7 ms·

Care to elaborate? I saw no such issue.

by genwin 14y ago

pdonis 14y ago
In the diagram of Frame X, which purports to be an inertial frame "centered" on the horizon, the horizon is shown as a vertical line. If this diagram is supposed to be a spacetime diagram, this is incorrect; the horizon is an outgoing lightlike surface, so it should appear in a spacetime diagram of Frame X as a 45-degree line going up and to the right, just like a light ray. However, if the diagram is just supposed to be a diagram of "space" at the horizon (not spacetime), then it is not correct because the direction to the left of the diagram, towards the singularity, is not a spacelike direction; that direction is supposed to be the inward radial direction, but that direction is a timelike direction, not a spacelike direction. In short, the diagram of Frame X can't be correct, so no valid logical argument can be based on it. [Edit: The argument given in words has the same problems, but it's easier to illustrate them in the diagram.]
- genwin 14y ago
  As I interpreted it, it's a diagram of a lab falling through a horizon, as viewed by someone at rest with respect to the lab. The horizon would be a plane traversing the lab; thus the horizon is drawn correctly. The singularity would be in one direction perpendicular to the horizon, whereas the escaping particle would be heading toward infinity in the opposite direction; thus those are drawn correctly. > that direction is supposed to be the inward radial direction, but that direction is a timelike direction, not a spacelike direction. It's an inward radial direction according to the diagram. The "but" part of your sentence doesn't offer evidence to invalidate that or otherwise show a problem. There's a coffee mug in front of me now. Regardless whether it's a spacelike or timelike direction, the mug is in that direction. Likewise to someone in that frame X the singularity is definitely in a particular direction. I'm not seeing a problem with the diagram.
  - pdonis 14y ago
    The horizon would be a plane traversing the lab No, it wouldn't. That's the point. The horizon is an outgoing lightlike surface; with respect to Frame X (or to any inertial frame that straddles the horizon), it's moving radially outward at the speed of light. It's not a plane stationary in space. The singularity would be in one direction perpendicular to the horizon No, it wouldn't. The singularity is to the future of the horizon; the direction from the horizon to the singularity is timelike, not spacelike. There's a coffee mug in front of me now. Regardless whether it's a spacelike or timelike direction, the mug is in that direction. This is not correct; timelike directions are fundamentally different from spacelike directions. What direction is next Tuesday from you now? That's a timelike direction, and it's not the same direction as the direction of a coffee mug, or any object that is in the space around you now. It's not even the same kind of direction. But that kind of direction--the kind that next Tuesday is in from you now--is the direction the singularity is in from the horizon. I'm not seeing a problem with the diagram. That's because you evidently don't understand what the curved spacetime around a black hole is like. It's a perfectly self-consistent model; but it doesn't work the way the web page author, and evidently you, think it works.
    - genwin 14y ago
      > The horizon is an outgoing lightlike surface; with respect to Frame X (or to any inertial frame that straddles the horizon), it's moving radially outward at the speed of light. It's not a plane stationary in space. "Lightlike surface" and plane are not incompatible ideas. Surface = plane in this case. The diagram or its caption doesn't say the horizon is stationary, it says the frame is falling through the horizon. Presumably the horizon is indeed moving in that frame at the speed of light (an outgoing lightlike surface). > What direction is next Tuesday from you now? The singularity is not a date; it's an object, like my coffee mug is. It's not invalid to show a direction to an object just because you'll reach the object next Tuesday. > That's because you evidently don't understand what the curved spacetime around a black hole is like. I've take a couple years of classes on this stuff. You're using the terminology inappropriately. The terms spacelike and timelike are not limited to black holes. By saying the diagram incorrectly shows the direction to the singularity you're implying that neither can I point to my coffee mug and say it's in that direction. But I can point to my coffee mug as validly as someone in frame X could point to the singularity. I can even point to a real purported singularity by walking outside and pointing to the direction of the center of the Milky Way. It's no more complex than that. Can I validly point to the center of the Milky Way? If yes, then there's no problem with the diagram in that regard. > It's a perfectly self-consistent model An assumption that should be set aside when considering an objection to it.

Care to elaborate? I saw no such issue.

by genwin 14y ago

Care to elaborate? I saw no such issue.

In the diagram of Frame X, which purports to be an inertial frame "centered" on the horizon, the horizon is shown as a vertical line. If this diagram is supposed to be a spacetime diagram, this is incorrect; the horizon is an outgoing lightlike surface, so it should appear in a spacetime diagram of Frame X as a 45-degree line going up and to the right, just like a light ray. However, if the diagram is just supposed to be a diagram of "space" at the horizon (not spacetime), then it is not correct because the direction to the left of the diagram, towards the singularity, is not a spacelike direction; that direction is supposed to be the inward radial direction, but that direction is a timelike direction, not a spacelike direction. In short, the diagram of Frame X can't be correct, so no valid logical argument can be based on it. [Edit: The argument given in words has the same problems, but it's easier to illustrate them in the diagram.]

genwin 14y ago
As I interpreted it, it's a diagram of a lab falling through a horizon, as viewed by someone at rest with respect to the lab. The horizon would be a plane traversing the lab; thus the horizon is drawn correctly. The singularity would be in one direction perpendicular to the horizon, whereas the escaping particle would be heading toward infinity in the opposite direction; thus those are drawn correctly. > that direction is supposed to be the inward radial direction, but that direction is a timelike direction, not a spacelike direction. It's an inward radial direction according to the diagram. The "but" part of your sentence doesn't offer evidence to invalidate that or otherwise show a problem. There's a coffee mug in front of me now. Regardless whether it's a spacelike or timelike direction, the mug is in that direction. Likewise to someone in that frame X the singularity is definitely in a particular direction. I'm not seeing a problem with the diagram.
- pdonis 14y ago
  The horizon would be a plane traversing the lab No, it wouldn't. That's the point. The horizon is an outgoing lightlike surface; with respect to Frame X (or to any inertial frame that straddles the horizon), it's moving radially outward at the speed of light. It's not a plane stationary in space. The singularity would be in one direction perpendicular to the horizon No, it wouldn't. The singularity is to the future of the horizon; the direction from the horizon to the singularity is timelike, not spacelike. There's a coffee mug in front of me now. Regardless whether it's a spacelike or timelike direction, the mug is in that direction. This is not correct; timelike directions are fundamentally different from spacelike directions. What direction is next Tuesday from you now? That's a timelike direction, and it's not the same direction as the direction of a coffee mug, or any object that is in the space around you now. It's not even the same kind of direction. But that kind of direction--the kind that next Tuesday is in from you now--is the direction the singularity is in from the horizon. I'm not seeing a problem with the diagram. That's because you evidently don't understand what the curved spacetime around a black hole is like. It's a perfectly self-consistent model; but it doesn't work the way the web page author, and evidently you, think it works.
  - genwin 14y ago
    > The horizon is an outgoing lightlike surface; with respect to Frame X (or to any inertial frame that straddles the horizon), it's moving radially outward at the speed of light. It's not a plane stationary in space. "Lightlike surface" and plane are not incompatible ideas. Surface = plane in this case. The diagram or its caption doesn't say the horizon is stationary, it says the frame is falling through the horizon. Presumably the horizon is indeed moving in that frame at the speed of light (an outgoing lightlike surface). > What direction is next Tuesday from you now? The singularity is not a date; it's an object, like my coffee mug is. It's not invalid to show a direction to an object just because you'll reach the object next Tuesday. > That's because you evidently don't understand what the curved spacetime around a black hole is like. I've take a couple years of classes on this stuff. You're using the terminology inappropriately. The terms spacelike and timelike are not limited to black holes. By saying the diagram incorrectly shows the direction to the singularity you're implying that neither can I point to my coffee mug and say it's in that direction. But I can point to my coffee mug as validly as someone in frame X could point to the singularity. I can even point to a real purported singularity by walking outside and pointing to the direction of the center of the Milky Way. It's no more complex than that. Can I validly point to the center of the Milky Way? If yes, then there's no problem with the diagram in that regard. > It's a perfectly self-consistent model An assumption that should be set aside when considering an objection to it.