# Gravitational Lag Thought Problem

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So to get this straight in my head (the problem not the answer) - the thought experiment is trying to remove all extraneous entities/forces to demonstrate that (assuming a non-instantaneous speed of gravitational interaction) the apparent centre of mass of object B which object A interprets as the direction of force between them must be slightly to the rear of the physical centre of mass of object B (and vice versa). The only way the apparent and physical centre of mass could be coincident is if the force/perturbation was propagated without delay. The fact that the apparent centre of mass is behind the object means there is a tiny retardant force - and the objects will slow as well as come together. the momentum should stay conserved - but if the objects are slowing it hasn't been

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But the synchronization was not part of the question, they are assumed to be synchronized.

How can it not be part of the question... or at the very least part of the answer? The OP brought the equidistant observer into the discussion him(her?)self in post #13. I don't think the assumption of synchronization is possible when talking about relativity.

During acceleration they are out of sync, but each would also see himself turning off the engines first.

I agree.

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My gut instinct is that the paradox relies on an intuitive but erroneous absolute movement through space - but from the frame of reference of either object the opposing ship is not moving. the fact that other observers are in relative motion to the pair does not impact on the calculations that the pilots would carry out regarding each other and of course not on the physical reality either.

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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.

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@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.

If I remember correctly this had to do with orbits at relativistic speeds (high enough to be significant) so it was not the same thing. I briefly tried to search for it.

It was something about whether gravitation was at light speed and how the lag would effect the result. Maybe Swansont will remember, but I think he said it happened at light speed, but that the effect was toward the current position.

I do know (don't we all) that the results have to be consistent in all frames, both inertial and otherwise, when looking at the same events. Your original post surmised something that would not be, and I think that is the assumption that is incorrect (the gravitational pull directly toward the earlier position in that frame)

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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.

The aberration of light occurs between objects that have a relative velocity with respect to each other, it does not occur between objects that do not have a relative motion, such as in the example.

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I believe your assumption that the two masses gravitate towards their 'previous' locations, and not their 'present' locations is inaccurate or misleading at best.

There is no 'present' location, the only true position is the 'previous' position. It isn't just gravity which acts at the speed of light, all information is constrained to travel at this speed, i.e. where you see it ( after the light has travelled to your eyes ) is where it is. You will not see it at a 'present' location which is farther ahead than the 'previous' location to which it gravitates.

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The aberration of light occurs between objects that have a relative velocity with respect to each other, it does not occur between objects that do not have a relative motion, such as in the example.

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).

Edited by md65536
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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?

Edited by DieDaily
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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?

Yes, you might think of it that way, but remember that in M1's frame everything off to its side in the Launcher frame appears to be slanted forward (along a line that is angled slightly forward of perpendicular). The point on the Launcher frame that is "less distant from M2's launcher" is also offset forward in M1's frame by exactly the same distance, making that point appear perpendicular in M1's frame.

You can prove that it works out "magically perfectly" simply by considering that light moves relative to each and every inertial frame, and imagining the path of a photon relative to M1.

Remember that a photon in M1's inertial frame will behave as if this is a rest frame. If you consider M1's frame to be moving forward relative to the launcher frame, then all the photons in M1's frame must also be considered moving forward or "dragged along with the frame" -- it's less confusing simply to treat it as a rest frame with any other frame moving. Since M1 doesn't "leave the photons behind" as it moves, the lateral delayed images never appear to be from behind.

Just to further clarify that point: All photons can be considered to "be in" every inertial frame. You can consider the launcher frame at rest and imagine photons relative to that frame, and then switch to a different frame and consider the same photons relative to that other frame... the same photons behave as if any inertial frame they are considered from is at rest.

All of the SR "paradoxes" I've seen so far are similar:

1. Relativity seems weird, and you can imagine weird situations.

2. Describe that situation without considering relativistic effects, and you deduce impossible situations.

3. Consider ALL applicable relativistic effects (time dilation, length contraction, lack of simultaneity, etc), which seem like further complications, and everything ends up working out perfectly.

They're all puzzles and this one's a good one.

It's not due to coincidence that relativistic effects happen to make everything work out by just the amount you need. They are essential to the consistency of the scenario.

Edited by md65536
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All of the SR "paradoxes" I've seen so far are similar:

1. Relativity seems weird, and you can imagine weird situations.

2. Describe that situation without considering relativistic effects, and you deduce impossible situations.

3. Consider ALL applicable relativistic effects (time dilation, length contraction, lack of simultaneity, etc), which seem like further complications, and everything ends up working out perfectly.

It's not due to coincidence that relativistic effects happen to make everything work out by just the amount you need. They are essential to the consistency of the scenario.

This is full of truth. If i were to explain calculus but were to leave out negative numbers and subtraction then a lot of it would be absolutely impossible as the framework would not be consistent. the subtraction and negative numbers are necessary for it all to work.

think of relativity like a machine if you remove a few gears(some relativistic effects like contractions and so on) then it will not work properly and will not represent true relativity but rather a broken version of it.

This is a fine example of a strawman fallacy. Its a bit more subtle because it does accurately use a proportion of the theory but it does miss out vital components which means it is not actually relativity they are arguing against but their own modification and thus leading to support of relativity through their own thought experiments.

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Accordingly, the drag force that I posited in the lab frame is maybe fully alive and well in the CM frame?

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.

But then... isn't it true that according to the launcher's frame, gravitons would also "approach M1 from behind and slow it down"?

The answer is... no, the paradox resolves itself exactly the same way.

Just as from M1's frame, everything in the launcher's frame appears slanted, everything in M1's frame appears slanted according to an observer in the launcher's frame (the launcher frame can be considered moving relative to M1's frame equally validly as M1's frame can be considered moving relative to the launcher's frame).

So now... sorry for the complication... consider this...

Imagine another observer in the "middle of the football field", equidistant from M1 and M2, which observes them passing by in the middle of their "race".

Imagine also a ruler connecting M1 and M2.

Since the M1+M2 frame is moving relative to the Middle observer, the ruler will appear bent to her. It would be the same as if the Middle observer were moving toward the midpoint between M1+M2 while M1, M2 were at rest. The middle of the ruler would appear farthest forward in the race according to Middle, while the M1 and M2 edges would slant back toward the launcher positions.

Now if you imagine photons or gravitons emitted from M1 or M2, as seen by Middle, they would appear to always travel along the ruler. They would travel in a straight line according to Middle (or according to anyone), but different parts of the apparently bent ruler would coincide with that straight line at different times, because the ruler is moving.

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.

So M1 and M2 converging would be essentially involve the ruler shortening.

The direction of the ruler represents M1's "side" in any frame. So, weirdly, you might say that Middle sees photons from M2 approaching the moving M1 from behind, but they hit M1 on the side, even though Middle sees that side slanting forward! This is only possible because M1 is moving forward while colliding with the photons.

Any additional details can make it more complicated, but it should always work out perfectly.

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I'm sorry, I haven't read all the replies so I may be repeating what some one else has already said here but

You are assuming your base stations were absolutely at rest to start with and that your rockets are absolutley in motion. Did you consider that your base stations are moving at speed and that the rockets are in effect slowing down?

Let's consider that 'your' space (as you described it) is full of imaginary points. These points are moving in random directions and speeds to each other but each point has constant speed and direction itself (uniform rectilinear translation). Now in your imagination you can jump from point to point and as you do you will consider yourself at rest for every point you visit. You will notice that your base stations will be travelling at a different speed and in a different direction for each point you visit. Eventually you may find a point where your base stations are not moving.

Exactly the same is true for your rockets (lets say they reach constant speed), relative to most points they are moving but to some points they are stationary.

Within a frame of reference rigidly attached to one of the rockets the other rocket will be at rest so there will be no lag. From the point of view of an object moving relative to the rockets there will be a lag such that from your point of view they will be attracted to a point behind where they actually are but you will also see them behind where they actually are and you will in fact see them being attracted exactly towards each others centre.

To put it another way, IF there was gravitational lag, these two objects would be continually moving into a weaker gravitational field and so they would diverge.

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Okay DieDaily,

I've spent most of the day reading and re-reading this entire thread, and I don't think that anyone has addressed these questions quite this way. I don’t see any paradox, CM is not violated, and what you see looking out the side window does not describe the effects of gravity.

Addressing the last first, light has to bridge the distance between the objects (ships.) Gravity doesn't, it's already in place. Light is emitted or reflected, there is a gap between photons. That gap gets wider as they leave the point source. (Which is where the concept of 'gravitons' breaks-down, for me.)

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).

Don’t forget that gravity is omnipresent and omnidirectional unless you just happened to create these two masses out in the intergalactic void, somewhere. Gravitational effect might propagate at the speed of light, but this matter has existed since shortly after the BB, and each atom that makes it up has had plenty of time to distort the curvature of space in all directions as much as any normal atom can.

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.

Hypothetical reason: ( Edited)

. . .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).

And the distance between this hypothetical gap, is also larger. So now the ‘attraction’ is less, by the difference in the SQUARE of the extra distance. And you’re still ‘running into’ gravitational effects that each mass would have ‘missed’ if they weren’t shot away at the new velocities.

I agree that this simple explanation may not hold for relativistic speeds, but then again, it might.

There’s a reason that there’s no ‘V’ for velocity in the (Newtonian) gravitational equation.

It just doesn’t matter.

Bill Wolfe

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• 2 months later...

Afternoon all, I found these posts after googleing 'gravitational lag'

I am by no means anywhere near as knowledgeable as most users who posted here are on this subject - but my mind tends to throw random things at me that just make me wonder...

The reason I ended up here is two fold, firstly I love the stars and thinking about the mind boggling distances and time frames involved. But that got me thinking about where these stars are actually located now, has anyone actually plotted what are galaxy actually looks like right now? Ok obviously we have not plotted every star, rock and cloud, but based on the substantial data we do have? Be interesting to see a virtualisation of our sky if light traveled instantly.

That then got me onto Gravitational Lag, and reading this post was brilliant thanks for all the time you guys must have spent getting this written for guys like me to read. My thoughts went from what is everything doing now - to how do we actually work out where everything is, as surely there must be a lag involved with the gravitational pulls experienced across the wide expanse that is a galaxy? There must be a huge 'wobble' going on, just very slowly and across vast distances.

Then I got thinking about how the universe is still expanding - and accelerating and we are not sure why (dark matter / energy?) Could it be that the lag involved in various forces (gravity, electro etc) has a part in this, that what we are 'seeing' is so out of context with what is 'really' happening we are being fooled into thinking most of the universe is invisible...?

There we go, rant done, sorry if I have hijacked a thread - feel free to move.

Dave

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• 1 month later...

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".

Edited by DieDaily
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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:

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!

Edited by DieDaily
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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".

No, that's a misleading way of putting it.

If "photons get dragged along with a frame" makes sense at all, then it's not one particular frame it happens to, but all inertial frames. Since this has already caused more confusion than good, I think this explanation should be retracted. What I meant by it was something like how the moon seems to "follow you" when you move. AND it seems to follow each individual who moves. BUT from your perspective, it doesn't seem to follow anyone else who moves independently of you. YET if you imagine someone else's perspective, you should imagine the moon seeming to follow them! If that's too confusing, then certainly my explanation will not be useful.

A similar (but not equivalent) thing happens with light. The difference between the moon and light is that with the moon it's only an illusion due to its great distance; move far enough (say a million killometers) in a straight line and the moon will not stay in the same place in the sky. With light, no matter how far or fast you move, the light will always be moving (not stationary as with the moon example) at the same speed relative to you. With light it's not just an illusion.

A simpler way of reasoning about this is that, instead of imagining light "being dragged along" with moving inertial frames but only from the perspective of observers in such a frame, it is simpler to just realize that any inertial frame is at rest according to observers in that frame. The above explanation tries to explain the same idea, but in a convoluted manner.

This is the root cause of most SR paradoxes: Light signals moves at c in your rest frame, and the same signals move at c according to anyone else's rest frame, even though these frames are not at rest relative to each other.

This is the resolution of most SR paradoxes: Time dilation and length contraction ensure that all of this happens consistently. It's only a matter of how complicated the details are for a given example.

Check out some videos such as this:

They should help visualize the kinds of relativistic effects (namely aberration) that are required to fully explain your paradox.

So, again, your paradox might be restated as such: Two objects moving together naively seem to have gravity (and light) from the other "come from behind" (thus slowing the objects) due to the delay in the travel time of gravitons and photons. Yet, in the rest frame of the moving objects, there is no movement at all, and those signals should seem to come from the side, so there must be no forward/backward acceleration. An external observer who sees the the objects moving, will see them subject to aberration, and will not observe signals between the two "coming from behind".

However, complicated details come up when you try to precisely describe the two objects' relative motion while accelerating from one inertial frame into a new one. Aberration (a result of length contraction and time dilation) resolves the paradox, ensuring that the photons we may have thought would seem to "come from behind" according to each object... will not. If we work out the details, we'll find that the 2 synchronized objects will always see each other "directly to the side" while in an inertial frame, consistent with the simpler example of treating them at rest relative to each other (while in an inertial frame).

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!

If you use instantaneous gravity you should use instantaneous transmission of light. I would not recommend this route.

If any information is transmitted faster than light, you'll derive all sorts of contradictions that involve violations of causality.

That is to say, the gravitational pull of an object will appear to come from the same place that light from the object appears to come. You will not be "pulled toward an object's current position" while "seeing the object in its past position".

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.

Relativistic effects also happen at Newtonian speeds.

The original paradox involves two objects slowing each other down due to delayed gravitational influence. If they are moving at Newtonian speeds, any angle (off of perpendicular) of incoming gravitons, according to any observer, will be negligible. The angle of aberration (for the same observer) will be correspondingly negligible. You must neglect both, or neither, or you'll derive "small inconsistencies" where there are none.

Edited by md65536
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• 3 weeks later...

That is to say, the gravitational pull of an object will appear to come from the same place that light from the object appears to come. You will not be "pulled toward an object's current position" while "seeing the object in its past position".

This is incorrect, according to Prof. Steve Carlip, here:

http://arxiv.org/abs/gr-qc/9909087

Edited by SpeedFreek
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The paper I posted above explains exactly how General Relativity deals with the aberration described in the OP.

For objects in relative uniform motion, or objects undergoing uniform acceleration, GR plays a neat trick on us, where velocity dependent interactions conspire to almost exactly cancel out any propagation delay for gravity.

A lot of people find this surprising but in GR gravity points at the instantaneous position of the source, rather than the retarded, light-delayed position, even though gravity propagates at c.

The surprising upshot of this is that, on Earth, the gravity of the Sun of course comes from the place the Sun was 8 minutes ago, but when it reaches Earth it combines with those velocity dependent factors such that the space-time curvature points the Earth towards the instantaneous position of the Sun, rather than the retarded position. The Earth therefore orbits the place the Sun is "now", not where it was 8 minutes ago.

The Earth is "falling" towards the instantaneous position of the Sun, rather than the retarded position where we see the Sun to be. This is evidenced by measurements of the peak acceleration of the Earth during a lunar eclipse - peak acceleration occurs after totality - not when we see the Sun and Moon to be lined up, but when the Moon is lined up with the "instantaneous" position of the Sun, which GR neatly extrapolates.

This extrapolation is exact except when there is a change in acceleration, in which case the extrapolation "misses" and leads to a loss of energy/momentum in the form of gravitational radiation. Due to the Earth's weakly changing acceleration, there is a gradual loss of energy in its orbit, but it is so small that it equates to only 300W per year (the energy of 3 light-bulbs!), and will have no major effect on our orbit during the lifetime of the Solar system.

So, when relative motion is involved, it is definitely wrong to say we are gravitationally attracted towards the place we see the source to be (the light-delayed, retarded position).

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A lot of people find this surprising but in GR gravity points at the instantaneous position of the source, rather than the retarded, light-delayed position, even though gravity propagates at c.

This certainly adds some complicated details and proves to me yet again that my understanding of relativity is inadequate. I'm not sure now what of my previous posts can be salvaged.

Note that this can only be true when the instantaneous position of the gravitational mass (sun) is known from the delayed light. Otherwise it is a violation of causality. This is just another way of saying:

This extrapolation is exact except when there is a change in acceleration, in which case the extrapolation "misses" and leads to a loss of energy/momentum in the form of gravitational radiation.

In light of these details, I'd like to change my answer:

- Ignore anything I've said.

- Assume no acceleration (at least until the thought experiment makes complete sense with constant velocity)

- Consider the frame of reference where the 2 objects are relatively at rest, which will be the simplest perspective.

- All other frames of reference will observe something that is consistent with that.

Clearly, in the rest frame the only gravitational attraction of the objects would be directly towards each other.

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In light of these details, I'd like to change my answer:

- Ignore anything I've said.

- Assume no acceleration (at least until the thought experiment makes complete sense with constant velocity)

- Consider the frame of reference where the 2 objects are relatively at rest, which will be the simplest perspective.

- All other frames of reference will observe something that is consistent with that.

Clearly, in the rest frame the only gravitational attraction of the objects would be directly towards each other.

Well this works with (classical) acceleration for pairs of objects too, on one condition.

The centre of mass is the centre of force.

If you have two equal massed opposite charges 'orbiting' each other you'll find that the magnetic and electric fields work out just right so that you can use the coulomb guage, ignore the magnetic force, and still get the right result.

Edited by Schrödinger's hat
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The following explanation comes courtesy of another forum from a user named publius, who knows GR well and has given me permission to repost his words. I do this to provide some sort of formalism, which I am not able to provide myself:

Let me elaborate on why EM behavior is so relevant. You'll also note Carlip started out with EM analogy, too, before he delved into the much more complex GR calculations.

First of all, EM is simpler. Second, we're all familiar with it, and no one disputes that EM influences propagate at 'c'. I mean, that's what the speed of light is all about. Third, we know that EM forces involve more than just a basic inverse square Coulomb interaction. There's the magnetic side, and what I like to call the "Maxwellian dance", which is the coupling between the two through time variation (or just go to the 4-vector form where it's all one tensor field, not two vector fields).

Thus, it is no great surprise that when a source charge is in motion, there will components to the field beyond the simple inverse square Coulomb part, and these components are velocity dependent. Indeed, calculating the fields directly is a bit of chore, so we use the simple potentials, and we learn that E = -del(phi) - dA/dt and B = curl A.

When a point charge is moving, there is an A, and it is the dA/dt part that is responsible for the "correction" from your basic inverse square Coulomb part, which comes from the gradient of the scalar potential part.

That's what makes the force point ahead of the retarded, light image position of the source.

Now, that falls right out of the equations, and should surprise no one.

Now, enter SR. From the spirit of relativity, we know that we should be able to switch to the frame of an inertially moving source charge and get the same invariant results as in a frame where the source is moving. Going to that frame, the source isn't moving, and the field is static, and pure inverse square Coulomb. We know that the test particle force has to point toward the static source.

Now, whether the force "misses" or not is an invariant. It cannot point at the source in one frame and not point at it in another!

Thus, we deduce that if EM is going to be compatible with SR, then it must somehow "extrapolate" for inertial motion in frames where a source is moving. It has to.

So, relatively simple EM does this "extrapolation" and in a way that should surprise no one.

Thus, the objection to "extrapolation" should be dispensed with. Then we move on to gravity. Because of the additional complexity of gravity, it extrapolates on higher order than EM. It's the same basic behavior at work, just doing it a little better than EM.

As we learn from EM, because of Lorentz invariance (compatibility with SR), we see that there must be these velocity dependent components of the forces (in the 4-vector form, you see that is nothing but the components of a tensor changing with coordinate transforms -- it's the same tensor, it just has different components in different frames).

So, if gravity is to be compatible with relativity, then by George, it's going to have to have velocity dependent components as well, as further, it's going to "extrapolate" to at least velocity as EM must.

But gravity also must obey the Equivalence Principle, which makes it more complex, and also requires it to "extrapolate" to second order, to acceleration, as well as velocity.

-------------------

The best way to think of it is the GR gravitational field contains information of the position, velocity, *and acceleration* of the sources and the first order of radiation is quadrapole. By contrast, the EM field contains only velocity and position information and the first order is dipole.

Let r be the light retarded position of the source, and v its velocity, and a its acceleration. That is, that's the position of vector, in your coordinates, of the light delayed image of the source you would see. It's rather straightfoward to show that the E field of a moving source points in the direction:

r + v(r/c)

(r/c) is the light travel mean time. If the source is moving at constant velocity, that points exactly at the instantanous position of the source. Hence EM can be said to "extrapolate" the velocity of the source. One can, as shown by Carlip, get that very quickly by the elegant and succinct, but more advanced, 4-vector formulation of EM, but you can get it from the more familiar 3-vector form Maxwell as well, it just takes more groking.

Now, as Carlip shows, GR gravity (in the weak field, low velocity limit) points along:

r + v(r/c) + 1/2 a (r/c)^2

IOW, it further extrapolates for the acceleration of the source in addition to velocity, something not in EM. And the magnitude of that acceleration in that limit is just GM/R^2, where R is that "extrapolated" position magnitude. And that's just instantaneous Newton!

So, as long as the source doesn't change acceleration, gravity points at the instantaneous position of the source, following Newton exactly (in the limit).

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