Halc

Quite plausible actually, not just in principle. In the inertial frame X of some planet in a galaxy 27 billion light years from here (distance measured in frame X), the universe is currently (simultaneous with us now) about 30 billion years old. Yes, the universe for such an observer would be quite different from what we see here since for one thing it appears to be over twice as old. Much more mature galaxies and such. Yes, we do know of galaxies moving at sufficient speed for this. The one I mention above would have a redshift of about z=1.3 as viewed from here, and the record holder is over z=11. Yes, I realize I'm replying to posts from January, before I registered I think.

In general, a superposition of states is known through demonstration of interference between the two states: Refraction patterns, positive/negative interference and such. I want to know how it is done for more macroscopic scenarios. They put a macroscopic object (one visible to the naked eye) into superposition. It was a sliver of material suspended in some kind of field, and in superposition of vibrating (like a xylophone bar) and just sitting there. What test was performed on such a system that couldn't be used to determine which of the two states it was in, but nevertheless demonstrated (over the course of multiple iterations of course) a pattern different than what would have been measured if the system was simply in one unknown state or the other, but not in superposition? The article I originally read on the subject was just based on a press release and did not report such details, but it seems to be the only one that matters. A different scenario will do as well, but firing buckyballs through slits does not count as a sufficiently macroscopic superposition.

Speed has nothing to do with it, since in your example, the situation is no different than the ship being stationary and the observer watching it go by being what moves at relativistic speed. Unruh radiation is observed in an accelerating reference frame, and has nothing to do with speed. Hawking radiation can be measured at any distance from an event horizon, but only by a hovering observer, not by one falling in.

Unruh radiation is not emitted by an accelerating ship. There is also no collision of matter going on in that scenario. There's merely a coordinate singularity inherent in a continuous accelerated reference frame, which, only in that ARF, emits faint radiation at the singularity similar to the Hawking radiation (which is also not emitted by any ship) emitted in say an inertial reference frame at the coordinate singularity of the event horizon of a black hole In both cases, the radiation is not emitted in coordinate systems where there exists no coordinate singularity there.

Einstein did not beg his conclusions. He posited two lightning strikes, but posited neither their simultaneity nor the absolute motion of either observer. The simultaneity of the strikes was concluded only after the respective observers took measurements of the events in question. Neither observer measured the motion (absolute or relative) of any object in that particular though experiment.

I am talking about universal time, and while I agree that there's no such thing, there seems to be no contradiction arising by postulating it. I'm proposing such a contradiction here. If the choice is relative to a particular observer, it's hardly objective. Another clock cannot be set to the universal time without agreeing on this privileged observer or privileged location in space. Points in space 50 billion light years away do not exist at all relative to a given observer, so his personal choice of coordinates do no in fact foliate all of spacetime. There is a choice that does foliate all points in an arbitrarily large scale, but as pointed out in this topic, it doesn't work for excessive local curvature such as black holes. There seems in fact to be no possible coordinate system that does, and that's the contradiction that arises from postulating universal (objective/absolute) time/space.

I'm talking about interpretations that deny the principle of relativity. There seem not to be infinitely many possible foliation schemes. As a matter of fact there doesn't seem to be any that foliate all of spacetime. The typical one suggested is the curved (non inertial) comoving frame corresponding locally to the inertial frame in which the CMB appears isotropic, but any frame like that does not properly foliate local deviations from flat space like black holes. If they did, then rjbeery would have grounds to stand on when trying to objectively determine if event X inside a black hole occurs before or after event Y somewhere outside it, particularly after the BH has evaporated. An objective foliation scheme should not in any way depend on an observer. Any two observers, no matter how separated and unable to communicate, should be able to sync their clocks simply by setting said clock to the current objective time, and then I suppose having the clock running at some rate which depends on the speed of the clock and its current gravitational potential. The latter requires a standard 'zero', which also seems undefined. For example, what is the gravitational potential at the surface of Earth? Nobody publishes that. They only publish the potential if Earth was in an otherwise empty universe, which it obviously isn't. Anyway, point is, there is no viable objective foliation scheme that includes all spacetime events. The lack of a viable scheme means that time and motion cannot be objective. The principle of relativity cannot be denied. Correct me if I'm wrong.

It seems that there is no coordinate system that foliates all of spacetime. This seems to be an interesting argument against any philosophy of time that posits an absolute coordinate system (a preferred frame of one sort or another). Presentism is only a subset of these philosophies. The inability to identify any coordinate system that can consistently map any pair of events as to which occurs first seems to me to be a fatal flaw in such a philosophy.

You've not given any indication of what you've done or what your current understanding of these terms is, so I don't know where help is needed. If you don't know the difference between an interrupt and a subroutine call, it seems you have to re-read the chapter(s) preceding this question.

Unclear how you might think so. Simple substitution yields 1-1/1 which is zero. Even if you ignore precedence rules and evaluate it as (1-A^2)/B^2 you still get zero. I can prove that 1 equals 2 using some sleight of hand, but not in the equation you present.

I've seen it demonstrated with a Kruskal-Szekeres diagram that an infalling observer can only witness a finite future as measured by an outside observer. He cannot see the universe end.

I never said any particular coordinate system wasn't meaningful. It isn't meaningful to compare the times of the two events you indicate. The Penrose diagram demonstrates the same thing in this case. An event within the black hole (an event that doesn't exist in the coordinate space discussed in my prior post, but does exist in the Penrose diagram) has no causal connection with the event after the evaporation. That makes it like any pair of events separated in a space-like manner: There is no objective comparison of their times. A-before-B is a relation dependent on the foliation of choice, because neither event is in the past or future light cone of the other.

No, I do not. It is not meaningful to compare the time of an event to an event not in your coordinate space. Use different coordinates if you want to do this.

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?