
Posts
2133 
Joined

Last visited

Days Won
7
Content Type
Profiles
Forums
Events
Posts posted by md65536


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 SIGHTLINE 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.
1 
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).
0 
Exactly. For massive particles we can interpret the parameter t as the proper time. As you see passing from t > t does not affect the geodesic equation.
For massless particles we cannot interpret the affine parameter as a proper time. We still have the Tsymmetry formally but it does not have such a clear interpretation as for massive particles.
So a geodesic is the same path, passing from t > t?
I think that implies that spacetime curvature is the same for t as for t? Or at least, there is no inversion of the curvature that would make timereversed gravity into a repulsive force.
If you send a signal to the moon and timereverse the process before it gets there, it will reverse course and return to you.
If you drop a neutron off a building and timereverse the process before it lands, it will continue to fall (I speculate).
Admittedly, this depends on some of my own interpretation, which is not accepted science. As you say, there is no clear interpretation.
Time doesn't exist, you certainly can't run it backwards
Ignoring whether my examples describe practical or possible realities, figuring out the theoretical implications can be useful in figuring out what is possible in the universe and hopefully ultimately how it all works.
Largescale Tsymmetrical time reversal is probably impossible (this very thread speculates one of several reasons why), and certainly impossible in any universal way that requires the existence of a fictional concept of "universal time", but it's useful in very small scale interactions such as those described by Feynman diagrams.
0 
Spoken like a true dogmatist. Not all cosmology is based on GR. And "curved spacetime" as a central concept is still a hot debate among ontologists (whom of course you despise, to your discredit.) It would broaden your horizons to study those papers on spacetime compiled by Deiks and all those references provided by Ross.
owl, you are a fool.
You are a pigeon, crapping on the chessboard that is this forum.
Since you don't understand analogy, I don't expect you to understand metaphor, so I apologize for my inaccurate insult.
Philosophy of science is fine and it has its place, but you are using it to discredit GR.
This is a Relativity forum, not a philosophy forum; hence the pigeon analogy and now metaphor.
If you can prove that GR is wrong using philosophy in a way that is generally accepted, then those philosophical arguments are relevant here.
But around here, GR is generally accepted science that has not been refuted in any accepted way, regardless of any "hot debate".
You have a LONG WAY to go to disprove GR using philosophical arguments. Until it is generally accepted, THOSE ARGUMENTS DO NOT BELONG HERE.
If you wish to try to refute GR using arguments that are not already accepted science, do it in the speculations forum.
You have two choices: 1). Learn and understand the concepts on which the theory is built. 2) Continue to babble incoherently making inane, irrelevant and nonsensical comments..
There's another choice: 3) Stop posting.
I'm a fool myself. But I'm trying, Ringo. I'm trying real hard to number 3.
1 
I read in Carl Sagan's Cosmos that traveling near the speed of light would warp things so that things that were behind you would squish into your forward cone of vision, but I never really made sense of that until now.
I 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.
0 
What if instead of thinking of the early universe of the big bang as expanding spacetime in some abstract sense, you just thought of it as a small, dense ball of matter? Then, think of the expansion of that ball as a process of stretching the contents out despite a limited amount of space between them. So instead of the contents "expanding into" space, they are actually stretching space between them like trying to expand a vacuum within the atmosphere. Another way to describe this would be to say that gravity originated as perfectly contracted spacetime and henceforth began expanding to allow more distance between particles/objects, yes some areas remain(ed) less expanded (e.g. galaxies, stars, planets, interstellar clouds, etc.) In this way, would it be necessary to view gravity as a force, or could it be viewed as simply varying degrees of expansion of spacetime? Also, could it be that the expansion was caused not by a "bang," i.e. pushing force from the center, but rather a "pull" as its surroundings were drawn outward for some reason?
If the universe were thought of as an expanding (inflating) ball... (it might not be valid to do this)...
Yes, I think you could define a changing measure of distance, such as "one unit = radius of the universe". Then using that measurement, the universe remains a ball with radius of one unit, and everything inside it shrinks and contracts into "patches" of greater density.
You might be able to reconcile gravitational acceleration with the equivalence principle, in that a frame under the influence of gravity is equivalent to an accelerating frame.
Perhaps something like... the strength of a gravitational field is related to the rate at which it contracts.
Everything shrinks relative to the size of the universe, so it always seems like there is more room in the universe... it appears to be expanding relative to everything.
Upon rereading your post, I don't think this is what you're talking about.
When you say "expand a vacuum within the atmosphere", do you imagine pushing everything else out of the way, so that the atmosphere (analogous to the universe) remains the same size, and everything outside of the vacuum gets pushed together (analogous to gravity)?
Or do you imagine that the atmosphere is being pulled larger, and everything in stays where it is, so that the distance between things remains the same but those distances diminish relative to the increasing size of the atmosphere? If you mean the latter, then no I don't think that the expansion of the universe explains the effect of gravity.
One interesting sideeffect of imagining the size of the universe being fixed and the size of everything else changing relative to that is this: If the universe started out as a singularity, couldn't it be considered to still be a singularity?
0 
I must be blind. Where is it T symmetric?
t only shows up squared, so the equation has the same value whether it is positive or negative. ???
It makes sense that a particle traveling along a geodesic would travel in the opposite direction along the same geodesic if time were reversed.
0 
I am not sure about Tsymmetry in general relativity as a whole as we do not usually have a good notion of space and time, rather just spacetime.
However, one can think about Tsymmetry in the context of the path of test particles.
The geodesic equation is
[math]\frac{d^{2}x^{\lambda}}{dt^{2}} + \Gamma^{\lambda}_{\mu \nu} \frac{dx^{\nu}}{dt} \frac{dx^{\mu}}{dt}[/math].
Clearly the above is Tsymmetric.
Gravitationally accelerated test particles do not move along a single geodesic.
If a black hole were time reversed and "became a white hole", yet we at an external perspective were not time reversed, the white hole would continue to gravitationally attract us.
What I'm not sure of is whether the particles inside that white hole would follow full reverse paths and appear to be gravitationally repelled from the white hole, or if they would only follow reverse geodesics, and remain gravitationally attracted to the white hole. Only the latter makes sense, because (I assume) the spacetime curvature of the timereversed black hole would remain the same as before, and that curvature is what dictates the gravitational acceleration.
But then again, like you said we don't have a good notion of space and time. I'm mistakenly thinking of curvature only as spatial curvature, so time reversal might imply changes to spacetime curvature that I can't clearly imagine.
0 
This is the same as the "light clock" example. Start off by bouncing a light back and forth between the objects. As seen from either object, the light passes directly between the two. Now accelerate the objects equally. repeat the experiment. The light will still bounce back and forth between the objects, and neither will see the light as coming "from behind" the other object. You can't tell any difference between before and after acceleration.
But how do you accelerate the objects at the same time according to all observers? You can't.
If I have a viewpoint from which the 2 objects are symmetrical, and I synchronize the start of their acceleration, then they'll always be symmetrical to me.
But each of the objects will see that they appear to have had a head start vs the other.
Assuming gravity waves behave exactly like light, an object's gravitational pull on me will always appear to come from exactly where the object appears to be.
So let's restate the problem with a different example:
Imagine 2 objects P and Q at the start of a race.
Imagine a very long start line, many light seconds long, with the objects separated by 1 lightsecond.
A light signal equidistant to P and Q starts the race. Suppose P and Q instantly accelerate to some significantly fast speed (so we consider only 2 inertial frames: at rest relative to the start line, and moving relative to it).
From P's perspective, it started the race 1 second ahead of Q. P won't see Q start the race for 1 second, and vice versa.
The resolution to the paradox is this: If we imagine any photons moving through space, we can imagine them moving along with whatever inertial frame we choose to consider, correct? So, imagine photons emitted from Q a fraction of a nanosecond after Q starts to move (assume it is essentially at the starting line) and traveling along the start line, perpendicular to the velocity of P and Q. From P's moving inertial frame, these photons will "move along with P" and remain incoming from a perpendicular direction.
This must mean that the start line appears to curve "forward" according to P. When it switches frames, it sees the start line stretching out to the side but now stretching slightly forward of perpendicular. It appears as if Q is "already ahead" of it. After 1 second, it appears to catch up to Q laterally at the same time that Q appears to start moving. They would remain "side by side" except for that first second (and if they stopped at the end line, Q would appear to be behind P for only that last second).
I read in Carl Sagan's Cosmos that traveling near the speed of light would warp things so that things that were behind you would squish into your forward cone of vision, but I never really made sense of that until now.
0 
I came across a definition of a white hole as a "timereversed black hole."
I assume that a white hole would only let light out.
However, this doesn't make sense to me. If you have a curved geodesic contained within a black hole event horizon, wouldn't light travel along the same path whether it was going forward in time or backward in time?
It seems to me that spacetime curvature would determine whether light etc would be confined to a space, or unable to enter that space.
A timereversed black hole would be gravitationally identical to a black hole.
Perhaps its spin would be reversed or something, but essentially its influence on the universe would be the same???
A white hole then would be a "spacetime inversion of a black hole", where the curvature is inverted or negated or something.
Extrapolating, it seems clear that gravitational attraction is independent of the direction of the arrow of time (it's probably still dependent on the rate of time or the magnitude of the arrow, if that makes sense). Gravitation is a oneway process, regardless of whether or not time is. ???
Or would a timereversal of a black hole allow light to escape along the same paths that let it in?
0 
It sounds like you're trying to imply some form of absolute perception. My point is that particles are only ultimately relative to each other insofar as they interact directly. Beyond direct interactions, you're only dealing with abstract spatial relations, which can't be more than a composite of overlaid orientations derived from various observations.
No, I agree everything's relative. I just think the additional dimensions are important. Since you reduced location to distance, I assumed you were talking about spherical coordinates while considering only the distance dimension.
Your example of orbiting the sun is not the best example, because the sun is essentially the same in any orientation. But if instead you were orbiting Earth, and say you wanted to land, then yes your relative distance is important, but if it mattered where on Earth you landed, and whether you landed on your head or on your butt, then relative orientation also matters.
But this is all beside the point because as soon as you add a third point that's not collinear, an angle dimension becomes relevant, and if you add a fourth point that's not coplanar to the other 3, a 3rd dimension becomes relevant. With 4 noncoplanar points, I don't think your example of choosing an arbitrary axis and origin where you can ignore a dimension, will work.
Certainly, the distinction between whether locations are considered relative or absolute is relevant to the thread, and I hadn't considered it in the original post. But I think that any theory that attempts to describe reality would have to consider locations to be relative.
0 
This is the way I begin thinking about location and energy without imagining a fixed coordinate system that defines things relative to something external to them: imagine you have two points that can't rotate. These two points can move in any way relative to each other but the one can only interpret its location relative to the other in terms of distance increasing or decreasing. It can experience changes in force and momentum as it changes directions of motion relative to other imaginary points, but its location can only be measured in relation to the only other existing point in its universe, which it only becomes more or less distant from. Does that make any sense?
You're describing relative location in terms of only distance, implying that one dimension is enough to define the relative location between 2 points exclusively.
The other spatial dimensions (representing orientation) are irrelevant  do you mean in general, or as it pertains to this thread?
I don't think I agree. I don't think the most elementary particles are onedimensional, and the relative orientation of 2 particles might be important especially when it comes to light, or velocities.
As it pertains to the conjecture, I'd say that the size and the shape of a particle's "spatial range" is what matters (the range perhaps defined by a probability wave that specifies the possible locations of the particle and the probability of it being in any particular location. A "larger wave" would mean less locational precision, which I'm suggesting corresponds to lower energy). Unless the possible range is isotropic (ie. it's shape would need to have spherical symmetry?), then the orientation would be important.
I am not sure what the op is saying but if you look at the Bohr model
then when you add energy to an orbiting electron it goes to a higher level and slows down
Its potential energy increases but its kinetic energy decreases.
as a result the particles wavelength is bigger and the particle is 'spread out' over a larger area.
i.e. less localized.
Yes... this seems to be in direct contradiction to my conjecture.
It would seem that the location of the particle (the electron?) is less precisely defined in a higher energy state.
Unless there's some other property that shrinks and allows greater precision, the conjecture does not account for electrons and must be wrong.
Electrons ruin all my ideas! Are you sure we have to consider their existence at all???
0 
No, these are not consistent with the definitions of the terms in standard physics. Potential energy depends on position, not velocity, and a force perpendicular to the motion will change velocity but does no work, so there is no transfer of energy.
Potential energy depending on location fits the conjecture better than velocity does.
Is it a general case? Does any change in relative position involve some change in potential energy?
I can't actually imagine how kinetic and/or potential energy relates to the idea. I shouldn't have mentioned it.
0 
France is a pretty big place. Can you be a bit more specific about where, exactly, in France this device is located?
This probably refers to the one built by Aldo Costa:
http://en.wikipedia.org/wiki/Aldo_Costa_(inventor)
"However, as with other devices of this kind, the energy created by the unbalanced weights falling is merely equal to what's required to lift them to become unbalanced in the first place."
Videos of it here:
http://www.blueman.name/Des_Videos_Remarquables.php?NumVideo=2274#NAVIGATION
Some explanation here:
http://www.besslerwheel.com/wwwboard/messages/241.html
"his wheel stalls"
0 
Energy is a frame dependant quantity, which is worse than just depending on the location (points on spacetime). Importantly, energy cannot be locally described by a tensor.
Meaning that energy takes different forms in different frames?
Is the total energy of a system (including for example the entire universe) invariant, and just changes form depending on frame of reference?
Perhaps I'm using the wrong word "location", if it means a precise point in space. Instead I want to describe position with a variable degree of uncertainty or precision. So size too, I guess... a quantum of energy has a range of uncertain possible locations.
How is 'location' in any sense absolute, or maybe I should say less than relative? To me, objects always move relative to the objects they exchange energy with.
I agree it's completely relative. So it's not location that's important, such as specified by some spatial coordinates relative to any origin. The values of those coordinates (or its distance from origin) don't affect something's energy or mass.
It would be precision of location that would be related to energy.
The conjecture might be restated: The energy of something is proportional* to the precision of its location.
(Now the specific location or whether it's relative to something else, doesn't matter.)
* I want to say "equivalent" but I don't know how to account for different forms of energy, or "somethings" that are made up of multiple quantities of energy and can thus have greater overall energy but may not have a proportional degree of locational uncertainty.
0 
Here are some aspects of relationships between location and energy:
1. To change an object's location requires energy. If an object has velocity relative to something else (such that relative location changes), it has potential energy. To change velocity requires a transfer of energy.
2. In a BoseEinstein condensate, which has very little thermal energy, the location of particles becomes undefined. Particles act as if they are simultaneously everywhere in the matter.
3. If an object falls into a black hole, light from it is redshifted indefinitely. Is it reasonable to say that one wavelength of the light is simultaneously traveling to our eyes at c, and stuck at the event horizon, so the infinite redshifting is equivalent to stretching that one wavelength of light across an everexpanding distance? As the light energy is lost to the black hole, its location becomes undefined... instead of being in a specific point, it gets stretched indefinitely.
4. According to the conjectured holographic principle, a location in our 3d universe maps to all locations on a 2d topological manifold and vice versa. In some vague sense, any quantum of energy can exist everywhere, but some property gives it locational definition in our 3d universe.
Can these ideas be combined into one relationship between location and energy?
The energy of something would be related to the degree to which that something is "focused" or welldefined locationally. Greater energy means sharper focus into a specific location. If you want to determine the precise location of something either you would need to use a lot of energy to do so, or that something would need to have a lot of energy. The more precision you need, the more energy is needed.
Mass, which is a form of energy, would be related to the specificness of location. More energy means more specific location. Inertia could be expressed in terms of specific location (including moving locations); the difficulty in overcoming inertia is related to the difficulty of modifying locational specification. This would probably imply that the location of a moving object is better defined (ie can more precisely be determined) than a similar stationary object???  is there any accepted theory that speaks to this?
One last conjecture in case there's nothing zany enough in the above: If location is emergent (which I believe it is, along with all of geometry), would this imply that energy is also emergent? I'd previously thought that energy was invariant and a fundamental aspect of the universe... I still think it must be, but I'm not sure.
(Energy is conserved  except for vacuum energy???  which means it is invariant, but it can be converted to different forms which are different for different observers, so the form that energy takes is not invariant. In conclusion I don't quite know what this means.)
Or does this conjecture make sense?: The form of a quantity of energy is equivalent to its location. (I don't think I said that right... anyone have ideas?)
0 
because if it's right then i dont understand how an object can be moving .866 c and still move at half lightspeed through time.
If for example it's a rocket moving at .866 c relative to "our inertial reference frame", its velocity is .866 c according to us.
No velocity is halved in this example. The Lorentz factor is 2.0, which means that according to us, a clock on the rocket ticks at a half rate.
However, lengths in the rocket's frame are also contracted by the same factor of 2.0, so both distance and time in the rocket's frame are scaled by the same amount, and the rocket's velocity = d/t remains unchanged at 0.866c despite time dilation and length contraction.
Lengths in the rocket's frame (including distance to it) are halved, and its time passes half as quickly, according to us.
what is the trejectory like then?
if a spaceship in an inertial frame were to shoot out a beam/pulse of light in front and backward and was moving at a steady speed, would the two beams be moving at the same speed away from the ship?
If we're in an inertial frame, its trajectory follows the curvature of space, which is a straight line in the absence of a gravitational field (essentially straight in this example. Einstein believed we'd never be able to detect spacetime curvature in our local weak gravity fields so let's say it's negligible).
Yes, the speed of light of the beams would be c in both directions, relative to us.
(They'd also both be c according to the rocket, or any other inertial frame.)
0 
It would not diminish GR to just refer to the curved path of objects, however, without the superfluous insistence on " curved spacetime" with ruts or grooves, or whatever which "guide" objects' trajectories.
And with that, I formally abandon this hopeless conversation. Thank you for your time.
0 
GR assumes that space is an entity
Citation? I don't think that's true.
You've stated in this thread that you don't consider space to be an entity. Would you then conclude that GR is based on false assumptions? Would you also say that because of this, GR can be safely ignored, and that an understanding of GR is irrelevant to this discussion?
Also, before you declare victory for the established fact of spacetime, please do the required* research into what the International Society for the Advanced Study of Spacetime (ISASS) has been debating for most of the last decade.
*(If you care about what spacetime is)
Any search will get you there... if your mind were not already 'made up.'
On the website that you are referencing, they have the question "Is Space Infinite?" on their Open Questions page: http://www.spacetime...nquestions.html
Your source does not seem to agree that the question has been answered.
Others in this thread accept that it remains an open question. So how is it that their minds are made up while yours is not?
It is amusing to watch you attempt to address the ontology of spacetime when you have no idea what spacetime is and harbor so many gross misconceptions regarding general relativity.
I also find it amusing, but at the same time it is really bothersome to see the same misinformation repeatedly posted. As someone who doesn't have a firm grasp of relativity, I find it harmful to my attempts to understand relativity, and I think it does not belong in a relativity forum.
I also think it's sad that what is claimed to be an expertise in the ontology of spacetime, seems to me to be based not only on a lack of understanding of relativity, but also some confusion about the very meaning of ontology (due to the apparent assumptions that for spacetime to have properties implies that it is an entity). I am not an expert on the philosophy of science, but to me this seems naive.
Btw, presentism is another study which inquires beyond local frames of reference and "time environments" and the usual "who sees what and when" of relativity. It can be ignored, but it will not go away. The most simple and obvious illustration of presentism is that now is now for both earth and sun even though it obviously takes over eight minutes for sunlight to travel to earth.
Then, this "now" can be extended to "now everywhere," that the universal present is not limited by lightspeed.
Now this is an interesting topic relevant to my interests. But I think discussion of it is off topic and probably belongs in the Speculations forum anyway.
0 
c is a constant in an inertial frame. If you are accelerating you are not in an inertial frame, and you will not measure the speed of light to be c. Acceleration due to rotation gives rise to the Sagnac effect.
In the context of the original post, is the Sagnac effect equivalent to saying that...
1. Rotation of the reference frame will cause the paths of light (aimed in different directions) to curve in different ways.
2. There is no possible common path (geodesic) that the light can travel in opposite directions, from the rotating reference point.
3. Light in opposite directions travels a different distance in each direction in a given time, due to the differently curved paths.
?
For the purpose of the thought experiment, it might suffice to imagine an inertial frame that approximates the Earth's motion through a portion of its orbit.
0 
if not then what speed would it take for time to be halved?
About .866 c
No, since we are not in an inertial frame. We orbit the sun, so we are in an accelerating frame. It's not a big effect, though.
??? The speed of light is invariably c, for all observers, regardless of relative motion.
There's nothing you can do to change that.
Acceleration won't change the speed of light. What effect are you speaking of?
0 
DrRocket is very fluent in math and the "higher dimensional" nonEuclidean geometries, for instance, while my forte' is in the philosophy of science, specifically the ontology of such "dimensions." The two realms of expertise are obviously not in communication in this thread, and DrR seems to believe that ontology is irrelevant to this discussion. (Correct me if I'm wrong.)
But you are giving a philosophical answer to a question that pertains to General Relativity, in a Sciences > Physics > Relativity forum, not a philosophy forum.
You could very well be right, but you can't prove it in terms of relativity, science, or math. The reasoning in what you considered the best answer is this: "I don't see how the universe couldn't be infinite." That's simply not acceptable. I think it does a disservice to anyone who comes here trying to understand relativity (and not the philosophy of science), to find answers that are based on not being able to see how some potential implications of GR can be real.
The question remains an open problem (whether considered from a scientific perspective, or a philosophical one).
If you had reasoning that addressed why closed (curved) space should be considered impossible, in terms of GR, that would be interesting.
0 
Since "antitime" doesn't seem to be defined, you might define it as negative time, so that an equal duration of time and antitime "annihilate" each other when added together.
But time and distance are abstractions, as swanstont has pointed out, whether positive or negative. If you push 2 things together, you're not actually physically destroying anything as you reduce the distance to 0.
Negative values of time and distance are useful for describing differences in the measurements.
If you move something closer to me, my distance to it changes by a negative value.
The difference between today and yesterday is 1 day.
Meanwhile, the length or magnitude of any distance or time will be nonnegative. It is probably easy to think of physical objects with lengths and events with durations, yet negative values may only come up when speaking of something relative to something else. So it might be easy to confuse distance as "something that is real", but it is only a measurement or a property of something real (or abstract).
0 
Unless you're speculating otherwise, spacetime usually consists of 3 spatial dimensions and 1 time dimension, so time and space are hard to compare. If you want to compare time to a 1D aspect of space, comparing time and spatial distance would be easier.
Antitime might be like antidistance. I don't know how that'd be defined, but I'd expect it to only be abstract, not anything "real".
0
Gravitational Lag Thought Problem
in Relativity
Posted
I thought about this some more and I think I see what you're saying...
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.