md65536

The aberration occurs between the moving rockets' frames, and the "launcher" frame. Think of it like 2 (very fast) runners on a (very large) football field. Due to aberration, the yard lines would not appear perpendicular to the runners, but instead slant forwards. This is crucial to this example because each of the traveling objects appears in their own frame to have a head start. During the head start, the other object appears to be in the launcher/football field frame; during the head start there is relative motion between each object and the other (from their own frames of reference). But due to aberration (a form of length contraction), they only appear to be catching up to a perpendicular line to each other, rather than appearing to have left the other behind. During the head start, the start line (including the other object) appears slanted forward. When they are at the same speed, there is no relative motion, and they are perpendicular to each other from either object's view point (or any viewpoint on the football field equidistant to each). But they still never appear to be at the same yard line, from either of the object's viewpoints. The yard lines do not appear perpendicular to them. Further, this allows for each object to appear to themselves to always be ahead in the race relative to the launcher/football field frame (which must be the case due to the delay of observations of the other object), and yet remain neither ahead nor behind the other in their own frame where the other is relatively stationary. This is the solution to the paradox. You can't ignore lack of symmetry from the objects' perspectives, so you can't ignore relative motion at the start of the "race", and so you can't ignore length contraction and still expect it all to work without problems (which also means that if you're doing the numbers, you can't ignore time dilation either).

So a geodesic is the same path, passing from t -> -t? I think that implies that spacetime curvature is the same for t as for -t? Or at least, there is no inversion of the curvature that would make time-reversed gravity into a repulsive force. If you send a signal to the moon and time-reverse the process before it gets there, it will reverse course and return to you. If you drop a neutron off a building and time-reverse the process before it lands, it will continue to fall (I speculate). Admittedly, this depends on some of my own interpretation, which is not accepted science. As you say, there is no clear interpretation. Ignoring whether my examples describe practical or possible realities, figuring out the theoretical implications can be useful in figuring out what is possible in the universe and hopefully ultimately how it all works. Large-scale T-symmetrical time reversal is probably impossible (this very thread speculates one of several reasons why), and certainly impossible in any universal way that requires the existence of a fictional concept of "universal time", but it's useful in very small scale interactions such as those described by Feynman diagrams.

owl, you are a fool. You are a pigeon, crapping on the chessboard that is this forum. Since you don't understand analogy, I don't expect you to understand metaphor, so I apologize for my inaccurate insult. Philosophy of science is fine and it has its place, but you are using it to discredit GR. This is a Relativity forum, not a philosophy forum; hence the pigeon analogy and now metaphor. If you can prove that GR is wrong using philosophy in a way that is generally accepted, then those philosophical arguments are relevant here. But around here, GR is generally accepted science that has not been refuted in any accepted way, regardless of any "hot debate". You have a LONG WAY to go to disprove GR using philosophical arguments. Until it is generally accepted, THOSE ARGUMENTS DO NOT BELONG HERE. If you wish to try to refute GR using arguments that are not already accepted science, do it in the speculations forum. There's another choice: 3) Stop posting. I'm a fool myself. But I'm trying, Ringo. I'm trying real hard to number 3.

I believe that my post fully resolves the paradox but no one has acknowledged or refuted it. If two rockets are separated by one lightsecond and are launched at the same time in their rest frame, they will each see themselves start to move one second before the other does. But length contraction will make perpendicular lines that are in the launchers' frame appear to curve forward. The other rocket will appear ahead of me (on one of those curved lines) until I catch up to it exactly at the point where it reaches the same speed as me. While traveling with the same velocity they are relatively at rest, and will be exactly perpendicular to each other, even though they each witnessed having a head start over the other. In short: The effects of length contraction ensure that nothing impossible happens. My previous post explains more. The principle is essentially this: http://en.wikipedia.org/wiki/Aberration_of_light I'm assuming that gravitons and photons behave identically.

If the universe were thought of as an expanding (inflating) ball... (it might not be valid to do this)... Yes, I think you could define a changing measure of distance, such as "one unit = radius of the universe". Then using that measurement, the universe remains a ball with radius of one unit, and everything inside it shrinks and contracts into "patches" of greater density. You might be able to reconcile gravitational acceleration with the equivalence principle, in that a frame under the influence of gravity is equivalent to an accelerating frame. Perhaps something like... the strength of a gravitational field is related to the rate at which it contracts. Everything shrinks relative to the size of the universe, so it always seems like there is more room in the universe... it appears to be expanding relative to everything. Upon re-reading your post, I don't think this is what you're talking about. When you say "expand a vacuum within the atmosphere", do you imagine pushing everything else out of the way, so that the atmosphere (analogous to the universe) remains the same size, and everything outside of the vacuum gets pushed together (analogous to gravity)? Or do you imagine that the atmosphere is being pulled larger, and everything in stays where it is, so that the distance between things remains the same but those distances diminish relative to the increasing size of the atmosphere? If you mean the latter, then no I don't think that the expansion of the universe explains the effect of gravity. One interesting side-effect of imagining the size of the universe being fixed and the size of everything else changing relative to that is this: If the universe started out as a singularity, couldn't it be considered to still be a singularity?

t only shows up squared, so the equation has the same value whether it is positive or negative. ??? It makes sense that a particle traveling along a geodesic would travel in the opposite direction along the same geodesic if time were reversed.

Gravitationally accelerated test particles do not move along a single geodesic. If a black hole were time reversed and "became a white hole", yet we at an external perspective were not time reversed, the white hole would continue to gravitationally attract us. What I'm not sure of is whether the particles inside that white hole would follow full reverse paths and appear to be gravitationally repelled from the white hole, or if they would only follow reverse geodesics, and remain gravitationally attracted to the white hole. Only the latter makes sense, because (I assume) the spacetime curvature of the time-reversed black hole would remain the same as before, and that curvature is what dictates the gravitational acceleration. But then again, like you said we don't have a good notion of space and time. I'm mistakenly thinking of curvature only as spatial curvature, so time reversal might imply changes to spacetime curvature that I can't clearly imagine.

But how do you accelerate the objects at the same time according to all observers? You can't. If I have a viewpoint from which the 2 objects are symmetrical, and I synchronize the start of their acceleration, then they'll always be symmetrical to me. But each of the objects will see that they appear to have had a head start vs the other. Assuming gravity waves behave exactly like light, an object's gravitational pull on me will always appear to come from exactly where the object appears to be. So let's restate the problem with a different example: Imagine 2 objects P and Q at the start of a race. Imagine a very long start line, many light seconds long, with the objects separated by 1 lightsecond. A light signal equidistant to P and Q starts the race. Suppose P and Q instantly accelerate to some significantly fast speed (so we consider only 2 inertial frames: at rest relative to the start line, and moving relative to it). From P's perspective, it started the race 1 second ahead of Q. P won't see Q start the race for 1 second, and vice versa. The resolution to the paradox is this: If we imagine any photons moving through space, we can imagine them moving along with whatever inertial frame we choose to consider, correct? So, imagine photons emitted from Q a fraction of a nanosecond after Q starts to move (assume it is essentially at the starting line) and traveling along the start line, perpendicular to the velocity of P and Q. From P's moving inertial frame, these photons will "move along with P" and remain incoming from a perpendicular direction. This must mean that the start line appears to curve "forward" according to P. When it switches frames, it sees the start line stretching out to the side but now stretching slightly forward of perpendicular. It appears as if Q is "already ahead" of it. After 1 second, it appears to catch up to Q laterally at the same time that Q appears to start moving. They would remain "side by side" except for that first second (and if they stopped at the end line, Q would appear to be behind P for only that last second). I read in Carl Sagan's Cosmos that traveling near the speed of light would warp things so that things that were behind you would squish into your forward cone of vision, but I never really made sense of that until now.

I came across a definition of a white hole as a "time-reversed black hole." I assume that a white hole would only let light out. However, this doesn't make sense to me. If you have a curved geodesic contained within a black hole event horizon, wouldn't light travel along the same path whether it was going forward in time or backward in time? It seems to me that spacetime curvature would determine whether light etc would be confined to a space, or unable to enter that space. A time-reversed black hole would be gravitationally identical to a black hole. Perhaps its spin would be reversed or something, but essentially its influence on the universe would be the same??? A white hole then would be a "spacetime inversion of a black hole", where the curvature is inverted or negated or something. Extrapolating, it seems clear that gravitational attraction is independent of the direction of the arrow of time (it's probably still dependent on the rate of time or the magnitude of the arrow, if that makes sense). Gravitation is a one-way process, regardless of whether or not time is. ??? Or would a time-reversal of a black hole allow light to escape along the same paths that let it in?

No, I agree everything's relative. I just think the additional dimensions are important. Since you reduced location to distance, I assumed you were talking about spherical coordinates while considering only the distance dimension. Your example of orbiting the sun is not the best example, because the sun is essentially the same in any orientation. But if instead you were orbiting Earth, and say you wanted to land, then yes your relative distance is important, but if it mattered where on Earth you landed, and whether you landed on your head or on your butt, then relative orientation also matters. But this is all beside the point because as soon as you add a third point that's not collinear, an angle dimension becomes relevant, and if you add a fourth point that's not coplanar to the other 3, a 3rd dimension becomes relevant. With 4 non-coplanar points, I don't think your example of choosing an arbitrary axis and origin where you can ignore a dimension, will work. Certainly, the distinction between whether locations are considered relative or absolute is relevant to the thread, and I hadn't considered it in the original post. But I think that any theory that attempts to describe reality would have to consider locations to be relative.

You're describing relative location in terms of only distance, implying that one dimension is enough to define the relative location between 2 points exclusively. The other spatial dimensions (representing orientation) are irrelevant -- do you mean in general, or as it pertains to this thread? I don't think I agree. I don't think the most elementary particles are one-dimensional, and the relative orientation of 2 particles might be important especially when it comes to light, or velocities. As it pertains to the conjecture, I'd say that the size and the shape of a particle's "spatial range" is what matters (the range perhaps defined by a probability wave that specifies the possible locations of the particle and the probability of it being in any particular location. A "larger wave" would mean less locational precision, which I'm suggesting corresponds to lower energy). Unless the possible range is isotropic (ie. it's shape would need to have spherical symmetry?), then the orientation would be important. Yes... this seems to be in direct contradiction to my conjecture. It would seem that the location of the particle (the electron?) is less precisely defined in a higher energy state. Unless there's some other property that shrinks and allows greater precision, the conjecture does not account for electrons and must be wrong. Electrons ruin all my ideas! Are you sure we have to consider their existence at all???

Potential energy depending on location fits the conjecture better than velocity does. Is it a general case? Does any change in relative position involve some change in potential energy? I can't actually imagine how kinetic and/or potential energy relates to the idea. I shouldn't have mentioned it.

This probably refers to the one built by Aldo Costa: http://en.wikipedia.org/wiki/Aldo_Costa_(inventor) "However, as with other devices of this kind, the energy created by the unbalanced weights falling is merely equal to what's required to lift them to become unbalanced in the first place." Videos of it here: http://www.blueman.name/Des_Videos_Remarquables.php?NumVideo=2274#NAVIGATION Some explanation here: http://www.besslerwheel.com/wwwboard/messages/241.html "his wheel stalls"

Meaning that energy takes different forms in different frames? Is the total energy of a system (including for example the entire universe) invariant, and just changes form depending on frame of reference? Perhaps I'm using the wrong word "location", if it means a precise point in space. Instead I want to describe position with a variable degree of uncertainty or precision. So size too, I guess... a quantum of energy has a range of uncertain possible locations. I agree it's completely relative. So it's not location that's important, such as specified by some spatial coordinates relative to any origin. The values of those coordinates (or its distance from origin) don't affect something's energy or mass. It would be precision of location that would be related to energy. The conjecture might be restated: The energy of something is proportional* to the precision of its location. (Now the specific location or whether it's relative to something else, doesn't matter.) * I want to say "equivalent" but I don't know how to account for different forms of energy, or "somethings" that are made up of multiple quantities of energy and can thus have greater overall energy but may not have a proportional degree of locational uncertainty.

Here are some aspects of relationships between location and energy: 1. To change an object's location requires energy. If an object has velocity relative to something else (such that relative location changes), it has potential energy. To change velocity requires a transfer of energy. 2. In a Bose-Einstein condensate, which has very little thermal energy, the location of particles becomes undefined. Particles act as if they are simultaneously everywhere in the matter. 3. If an object falls into a black hole, light from it is redshifted indefinitely. Is it reasonable to say that one wavelength of the light is simultaneously traveling to our eyes at c, and stuck at the event horizon, so the infinite redshifting is equivalent to stretching that one wavelength of light across an ever-expanding distance? As the light energy is lost to the black hole, its location becomes undefined... instead of being in a specific point, it gets stretched indefinitely. 4. According to the conjectured holographic principle, a location in our 3d universe maps to all locations on a 2d topological manifold and vice versa. In some vague sense, any quantum of energy can exist everywhere, but some property gives it locational definition in our 3d universe. Can these ideas be combined into one relationship between location and energy? The energy of something would be related to the degree to which that something is "focused" or well-defined locationally. Greater energy means sharper focus into a specific location. If you want to determine the precise location of something either you would need to use a lot of energy to do so, or that something would need to have a lot of energy. The more precision you need, the more energy is needed. Mass, which is a form of energy, would be related to the specificness of location. More energy means more specific location. Inertia could be expressed in terms of specific location (including moving locations); the difficulty in overcoming inertia is related to the difficulty of modifying locational specification. This would probably imply that the location of a moving object is better defined (ie can more precisely be determined) than a similar stationary object??? -- is there any accepted theory that speaks to this? One last conjecture in case there's nothing zany enough in the above: If location is emergent (which I believe it is, along with all of geometry), would this imply that energy is also emergent? I'd previously thought that energy was invariant and a fundamental aspect of the universe... I still think it must be, but I'm not sure. (Energy is conserved -- except for vacuum energy??? -- which means it is invariant, but it can be converted to different forms which are different for different observers, so the form that energy takes is not invariant. In conclusion I don't quite know what this means.) Or does this conjecture make sense?: The form of a quantity of energy is equivalent to its location. (I don't think I said that right... anyone have ideas?)

If for example it's a rocket moving at .866 c relative to "our inertial reference frame", its velocity is .866 c according to us. No velocity is halved in this example. The Lorentz factor is 2.0, which means that according to us, a clock on the rocket ticks at a half rate. However, lengths in the rocket's frame are also contracted by the same factor of 2.0, so both distance and time in the rocket's frame are scaled by the same amount, and the rocket's velocity = d/t remains unchanged at 0.866c despite time dilation and length contraction. Lengths in the rocket's frame (including distance to it) are halved, and its time passes half as quickly, according to us. If we're in an inertial frame, its trajectory follows the curvature of space, which is a straight line in the absence of a gravitational field (essentially straight in this example. Einstein believed we'd never be able to detect spacetime curvature in our local weak gravity fields so let's say it's negligible). Yes, the speed of light of the beams would be c in both directions, relative to us. (They'd also both be c according to the rocket, or any other inertial frame.)

And with that, I formally abandon this hopeless conversation. Thank you for your time.

Citation? I don't think that's true. You've stated in this thread that you don't consider space to be an entity. Would you then conclude that GR is based on false assumptions? Would you also say that because of this, GR can be safely ignored, and that an understanding of GR is irrelevant to this discussion? On the website that you are referencing, they have the question "Is Space Infinite?" on their Open Questions page: http://www.spacetime...nquestions.html Your source does not seem to agree that the question has been answered. Others in this thread accept that it remains an open question. So how is it that their minds are made up while yours is not? I also find it amusing, but at the same time it is really bothersome to see the same misinformation repeatedly posted. As someone who doesn't have a firm grasp of relativity, I find it harmful to my attempts to understand relativity, and I think it does not belong in a relativity forum. I also think it's sad that what is claimed to be an expertise in the ontology of spacetime, seems to me to be based not only on a lack of understanding of relativity, but also some confusion about the very meaning of ontology (due to the apparent assumptions that for spacetime to have properties implies that it is an entity). I am not an expert on the philosophy of science, but to me this seems naive. Now this is an interesting topic relevant to my interests. But I think discussion of it is off topic and probably belongs in the Speculations forum anyway.

In the context of the original post, is the Sagnac effect equivalent to saying that... 1. Rotation of the reference frame will cause the paths of light (aimed in different directions) to curve in different ways. 2. There is no possible common path (geodesic) that the light can travel in opposite directions, from the rotating reference point. 3. Light in opposite directions travels a different distance in each direction in a given time, due to the differently curved paths. ? For the purpose of the thought experiment, it might suffice to imagine an inertial frame that approximates the Earth's motion through a portion of its orbit.

About .866 c ??? The speed of light is invariably c, for all observers, regardless of relative motion. There's nothing you can do to change that. Acceleration won't change the speed of light. What effect are you speaking of?

But you are giving a philosophical answer to a question that pertains to General Relativity, in a Sciences > Physics > Relativity forum, not a philosophy forum. You could very well be right, but you can't prove it in terms of relativity, science, or math. The reasoning in what you considered the best answer is this: "I don't see how the universe couldn't be infinite." That's simply not acceptable. I think it does a disservice to anyone who comes here trying to understand relativity (and not the philosophy of science), to find answers that are based on not being able to see how some potential implications of GR can be real. The question remains an open problem (whether considered from a scientific perspective, or a philosophical one). If you had reasoning that addressed why closed (curved) space should be considered impossible, in terms of GR, that would be interesting.

Since "anti-time" doesn't seem to be defined, you might define it as negative time, so that an equal duration of time and anti-time "annihilate" each other when added together. But time and distance are abstractions, as swanstont has pointed out, whether positive or negative. If you push 2 things together, you're not actually physically destroying anything as you reduce the distance to 0. Negative values of time and distance are useful for describing differences in the measurements. If you move something closer to me, my distance to it changes by a negative value. The difference between today and yesterday is -1 day. Meanwhile, the length or magnitude of any distance or time will be non-negative. It is probably easy to think of physical objects with lengths and events with durations, yet negative values may only come up when speaking of something relative to something else. So it might be easy to confuse distance as "something that is real", but it is only a measurement or a property of something real (or abstract).

Unless you're speculating otherwise, spacetime usually consists of 3 spatial dimensions and 1 time dimension, so time and space are hard to compare. If you want to compare time to a 1D aspect of space, comparing time and spatial distance would be easier. Anti-time might be like anti-distance. I don't know how that'd be defined, but I'd expect it to only be abstract, not anything "real".

The bounded infinite spaces I proposed are metric spaces that are only bounded according to a different metric. I don't think they can be called bounded metric spaces. Pure imbecility!, sorry about that. I think we should stop talking about boundaries, because that only answers the question about whether or not space is infinite, if there IS a boundary. Since no one is arguing for the existence of a boundary, we may as well assume there is no boundary. For a metric space to be finite and have no boundary, does this mean that no spatial dimension has a bound, yet the distance metric has an upper bound? Is it a confusion of spatial dimensions and the distance metric that is causing all the trouble?

If there's no boundary either way (whether or not space is finite) I don't see what it would prove to imagine such a space. I won't posit it (as in, "assume the existence of") because that goes against the assumptions that DrRocket laid out early in this thread: "Under the assumptions of homogeneity and isotropy it can be decomposed as a one-parameter foliation of space-like 3-dimensional hypersurfaces (aka "slices"), without boundary." I have no special understanding that supersedes all of known science, that would even suggest that space (whether finite or not) has a boundary. But for the sake of imagination, I'll try anyway. Here's how to imagine it. Imagine first a flat and infinite homogeneous space, which is what I think you are claiming is the only possibility. Now curve or stretch that space so that you map any point at a distance of d from some arbitrary point, to a distance of 1/(d+1). This effectively turns space inside out, which I know is weird. All of space is now contained in a sphere with a radius of 1 unit. This is an infinite bounded space; if we remove the singularity at the center, it becomes a finite bounded space. Imagine existing within this sphere. There is NO SPACETIME beyond the sphere. There is no emptiness, there is no volume to the emptiness, there is no measurement of the emptiness. All of space, all emptiness and all "stuff" (energy and matter) within that space, are contained within the sphere. Now, I will admit this: I don't know if this even counts as a bounded space, because from within the universe, you can still measure space with your original mapping in which the space was flat and infinite and unbounded. It requires defining distance from some external perspective, which has its own measure of distance, which we might again be compelled to imagine as another space in which the first is embedded. We must resist that compulsion, but in doing so I may be forced to concede that this is an abstract concept only, which may not have any possible real existence in any way. But that doesn't even matter, because this space requires severe curvature. It is not homogeneous and isotropic in terms of curvature or distance. This whole discussion of bounded space may be a complete waste of time discussing, because even if it does make sense (I'm not sure it does) and even if it made sense and you understood it (doubtful), it's still not the finite space that we should be talking about, which is closed, unbounded space of a constant curvature. I know that you and michel123456 don't get it that space can have properties such as curvature without making it an entity (which by the way I'm taking to mean "The existence of something considered apart from its properties"), and I don't know if anyone gets anything out of what I'm saying, so it probably indicates "pure imbecility" on my part to bother writing at all. Yes, it does seem to indicate moderate or severe mental retardation. Thank you. I don't understand what you are saying here. Ontology is a branch of philosophy dealing with existence. An entity is something that has a physical existence. What is the ontology of a non-entity? I think there is none. There's only a problem if spacetime is an entity. I also don't get how defining something's properties makes it mysterious. "Nothing" was a bad word for me to use, because it is too ambiguous. It can be used as a name for empty space, or it has even been used to describe vacuum energy (which I'd agree could be an entity with an "ontological problem"), or something that has no properties, but I meant only that it has no physical existence apart from its properties. It is nothing besides its properties. I don't think that's an axiom at all.