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md65536

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Everything posted by md65536

  1. This is what I got from your posts: 1) A black hole and all the events in its interior can be described in the coordinates of an observer at infinity. 2) A Penrose diagram of an evaporating black hole shows that the formation and disappearance of a black hole have the same time coordinate. 3) If an event A has a coordinate time that is less than the coordinate time of an event B, then A happened before B (maybe even in B's past?). Problems with this: (1) The interior events do not have meaningful time coordinates for this observer. (2) If that's what the diagram really shows, then the coordinates used in that diagram can't be the same as for the observer in (1). (3) You're comparing coordinate times of events that have no causal connections, and their ordering is irrelevant, but you see "logic problems" by treating it as something physical.
  2. I'm not seeing any problem, except maybe mixing of different time coordinates. In my understanding, the point of having the observer at infinity is that it is "shielded" from any effects of spacetime curvature. In its coordinates, you could say eg. the black hole formed very far away and at coordinate time (ie. observer's local time) t=0, remained at rest, had a lifetime of 100 units of coordinate time, and finished evaporating at t=100, then sometime later at t>100 some other event happened at the location of the black hole. The same could be said if instead of a black hole, you're talking about a snowball with negligible mass. Neither has any effect on the coordinate time of the observer at infinity. There is nothing contradictory in the coordinate times of this observer on its own. So clearly we're comparing the times of different observers???, but it's not clear to me what other times you're speaking about here. Also, it should be possible to choose foliations of spacetime such that any events in the interior of the black hole are assigned meaningless coordinate times anywhere in [0, 100]. However, they would have no physical significance to the observer, and there'd be no way to break causality or create a contradiction through your choice.
  3. Earlier you wrote: Can you remind us of the situation you're describing (I've lost track)? Whose coordinate time are you talking about here? It sounds elsewhere like you're talking about a Schwarzschild black hole, at rest (and evaporating) in the coordinates of an observer at infinity. However it also sounds like the Penrose diagram doesn't show those time coordinates, and the statement above doesn't match those coordinates either??? When you speak of time, if you could mention in each case whose coordinates you're referring to, that might make it clearer.
  4. You're speaking of a general case, but if you compared two observers in flat spacetime (eg. at infinity, or in the location of a single event), wouldn't it have to be the case? I didn't see it specified what observers are being compared (eg. infalling vs. one at infinity), but if you're given the choice of which observers to compare, it should be possible? I think this is related to https://en.wikipedia.org/wiki/Black_hole_complementarity I don't think the issue is settled in accepted science. However, seeing the infalling object reach the event horizon doesn't make sense (unless the BH has zero size). Maybe the object evaporates just like the BH does. Maybe the object simply fades out of existence as it's infinitely red-shifted to nothing.
  5. Doesn't the null surface correspond with the event horizon, which has the same physical significance (re. light-like intervals, causality, etc.) regardless of coordinates? Whether or not the event horizon at the Schwarzschild radius is a singularity depends on choice of coordinates, but that doesn't determine its existence or behaviour. It's still an event horizon.
  6. The null surface is the event horizon? Isn't it located at the same place in different coordinates, just with different numerical representations in the different coordinate systems? What are you asking is invariant? There are aspects of spacelike and timelike things that are relative, and other aspects that are invariant, right? Mordred, can you please answer my previous question so that I know I'm not just wasting my time here? Is rapidity some kind of acceleration?
  7. Exploring the causal connections with black holes seems related enough to the topic. I'd say that causal connections are invariant. I think light cones are invariant. A light signal from one event either reaches (causes) another event, or it doesn't. That doesn't change depending on observer. I don't know what you mean by "experience" but of course different observers will see things appear differently, observe different parts of spacetime etc. Obviously if a particle can survive (as expected) falling into a BH, there can be causal connections from outside to in. As far as I know, it is not known exactly what an observer inside the black hole would observe, as that requires some speculative extrapolation of testable physics. It is only causal connections from inside to out that are prohibited.
  8. I don't think that's correct. It did exist, and it evaporated in the observer's past. It's only the interior events that aren't causally connected to the observer in the moment described. How is this relevant to the thread? Your link confirms that rapidity is not acceleration. Quote: "rapidity η (v) ≡ tanh^−1 (v)". Constant rapidity implies constant velocity. Do you understand that rapidity is not acceleration? See https://en.wikipedia.org/wiki/Rapidity : If you still think rapidity is acceleration or requires acceleration or whatever, can you please provide a definition that you're using?
  9. Sure, if you're using hyperbolic functions with the Lorentz transformation. Not relevant here. It isn't. Have you actually read your link? You should. None of these terms are relevant to this thread. They're worse than irrelevant when used incorrectly.
  10. ??? From https://en.wikipedia.org/wiki/Lorentz_transformation : "Transformations describing relative motion with constant (uniform) velocity and without rotation of the space coordinate axes are called boosts, and the relative velocity between the frames is the parameter of the transformation." Do you think a boost is an acceleration? Can you please provide references to the definitions you're using (including rapidity)? I don't trust what you're saying because it's not making any sense to me with respect to anything else I read.
  11. You keep referring to rapidity as acceleration. The only definitions I've seen are that it's a measure of relativistic velocity. What definition are you using? Your statement makes as little sense as saying an infalling observer is undergoing velocity.
  12. Are you saying that you get different light cones with different coordinate choices? But if you have light from one event reaching another event on its future light cone, that doesn't change depending on coordinates, so I don't know what you mean. This makes no sense to me. Isn't it the events that have light cones, not observers? For example, if you have an event where an infalling observer contacts a hovering observer as it passes, that event has a light cone. Are you saying it has different light cones for the different observers?
  13. Is it fair to say your argument is basically, "if a black hole's entire existence is within an event's past light cone, then any interior events of the black hole are also within that event's past light cone"? I think the argument is false. The interior events are not in your past light cone. For one thing, a light cone is based on the paths of light from one event to another, and a black hole doesn't have such paths from interior events to exterior. I think what you're doing is using a mathematical definition of a light cone in "Your" flat spacetime. Then with a black hole placed in that past light cone, you're effectively assigning flat spacetime coordinates to events within the black hole, like you might do if the black hole wasn't there at all and the spacetime remained flat. You're effectively giving physically meaningless flat-spacetime coordinates to events in a curved spacetime, which I think is okay, but then you're drawing conclusions about those events based on physics that applies in flat spacetimes, which is not correct. In the curved spacetime, the black hole's interior events are geometrically outside of your past light cone, I think... or, I have no idea. Maybe another way to put it is that black holes tilt light cones, and you're not accounting for that. As an amateur, I think I'm missing the maths and vocab that would make this clear and precise. edit: Thinking more about tilted light cones... Say the event of the BH evaporating is in your past light cone. You can say there's a causal connection between you and it because its future light cone intersects your past light cone. But for an event within the BH's horizon, the event's future light cone is tilted more than 45 degrees such that its future light cone does not intersect your past light cone, and there is no causal connection. I suspect there's more to it than that.
  14. 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.
  15. 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?
  16. 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?
  17. 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?)
  18. 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).
  19. 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:
  20. 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).
  21. 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.
  22. 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.
  23. 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?
  24. 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.
  25. 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.
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