an issue with your conjecture. The problem with imprecision is that you could be talking about something that disobeys causality, or you could be talking about dark matter, or any number of things that can't be precisely distinguished.

The short answer is causality. Causality is the answer that still remains, as to why there can be no gravitational attraction by matter that is beyond our cosmic horizon. Do you accept that gravitational effects cannot propagate faster than c? If not, then your proposal is in conflict with special relativity, which is a problem because special relativity is consistent with all observed phenomena and is well accepted. Can you explain how causality doesn't apply, or how it can be circumvented? If your proposal conflicts with causality, then I'm afraid you're going to have to provide a lot of pretty convincing evidence before I could consider the possible reality of your idea. If you accept special relativity but don't get how it applies here, I could try to provide a clearer example. If I am misunderstanding what you mean by "cosmic horizon", then some clarification would be helpful to me.

No, magnification is not the same as being closer. The difference is best illustrated with cameras, and the difference between zoom and tracking: It's also easy to experiment by playing around with the "view angle" in a video game. As for "energy"... a telescope's front lens is usually bigger than your eye, and it focuses that larger area into the smaller eyepiece area, which means that it allows more incoming energy to enter your eye than without the telescope.