If such objects existed in our inertial frame, light from them would reach us in finite time, so these objects don't exist in that frame, and thus the frame doesn't foliate all of spacetime. — noAxioms

As you can see, any event can be located in an inertial frame, but only those events within our past light cone can be detected by us now. Events outside that cone are still in the reference frame but cannot influence us.

Gravitation can't be accurately described by inertial frames but require curvilinear coordinate systems.

For example, the current inertial frame of Earth won't do: There are objects beyond our event horizon (events from which light can never reach us even in infinite time). If such objects existed in our inertial frame, light from them would reach us in finite time, so these objects don't exist in that frame, and thus the frame doesn't foliate all of spacetime. — noAxioms

I don't get this. Why would they have to reach us? The light will never reach us because of cosmic expansion whether they exist or not, so the fact that we don't see them doesn't mean they don't exist.

That coordinate system works great for large distances, but completely fails where there is large curvature of spacetime: black holes. Any such non-local foliation does not cover the events within the black hole, and thus do not constitute a foliation of all spacetime. — noAxioms

I'm not sure about that. As far as I know, any spacetime that doesn't allow for closed timelike curves is open to being sliced into global hypersurfaces so they should be allowed in universes with black holes. At least, all the discussions I've seen about the idea of an absolute present in GR seem to mention closed timelike curves as being problematic for the concept, but nothing about black holes precluding them.

In other words, time travel is problematic for presentism (who knew right?), so it would be a problem for them if we lived in a world where time travel is possible, but I don't think they should lose sleep over their possibility since closed timelike curves have a number of other wild consequences to them (such as retrocausality) which make their existence unlikely.

Thanks for your initial responses.

I've been in discussion about this on physics sites, but they don't care so much there about the metaphysical implications to absolute time interpretations.

As you can see, any event can be located in an inertial frame, but only those events within our past light cone can be detected by us now. Events outside that cone are still in the reference frame but cannot influence us. — Kenosha Kid

You've drawn flat Minkowski spacetime (with arbitrary inertial frame) in which light from any spatial location will reach any other location. That makes it an inappropriate model of the large scale universe where light that is currently say 17 GLY away will never get here, not in 17 billion years or ever.
Earth has an event horizon, and Minkowski spacetime does not. The universe cannot be foliated with such a coordinate system.

Gravitation can't be accurately described by inertial frames but require curvilinear coordinate systems. — Kenosha Kid

You can still foliate reasonable gravitation in 'bent' Minkowski spacetime, but not black holes. So for instance, a device measuring absolute time here on Earth would run apparently faster than one on the surface of Saturn due to the lower gravitational potential here on Earth. The same device on a ship with relativistic absolute speed would similarly appear to run faster (than the clock next to it) than it would if the ship had low peculiar velocity.

I don't get this. Why would they have to reach us? — Mr Bee

There's no requirement for light to reach any location from any other since there are very much cases where that does not occur. My point was that in an inertial frame, light can reach location X from Y given enough time, and thus such a model is not a model of our universe.

The light will never reach us because of cosmic expansion, so the fact that we don't see them doesn't mean they don't exist.

If there is a boundary to an inertial frame, then event outside that boundary do not exist in that frame. An inertial frame does support cosmic expansion, but it does not support acceleration of that expansion. So given no such acceleration, there would be no event horizon and light will eventually get from location X to Y given time. And even locally, an inertial frame cannot foliate the interior of black holes, so it fails twice.

I'm not sure about that. As far as I know, any spacetime that doesn't allow for closed timelike curves is open to being sliced into global hypersurfaces.

There are indeed ways to do it with a single black hole, but you must assume the black hole is at some kind of privileged location. So consider 3 events: A clock is dropped into a black hole. Event A is that clock 1 second (measured on that clock) after passing the event horizon. The black hole is big enough that it survives at least one second. The rock is dropped from a hovering location outside, which shines light down on the dropped clock. At some point the last light is emitted from this location that will catch up to the dropped clock before it hits the singularity. Event B is that hovering location 1 second after that last light goes out.
Event C is at the location of the former black hole after it has evaporated.
Yes, you can come up with various schemes to order these three events, but do any of those schemes order all of spacetime? OK, C occurs after B since it is in the future light cone of B. That's easy. Not so easy with event A.


I'm not suggesting retrocausality anywhere. Event A is not causally connected with either B or C, so no objective ordering scheme is going to produce a contradiction unless B is in A's future but C is in A's past.

noAxioms!

Two quick questions:

1. Does black hole time travel increase or decrease Time ( I can't remember)?
2. Do black holes contribute to Multiverse theories at all?

You've drawn flat Minkowski spacetime (with arbitrary inertial frame) in which light from any spatial location will reach any other location. That makes it an inappropriate model of the large scale universe where light that is currently say 17 GLY away will never get here, not in 17 billion years or ever.
Earth has an event horizon, and Minkowski spacetime does not. — noAxioms

It's perfectly appropriate for that: that's just light further outside the light cone. It being further away just means its further away. Minkowski spacetime is not appropriate for gravity, though.

You can still foliate reasonable gravitration in 'bent' Minkowski spacetime, but not black holes. — noAxioms

Not sure what you mean. Never heard of 'bent' Minkowski spacetime or anything in which that would make sense. Minkowski spacetime is, as you said, flat.

So for instance, a device measuring absolute time here on Earth would run apparently faster than one on the surface of Saturn due to the lower gravitational potential here on Earth. The same device on a ship with relativistic absolute speed would similarly appear to run faster (than the clock next to it) than it would if the ship had low peculiar velocity. — noAxioms

Is this what you mean? Well, this is exactly how you do GR in practise: you treat, at any given event, the spacetime as that of SR. That was Einstein's devised approximation.

1. Does black hole time travel increase or decrease Time ( I can't remember)? — 3017amen

Black holes slow down time, right to a standstill at the singularity.

2. Do black holes contribute to Multiverse theories at all? — 3017amen

Yes, Smolin's multiverse theory, also once forwarded by Hawking, is that black holes are baby universe that inherit laws of physics from the parent universe. This is cosmological Darwinism.

My point was that in an inertial frame, light can reach location A from B given enough time, and thus such a model is not a model of our universe. — noAxioms

I don't see how that is a consequence of a global inertial frame. Light may not reach us for other reasons unrelated to it, one possibility being the cosmic expansion of the universe being faster than light.

If there is a boundary to an inertial frame, then event outside that boundary do not exist in that frame. — noAxioms

You seem to be mixing up the boundary of the observable universe with the "boundary" of an inertial frame, the latter of which I don't really understand. They are both not the same.

There are indeed ways to do it with a single black hole, but you must assume the black hole is at some kind of privileged location. So consider 3 events: A clock is dropped into a black hole. Event A is that clock 1 second (measured on that clock) after passing the event horizon. The black hole is big enough that it survives at least one second. The rock is dropped from a hovering location outside, which shines light down on the dropped clock. At some point the last light is emitted from this location that will catch up to the dropped clock before it hits the singularity. Event B is that hovering location 1 second after that last light goes out.
Event C is at the location of the former black hole after it has evaporated.
Yes, you can come up with various schemes to order these three events, but do any of those schemes order all of spacetime? OK, C occurs after B since it is in the future light cone of B. That's easy. Not so easy with event A.

I'm not suggesting retrocausality anywhere. Event A is not causally connected with either B or C, so no objective ordering scheme is going to produce a contradiction unless B is in A's future but C is in A's past. — noAxioms

I don't really have the expertise to properly address this (hopefully someone like @Kenosha Kid can chime in here and give his input). My understanding is that it is mainly spacetimes with closed timelike curves that preclude the existence of global hypersurfaces, but I haven't heard anything about black holes doing the same.

Two quick questions:

1. Does black hole time travel increase or decrease Time ( I can't remember)?
2. Do black holes contribute to Multiverse theories at all? — 3017amen

Time slows (is more dilated) when deep in a gravity well, So clocks on Earth for instance run objectively slower than say GPS clocks (which are very high up and not moving fast). Those GPS clocks are slowed due to their orbital motion, but the gravity effect is greater at that altitude. Clocks on the ISS run slower than the ones on the ground due to minimal gravitational potential difference in low orbit, coupled with significant dilation from the higher orbital velocity. So at an altitude of 1.5 R (R being Earth's radius), the two effects cancel out and orbiting clocks can be synced indefinitely with those on the ground.

Similarly, from the PoV of the distant observer, a clock falling into a black hole freezes on the event horizon. It doesn't just appear to freeze. Coordinate time slows and actually stops there.
From the PoV of the observer falling in, he sails right in without a hitch, and the universe behind him appears to speed up, but not infinitely so. There's definitely a time outside the black hole beyond which is not part of his past light cone, and thus is not observable.

About the multiverse thing, I think there are theories that a black hole in one universe is a white hole from the perspective of the interior spacetime. I think we're possibly supposed to be in such a white hole in some of these theories, except I don't see how we could be expanding then. There's no singularity (big crunch) at the end of time like one would expect from a geometry with an abrupt cessation of time like that.

I don't really have the expertise to properly address this (hopefully someone like Kenosha Kid can chime in here and give his input). — Mr Bee

I got lost at:

The rock is dropped from a hovering location outside, which shines light down on the dropped clock. — noAxioms

It's not clear what frame of reference we're in here. From the perspective of an observer outside the event horizon (with some magic blackholescope), the clock will accelerate toward the singularity and run slower and slower. Any photons emitted from the rock (which is getting further and further away from the clock) will still travel at the speed of light and catch up with the clock, because the clock cannot move at the speed of light. Effectively, there will be a time at the singularity in which no more photons can hit the clock because the clock has no future. From this perspective, the clock is part of the singularity at this point.

From the rest frame of the clock, it is in perpetual free fall. Eventually the rock will simply recede so far into the distance it cannot be detected. The limit of this is an event horizon for the rock after which no more new light can reach the clock. However! If we call Event A the first photon emitted that will reach the clock and Event B the last photon emitted by the rock that can reach the clock, there is still light emitted between A and B that the clock has not yet "seen". So the light ought to get dimmer and ever redshifted, but should never stop. The last photon emitted by the rock that the clock will ever see must be when the clock has no future, which is, in the clock's rest frame, at t=infinity.

It's perfectly appropriate for that: that's just light further outside the light cone. It being further away just means its further away. Minkowski spacetime is not appropriate for gravity, though. — Kenosha Kid

You don't comprehend my explanation, so I'll try to comprehend your vision.

Perhaps you can explain a distant galaxy then using this coordinate system. Gravity at very large scales is negligible, so space is effectively flat so long as we're not noticing lensing effects and such.
So take GN-z11, a very distant thing with redshift of over 11.
Using your coordinate system, where (and when) is the event when the light was emitted that we see of it today? The wiki site says it was emitted 13.4 billion years ago, but it could not have got far enough away in only 400M years for light to take that long. Of course, wiki isn't using inertial coordinates when making that statement, so kindly describe the situation in those terms. Where is the emission event? If it vanishes today, will we ever see that from here if we wait long enough?

I don't see how that is a consequence of a global inertial frame. Light may not reach us for other reasons unrelated to it, one of which is the cosmic expansion of the universe being faster than light. — Mr Bee

There is no cosmic expansion under inertial spacetime. There is only an explosion of stuff from a point, with nothing moving at faster than c.

If there is a boundary to an inertial frame, then event outside that boundary do not exist in that frame.
— noAxioms

You seem to be mixing up the boundary of the observable universe with the "boundary" of an inertial frame, the latter of which I don't really understand. They are both not the same.

They are indeed not the same. The boundary of our inertial frame is much less than the 47 BLY radius of the observerable universe, and even less than the ~16 BLY distance to the event horizon. The current radius of our inertial frame must be 13.8 BLY because nothing outside that radius could have come from the big bang without moving faster than c, and nothing moves faster than c in an inertial frame.

My understanding is that it is mainly spacetimes with closed timelike curves that preclude the existence of global hypersurfaces, but I haven't heard anything about black holes doing the same.

Your understanding here is fine. Nobody is proposing a closed timelike curve. Any foliation, objective or not, would preclude that.

I got lost at:

The [clock] is dropped from a hovering location outside, which shines light down on the dropped clock.
— noAxioms

It's not clear what frame of reference we're in here. — Kenosha Kid

First of all, I meant dropping a clock, which seem more useful than dropping a glowing rock. I used a rock at first and neglected to change them all to 'clock'. But it moves like the rock: not under propulsion or anything.

The light shines from the hovering station. It can be light from the clock displaying the time if you will. The time is the proper time of the hovering space station that maintains a constant distance from the black hole. We can build a shell around if you like it so we don't need to expend fuel to stay indefinitely at that location.

From the perspective of an observer outside the event horizon (with some magic blackholescope), the clock will accelerate toward the singularity and run slower and slower. Any photons emitted from the rock (which is getting further and further away from the clock) will still travel at the speed of light and catch up with the clock, because the clock cannot move at the speed of light.

I've caused confusion. The rock and the dropped clock are the same thing. The space station can watch it fall in, but if it reads time T when it crosses the event horizon, then the space station will never see the clock read anything after T. It will appear from the space station to slow and approach but never reach T. Event B is that clock when it reads T+1.

From the rest frame of the clock, it is in perpetual free fall. Eventually the rock will simply recede so far into the distance it cannot be detected.

Again, they are the same thing, so the clock indeed will eventually reach the abrupt end of time and tick it's last, so to speak. This is assuming the clock is a point device that isn't destroyed by excessive violence like tidal forces before it gets to the singularity.

If you want to describe a clock and a rock dropped say at separate times, you need to lay out the scenario. I never meant for there to be two things falling like that.

As No Axioms already explained, relativity tells us that extreme gravitational wells like black holes will severely dilate time (if you've ever seen the movie Interstellar, they cover this reasonably well with the extreme time dilation experienced on the "water world" planet they first visit, close to the black hole Gargantua)- we can and have even measured this in less extreme cases, like in Earth orbit, and indeed GPS satellites would quickly cease to operate effectively if this was not accounted + corrected for. So time "runs slower" in such a gravitational field. To an outside observer, an astronaut falling into a black hole moves increasingly slowly... until they appear to freeze entirely at the event horizon.

Worse, at the event horizon, time dilation becomes so extremely that, from the perspective of the outside observer, events there do not ever occur- not even after an infinite amount of time has passed. They are dilated infinitely far into the future. So from the perspective of the outside observer the infalling astronaut never actually crossed the event horizon (although from the astronaut's perspective they certainly do- though they don't necessarily notice anything special when they cross the point of no return), and events inside the black hole cannot be consistently assigned a spot on any outside observers timeline: those events are dilated infinitely distant into the future- they never occur, from the perspective of those outside of it, even after an infinite amount of time has elapsed. But of course to those inside, these events are very real: including/especially the astronauts inevitable demise inside the black hole!

And I'm not sure that black holes directly imply any multiverse theories, the way that e.g. a geometrically flat, infinitely extended (spatially) universe implies a cosmological multiverse, or some interpretations of QM imply a quantum multiverse. But black holes do figure prominently into at least some "multiverse(ish)" hypotheses, like Smolin's cosmological natural selection hypothesis where "baby" universes are spawned within black holes (and so you get this nested hierarchy of universes within universes and so on). It is at least highly intriguing that the only place where conditions approach those of the early (Big Bang) universe are the interiors of black holes, and maybe even moreso the fact that a time-reversed black hole (i.e. a white hole) looks eerily similar to the Big Bang itself.

The wiki site says it was emitted 13.4 billion years ago, but it could not have got far enough away in only 400M years for light to take that long. Of course, wiki isn't using inertial coordinates when making that statement, so kindly describe the situation in those terms. Where is the emission event? — noAxioms

Right. So, first, there was a supposed stupendous inflation period in the early universe that cannot be described by any inertial frame. Second, it is unexpected that the galaxy would have formed 400M years after the big bang, i.e. it is a cosmological and astronomical mystery but a) that doesn't stop it being 13.4 billion light years away from us when it did form and b) such a mystery can be a sign of an incomplete or faulty model. Cosmology is still in its infancy and while recent successes like gravity wave detection and the black hole image speak well of the underlying theory (general relativity), it is likely that the cosmological model has some kinks to work out yet.

One possibility is that there exist some regions where inflation carried on a lot longer than others. A longer period of inflation between us and GN-z11, for instance, might explain why it could have formed less than 13.4B LY away from us but still appear 13.4B years old. Or maybe it turns out 400M years is long enough to start making galaxies. I'm sure the answer will be profound.

I've caused confusion. The rock and the dropped clock are the same thing. The space station can watch it fall in, but if it reads time T when it crosses the event horizon, then the space station will never see the clock read anything after T. It will appear from the space station to slow and approach but never reach T. Event B is that clock when it reads T+1. — noAxioms

I understand, I think. There are two related effects going on here, and I was referring to the first with my magic blackholescope: from the observer's point of view, time slows down for the clock the faster it moves due to the BH's gravitational pull; light emitted from the clock is also redshifted by gravity.

So it is true to say that, if the clock were a regular emitter for instance, light from the clock would reach the observer ever more slowly. And it is also true to say that no more light will reach the observer once the clock passes the event horizon. But the second is not a continuation of the first because the clock will still have a subluminal velocity even at the event horizon, therefore its time will not have slowed to a standstill. Rather, the light from the clock is redshifted to zero frequency at the event horizon. The light will appear redder, go through infrared, then microwave, then radiowave frequency bands then, at the horizon, will disappear.

. It is at least highly intriguing that the only place where conditions approach those of the early (Big Bang) universe are the interiors of black holes, and maybe even moreso the fact that a time-reversed black hole (i.e. a white hole) looks eerily similar to the Big Bang itself. — Enai De A Lukal

In you all's learn-ed opinion, since science namely theoretical physics, seem to be split on what existence was like before the Big Bang, could multiverse theories be an attempt to explain causation prior to the Big Bang?

Because multiverse theories cannot be falsified, I realize that it seems the floodgates tend to open-up allowing for all sorts of radical ideas. I'm in the process of studying this a bit more, and was also wondering how it could possibly square with the concept of eternity, Platonism, and unchanging timelessness.

As a very rudimentary example, what in theory, would exist outside of the block universe?

Hi 3017. That might be more on-topic here: https://thephilosophyforum.com/discussion/8635/dark-matter-possibly-preceded-the-big-bang-by-3-billion-years

You have to be careful distinguishing different types of multiverses, since what is true of one isn't necessarily true of the other- they are posited in different contexts and for different motivations (i.e. to address different types of problems/concerns, or to explain different kinds of observations) and can be structured entirely differently from one another (i.e. how the different universes relate or exist relative to one another- do they just precede one another in time? Do they exist alongside one another but are causally disconnected? etc.). Cyclical cosmologies (at least a few of which can be characterized as "multiverses")- where the expansionary phase of the universe is follow by a contracting phase which is in turn follow by an expansionary phase and so on- can and do speak to a pre-Big Bang epoch- and the removal of the hypothetical t=0 singularity is considered a feature of loop quantum cosmology (and hopefully other candidates for a successful quantum theory of gravity).

Its also not the case that multiverse theories are generically untestable or unfalsifiable. Some of them certainly seem to be, others not, and this differs from case to case in the same way multiverse theories themselves differ (i.e. as mentioned above). So its difficult to talk about "multiverse theories" in general with any accuracy, since they don't have all that much in common once you get into the details. Have to be sure to specify what flavor of multiverse you have in mind.

The wiki site says it was emitted 13.4 billion years ago, but it could not have got far enough away in only 400M years for light to take that long. Of course, wiki isn't using inertial coordinates when making that statement, so kindly describe the situation in those terms. Where is the emission event?
— noAxioms

Right. So, first, there was a supposed stupendous inflation period in the early universe that cannot be described by any inertial frame. — Kenosha Kid

GN-z11 is about 2/3 of the way to the edge of the visible universe. Immediately after inflation, the size of the visible universe was anywhere from a grain of sand to a city block, depending on your model. A 1 meter head start isn't going to get that object (or rather, the material that would eventually become it) out far enough to be 13.4 GLY away when that light is emitten only 400 MYr later

Second, it is unexpected that the galaxy would have formed 400M years after the big bang

OK, you're allowed to give it more time, but how long do you want? It's going to take 13.4 billion years to get far enough away, at which point there's no time left to send the light back to us here.

i.e. it is a cosmological and astronomical mystery but a) that doesn't stop it being 13.4 billion light years away from us when it did form

Actually it does stop it. It's not a mystery, it's a physical impossibility in an inertial coordinate system for something to move 13.4 BLY away and then send a signal back, all in 13.8 BYr. Waving your hand around and spreading 'I don't know/it's a mystery' dust all over the place isn't a viable model.

I take it you're not familiar with the comoving coordinate system (which does foliate spacetime to any distance) or the FRW models of the universe (from which that 13.4 BY figure comes). I'm not here to debate the viability of an inertial coordinate system to describe the universe. Trust me, it isn't a candidate. I'm here to discuss my argument against absolute time, with people who know their physics sufficiently to comment productively on it. This is not that discussion.

could multiverse theories be an attempt to explain causation prior to the Big Bang? — 3017amen

There are at least six kinds of multiverses discussed. Tegmark enumerated them as Level 1 (other Hubble spheres), Level 2 (other bubbles in eternal inflation theory), Level 3 (other quantum worlds), and Level 4 (other unrelated structures). There is also the Smolin evolutionary thing where the interiors of black holes are considered to be other universes. If Level 1 is our universe but spatially 'not here', then there should be a Level 0 which is our universe but temporally 'not now'. That's six at least.
Of those, it is probably the Level 2 multiverse that most qualifies as an attempt to explain causation of the Big Bang. It is also the model that explains the fine-tuning argument.
The Smolin evolutionary thing also seems to attempt this, but each universe created is of infinitesimal magnitude (matter and energy and such) compared to its parent, so it's hard to see how that can continue for enough generations for evolution to be effective.

As a very rudimentary example, what in theory, would exist outside of the block universe?

Whether it is interpreted as block or not seems immaterial. Look into eternal inflation theory. Wiki has a terse entry on it. I found a more comprehensive description in Tegmark's Mathematical Universe with some illustrations that help with visualization. There are other 'universes' that have different number of spatial and temporal dimensions, and the vast majority of them cannot produce complex physical states.

Worse, at the event horizon, time dilation becomes so extremely that, from the perspective of the outside observer, events there do not ever occur- not even after an infinite amount of time has passed. — Enai De A Lukal

I need your opinion then. OK a foliation based on the perspective some outside observer cannot account for events beyond the event horizon, and thus seems to not to be a viable candidate for an objective foliation of all of spactime. Is there some other coordinate system that is actually up to the task? If not, is this a valid falsification of objective space and time such as is proposed by Lorentz Ether Theory? This is not even including those interpretations that additionally posit a preferred moment in time.

So you drop an absolutist into a black hole, then ask him, what's your brother doing now? His inability to give a coherent answer seems to falsify his view, but then until we drop him in like that, I suppose he's free to deny the interior events altogether, which seems to be the only recourse.

the current inertial frame of Earth won't do: There are objects beyond our event horizon (events from which light can never reach us even in infinite time). — noAxioms

I don't see why an absolute coordinate system would be obligated to propagate that the speed of light. Hence, those events that are beyond our event horizon nevertheless might have a particular position in an absolute coordinate system.

The answer to your question seems to me to be that any coordinate system might be set up as absolute; relativistic physics specifies how we translate from any frame to any other frame, so calling any frame of reference absolute becomes simply irrelevant.

Yeah I would assume that the extreme time dilation in the vicinity of a black hole- culminating in the infinite time dilation at the event horizon itself (and the absolutely off-the-wall implications that carries)- would be very problematic for any form of absolutist wrt spacetime... but then I'm not familiar with this debate (absolutism vs. relationism) outside of Smolin's discussion in the context of his cosmological natural selection (which was largely historical in nature), and I would have assumed that relativity in general made any sort of absolutism about spacetime a non-starter and more or less settled the matter..

but as that is evidently not the case (if the philosophical debate persists to this day), I think I must be missing quite a few of the relevant issues. I'm actually reading the Stanford entry on this right now, to get a bit more background on this particular dispute.

Thanks for your input as always. What are your thoughts on the general idea that black holes preclude a global slicing of spacetime? I always assumed it was just closed timelike curves would make them impossible but noAxioms apparently thinks otherwise.

the current inertial frame of Earth won't do: There are objects beyond our event horizon (events from which light can never reach us even in infinite time).
— noAxioms

I don't see why an absolute coordinate system would be obligated to propagate that the speed of light. — Banno

A coordinate system doesn't propagate. You mean light propagates at c in a coordinate system. This is more or less true for an intertial coordinate system, with variation on speed due to changes in gravitational potential. So light from another star often gets to us at slightly greater than c due to most of the trip taking place in space at higher gravitational potential than we have here.
Light in an inertial coordinate system can get from any location to any other in a time dependent on the separation of the two locations. This does not describe our actual universe.

Hence, those events that are beyond our event horizon nevertheless might have a particular position in an absolute coordinate system.

They do in some coordinate systems, but they don't have a particular position in our inertial frame.

The answer to your question seems to me to be that any coordinate system might be set up as absolute; relativistic physics specifies how we translate from any frame to any other frame, so calling any frame of reference absolute becomes simply irrelevant.

No coordinate system works. That's been my point. Every choice leaves parts of spacetime unordered. As Enai puts it: There are always events that cannot be consistently assigned a spot on any choice of objective timeline.

A coordinate system doesn't propagate. — noAxioms

Indeed; that is exactly my point.

As Enai puts it: There are always events that cannot be consistently assigned a spot on any choice of objective timeline. — noAxioms

events inside the black hole cannot be consistently assigned a spot on any outside observers timeline... — Enai De A Lukal

These are not the same.

Not literally, sure, but I think the upshot is the same: if the events at/beneath the event horizon do not ever occur from the perspective of the outside universe, any timeline including those events will be inconsistent with that of the outside universe. But any timeline not including those events will be inconsistent with that of e.g. the infalling astronaut- from their perspective, they most definitely cross the event horizon, and go on to meet whatever unpleasant fate awaits them within the black hole (probably being turned into a human spaghetti-noodle).

But so this is why- from my admittedly extremely limited/rough understanding of this debate- its hard to see how this isn't fatal for any "absolutist" notion of spacetime: what is absolute here, if there are collections of events (black holes) that do not ever occur from the perspective of the outside universe, and no self-consistent timeline that includes them both?

Hang on, I'm not following. For someone outside the hole the astronaut falls forever, For the astronaut, the fall occurs over a finite time.

If someone outside the hole applies the appropriate transformations to their forever-falling astronaut, they will find that form the astronaut's perspective the fall is finite.

If the astronaut applies the appropriate transformation, they will find that for someone outside the hole the fall takes forever - or more.

I don't see any inconsistency. What did I miss?

Every choice leaves parts of spacetime unordered. — noAxioms

I do not see that this has been shown.

Actually it does stop it. It's not a mystery, it's a physical impossibility in an inertial coordinate system for something to move 13.4 BLY away and then send a signal back, all in 13.8 BYr. — noAxioms

That is a limitation of inertial frames, not of the physical universe. Also, you seem to think that if we see light from a star 13.4B LY away, there must have been a time when that star was very close to us. That is not right. It didn't have to "move 13.4 BLY away and then send a signal back". Stars did not emerge from the big bang.

I'm here to discuss my argument against absolute time, with people who know their physics sufficiently to comment productively on it. This is not that discussion. — noAxioms

You mean pretend physics, which requires a pretend physicist to discuss it with? Fair point, I am not that person. Gimme a holler if you need someone who taught relativity at university though. I'm sure it won't measure up to pretend physics but it has its place.

What are your thoughts on the general idea that black holes preclude a global slicing of spacetime? I always assumed it was just closed timelike curves would make them impossible but noAxioms apparently thinks otherwise. — Mr Bee

My experience is that slicing is not precluded. It depends on the origin of reference frame. If it's outside the event horizon, you can still slice, but if the slice intersects the horizon you have to treat the exterior and interior separately. This isn't particular to slicing. Spherically symmetric slicing for some model black holes with the origin inside the horizon have also been shown to work.

Good to know, thanks. Again it's nice having an expert around to keep us philosophers in check :smile: .

I'm not particularly an expert on GR (my field was QM), so you oughtn't to assume an overriding authority from me. However I know enough to have lectured a syllabus and have an interest in it.

This question seems based on an error. It's worth reiterating though that the problems expressed here are not physical problems. The Einstein equations are notoriously difficult to solve exactly (there are only a handful of known exact solutions) and, as I said earlier, the easiest way to solve them is to treat spacetime as a series of locally flat spacetimes (slicing or threading). As with any such approximation, this brings with it certain problems (e.g. sensitivity to initial conditions not captured by the initial inertial frame) and has certain limits (where spacetime cannot be shown to asymptotically approach flat spacetime, such as at the centre of a black hole). Black holes are not features of special relativity, only exact GR.

So there is little profundity to be found from these problems. They have to be overcome not to get a better idea of spacetime directly, but to numerically solve approximations to the Einstein equation and (hopefully) gain insight about spacetime that way, i.e. they are pragmatic only*. Any generalisation about these problems to the physical universe is seriously flawed.

*They are more important to quantum gravity because SR is the only feasible consistent way of describing Einsteinian gravity (as opposed to e.g. gravitons) quantum mechanically. But, still, this is a practical problem rather than a fundamental mystery of the universe.

If someone outside the hole applies the appropriate transformations to their forever-falling astronaut, they will find that form the astronaut's perspective the fall is finite. — Banno

No such transformation exists since the astronaut never crosses the event horizon, so there can be no transformation of events beyond that from either frame to the other.

If the astronaut applies the appropriate transformation, they will find that for someone outside the hoel the fall takes forever - or more.

He cannot apply the transformation, which is what is meant by events that cannot be consistently assigned a spot on the outside observer's timeline. His events do not exist at all on that outside timeline.

That is a limitation of inertial frames, not of the physical universe. — Kenosha Kid

Exactly, which is why I say that inertial frames do not describe the universe.

Also, you seem to think that if we see light from a star 13.4B LY away, there must have been a time when that star was very close to us. That is not right. It didn't have to "move 13.4 BLY away and then send a signal back". Stars did not emerge from the big bang.

The material/energy from which they are comprised very much did.
Cosmologists estimate that the light we see now from GN-z11 was emitted when the universe was around 0.4 BY old, and was emitted at a proper distance from here of about 2.8 BLY at the time, which is closer than the emission distance of other galaxies with somewhat lower redshift. Light from a galaxy with redshift z=2 for instance was emitted at a proper distance of around 5.8 BLY away. That has the unintuitive effect that the more distant galaxy (the one receding faster) appears larger (greater angular measure) than a similar size object that is closer. Were the same two objects to be viewed in a Minkowski inertial universe, the angular measure of the higher redshift object would be smaller.

The material/energy from which they are comprised very much did. — noAxioms

Yes, that's true. But when we gaze at a galaxy 13.4B LY away, we are not seeing the material and energy that would later form that galaxy, we are seeing the formed galaxy. Ergo the galaxy did not form close to us then "move" 13.4B LY away from us. It was 13.4B LY away from us when it emitted the light we are seeing now.

Exactly, which is why I say that inertial frames do not describe the universe. — noAxioms

For sure, LETs can't describe black holes. There's no aether definable at or within the event horizon, although people have tried. You don't need to foliate spacetime to get to this conclusion, nor consider events outside the light-cone as being outside the entire reference frame. Black holes are curvatures of spacetime, i.e. assuming they exist is assuming your conclusion. The natural questions would be: what is the closest thing to a black hole in LET (the static aether), and is it consistent with empirical evidence?