md65536

The definition you quoted, "The black hole region, B, of such a spacetime is defined to be the points of M not contained in the causal past of future null infinity." If there was a black hole then there were such points, which means there must be an event horizon. There's no contradiction there. Can you give an example of an event from inside the theoretical MBH's horizon that causes an effect outside, such that it has some recorded effect "in the lab the next morning"? If so, then you're on to something. If not, you're making extraordinary claims without evidence. It's events that are in past light cones, not spatial regions. Assuming you know that, you mean something like that all the events at that location in a given Euclidean coordinate system, but with earlier times, are in our event's past light cone. However, the events within the past black hole's event horizon are not part of that Euclidean coordinate system, I think. If you were claiming that black hole event horizons can't exist in a Euclidean spacetime, I think you'd be right.

The (Riemann) curvature has one tensor value for each location+time, and that one tensor value is made up of "other stuff" that gives you the different scalar curvature values in different directions? The "other stuff"'s beyond me and probably not important for the conversation but wikipedia says it's "the Christoffel symbols and their first partial derivatives"... with values corresponding to the 4 dimensions? And there's a scalar curvature in the direction of time as well as any other direction?

Edit: I'm trying to wrap my head around this. Does this mean that the curvature has a specific value for every event in 4D spacetime (ie. a field), and that at each event, it's the same for all observers? Conversely, something like the magnetic field also has a value for every event in 4D spacetime, but the value at a given event can differ depending on inertial frame. Then 'globally' would refer to all of 4D spacetime, not 'spatially everywhere at a particular moment' like I've been thinking of it? If so then then my original reply below might not make sense. ---- Is the curvature locally frame independent, or globally? It is time-dependent, right? OP's experiment involves changing curvature? If you set up two of OP's experiment, say some light years apart, then the relative timing of the experiments depends on inertial frame. Can the global curvature (or the tensor field?) be described without that mattering? Does the concept of a "global curvature at a given time (a Cauchy surface?)" even make sense? Or does the tensor field necessarily extend through time or something? Now I'm confused. My guess would be that it's all local, and trying to apply it globally to causally disconnected 4D regions would require some arbitrary choice of ... how you want to connect the regions into a global thing. Basically, OP's experiment describes an event at the midpoint observer's location, and all observers everywhere in the universe agree on the spacetime curvature near that event?

I have more questions about my understanding of this than I have answers... hopefully someone can correct me. You're specifying a moment in time here. The curvature of a static spacetime should be frame-independent, but if it's changing over time in different locations, the timing of those changes will be frame-dependent (right?), and you won't have a single description of the spacetime at a given moment (eg. the moment of some event), because there are no frame-independent individual moments that span the space. The frame is still needed to define the moment. You're specifying the moment, and you have the choice of specifying whose frame of reference you're using. Since you didn't specify any other frame, the midpoint observer's frame (ie. the frame where the two black holes are symmetric) is the only sensible frame of reference that can be assumed by your description. (However, your description is missing some info, like whether you mean the black holes are traveling relative to each other at c/1000, or that's their closing speed according to the midpoint observer, and neither seems like your obvious intention.) Changes in spacetime curvature are propagated as gravitational waves, and they propagate when there is a change in acceleration of a mass (right?). When you have two masses approaching each other head-on in freefall, it is symmetric and no gravitational waves are emitted (right?). I'm guessing that means that there's no frame-dependence here, and all observers (all frames) would agree on the mathematical description of the spacetime at the moment that the two black holes are 100 light seconds apart according to the midpoint observer. Also, I suspect that if what you were describing wasn't symmetric, it would matter that the black holes are approaching each other (rather than eg. moving apart after a flyby). In your example, without any gravitational waves being propagated, I suspect that you'd have the same curvature with the masses at the given separation, regardless of their speed. (Right?)

Quote from https://en.wikipedia.org/wiki/Anti-gravity: Also, you're getting a lot of answers to "why" things fall toward each other. If people didn't have answers, you'd probably see something like "Science doesn't deal with 'why', it deals with 'what'", and that applies here too. The answers aren't the root cause of attraction or anything like that, they're just other measurements that correspond. Masses correspond with a certain geometry of spacetime, geodesics of that geometry have certain configurations. If 'what' makes sense enough, you tend to stop thinking about 'why' (eg. one wouldn't wonder "why can't a circle curve outward instead of in on itself?" if one knows what a circle is).

To do it from a diagram like that, you can rotate the image 180 degrees, then overlap the ellipses. Here the two suns are the foci. Obviously the accuracy will be limited by image quality but for example you can see that the foci of Mercury's ellipse are farther apart than Earth's, and that Mercury is on the order of 3/2 as far from the sun at aphelion as it is at perihelion. Mercury: Earth:

Couldn't you just find the distance from the first focus to Mercury at perihelion, and the distance from the first focus to Mercury at aphelion, then take a vector from the first focus toward the point of aphelion, with a length that's the difference of the two distances? Even if those values are determined by an accurate-enough simulation, that should be easy. According to wikipedia, the difference is 23.8 million km, so that's approximately how far apart the foci should be (neglecting the sun's wobble). That's more than half the distance between Mercury and the sun at perihelion. Mercury's orbit eccentricity is huge (0.2056) compared to Earth's (0.0167).

If you're simulating Newtonian gravity, then all you need to get an elliptical orbit is to give the smaller mass a velocity. Then calculate updated positions and velocities, using gravity for acceleration. The data would be mass of the sun, location of the planet relative to center of sun, and velocity at that location. Or if accurate relative positions aren't important, just distance from the center of the sun at apogee or perigee, and speed at that point (oriented 90 degrees from the sun) will do. Simply updating position, velocity, and acceleration iteratively ("Euler method") can give a good approximation for simple visualization. I'd be curious to see if you can find eg. the max deviation in distance between Mercury and the sun, based only on those data. You would know you have a small enough step size, when making it a lot smaller (eg. half) doesn't change the results much.

As MigL suggested, your idea is to warp space with a system of energy that has much more mass than the ship? And it pulls you along as you fall toward it? But to travel anywhere, wouldn't you have to accelerate it (using much more energy than accelerating the ship, since it's much more massive)? Are you imagining something with a lot of gravitational mass but little inertial mass? I don't think anything known or predicted is like that.

Is that a fact? A spacetime interval can have a length that's positive, negative, or zero, so that value is not always negative. Also, you're talking about a metric signature (+ + + -) which is only a convention, but so is (- - - +). A measure of proper time uses the latter. Then, ds^2 is negative for spacelike intervals, and positive for timelike. As for physical significance, could you say that the proper time along a spacelike interval is imaginary?

I agree that shutting it down was justified, but it went from indulging OP's avoidance of simple questions, to brushing off everyone's questions, with no warning and nothing in between. A warning a few pages earlier could have prevented both rambling posts AND people bothering to continue asking serious questions. Also, the topic was started in Relativity I think, and I was reading it only through notifications of replies. I didn't see any indication that it was moved to Speculations, and that replies were no longer considered worth anything.

For example, a post on SR that was moved to speculations was closed recently. The reply immediately before it was closed was from someone asking questions to OP. The problem is that the topic was closed only due to OP's behavior, but there were other people in the thread. This suggests that OP "owns" a bad topic, even if others are discussing reasonably. It would be nice to instead see a warning, like "Stop posting what you're posting. You have a chance to answer questions others have asked. If you don't take it, the thread will be closed." Or a warning to others: "Don't bother asking any questions, we're not giving OP more chances to answer." Even if all indications are that anyone else posting in the thread is having their time wasted, it's still good to know whether our questions or corrections or suggestions made any difference. If closing a topic is justified, the note about its closing could address everyone participating in the discussion.

Are you talking about some aspects of SR that can be observed without referring to different clocks etc., or are you saying all of SR can be understood without them? If you separate two clocks and bring them together again, one might have measured a longer time than the other. Do you explain that without saying one ran faster or slower than the other, or is that not one of the aspects of SR that you're talking about, or are you saying that wouldn't happen?

Yes, extra connections don't seem to add any meaning. The Krasnikov tube wiki you linked has an example with 2 one-way tubes that can bring you to Earth 6000 years before you departed. Not that that's assumed to be possible, but a connection between Earth 6000 years apart wouldn't make it a common 'now' away from that connection.

Does GR tell you how much time is measured outside the warp "bubble" or at the other end of a wormhole? Or "when" it is on the other side? With the Alcubierre drive, is there a horizon between inside and outside, so you can't interact with the outside? Suppose there was a way to create the warp in one place, and something else to cancel it out in another place, so you could travel there. Then suppose there was a way to do that in the opposite direction, so you can come back. Does GR tell you when you'd come back? Eg. if you could spend a day traveling at 10c, then immediately spend a day returning at 10c, is the idea that you could return to Earth with 2 Earth days having passed? Or is it some other time or unknown or undefined? When it comes to the wormholes, "when" is it on the other side of the wormhole? Is that arbitrary? Can you have a wormhole or a series of them connecting you to beyond our visible universe? I can't make sense of the idea of "now" on the other end of a set of wormholes, yet no universal now. For example, if you had 3 extremely distant events A, B, and C, each connected to each other with a wormhole, either the relative timing of the events would be arbitrary, or it would establish a common 'now' between the 3 locations???

Populated with what? Measurements of A? Or a prediction, based on the LT or the underlying definition of simultaneity? If simultaneity was not defined, could B say what the time at A "really" was? Is there for B, a physical "now" at the distant location A independent of that definition? Would you say that Einstein was wrong in writing that such a definition is needed? I didn't say "current". I said B can measure the total ageing of A without ever considering what the "current" or "real" time at A might be. It can measure what the time at A appears to be, using only the local current time at B. Why? He didn't, and got the right answer, never assuming anything at all about simultaneity. You say the speed of light must be considered, but don't you mean the one-way speed of light? B only needs to care about incoming light from A, to determine everything it needs to know about A, right? What is the one-way speed of incoming light? How do you know that light takes time to arrive? I'll just tell you the answer: You know it because the time it takes incoming light to cross a fixed distance is defined to be the same as the time it takes outgoing light to cross the same distance. You're wrong to say you "must" come to the same conclusion to be able to predict the ageing of A. I've just shown, B can predict the total ageing of A using only the relativistic Doppler effect, which is a real measurement that can be made without relying on any definition of simultaneity, and gives you the same answer regardless of how you define the "current time at a distant location." I'll just assume you're still using your own meaning of the word 'theory'. Both the LT and the relativistic Doppler effect can accurately let B predict the total ageing of A. Would you say there is no way to know which one matches reality? So, accepting that you can't know the answer to the question, you conclude that it must be the answer most reasonable to you? Can you conceive of the idea that the inability to measure the 1-way speed of light is the one "theory" that matches what is real??? It's not that a way to measure it hasn't been figured out yet, it's that there's no accepted theoretical way in which such a measure can meaningfully be made. It's like saying "Measurements of the Ether are all consistent with the fact that it doesn't exist," and someone arguing "I agree. Even though it exists, we may never have the ability to detect it." I agree! Einstein in fact did say something along those lines. He said, "in reality it assumes absolutely nothing about light" as I've quoted. In his 1905 paper he wrote, and then defined the equal timing of light signals in opposite directions. Thus he literally said that 1) we "might content ourselves" with an alternative, which I take to mean that it can provide workable solutions, and 2) a justification of the definition he used is that it is more practical. He knew what he was doing and didn't get mired in trying to base the theory on what he thought to be "real", only what agrees with experience.

What's the definition of a clock's "existence" in another observer's frame? What if B doesn't know of relativity, and says "A's existence spans 2 of its years on my outbound journey, and 8 years on my inbound, and I've measured that to be true"? How can you prove to B that it's wrong and that your description of existence is the right one? Can you convince it that what it measures (2 + 8 years observed) is wrong and your numbers (unmeasured, but later verified to be consistent with a particular definition of simultaneity) are the ONLY ones that can be real? And can you do this without relying on Einstein's definition of simultaneity or an equivalent? Do you think that when Einstein defined simultaneity in such a way that real-world events could be tested against that definition to determine if they fit it or not, he actually did much more than that, and actually defined existence? Or could it be that his definition so perfectly aligns with your assumptions about reality, that you figure he is proving your assumptions correct simply by definition?

That's wrong. B can SEE A ageing. B predicts that A's clock can be seen ticking at a rate of 0.5x its own, for 4 of B's years, and then ignores whatever happens at A while B turns around, then predicts A's clock can be seen ticking at a rate of 2x its own, for 4 of B's years. So it predicts A will be seen ageing 2+8 = 10 years, plus whatever it ignored. Why must it predict 6.4y, when it can predict the correct value? The rest of your post, you just keep repeating a similar false claim over and over. There's no such thing. Distant simultaneity isn't sensed. B doesn't "sense" a change in the time at A while it turns around (in negligible time). The coordinate time at A changes BY DEFINITION of simultaneity given by Einstein. Do you not accept that? You say his definition is a convention and then give pages and pages and pages of arguments that it's not. I've not convinced you of anything, and I'm repeating the same thing over and over, I give up. No thanks. I don't think that all of the unnecessary complications you're adding will help to understand the uncomplicated case. So start with something that makes sense. Don't just make random changes, choose the idea that you're trying to model. If you only change things that do not influence any real measuring device readings then the end result should agree with reality. Assume your "fused spacetime continuum" if you want. Just *don't* change something that doesn't affect real measurements, end up with something that agrees with reality, and then conclude that your changes must represent "true reality". (For example, choosing a random privileged frame will agree with reality, that doesn't make its privilege real.) Also don't take existing definitions that don't affect real measurements and conclude that they must represent "true reality".

There's another simplification that can be made. How do you know what's a realistic acceleration? We could be talking about twin neutrinos. If we're talking about rockets, the physical properties of the rockets aren't given. That's fine because they don't matter. The mass of the object that accelerates doesn't factor into the SR equations. Therefore it can be simplified out. We can talk about abstract twin particles. Imagining they're something specific, just adds red herrings. Sure, but they're synchronized only (generally speaking) in the Earth/A/X inertial frame. Ie. B is momentarily at Planet X and at rest with it. B's now in A's inertial frame, and agrees with A's (X's) measurements: A is 3 LY away, and A's clock is Einstein-synchronized to X's, which reads 5 years (per OP's specs, halfway---according to any of A, B, C---through the experiment). Nah! How would you measure that sweep at A? You can definitely predict it, using SR, but if you didn't know SR but had any conceivable measuring device you can imagine, how would such a device measure (not predict) that sweep? If you can unambiguously measure it, I'll agree it's the only outcome consistent with reality. Just checking we're on the same page: What does X's clock read when B reaches it, comes to rest with it, and then leaves again (all in negligible B's proper time)? That's what makes it a philosophical argument, not a scientific one. Scientific theories do not pick a choice they think is "real" based on Occam's razor. You don't settle eg. Copenhagen interpretation or string theory based on Occam's razor. You also don't have to because the questions answered by science are about quantitative predictions, not "which model is the one true description of reality?". The conventions used in SR are not about picking a choice that one thinks is "real", it's about ... again, in Einstein's translated words: "that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled." Ie. it is chosen because it is useful in making measurements. Any conventions that give you measurable predictions that equally agree with reality, are equally real. You need a different measurement given by different conventions, to be able to physically evaluate which is more "true-to-nature". Occam's razor tells you nothing about that, but it can tell you which are more practical than others.

A possible way forward is to treat c as a constant local speed of light, as it is in GR. It might be possible not to worry about the speed of anything measured from a distance, in your equations? I don't recommend following any of my advice on anything, unless you agree with it! I'm 100% sure you understand the technical details better than I do. If you're interested in testing whether your results are in agreement with SR, you might try deriving the Doppler effect including any of your alterations. If it doesn't give the exact same values as SR, it's not going to agree with real measurements as SR does. But also, I'm not sure what you're working to accomplish, so I don't want to suggest more work. I think we'll never agree, because of philosophical differences. Of course, SR doesn't depend on philosophy, and I think anything "purely" philosophical is not part of the theory. The way I see it... SR is correct, independent of experimental validation. The theory is purely mathematical. You start with some assumptions and mathematical rules, and you end up with some consequences. It is an exact, error-free model. Experimental validation deals with how well that model corresponds with reality, not whether or not it is correct (or complete, or whatever). We find that when measuring the universe, it really does seem to adhere to the assumptions and rules that SR uses, and thus the predictions made by SR are accurate in the real world. Philosophically, the only things I treat as "real" are what are measurable. If there's some mathematical prediction or description, like "A sweeping contiguously through time relative to B in the instant B accelerates", but it is not measurable, for me it's just a part of the model, not something real. For me, it makes so much more sense when everything "optional" is left out (cut off by Occam's razor). That's why I like OP's experiment. Changing from "B and C pass by each other" to "B turns around" doesn't change the prediction, so there's nothing real in that left to figure out.

Celeritas, I haven't followed the math very well. But back to an earlier subtopic, I think I'll no longer say that B turning around "doesn't cause" the difference in ageing seen at event AC (when A and C pass), because I don't know the meaning of that statement precisely enough. Here, C can refer to OP's C clock, or to B after an instant turnaround at event BC. Speaking in terms of causality, event BC *can* be causally related to event AC. AB is also causally related to AC (and to BC). Indeed, all events on all three clocks' worldlines between the events mentioned, can be causally related to AC. So you could say "A remaining inertial causes the difference in ageing seen at event AC", and "The entire time A and B/C are separated causes the difference at AC". You could also say something like "A and B passing causes BC" and get into interpretations, just like "B turning causes AC" is interpretive, but causal influence is possible. In terms of causality, the event BC is not causally related to any events on A's world line between proper times 2 years to 8 years. Therefore technically, B turning around doesn't cause (or is affected by) any events at A within that range. Back to what the LT says, if there is some physical change in the relative time at A when B accelerates (which I don't accept), that change is causally restricted to within event BC's light cone. For example, if B randomly decided only at event BC, whether to turn around or remain inertial, then A would not be able to detect any change due to that decision, until it had aged 8 years since leaving B, at which point it is able to see whether B turned or not. Yes, "who is ageing less" ie. "whose clock is running relatively slower" is relative and generally depends on reference frame. That's why in the twin paradox experiment, the relative ageing is only compared when the twins are together (ie. at individual events). When they're together, the difference in their ageing is not frame dependent, so all observers agree on it. In your experiments, different observers disagree, as per special relativity, but that's no argument against the the twin paradox, in which everyone agrees on the outcome.

Ideally that would come from what you're trying to model. Or if you're seeing what happens with an arbitrary value, or if it's a value that can be chosen for convenience without modelling anything physical, then you can choose. It's beyond me at this point. I was surprised it worked for you, I'd assumed that with so many details and definitions that can be adjusted, it would be much likelier to come up with something that doesn't work. On the other hand, with all the measurements related, it might just need letting the related things conform to whatever changes you make. It's definitely messy that way, but maybe not a problem. For example, if you change the definition of speed, you might end up with a measure of momentum that is no longer constant for an inertial mass, and say "oh, this must be wrong," but if you're redefining everything, your alternative definition doesn't have to have the same properties as the standard definition. It might not be wrong, just less useful. I don't know what's happening with your x coordinates, but maybe something like that is expected? Proper time and proper lengths are measured differently. Proper times can be measured by a moving clock, but proper lengths are measured in a rest frame. The ruler distance along a world line is not invariant. In my example when I messed with the definitions, I ended up with an altered meaning of being at rest, and so distances didn't have the same intuitive properties as usual. It's a bit of a rabbit hole. If you're looking at something like the speed of light as "just a definition", and with distance defined by speed of light, it's also "just a definition." If that seems wrong, consider that the definition of a metre has changed several times in history, and each time the measured value of a given length changes slightly, but nothing physically changed with each new definition.

Sure, I think I'm in agreement. Clocks passing or the intersection of world lines are events. Does it make it easier to deal with them as events? I think that 1-way speed of light differing from 2-way speed has turned out to be too complicated for me to handle. I don't even know if it can work, or how. In all the toy examples I've tried, if there's an easy-enough way to make some modification of simultaneity match the predictions of SR, I keep ending up with definitions where 1-way speed equals 2-way speed. Every time I've mentioned the definition of simultaneity I speak of the time it takes light to go in the 2 directions. It's easy to find alternative timing values that are still in agreement with SR; just borrow the measurements from another reference frame. Assuming standard SR agrees with reality in that frame, there's a set of definitions with which those same measurements agree with reality. But that trick doesn't work with the speed of light, because it's the same in the different reference frames. Even if you can get different speeds of light to work, there are other ways to get different working time/space coordinates that don't require a change in the speed of light.

Those are proper times, though. You're talking about the time of an event that is measured by a clock that passes through the event. All observers agree that B's clock is at 4 years when it passes C. "The time at B" is a coordinate time for A for events at A. For example, if you have an event "half way through A's world line", which A's world line intersects at a proper time of 5 years, all observers will agree that A passes through that event at 5 years. What they don't agree on is the coordinate time at B or C relative to that event. For instance, A says that "half way through A's world line" is simultaneous with B and C's passing. Inertial B says that event happens before B and C's passing. C says it happens after. Sorry, I'm trying to look at this in too many ways. But alright, let's stick with 1-way <> 2-way speed. How are you defining that? You have the definition of simultaneity: "The time required for light to go from a to b is the same as the time required by light to go from b to a in a stationary system." Are you changing that, or leaving that alone? Are you leaving c as a constant, or will you replace it with a variable that depends on direction (and if so, how?). Finally are you leaving distance defined by c, or changing that? Will you have distance measured differently in different directions, or maybe change both c and the definition of distance so that distance is the same in different directions? In SR, the 1-way speed of light is the same as the 2-way by definition. If you want to consider an alternative, you're going to have to change at least one of the definitions. If you want it to be consistent, and to agree with reality, I think you'll have to change multiple definitions. Which definitions are you changing? I used the example of choosing a preferred inertial frame with which to define all the relative measurements. This is a bad alternative because it has no benefits for any other observers except the preferred frame. However, it is an easy way to make sure that all of the measurements are at least consistent, and can be physically verified (remembering that the one-way speed of light is a definition, not a measurement), and must give the same predictions (but with different coordinates) that SR does.

Good idea. In that case the twins are symmetrical. There are observers that can measure A and B symmetrically, the simplest being one for which the speeds of A and B are both 1/3 c (so the composition is .6 c). Which twin ages more, is relative.