Halc

In the coordinate space defined by such an observer, the black hole doesn't exist and never (yet) existed. Any object tossed in (from the perspective of this specific observer) was still outside the event horizon, even a moment before the evaporation completes. There is no line of simultaneity reaching from any point on this observers worldline into the black hole. Said hyperplane of simultaneity always remains unbroken (no hole in it), clean to the other side. It's as if all events comprising that region of spacetime exist only entirely in the future of this observer, even when the black hole is evaporated.

Edit doesn't work and all the quotes were nullified, so posting this again. Robert Wald: An asymptotically flat [and strongly asymptotically predictable] spacetime M is said to contain a black hole if not every point of M is contained in the causal past of future null infinity. 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. The boundary of B in M is called the event horizon. rjbeery: My issue is that this, and almost any, definition makes finite black holes a logical impossibility. I don't find it a logical impossibility. The definition puts us in a black hole actually, since any location in space beyond the visible universe at t=infinity (currently a location about 65 BLY away) is not in our future light cone, nor are we in its past light cone. As for the more classic black hole, yes, any event within it is not containied within the causal past of an event near where the black hole completed its evaporation yesterday. That makes it existing by that definition, not a logical impossibility at all. rjbeery: In other words, any process (e.g. Hawking radiation, which I generically refer to as "evaporation"') that eventually eliminates the event horizon has, by the definition of black holes, negated that black hole's existence for all time, including the past. Evaporation and event horizons are mutually exclusive ideas. For these to be mutually exclusive, I think you need to make some additional premises which are simply not axiomatic. For one, my personal destruction (death say) does not negate my existence for all time, I still exist in 2020. So not sure what you mean by those words. Sure, it doesn't exist at that future time, but that future time is not 'all time', despite your assertion otherwise. Perhaps if you state the contradiction formally. rjbeery: We come back the next morning and have equipment that recorded the MBH's existence. We can also verify that the MBH no longer exists. This clearly puts the entire history of this MBH in our causal past It does not put the interior events in our causal past, so this is not clear at all. The mathematics can be used to explore whether or not any of the events (I hate calling them points) of M inside said event horizon are in fact contained in the causal future of events outside the event horizon. It is after all just a mathematical singularity. A rock fall through a Rindler horizon (another mathematical singularity, not a physical one) effortlessly and without notice by the rock. But it is arguable that a similar rock cannot be dropped into a black hole, instead forming a dense timeless shell. I'm having a hard time finding links on this interpretation.

Poorly worded, but I think enough clues are there to work out what you have in mind. Let me know if I get this wrong. In some frame, points A and B are stationary objects and nearly a light-month apart. "The rest of us" are stationary in that frame. For "themselves", we're referring to the people in the ship. The don't move at all in their own frame. The object B comes at them from nearly 10 light seconds away and takes 10 seconds to get to them. Now as for your question: No, to everyone else, they're moving at nearly light speed, taking a month to go nearly a light month. To themselves, by definition, they're not moving at all, which is slower than 'incredibly slowly'. It is A and B that takes a 10 second journey in that frame of reference, each moving at nearly light speed.

One should also mention Everett's RSF interpretation, which posits pretty much what you said there, and no more. More precisely: "All isolated systems evolve according to the Schrodinger equation". That's it. No wave function collapse, and no metaphysical spawning of new worlds.

Read my post again as well. MWI does not claim that the worlds split before the photon goes through the slits. So still one world, with interference. The split happens when it is measured: when the dot appears on the target. One world for each possible location for the dot, which is a lot more than 2 worlds. MWI does not claim that it passes through one slit in each of 2 worlds. Still the same world at that point.

MWI (DeWitt) posits splitting of worlds at time of measurement, not photons going through different slits in different worlds. RSF (Everett) does not posit any ontological split at all. I do believe that there is a fatal flaw in the DeWitt version, but it isn't that.

Yes, as they accelerate, there is a time in any frame where the speed crosses that particular rate of the two objects approaching at c/1000. You can't get from slow to fast without crossing 'medium'. Maybe I'm misunderstanding the question. I don't think the spacetime curvature is frame dependent, similar to the way events are absolute, not frame dependent. As I said, the curvature at the point between the masses is a saddle shape: positive curvature in one direction, negative in another. This is true in any frame. Something like c/2000 actually, and that depends on which frame measured the c/1000 approach of the two BH's to each other.

For one, the black holes would be accelerating towards each other, not moving at that constant speed. That speed of course is relative to your frame of choice, which in this case is your point in the middle, a sort of saddle-point of unstable equilibrium. Time would dilate as the two black holes approached, so they'd appear to approach faster than the speed measured by a distant observer.

OK, I've seen that paper before but didn't exactly see how it applied since I'm not committing any of the misconceptions mentioned. That said, I read it more carefully and the misconception I'm making is assuming that scalefactor was a linear function, whereas it is in fact based on complicated solutions to Einstein's field equations in the FRW models. They graph various models with this and that tuning, yielding this, which I've also seen before, but without making the connection: The consensus model seems to be the purple one there, the only one giving an age-of-universe as about 13.8 BY. The slope of that line is the expansion rate at various times, and yes, expansion was much quicker in the first billion years than it is now, which accounts for the nonlinear scalefactor on the right side of the diagram in my prior post. It is even more evident in the similar diagram top of page 3 of the originally linked doc, which shows the future as well as the past, and shows the scalefactor once again compressing as the expansion accelerates from its current low level, which seems to have changed very little from its minimum about 5 BY ago. This nonlinear scalefactor accounts for the curvature of the worldlines in all these diagrams, including the one I first posted. You said that one was from old data, but I see nothing particularly wrong with it. Problem is that popular articles talk about how the expansion is accelerating (dark energy and all), but not that it had been slowing in the past. So that prompted my initial post asking how GN-z11 could have got 2.66 BLY away in only 400 MY when its present recession velocity is only slightly over 2c. That's a significant reduction in expansion rate that the texts seem to rarely talk about. Anyway, Thanks Mordred for pointing me in the direction where I could find my answers.

Here's another dated image, unsure of origin, but one I see used a lot: GN-z11 worldline is very close to the 3rd dotted line. The resolution is too low to see where (distance) it crosses the light cone in the upper image. 4th dotted line is close to today's CMB. The lower image shows straight worldlines, and the upper can be supposedly generated from it by multiplying distances by that scalefactor on the right, but notice the scalefactor is either mislabeled or something, because there's no zero at the bottom, but rather something around 0.1, which would not produce a singularity as depicted in the upper diagram. It is that scalefactor that I suspect is the culprit. Notice the 0.2 is already closer to 0.4 than the spacing between the numbers above. So I suspect it does go to 0, but very compressed near the bottom, which would be decelerating expansion (numbers getting further apart over time), not accelerating expansion. The worldlines are curved just as they are in my prior diagram, and they would be straight if the scalefactor went evenly from 0 to 1, but that would put the emission-proper-distance of the 3rd dotted line at far less than 2.66 GLY. No matter how accurate of a picture we get, either the number reported for distant things are wrong, or those worldlines really are curved. The lower picture shows the difference between Hubble sphere (is Hubble Horizon?) and your description of Hubble distance. The latter would be a vertical worldline intersecting the event where blue 'now' and purple 'Hubble sphere' lines meet, correct? But if there was no expansion, the lower picture would be meaningless as there would be no scalefactor. In fact, the Hubble distance as you define it would be the edge of the universe, which, without expansion, would effectlively be flat Minkowski spacetime. I took the time to draw a picture of the universe using those coordinates rather than comoving coordinates. I could not include dark energy, but by leaving that off, I could foliate all of spacetime with an inertial reference frame. The light cone becomes a straight line. Distant things like GN-z11 are not so distant since speeds add the relativistic way, not linear, so nothing recedes at superluminal speeds. Alas, it fails empirical tests since really old things appear smaller (angular diameter) using the Minkowski spacetime, while they appear larger than younger 'closer' objects in reality.

The graph doesn't label redshifts beyond 10. The hubble distance (v=c line on right) is closer than the particle horizon, which is the 'today's horizon' line on left. Not sure what 'Hubble horizon' is as distinct from Hubble distance. Are you aware of such a graph (especially one that shows redshifts and worldlines out to a good percentage of visible universe) with more realistic data? Anyway, graph aside, the numbers quoted for GN-z11 are actual reported numbers, not something coming from a graph. My primary concern is those number and not a picture which may or may not accurately reflect reality. It is unrealistic to draw a graph (comoving coordinates, proper distance) with GN-z11 crossing the events reported and not have that worldline curve upward (slowing).

Wiki does give emission proper distance if you look close. I estimated it at 2.8 BLY based on inspection of the diagram above, but it says 2.66 BLY on the site. So it went from 0 to 2.66 in 0.4 BY, or an average of 6.5c, and in the next 13.4 BY it went from there to 32 BLY distant, an average of 2.2c. It is that falling off of recession speed that I'm trying to understand. If expansion is supposedly accelerating due to dark energy or a positive cosmological constant, then why has the recession speed of GN-z11 fallen by at least a factor of 3 between the event that we see and its present speed?

I need help understanding the diagrams I see showing worldlines of distant objects on a cosmological scale. From this paper http://people.virginia.edu/~dmw8f/astr5630/Topic16/t16_light_cones.html there appears this diagram, which appears in similar format on other sites. It is called the concordance model here. Note that this is comoving coordinates, plotting proper distance, not a spacetime diagram of an inertial reference frame, which would not be able to foliate all of spacetime like this does. It would seem that if space expansion was constant (no acceleration, no dark energy), then those worldlines (blue on left, dotted black on right) would be straight. That they curve upward suggests that expansion is slowing, not accelerating. Accelerated expansion would curve them outward, no? It is here where I need an explanation. Take for example GN-z11, the most distant galaxy visible. It is listed on wiki as having a red shift of 11.09, and has a 'present proper distance' of 32 billion light years, which corresponds to a worldline labeled 'v = 2.3c'. It would cross the red light cone at about t=400MY, proper distance of about 2.8 BLY. See the redshift markings on the right side of the red light cone, and where 11 would be on that line. Wiki agrees with this, saying what we see now was emitted when the universe was 400MY old. It gives no proper distance at the time. If it took .4BY to get 2.8BLY away, it was receding at an average speed of 7c up until then, but around 2c now. That appears to be deceleration, not acceleration. Where am I going wrong?

This is correct. I have a balloon and a rock of the same volume, but very much different weight, but the buoyancy of both is the same: The weight of both is reduced by the same amount when submerged in say water. The buoyant force on the rock is not enough to counter its weight, so it still sinks. The force on the balloon is far greater than the force of its weight, so the balloon will rise to the surface.

Through spacetime, any geodesic traces a (locally) straight line, not curved at all. So a bullet going from me to a target follows a straight line, not a parabola. Similarly, the ball tossed in what appears to be a high arc to the basket also traces a straight line through bent (non-Euclidean) spacetime,. The apple doesn't fall up because spacetime isn't bent in a way that would allow that to be a straight line.

Indeed, and nobody is claiming they are, although your choice of the term 'particles' carries a bit of that connotation. If one quantum particle is sent through a double slit, we observe one point (where it is measured), something a wave sent through the slits will not do. The probability curve of where that measurement will be taken is what resembles an interference pattern. No wave exhibits quantized behavior like that. Sound (an example of an actual wave) passed through slits will be measured in all locations, not just one, and its intensity (yes, an interference pattern) will drop off as a function of distance from source to measurement. A photon or electron exhibits no similar behavior, being measured at full mass/energy at the measurement location and not measured at all at any other location. Sound (or any other real wave) ceases to propagate if you take away its medium. There is no medium for a photon or molecule passing through the slits, and yet they still arrive at the measurement location.

No, they're not. If measured in the right way, they share some properties with waves, but they also behave in ways that waves definitely do not. This doesn't follow. Just because I'm made up of cells doesn't imply that I am a cell.

I know the thought experiment well. You statement that the observer in the middle of the train boths observes the strikes simultaneously and not simultaneously cannot be correct. OK, you meant something else, but also wrong: There is no actual to it. Simultaneity of spatially separated events is frame dependent and there is no ordering that is more actual than another. The thought experiment classically suggests the strikes take place simultaneously in (and only in) the platform frame, which, as I said, is no more special than any other frame. Thus the guy on the train sees one strike before the other (because in the frame of the train, the one strike is actually before the other), and does not "experience lightning hit the front and back simulataneously" as you posted. Neither frame is 'correct'. Better worded is that according to Einstein, each observer is correct relative to the frame of reference in which he is respectively stationary.

This is a self-contradictory statement, and is thus wrong. He cannot both experience (observe) the two events simultaneously, and also one before the other.

By 'ends' I mean the bottom. If all the land and ice were spread evenly across the globe (like in waterworld), the bottom of the atmosphere would be something like 400m higher than current sea level, and pressure there would be no different than it is now. You get a lower figure with your method, but I was taking into account the current volume of ice which displaces atmosphere in addition to what the land does. I used 840 (reddit), more than 1/3 (more like 3/8), and used projected sea level rise from global warming charts to estimate ice volume. 400 is probably still a bit high. 360 maybe?

If you want a more accurate mass estimate, multiply the surface area by the pressure at an altitude of something like 400m, which is close to the average altitude where the atmosphere ends worldwide.

Not saying Earth masses less than the atmosphere. Earth is in freefall, hence has no weight. You can place Earth on top of me, in which case it would weigh about 900 Newtons, still considerably less than the atmosphere collective weight. A 20 digit number of Newtons is more weight than zero. On the other hand, weight is a force, no? Force is a vector, and adding all the force applied by the atmosphere pretty much (not completely) cancels itself out, leaving many fewer digits of actual net force (weight?) on Earth.

Venus orbits the same direction as all the other planets. But it spins on its own axis backwards, so it has one more day per year than its sidereal spin rate, as opposed to one less like all the other planets. Earth for instance experiences 365.25 days per year, but spins at a rate of about 366.25 times. Venus spins so slow that it goes around about once per Venus year, giving it just two days in its year.

First of all, weight is a force, measured in say Newtons. I did the pressure * area thing and got 5.1x10^19 Newtons. That's far heavier than Earth itself since Earth, unlike the atmosphere, is not resting on anything and is thus weightless. This is my first test post and it didn't take the html ¹⁹