DieDaily

Okay, I finally did some dedicated research into this problem. This very same problem, it turns out, has bugged the heck out of the great scientists too, and many of them have solved it by concluding that gravity propagates virtually instantaneously (at minimum 108 or 1010 times faster than c), such as Laplace and, I will argue, Einstein. I'll give citations for this because it may seem controversial (after all, isn't NO THING WHATSOEVER allowed to go faster than light in vacuum?...well, we know from quantum coupling experiments and so forth that this is not actually the case...but, I'd better have good citations so you all don't try to up and blow my head clean-off). I'm a fluid dynamics guy, with a bit of a newly budding interest in plasma; but, basically, I'm a straight-up Computational Physics guy with a background mostly in hydrodynamics. Since an increasingly large subset of cosmologists now basically rely upon my own familiar models and arguments, those of classical hydrodynamics and classical thermodynamics, for instance, they now model galaxies, speculative thermal artifacts in the CBM, various sorts of structure formation, etc., I began to get an interest in cosmology that was at the outset based merely and solely upon this apparent commonality. Without knowing what I was getting into (my relativity training is scant, naive, and purely undergraduate) I began to wonder if maybe a novel modelling approach could prove useful, especially that basically "cellular automaton" (CA) approach in which I specialize. (Yes, I know, modelers always go nuts and see their own model everywhere...I know this...), So, in CA modelling, everything is really neat, really clear, and and really well-kept and tidy. First, we CA guys always quantize space in the form of a lattice. Duh, we're using computers. We often choose isotropic structures like hexagonal (for 2D) or else maybe a 3D slice of a 4D face-centered hypercubic (for 3D scenarios) because these lattices can are, pretty much indisputably, fully isotropic. Simple XY grids generally are not isotropic, so, we leave them to the retards. After defining a spatial grid, we make up some absurdly simplistic rules for propagation and collision that will be enforced by each cell of the grid (yep, this is paralleliable, unlike closed-form approaches, so we merely need more hardware to do whatever we want). I said simplistic, and, I mean, man, can the rules we use ever be simplistic like you could not imagine. After defining a space, and then defining the transport/propagation rules of that space, we merely dump in a ton of actors, "classical billiard balls" for all we care, as long as momentum and energy are conserved (and a few other things like exclusion, etc. but nothing majorly complex). Last, we execute our program, and then we are surprisingly awed by the richness that results from these simple, trivial, merely Pythagorean assumptions. Heck, really the only time we even need to use calculus is during the theoretical retrospective that is needed for writing up the paper afterward. Galilean (and even Lorentz) invariance just pops right out of these models, even if we choose nutty collision rules, from straight out of nowhere. We get full and complete Stokes-Navier behavior. We get a rich and inclusive set of thermodynamic behaviors. We can even take a hunk of pumice, slice it, scan/digitize it, run it, and see flow through a porous medium (complete with whetting) that is very close to physical/experimental. I was stuck on this relativity problem primarily because I don't see why some similarly elegant (and almost unthinkably simplistic and arbitrary) set of rules APPLIED PROBABILISTICALLY AND INDEPENDENTLY TO EACH CELL OF SPACE (i.e. to a triangular-ish lattice of quantized units of space) that pops out physicality just as splendidly. And let me be clear about this: I have made models, just for fun, with truly retarded transport mechanisms. Things like "If the iteration is not divisible by seven then all particles of unlike color that are 3 lattice units apart shall undergo a spooky attraction of 0.025 lattice units per iteration provided that they are of the same color". When I do this sort of thing, provided that I conserve momentum and energy, all I end up with is a perfectly physical phase separation...the purely viscous effect of immiscibility that results in the formation of ganglia (blobs) or a phase boundary (if I start the two phases separated within their own hemispheres)...and the I look at the this viscous fingering (which has a spatial period...the fingers have a mean separation) that turns out to be just the period that is predicted by their viscosities. (For example, take an aquarium with half water over half oil and quickly eliminate the membrane that holds them apart. You get "viscous fingering" with fingers that have a width that is predictable from the two calculable viscosity values. I observe very closely similar widths even when using my retardo-rules of collision.) So, with this present relativity problem, I'm really interested in how to model gravity in a spatially discrete universe (does there really exist such a thing as Planck length? If there does, why should this approach present an insurmountable problem?). Every time I use merely light-speed gravity, I get shit, shit, shit. When I use instantaneous gravity, I get very interesting results that seem to be more consistent with the physical/observed. See my dilemma? Turns out, everybody uses instantaneous gravity. Everybody. Whether they study orbital mechanics, or galactic mechanics, it's the same. That's the basic motivation I had for asking this question. But, back to relativity, here's what I've learned in a nutshell: In GR, gravity is not a force, it is a geometrical effect. Period. Gravitons are not exactly postulated as possible force carriers in SR/GR. Gravity is postulated as a mass/energy induced "distortion" in the fabric of space-time (geometry) which we then merely perceive and treat more or less as though it were an actual force. (Obviously I knew about this curvature aspect, but I truly did not know that it was basically an instantaneously propagated distortion, though that's exactly what I suspected had to be the case...my big plan was to prove it using this thought argument). Thus, the gravity problem is really nothing like the photon problem at all (for instance gravity ignores space-time curvature!, which is why black holes do emit gravity, despite a c or greater escape velocity which even traps all photons, and also why black holes never in any way distort or deflect the gravity of any other bodies with respect to any additional body's frame of reference...gravity passes through back holes just as though they did not exist at all, just as gravity passes through everything else in the universe unimpeded and unaltered). All of our argumentation which was predicated predicated upon the assumption that the photon problem and the gravity problem had any semblance of equivalence, was completely worthless and misguided. The charged particle analogy was possibly not a total wreck, since it had better similarity in some ways (i.e. non-accelerating charges never "radiate" whereas light emitters always do radiate, regardless), but it too was otherwise probably not a safe analogy unless The Greats say that EM forces also act at great distances effectively instantaneously (and I don't think they do). In short: masses/energies that are not accelerating, regardless of their velocities in any non-accelerating frame, never emit gravitons. Only accelerating entities "gravitationally radiate", and when they do, the proposed gravitons are not force-carriers since they never affect the perceived gravitational force "emitted" by the body in question or "perceived" by some body that is then affected. Instead, gravitons are associated with a special sort of acceleration-induced "ripple" in an object's gravity well. Said ripple is indeed proposed to travel at mere light-speed, strangely. Put another way: an incident ensemble of gravitons will be detectable not as any sort of change in gravitational force, but merely as a disturbance in "perceived length" and then only relative to some other axis of perceived length along which fewer or no gravitons are incident. Frankly, I don't buy it. But I have no right not to buy it, because I don't know precisely why I don't buy it. So, don't take that as part of my argument. My only argument here is going to be that gravity informs distant realms more-or-less instantaneously. By that I mean eight or more orders of magnitude faster than light does. Still, this argument that gravity is, for all intents and purposes, effectively instantaneous ("propagating" at minimum 108 or 1010 times faster than c and possibly much faster yet) is not a merely intuitive one, even though it also happens to be intuitively satisfying. I certainly need establish this with citations, preferably citations from The Greats. 1. There is no software, nor any closed-form method of physical reckoning used by physical navigators, that has EVER given physical results (==results consistent with observation and experiment) once she has stipulated a merely light-speed propagation of gravitational information. Introducing such a limit destroys all classical orbits (the objects will diverge) as well as relativistic orbits (binaries do NOT behave as though they cannot "extrapolate" the "actual, present" location of the other). Every astronaut is always shown how to use what "is seen in the visible sky" merely in order to then deduce the "actual, present-time location" of the ship, planet or sun, in order to then conduct a calculation that is based upon these real (ha ha, objective frame) positions, and lastly they are taught to translate them back into their "perceived" (i.e. retarded) positions for the sake of navigation-by-perceived-position. I do not believe that this is a controversial statement. 2. The "speed of gravity", in Newtons laws, is infinite/instantaneous. There is no dissent about this (take, for example, Misner et al., 1973, p. 177, and many others, which nobody has ever deigned to refute or impudiate in any way). Nobody has ever credibly argued against this, ever, because it is widely and automatically agreed that this is the case. Again, this is NOT a controversial statement. I would even venture that there does not exist ANY solution for Newton's equations that does not imply instantaneous instant-gravity-at-a-distance. Yet, the most fundamental precept of Einstein's relativity is that Newtonian gravity, which is said to apply when all velocities are low enough (the "weak-field" limit), is a consistent special case of GR/SR. This also is NOT a controversial statement. Therefore, it is a fact that for low velocities, gravitational influence is faster-than-light if Einstein was correct in this. Period. End of story. 3. Total lunar eclipses reach maximum optical eclipse roughly 40 seconds (38±1.9) before the sun and moon are in gravitational alignment. This is NOT a controversial statement. Why does it happen? Because photons do lag, while gravitational information does not lag? This is, at least, a simple/elegant argument worthy of your consideration discussion. 4. Binary pulsars seem to act based upon predictions of each other's "future position, velocity, and acceleration", but they do so faster than any speed-of-light-based-lag-time between them could possibly allow for. Sure, so far, for one binary (PSR 1913+16) it has been speculated that, given the experimenter's assumed decay rates, which the experimenters themselves concede is "not model-independent", seems to indicate a finite "speed of gravity" (Hulse, Taylor 1974). Many propose that the presumed decay rate is owing to "gravitational radiation" (like Weisberg et al. 1981). Later, PSR B1534+12, was given similar treatment but the results did not lead to such a precise a result. In effect the investigators seem to be arguing that the "residual motion-damping" implies a failure of 'retardation' effects (e.g. gravity lag-time--a lot like what I proposed in this thread, if not identical) to completely cancel the opposing 'noncentral, velocity-dependent" effects (the proposed compensating factor espoused by many scholars of relativity) and thus, they say, the gravity-lag-drag that results from the finite propagation of gravitational information does indeed predominate in these rare, high-energy cases. They may very well be right. This remains to be seen, however. In the mean time, we're all pretty much free to speculate, and we must note that there are huge problems with both of these studies. Sure, a Nobel prize resulted...whatever that now means...but the error bars, among other things, were extravagant. 5. The U.S. Naval Observatory, and the Jet Propulsion Laboratory's "Development Ephemerides" project attacked this problem head-on. They used various pulsars of known and reliable period (and, of course, location) to establish a "cosmological context" (ha ha, a cosmological frame) and then set out to determine "are we attracted to the apparent location of the sun (as in toward the incident direction of it's photons) as opposed to the "real, objective" location of the sun? (ha ha, an objective frame as in "where the Suin really must be at present despite frame-induced appearances"). They used 20 or so long-observed pulsars as "very distant, very reliable beacons" to orient themselves within something like an objective, cosmological, rest frame. Guess what they determined? "The Earth accelerates toward a point that leads by 20 arc seconds the visible position of the Sun...i.e. the position that the Sun will appear to be 8.3 minutes from the present is what we gravitate toward". The direction of incident photons from the Sun had nothing to do with anything. 6. In 1960, Synge, much like I did in this thread, stated: "Suppose that a man, standing on the earth, holds in his hand a heavy club. At first the club hangs down toward the ground, but at a certain moment the man raises it quickly over his head. Any theory of gravitation recognizes that the club produces a gravitational field, however minute it may be, and that the action of the man changes that field, not only in his neighborhood, but throughout the whole universe. According to Newtonian theory, the effect is instantaneously felt on the moon, on the sun and in every remote nebula. Since we are not concerned with Newtonian theory, we do not have to discuss the absurdity of this. As relativists, familiar with the idea that no causal effect can travel faster than light, ..., we would guess that the change in the gravitational field of the moving club travels out into space with the speed of light. And we would call this moving disturbance a gravitational wave. Thus, on a very general basis, we must regard the physical existence of gravitational waves, so understood, as self-evident." Never mind that a club, and it's movement, is non-relativistic. Never mind that Einstein and most everyone else has stated that Newtonian mechanics and Eisenstein mechanics are fully equivalent as a special case (which this certainly qualifies as). Does any of this unequivocally prove my point? Maybe, but, honestly, no, probably not. "Proof" is a relative term now. Is it therefore possible instead that "the speed of gravity" is simply a confusing phrase with no universally agreeable meaning? Probably. Things seems to go that way! As, well, perhaps, they ought to do. Might we again have a case of "this question cannot be sensibly posed"? Sigh. Perhaps. But does anyone have any meat on this? I would like to construct a representation (a model) here. Why should I not use instantaneous gravity (especially since EVERYONE else is!) when that's the only way I ever get any physical results!!! Please help!

Hi everybody, sorry for disappearing for so long after instigating this, I've been very busy, but that's no excuse because, I know...we all are. Also, I have to again remark that the comments have been impeccably courteous and non-dismissive and, in a many cases, educational. Yet, some of the responses seem simply to be not correct or else they introduce assumptions that I did not. I think much of the problem rests with me. I made a very general and non-rigorous hypothesis; I didn't proffer a specific experimental setup until later; and, then I kept refining that setup to try and isolate the proposed, hypothetical effect that I want to resolve (including disprove). So, how about I do a little retrospective commentary in response to the comments that I feel are either wrong or beside the point, while acknowledging those which are right (that actually do seem to offer a solution and are on-target). In a subsequent comment I hope to then put forward a final revision of an experimental setup that should hopefully make it possible to resolve all of this in an understandable manner, one way or the other. 1. In comment #4 Dr. Rocket points out that using General Relativity (non-flat space-time...we can consider Special Relativity as the flat space-time special case of GR) it's not so easy to prove that energy (or momentum) is conserved. I think I should not have stated that it "100% is conserved". He is right that it can't be easily proved, and I was not only therefore possibly wrong in my assertion (because this depends primarily upon how you define things, and Timo later agrees that a sensible definition may not actually be possible), but also I was tactically wrong to allow GR to leak into this debate at all. General Relativity needs have little or nothing to do with this problem, as my later points will reinforce. Explicitly: this can be purely a SR problem, and I intended it to be purely a SR problem. That's why I took pains to stipulate that no other masses were around nearby, or else that they at least were around only very distantly, and even so in an ambient and isotropic manner that could provide no net effect in any given direction as distinguishable from any other given direction. In comment #5 I counter-argued that only SR should hopefully apply. 2. In comment #6 Janus states that "You're assuming something that Relativity denies, that there is such a thing as 'absolute motion'. Essentially you are saying that there would be a method of determining whether or not the objects are 'moving" or not. Relativity states that no such test is possible." I respond in the first half of my comment #13 that I don't dispute this at all, yet I don't agree that my proposition requires or suggests the existence of any privileged frame(s). This is where I first start to define a rigorously described experimental setup, which I should have done right at the start and didn't. I attempt to make it very clear that I use the lab frame to establish time-of-launch simultaneity (obviously only in the lab-frame), parallel initial launch vectors (obviously with respect to the lab-frame, including identical speeds as well as parallel headings), and then I offer ongoing lab-frame-based telemetry from a CM-located, zero-or-effectively-infinitesimal-mass probe that uses the readings of instruments to continue to validate these assertions as time goes on within the experiment. I note that the "ambient universe" has nothing to do with anything, as per most if not all thought problems of this sort. Yet, let's be very clear, I don't say he's wrong. I merely state that we can think about this problem without recourse to any privileged frames (i.e. or absolute motions). 3. In comment #7 Dr. Rocket tries to push home his point that "There is no such thing as gravity in flat spacetime. Gravitation is a manifestation of curvature." and I counter in in the latter half of my point #13 that "this is obvious and goes without saying". I explain that obviously the two test masses themselves bend space-time because they have mass. I specify that I only meant that they were the only two actors under consideration and that if they didn't themselves bend local space-time then my thought-problem would be meaningless...because the two test masses would not experience any mutual gravitation. Again, Dr Rocket is completely correct that it is absurd to consider a flat local space-time (I agree), but I think I properly explained that this is beside the point. I explained that what I meant to say, and what I thought I had already said, was that the AMBIENT (or "extra-experimentally induced") curvature was zero...that any and all significant curvature would be owing purely to the two test masses under consideration...that they are the only actors...that we can consider them to be in strict isolation from the rest of the universe and without any interference from it. Virtually every thought problem with a local domain-of-interest has always been posed this way, such as the Twin Paradox, I merely do it too, and I stand by my remarks. But I never argue that Dr. Rocket is wrong. I merely argue that his arguments, while correct, need not be material to the case that I'm trying to examine. Again, at least in part, my shoddy and ambiguous setup of the specifics of the problem is possibly to blame. 4. In comment #12, md65536 gets bold and lays it all out. But, still, while I do agree throughout this thread that most of what he says is correct, I do go on to argue in comment #13 that some of his arguments do not apply--that they are simply beside the point (as opposed to incorrect). On the other hand, he makes the first argument that so far I actually cannot either refute or dismiss. He says, rather brilliantly and incisively, that: "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.". Well, this is very much to the point, entirely relevant, and it basically delineates the crux of everything that I'm asking. No other argument in this thread even comes close to destroying my hypothesis as fundamentally as this one does. If any argument has killed my thesis, then this is the one. Yet, wait, despite it, my hypothesis MIGHT not be completely DOA just yet, as I will explain later. 5. In comment #13, I deal with all of the above points save for one. Comment #13 is worth reading, even if I do miss out on this one single thing, the only important thing so far: md65536's assertion that "these photons will 'move along with P'". His assertion remains, in my mind, the sole argument found anywhere within this thread upon which my proposition will stand or fall. More on this later, but it seems to me that even though md65536 makes some incorrect claims in subsequent posts, that this argument basically kills my argument...unless I can successfully worm my way out from under it, which I will try to do (somewhat desperately!). 6. What I say to Spyman in comment #15 is not quite right. I do make a big mistake here. I stated "[in reference to his comment that:] 'Since both projectiles are not moving [in their mutual frame] they can not observe any lag in space neither for gravity nor EM radiation.' [so, I argue, what he is saying] is tantamount to stating that any radar pings from one object to the other (and back) will occur INSTANTANEOUSLY. You said it, not I. But, is this really true? Remember, you have just stated that there is no EM lag [in which I am wrong]. If so, there is no travel time for signals that are either emitted or reflected (bounced back) between the two. Are you sure of that?". My assertion was at best dubious, and I can't necessarily stand by it. If my proposed, mysterious lag-drag artifact is in error, then I now see that it could still be in error in a way that does not require a lack of EM lag (instantaneous information transfer). This was not clear to me at the time. It now is, basically due to the above-mentioned md65536 comment. On the other hand, I will propose a possible, but weak, counter-argument later, and I would like to see this counter-argument defeated before I admit total defeat. 7. In comment #20 J.C.MacSwell states: "My understanding: In the reference frame you are using the gravitational vector points toward the current position (assuming no acceleration other than that of their convergence).That way the effect would be consistent in all frames. IIRC Swansont pointed this out to me in a thread a few years back." but he never elaborates on this after my request that he should please do so. Never-the-less, he's made a very good point, potentially...if only he would elaborate. In my defense, though, I never have argued a privileged frame. I do expect to resolve this in a (obviously non-inertial) frame-independent way, i.e. in a manner that satisfies all possible non-accelerating frames (no GR!). 8. In comment #22, Spyman makes valid arguments about frame. For instance, in response to my own statement that: "Also, very importantly, I never argued that he would not experience a gravitational force in the direction 'that he sees it'..." he responds "I did not think you did either, sorry if I was unclear and appeared to argue that you did." and goes on to explain that "No, I said no lag in 'space', there will of course be lag in 'time', so there is no instantaneous action." As far as I can tell, he is probably right, and he making the same crucial argument that md65536 does (acknowledged in my point 4. above) that incident photons (==same for force carriers) will still appear to strike not from a past location, but from the present one, basically because those particles will be [in my own paraphrasing here:] "carried along within the frame that launched them". This is just what md65536 had previously said, and it remains the one and only argument that I have to overcome. I'm not sure that I can, but...later, I'll try. 9. In comment #23 losfomot points to another thread that relates to my question. If he's right, and he may well be, then my whole hypothesis merely results from my having naively confused the classical and relativistic viewpoints. In this thread many of the same players make many of the same arguments! Simultaneity, instantaneity, frame-independence... Oh, oh, I guess there really is nothing new under the Sun! Yet, later, I hope to introduce something that is at least a little bit novel! 10. In comment #28 imatfaal independently reinforces md65536's point by saying, brilliantly: "If you think of it as exchange of massless particles it also makes sense. In a non-accelerating frame of reference a beam of photons or gravitons that is emitted perpendicular to motion stays perpendicular to motion. If this was not the case one could determine velocity in absolute terms by shining a light across a box and measuring the deflection - it is only acceleration (or equiv) that would deflect the beam. If the beam of gravitons is emitted and received perpendicular to the direction of motion then the attraction must also be perpendicular." This is the same argument [the following in my words] that: "emitted photons will be dragged along apparently transversely with the apparent transverse motion of the rest-frame of the emitter". Hmmm. 11. In comment #30, md65536 is seems wrong because I don't ever propose that the test masses are moving at non-Newtonian speeds. I don't see how, in this experiment, any lines "appear to bend forward" or how "the other ship appears to be ahead of me" except in time. But, this does not invalidate what he said prior, which seems bang-on. 12. MigL, in comment #31, says things which I do not understand. They seem to support my argument, under the auspices of undermining it. Again, I just don't understand what he is getting at, so I can't really disagree. He does state, however, that "You will not see it at a 'present' location which is farther ahead than the 'previous' location to which it gravitates." which seems to support my position, not contradict it? md65536, imatfaal, and losfomot argue the exact opposite of this statement of MigL's, as far as I can tell. Again, this might boil down to a lack of understanding on my part of his comment. 13. In comment #32 and #34 what md65536 says seems dubious. He may be assuming that the test masses have relativistic velocities in the lab frame. I never said that they must, and I did say that they need not. I did say that the latter case is easier to solve so that this non-relativistic-observer-speed (in the lab frame) case is the one we'd do best to consider. As far as I can see, in no way does anything in the side (or any) window of either test mass (even the reference lines of the lab-frame football field) "bend forward", any more than it does when I take a non-relativistic ride in my car. Hence his statement in both comments that "the lines will appear to be bent forward" seems flawed to me, even and especially from various trivial considerations. When I look out of the window of, say, my non-relativistic-speed motorcar, I can see many distant stars in the night sky, some vastly more distant than others, and yet these are not bent forward in my window, and the most distant of those stars is certainly not proportionately more forward-bent than the closer ones are (since none of them are at all). I can't see how the appearance of the night sky would be visually warped, no matter how hard I press my foot on my non-relativistic gas pedal. The same holds for my thought-problem (?). If I were at rest in the lab frame, or in motion in the test-mass frame, the huge football field in space complete with luminous yard lines and so forth would not visually distort spatially. Sure, the further away parts will be reporting visual information that is arriving from the proportionately more distant past. The further away, spatially, then the more distant in time, naturally. But no visual distortion is required or could even be observed (?). Even if I had stipulated that the test masses were going so fast (relativistic) that I was seeing the ambient star-field increasingly collected toward my front window, that field would not internally distort in a distance-based manner (the far stars would not be displaced one iota more-so than the near ones). There could be no "curvature" in the "perceived lines of the football field" or in the "start and finish lines of the race". I guess this last observation is the very frame-drag argument that might be the undoing of my own argument!, but it does seem to stand in contradiction to md65536's comments #32 and #34. 14. In comment #33, I finally nail down every aspect of the experiment in rigorous terms. It's the first comment in which I actually am pretty rigorous. I lay out everything in the physical experiment, and I lay out the paradox in terms of it. #33 should have been #1. I should have just started out by posing comment #33. 15, In comment #35 insane_alien argues that my proposed paradox is a straw man argument. I feel that this is not fair. If I had made a straw man argument then I would have: 1. made up a false theory of SR that is was superficially similar while subtly unequivalent; 2. demolished my false theory; 3. claimed that since my false theory possessed flaws then so must the real theory. I can't see how I've done anything of the sort. This whole problem is predicated like this: 1. Here is a thought problem; 2. Use the real and unadulterated theory of SR to confirm/dismiss it one way or the other. Whatever I got right or wrong about SR, there was no straw man. The invitation to all of you is to use SR to explain why this paradox is wrong, is simply that: use the real SR to explain why I am wrong. There is no substitute theory, no slight of hand, so maybe insane_alien has been a bit unfair. I posed this thought problem in good faith. 16. In comment #36 md65536 states "In my example, in the launcher's frame, light from M2's launcher seems to be moving somewhat forward to catch up to M1. Meanwhile from M1's frame, that same light is moving toward M1 totally perpendicularly. This is why everything in the launcher frame appears slanted to the moving M1; light that appears to be coming from behind M1 according to one frame, appears to be coming from the side in another frame.". Well, I'm not sure that I really understand any of this, especially as a counter-argument. I do not understand what "light from M2's launcher frame seems to be moving somewhat forward to catch up to M1" means. I don't understand how the visual field could be in any way distorted for any case in which the perceiver is moving slowly with respect to the emitter, whatever the distance between them might be. If it were so, would that not prove my point? md65536 makes arguments based on rulers being bent (length contraction), yet there are no relativistic (in any frame that I propose) velocities, and likewise with time. Unless I'm missing something, these factors simply are not in play. I can't see how any rulers would contract or any times would dilate. I've made this problem one of very low velocities and very long distances (transit times). I'm not conceding that I could not have made a fully Lorentz-invariant argument for higher speeds, but I just don't think we need to go there. I don't have the months or years of desk-time required to go there! My position is that we can resolve this question using extremely low velocities (with respect to both of the frames I refer to, neither of which are privileged or cosmological) and that I have only proposed that the distances be large in order to have resulting effects that are more poignant due to the resulting perceptible lag in time--i.e. so that they would be very easily discernible to the human nervous system of the test observers for the sake of easy argument. So, when md65536 states: "Any observer would see M1 and M2 being pulled by each other in the direction of the ruler, even if that ruler is bent according to some observers. It's weird but it's consistent.", then I must reject any and all bending of rulers (in all proposed frames). Again, his earlier argument was great, devastating really, but this more recent one I just don't understand or give any credit to. 17. In comment #38, Bill Wolfe, as "StrontiDog" makes some perplexing comments like: "light has to bridge the distance between the objects (ships.) Gravity doesn't, it's already in place." and "Basically, any 'drag' caused by the fact that M1 is 'outrunning' the center of gravity of M2, is vectored perfectly by the fact that it is now 'running into' the gravitational influence ALREADY IN PLACE that it would have 'missed' if the two objects hadn't been simultaneously fired on parallel trajectories from some arbitrary 'still' point in space. And vice versa.". I certainly don't understand this. I think that if what Bill is saying is true, then everything we've said about the finite © propagation speed of force-carrying particles must be false. Forgive me if I'm wrong, Bill, but I think that you are saying that the shape of gravity-wells is predetermined in advance by an omniscient actor and is never time-dependent in it's evolution, if it even has an evolution. Hence, no gravity waves. Is this what you meant to say? You point out that Newton's law of gravitation is velocity-independent (no v in it) and, while a part of me hesitates to say that this has nothing to do with anything, maybe you've got something there. But please come back and expand on this. Barring this, I would have to provisionally lump your comment in with the ones that are "beside the point". ------ So, as far as I can tell so far, my whole argument will live or die based upon whether photons that are emitted by a moving emitter are ..."dragged along within the frame of that which emitted them".

Fantastic responses from everyone. So courteous! If you don't like long posts and want to get to the meat, skip down to the label "CM FRAME VERSION:" Ok, @md65536, your first post was by light years the most specific and bold. But I don't think it resolves the [apparent] paradox here, although I agree with all of your initial setup points (!), and they were more specific and committal than any of the other comments, to boot. But, I think that your arguments actually aggravate and reinforce the possible existence of the paradox, as I will explain. Let me clear a few things up first: 1. Frames: every solution has to be valid in all frames, period. J.C.MaxSwell points out that all of us deeply know this. It's about as integral a concept as could exist for us. The "lab frame" (that of the effectively massless launchers) is required for the problem to work. Without two frames, there might not even be a paradox to discuss, but 50% of the reason for the "lab frame" was just to set up initial conditions. I had to show that the two masses were, INITIALLY, launched at the "exact same time" and along the "exact same vector", and that they really did recede away, thus they really did have non-zero velocity (in the lab frame). The other 50% of the reason for including a lab frame is not related to the proper setup of the initial conditions, but rather is to demonstrate that the two masses do not need to have anything like "absolute motion". We could assume that the entire lab frame is translated at some massive, relativistic velocity, or that it is somehow at "cosmological rest". We just don't care at all. We can assume that the test masses never moved, but instead the launchers got shot backward (A SEEMING CLUE!). It doesn't matter at all. In my mind, absolute motion has nothing to do with anything, ever. I'm not in any way proposing, for instance, some stationary aether or omniscient/privileged frame. Instead, I'm trying to show that there may be a paradox here, which is not exactly trivial to resolve. It may be true (if relativity is true to reality) that two massive probes launched in parallel into an otherwise flat space-time do in fact decelerate mysteriously and thereby violate conservation of momentum. Or it may not be...but I don't think that it's a trivial or ill-posed question. But point 1. here is just "let's agree that the solution must hold in all frames". 2. Simultaneity of launch, exactly parallel initial motion: Just as the "lab/launcher frame" is needed to assure initial conditions and assure that there is indeed some relative motion, I also needed to deal with the timing and direction. So I then had to introduce an "effectively massless probe" that is PROVEN (by it's incessant radar pinging of both launchers AND both projectiles too) to be 2A.: equidistant from the launchers and equidistant from the test masses THROUGHOUT THE EXPERIMENT, and 2B.: non-moving with respect to the launchers, but also moving away from the test masses (the latter because pings returned from the test masses are always more delayed and also more red-shifted than the previous ping, although decreasingly so as their trajectories take them ever more out of the orthogonal and into line). I'll now go even further and also add that there is an effectively massless Physicist in residence on the central probe (he has an effectively massless pet cow on board, but the cow is perfectly spherical). As well as noticing visually that the two test masses are zooming away at the identical increasing redshift and also at identical apparent angles, he additionally employs math to assure himself that the two objects started out travelling in parallel. His theoretical knowledge allows him to detect whether or not there is eventually an unexpected mystery-drag. He expects that the projectiles will start to converge (mutual gravitational attraction) but he is also in a position to notice if there is some additional mysterious drag in the direction of his own position. If there is some mysterious drag he will see it as lower than expected redshifts and return times in his radar pings. But point 2. here is just "let's agree that the test masses were shot at the same time and along the exact same vector (i.e. parallel to each other) with respect to the frame of the probe." I define the probe's frame as the "lab frame". 3. The EM or "photon-like" nature of gravity in the standard theory: I assume that the travelling mass problem is the same as the travelling opposite charge problem is the same as the observed incident photon problem. I assume that we feel gravitational pull (or electric attraction) from any object with mass (or opposite charge) and that this force appears to us to be exactly along the "line of sight". This "line of sight" is nothing other than the direction from which incident photons from that object strike us. Period. So, while I don't need to posit discreet gravitons, they do work well for this thought experiment. We could posit light-speed massless force carriers for the opposite charge problem. Of course, in the third case, we have non-controversial information carriers that we know as photons. So point 3. here is just "the propagation-aspect of gravitons (or "charge-ons" or whatever) is identical to the propagation-aspect of photons". So, I've said that I agree with md65536's setup observations, and I'm about to try to use those to the advantage of the paradox position. Also, Janus was the first to point out, others agreed, and I also agree, that the CM frame of the two projectiles is of special interest. At first glance, setting up shop in their CM frame (and calling it the rest frame, which is fine) appears to unravel the whole paradox trivially. So let's do that, and see if it really does trivialize the paradox. CM FRAME VERSION: From the perspective of the CM frame, the two projectiles never moved. They started off at some distance apart in launch tubes, and then the launchers and the probe shot away from them. Initially at rest with respect to each other, the test masses then remained so, except that they slowly gravitated together and all was well and fine, violating nothing, they did not mysteriously violate conservation of momentum by dragging toward the launchers. Simple as pie, right? Well, maybe not. This is not a bad argument at all, but it's not quite right, in my mind. The reasoning behind why I think it is not a solution (but actually a reinforcement of the paradox) I will derive from md65536's accurate visualizations. md65536 points out that each projectile will visually experience having been launched before the other one. So, even though the lab-frame probe proves that they were launched simultaneously both in the lab/probe and projectile-CM frames, each test mass sees itself as having been launched first. But, since we are now abandoning the lab/probe frame, we can and must re-phrase this as follows: Each projectile experienced that it's own launcher shot away from it (centered in the rear window) before it experienced that the other launcher shot away from the other test mass. There was a time lag because the photons (and from 3. above therefore the gravitons) took a while to get to it. So, for all times, t, after launch, either projectile will see, out the side window, that the other "receding launcher" appears to be less distant from the other test mass than it's own launcher is from itself. Sure, it will see the other mass directly to it's side and it's own launcher directly behind itself, 90 degrees separated. All is well and fine, right? What a great frame! Well, maybe not. So, here comes the possibly controversial part, but I think it's not trivial or easily dismissed. Let's call the test masses M1 and M2, and their respective launchers are L1 and L2. Let's say the launch velocities, v (==v1=v2), is very small compared to c (I don't require that, I do think I have a Lorentz-invariant paradox to resolve here, but it sure makes life tons easier and we can always tackle that later if we're feeling suicidally under-worked). Likewise, M1 and M2 are not super-massive black holes or anything, just reasonably modest masses that will not elicit any spectacular accelerations from the other. Let's assume, again just for ease, that the two launchers/masses are initially separated by quite a large distance, such that there is a definite perceptible lag to the naked eye. At some time t1, M1 perceives that L1 (its own launcher, out the rear window) has receded by about, let's say, 10,000km. But, M1's crew notices, by looking out the side window, that M2 appears to be only 1km from it's launcher L2. This means that photons that are striking M1 were emitted sometime previously when M2 was only 1km away from it's launcher and are arriving only now after some transit time. Since this is true of the photons, this must also be true of the gravitons. (3. above, we have all agreed on this many times in this thread). Therefore, the gravitational attraction of M1 toward M2 is an attraction that is aimed toward a point in space that is 1km from L2! Likewise, symmetrically, M2 is being attracted to a point that is only 1km from L1! So, at any subsequent time, t, each test mass MUST be experiencing a force that is directed to a point that is less distant from the opposite launcher, than either mass perceives itself to be from it's own launcher. This means that the net force on M1 and M2 will ALWAYS be mysteriously directed a bit toward the other's launcher, EVEN THOUGH ORTHOGONALLY TO THE SIGHT-LINE OF IT'S OWN LAUNCHER. Accordingly, the drag force that I posited in the lab frame is maybe fully alive and well in the CM frame? Or is it?

@J.C.MacSwell. There no accelerations (other than that of their expected convergence, [and possibly also that of my thought-conjectured "lag-drag"]). So, PLEASE tell me more about how and why? What did this IIRC Swansont say a few years back? What is his counter-argument or explanation? Please note that if my hypothesis is correct then the CM frame is obviously non-inertial.

@imatfaal, well, thank you sir. I am, in fact, Welsh/Irish of decent (my real last name starts with "Mc", lol) as well as an equal amount of German genes also! Let me console you: I do have that learning you speak of and perhaps I even have that mindset you refer to also. I am a professional Physicist associated with a leading department (not that that really matters). Yet, like you, I notice contrary viewpoints (in my case amongst my students)...hence this post. I am delighted to be here in this forum; it's one of the few pseudo-academic sojourns I've ever made into the wonderful collective madness of the Internet. I must confess that, in the coffee room, my associates and I have a little bet going (for money)...about whether the people who visit this site will react dogmatically (insensate animals) or sentiently (doubting investigators or erudite explainers). No value judgement there...just recapping the supposedly fundamental precepts of truly scientific skepticism. Thus far, my colleagues and I are still at odds (cash-wise), because nobody has substantively answered in either way. Your response, however, we feel must be tallied within the margin of the latter category, although there was quite a bit of argument along the lines of whether or not you are entitled to have a valid viewpoint. I'm afraid that there was insufficient specific math in your comment to definitively decide this question. So, you may have cost me some cash! We (I, mostly) were primarily expecting two things: anger and incoherence. So far, I'm pleasantly disappointed.

Thanks! Much appreciated! And I too am awaiting the clear, concise death-blow to my thought problem! As per the massless launchers...let's ignore them. We could assume that the test masses had internal propulsion, such as chemical rockets, in which case we don't even need to stipulate that the launchers recoiled. Let alone recoiled infinitely quickly due their infinitesimal masses! But good observation!

Look, what I am saying is that regardless of how we pose this question: 1. Gravitational force (space-time curvature) 2. Opposite electrical charges force (definitely analogous) 3. Inspection of the direction of incident photons (hopefully completely analogous) We must (?) admit that the incident gravitational(1.)/electromagnetic(2.)/visual(3.) information is "lagged"--that the information that one test particle receives has undergone some lag--a time interval has elapsed between the emission time and reception time. Isn't NOT admitting this notion tantamount to admitting that the information "traveled" at an infinite velocity? If it was finite, then WHY does one particle NOT see (attract to) the "past state", rather than the "present state" (which could only be discernible via faster-than-light information transfer)? I don't see how this is in any way frame-dependent. I don't see how I am proposing some privileged-frame scenario. @Spyman: If this is true, then the "pilot" looks out his back window and sees his launch station directly behind (180 degrees) and out the side window he sees the other object at precisely 90 degrees (or 270 for the other one). If you are willing to agree to this, then we can go forward, but are you sure that you want to agree to that? [Edit follows:] But I would certainly not hesitate to add that you have hit on the crux of the matter--the rest frame--and that this frame, in this thought experiment, would undergo a mysterious deceleration that would occur absent external forces. Also, very importantly, I never argued that he would not experience a gravitational force in the direction "that he sees it"...that is actually integral to my argument...it's the basis upon which I rest my claim that scenarios 1., 2., and 3. above are analogous. Last, what you state: "Since both projectiles are not moving they can not observe any lag in space neither for gravity nor EM radiation." is tantamount to stating that any radar pings from one object to the other (and back) will occur INSTANTANEOUSLY. You said it, not I. But, is this really true? Remember, you have just stated that there is no EM lag. If so, there is no travel time for signals that are either emitted or reflected (bounced back) between the two. Are you sure of that?

I'm gratified by the thoughtful, smart responses. But, if I may, I would like to "narrow down" what I am talking about, by drawing directly upon your well-considered responses. I thought about a more rigorous (long and boring) definition of this thought experiment, but went for conciseness, trying to cut to the heart of the issue. I think I should now be more rigorous in defining it, because my previous decision seems to have been in error. @Janus: who states: I don't follow your reasoning. First, in no way did I intend (nor, I think, have I in any way suggested) any notion whatsoever of "absolute motion". More rigorously: the problem is defined such that there exist two base stations in some far reach of empty, inter-supercluster space (let's say for simplicity that these stations are effectively massless, or "extremely low mass", but ultimately it doesn't matter whether they are...it's merely a slightly more complex version of the exact same problem which resolves in the exact same way). These two base stations sight each other. They each rotate their launchers exactly 90 degrees from the sight-line of the other station. They then each eject a mass into a "flat space-time" (meaning simply that there are no other nearby NET sources of gravity--i.e. we don't care that there exists some huge ambient distribution of masses in the universe because these masses are both remote and, let's say, equally distributed along every direction/range--such that there is no ambient net force on our local system). Obviously, I hope, you can see that I don't mean to propose that these two test masses themselves fail to "bend space-time". So, these two test masses initially set out along exactly parallel paths at some velocity (non-relativistic, for our purposes, but that does not really matter either...the same will likely hold for any velocity up to and including "c"). We know that they are moving away from the base stations (the launchers) because, let's say, there is a radar transceiver on each station, bouncing waves off each projectile and these pings are taking longer to bounce back with each successive ping, which is, say, iterated once per second. We know that they are not initially convergent due to the fact that they were launched at precisely 90 degrees to the sight-line of the other station. Furthermore, let's talk about their simultaneity. We suppose a midpoint probe/observer that is equidistant from the two base stations...in fact it is directly between them, let's say. When the two base stations launched their test masses, that midpoint probe noticed and registered these launch events. It registered the EMR "launch signals" that were released from the launchers of each base station at the time of launch. It also visually noticed that each test mass left "at the same apparent time" and it noticed that as it bounces it's own radar signals off of the two base stations at an interval of once every second, that the reflected signals always return simultaneously (confirming that it was really and truly equidistant between them, especially given how flat space-time is here). Furthermore, it notices, throughout the experiment, that radar pings that are aimed at the two test objects keep arriving simultaneously. Last, it is noticed that the radar pings from the test objects have increasing red shifts as time goes on (and their velocity becomes less orthogonal to the pings as they get more distant, thus ever increasing the red-shift.) So, purely from instrumentation, we know that: the objects are moving away, and that they are travelling (initially) parallel. As a reminder, we expect that they will converge due to mutual gravitational attraction. What we DO NOT expect is that there will be CM-frame drag due to the time-lag between when "gravitons are emitted" and when "gravitons are received". Please, let's not get side-tracked by the word "gravitons". It's an identical problem absent discrete, finite-speed, force-carrying particles. The key here is the "finite speed" of the mechanism of propagation of gravitational information...NOT the specific nature of that information. What we have here is not some spooky "entire universe". It is not subject to the vagaries of entire-universe integrals wherein we wring our hands about what is or is not conserved GLOBALLY. GLOBAL need never enter into this. In fact, it's quite the opposite. It is merely a clearly defined, effectively isolated local system being proposed here. When I say that "space time is flat" in this area, I do not mean that each of the two objects is not attracting the other one. That was, I hoped, abundantly obvious and clear--in fact it's the essential issue around which the whole exercise is defined and built. Obviously, the two objects attract each other. As I stated, the whole point of this exercise obviously rests on this. What I AM saying is that all of the local curvature of space-time is exclusively whatever curvature the two objects themselves impose on it (all other curvature, the ambient curvature, being direction/range invariant and therefor NOT capable of any NET force on our local system...we don't care if we are amid some local minima or maxima because we assume here that it is directionally invariant...a good assumption in deep inter-cluster space...at the very least, in real-universe terms, these ambient effects are too many orders of magnitude too small to matter for our argument). So when ajb states: I would respond that this should go without saying. Obviously the two masses are themselves curving space time. While this is a true no-brainer, I definitely do need to apologize for not making it explicit...I should have done so. Even more explicitly: THE TWO OBJECTS CURVE SPACE TIME (AND ARE THEREFORE GRAVITATIONALLY ATTRACTED TO ONE ANOTHER) BUT NOTHING ELSE DISCERNIBLY DOES SO. Now that I have clarified things, in my mind the following evasions are no longer permissible: 1. That I have implied "absolute motion". I certainly have not. The two test masses move relative to the massless base stations and they slow down due to my conjectured "gravitational-lag drag" relative to them also. "Absolute motion" has nothing to do with anything, least of all this thought experiment. 2. Space-time is not flat here, but it is completely flat OTHER THAN the curvature introduced by the two test masses. This is the whole point of the exercise...to isolate two masses travelling in parallel in order to decide whether gravitons with non-infinite speed would actually act as a generalized drag force on parallel forward motion. (For the sake of the thought experiment, I assert that they would indeed do so and invite you resolve: WHY DON'T THEY?.) 3. Changes in the space-time curvature "caused" by these masses, propagate across space non-instantaneously, for instance: no faster than the speed of light. 4. Therefore the "perceived" curvature (gravitational acceleration) of one test object reflects the "stale" state of the curvature "caused/initiated" by the other mass. In effect, there is this dilemma: either the other mass instantaneously and at a distance "updated" the first object as to it's "real and present" location (and therefore its "real and present" space-time gravity well) IN WHICH CASE THE TWO OBJECTS ARE DRAWN DIRECTLY TOWARD ONE ANOTHER (violating nothing) or else, as I suggest, they must respond instead to "stale data". They must be drawn toward the "previous location" of each other, clearly resulting in rearward drag. IF THIS IS NOT SO, THEN WHAT IS THE MECHANISM WHICH "UPDATES" THE "PERCEIVED" SPACE-TIME CURVATURE CAUSED BY ONE OBJECT IN REAL TIME AT THE LOCATION OF THAT DISTANT OTHER OBJECT? Another equally firm way of putting it is to imagine SCENARIO B: infinitely fast (instantaneous) updating (across any distance) of gravitational force/curvature. Surely even the most jaundiced can imagine, for arguments' sake, a universe in which gravitons have infinite speed. Ok, if you can do that, then take a look at the DIFFERENCE between that scenario and the finite-speed graviton scenario. ARE THEY IDENTICAL? IF NOT, HOW SO? I hope this thought problem is more clearly stated now. I sense that in each response there is a retreat to the "general, whole-universe" case, and also the notion that "the problem is ill-posed". Guys and gals, I've presented a whole universe here. There are two massless launchers (or if that troubles you, let's say that these two objects happened to find themselves, for whatever reason, travelling apace and in parallel for some unknown reason but minus any launchers). There are two masses, which for all intents and purposes, are the only two masses in the universe. Third, we have another frame consisting of a detector midway between the launchers (and therefore equidistant from the test masses at all initial and subsequent times) which confirms via radar that those masses are really receding from the launchers...or, if you like, eliminate the launchers and assume that some probe is merely anywhere that is equidistant between the masses. (Does this imply "absolute motion"? Hell no, there is no such thing as absolute motion...there are no privileged frames...and I do not propose a privileged frame! Gawd, no!) So let's get to the heart of the matter. Take lagged gravity. Take gravity that is instantaneous over any distance. Is there a difference between them in terms of how things would play out? If you can argue that lagged gravity does not cause motion-damping in this case, then how now with instantaneous gravity? Would that, equally mysteriously, accelerate them? Would it leave them alone to proceed undamped? Would the two be the same in every way?

@Dr Rocket. Absolutely, and I invite the precision that will be required to solve this "paradox". This is a "flat space-time" problem. There are no external gravitational effects, no super-massive neighbors, no hyper-relativistic velocities, etc., and we're not talking about whether "the entire universe conserves...this or that..."; merely the local system. Really, it's a very simple, very clear, flat-space local problem. I don't imagine anyone will need to hedge, hum or haw, or try to divert the discussion to larger, less relevant things in order to solve it. It's clearly stated...knock it down! And, if you like, I would welcome a little of that precision. Especially if it's right on the stated target!

@timo: I think you are right to assume that if there were a problem with my reasoning, it would reside in "a)". It would have to be. It certainly does not reside in the later steps, which are airtight. But your b) is not right, in my mind. Regardless of what energy (although I do not raise the energy question) and momentum (I do raise that) the gravitational field can "carry" there is NEVER any reason for a CM frame (or any system) to change its net momentum absent forces that are completely external to that frame and it's constituents. No such external forces are allowed in this thought problem. As for your c) I would state that momentum is in fact big-time conserved in general relativity, 100%. As you state, I think my "argument" does in fact hold equally well for travelling charges, if they are opposite. (If they are alike, then the CM frame should speed up, as a "backward repulsive force" (==forward force) would replace a "backward attractive force" (==gravity-lag drag). Not only do I think that your "travelling charges problem" maps extremely well onto this apparent paradox, but also we could consider it in terms of visible light, which is equivalent and much more intuitively satisfying. With these two masses advancing in parallel to one another, let's say they are ships with windows. They look back at the two base-stations that shot them out, and those stations are exactly in the middle of their rear windows. But when they look at eachother out of their side windows, are they seen to be exactly 90 degrees to the side? I believe: NO. They each see the other's previous position. How lagged that position is, relates to how much time has passed since the photons came off the other object. That places the other object visibly "behind its actual, current position". If you don't think that non-instantaneous gravity exerts drag on two objects moving in parallel, then wouldn't you also have to concede that looking out your side window you would see the other object directly to the side and not lagging behind a little bit? Just like your travelling charge scenario, this one too is analogous, yes?

Hypothesis: If gravity is not instantaneous then any two masses travelling parallel to one another will not only converge, as one would expect, but they will also decelerate against the axis of their mutual forward motion, violating the law of conservation of momentum. (Their CM frame will slow down, even though there are no external forces on the objects in that frame). Hypothetical reason: Both objects will be "experiencing the arrival of" some gravity from the other object, but it will have been "time-lagged" (i.e. delayed in it's arrival by the constraint that gravity is not instantaneously acting at a distance--that it, for instance, propagates a the speed of light). Therefore, each object will be vectored not toward the other object's "present" location, but toward some "previous" location of it (time has passed during the transmission of the force, after all). The force will unexpectedly draw the objects toward their "previous positions" that are "behind their present positions", and thereby retard their forward velocity (in addition, of course, to drawing them toward one-another as we expected). Question: How does the theory of relativity cope with this paradox?