I've not read the whole thread, but responders are not always in accordance with physics. Mostly I see Tegmark's works countered with argument from incredulity, especially in the other thread that actually discusses MWI and level-4 universes. My interpretation of choice is probably RQM, not MWI.

MWI is unrelated to a level-1 multiverse. The argument that there are infinite copies of yourself seems to presume counterfactuals, which MWI does not, so right there Tegmark's stated preferences precludes the existence of an identical copy of yourself out there. So I will proceed under the premise of 1) a universe of infinite spatial extent, and 2) a quantum interpretation that supports counterfactuals, such as Bohmian mechanics.

I want to discuss his first type (I won't give my opinion about the other three as this probably gets me in trouble...). In an infinite universe, so Tegmark conjectures, there are infinite Hubble volumes and in this infinity an infinite of exact copies of you and me exist. — Cornwell1

Funny that it's worded that way. Hubble volumes have nothing to do with it. We can see objects that are currently outside our Hubble volume, so clearly those objects have a causal influence on us.

This can't be true because all Hubble volumes interact with their surroundings.

Fallicious reasoning. A given state (say current state of Earth) has a finite set of events in its past light cone, which was (as measured in proper distance) was merely the size of a grapefruit at the end of the inflation epoch, grew to a maximum proper size of nearly 6 billion light years around 7 billion years ago, and is today the size of Earth. By definition (and assuming cause and effect cannot happen faster than light), no event inside that past light cone can interact with an event inside that light cone.

So all we need for an identical Earth is for some finite volume of space (a similar light cone) out there with identical state. There are only a finite number of possible states for this finite volume, which Tegmark computes, hence there must be infinite copies given an infinite number of rolls of this finite sided die.

Suppose there is such a copy in a Hubble volume identical to the one we live in. How can this be? Near the border of our volume, there is interaction with stuff outside of the volume

Yes, which is why Hubble volume is useless. It affect the thing at the edge of the Hubble volume, but it doesn't effect you, so it matters not. Use past light cone instead of Hubble volume, and the logic works.

Tegmark's argument does not proceed along these my lines at all, and nor the one you describe. He does use a Hubble volume (like that matters. Only Earth matters). He computes that any finite volume can, at any given time, be only in some finite number of states. It's causal past is not considered. Since it is a current state, influence from the outside of the arbitrary volume is similarly moot. Infinite volumes divided by finite states makes for a vanishingly small probability of each state not appearing elsewhere.

which creates a difference between our volume and the identical volume somewhere else.

No it doesn't. It might mean that the identical (arbitrary) volume evolves subsequently differently, but that has no effect on the existence of the copy of you already at the center.

Am I right or am I left?
Worth a poll?

Polls get you opinions. The above is logic, not opinion.

Extra credit: Tegmark's argument (finite state possibilities of a given volume) is stronger than mine (worded from a causality standpoint). Can you point out why?

Personally (opinion here) I don't think there's an exact copy of me out there, but only because I don't accept all the premises I list above, not because the logic is faulty. I do accept the infinite spatial extent premise, without which the argument is meaningless. If it's finite at all, it's probably smaller than the insane large number that Tegmark computed for the nearest copy.

Been reading most of this thread without interfering, but this comment struck me wrong.

My intuitive sense is that people have no feel for what might be beyond the physical because they're instinctively oriented around the world of sensory detection - that only what can be sensed, weighed, measured by the senses or by scientific instruments is real. — Wayfarer

Only by physical instruments. Any physical instrument can serve as a scientific one, so maybe the distinction is unnecessary, but your choice of words seems to limit your thinking only to 'gadgetry', so to speak, as illustrated by your following comment:

Obviously today's scientific instruments are unthinkably powerful but people still have trouble understanding the sense that there might be some dimension or domain that is not available to apprehension by those means.

But the human body (among other things perhaps) is such a physical instrument, hardly 'unthinkably powerful' and yet you assert this other domain is available to it. That means a physical device (your body) is measuring this domain somewhere. All you have to do is investigate where, which is after all a scientific endeavor. Perhaps we can build a simple device that measures the same thing.

It is irrefutable that only a consciousness brings the wave function to collapse. — SolarWind

It is even more irrefutable that wave function collapse does not require consciousness. It seems that others are pointing this out. Wigner himself abandoned this interpretation when it was shown to logically lead to solipsism. Solipsism is another irrefutable thing.

Almost all quantum experiments take place without a human observer, except to gather the data afterwards.

What counts as an observer? — TiredThinker

Metaphysically, it is one system interacting with another, in any way.
Epistemologically, it seems to be a function of awareness, be it human or otherwise.

Can they use an electronic eye to see and record where the photon actually goes

You can't watch a photon. If you measure its path, any interference disappears.

and half the time delete the results before a human becomes aware of it

Human awareness does not play a metaphysical role (except in the Wigner interpretation). A result can be kept in superposition, but I know of no way to 'delete' a measured result.

I want to know if the electronic eye is interfering with the experiment and collapsing the wave function, or if it is awareness by a conscious human being.

The E-eye is not necessary either. Any interaction (the photon hitting the far wall in a room with no people or sensory devices) is enough to collapse the wave function, in interpretations with wave function collapse.

The guy didn't behave the same afterwards, whereas the zombie behaves indistinguishably from a 'human' in the same situation, so it doesn't really fit the definition.

Nice example though. Be interesting to have the dualists give their explanation of it. Somehow the surgery seems to have cut off the 'uplink' for 'mal-data' to wherever it gets 'processed' in a way that could be interpreted as pain. The data still gets through to say the rational area, but not to the area which causes distress. How might a dualist explain the 'mind' still getting the data for pain, but not feeling it? It's not like the mind was modified, only some connection in the brain.

Just for info, I do notice that there's multiple 'minds' in me. They hold different (contradictory even) beliefs, and one of the two is clearly in charge, but the other isn't epiphenomenal. But both of them seem physical. No funny external magic thingy.

User whatever terms you like, but your first person experiences of warmth, pain, color, etc. are not part of the physical descriptions of the world. — Marchesk

Your opinion is noted, but it provides negligible evidence falsifying an alternate one.

I find the p-zombie description not only possible, but a more accurate description of what's going on. A biological being such as you describe (with agency) would have evolved differently than what we see. Everybody tends to selection-bias that away. I did an old thread on the subject on the defunct PF. Can't reference it anymore. :sad:

Is the thermostat biologically equivalent to you? — Marchesk

Most thermostats are not biological, and are thus not the biological equivalent of anything.
I am, however, presenting one as a crude mechanical equivalent of "processing data which could be interpreted as 'feeling warmth'", which is what I claim noAx does.
Sorry for the 3rd person reference, but some of the prior posts have been getting a bit undefined as to what exactly 'I' refers. noAx is the physical biological human.

But this isn't about what words you can and can't use if you subscribe to this or that.

Yes it is. Chalmers forbids the usage of 'feels warmth' for the zombie, and the thermostat is a zombie, lacking the added bit that is the difference between zombies and humans. So the word is forbidden, despite the fact that the thermostat measures (via physics!) temperature and reacts to it, exactly as the zombie does. The vocabulary is reserved (by proponents of the existence of the ';additional bit') for objects that have that additional supernatural bit, as evidenced by assertions of 'lies' when the zombie claims that he also feels warmth.
I chose the thermostat since it is the ultimate in trivial data processing. A sensor and a single mercury switch is enough, the opposite end of the complexity spectrum compared to noAx, but fundamentally doing the same thing.
A rock also reacts to warmth, possibly by breaking, but it lacks both explicit sensor and an information processor, at least of the sort with which we're typically familiar.

It's about the fact that you do feel warmth.

Chalmers claims that the feeling of warmth can only be had by some supernatural experiencer, and since noAx is not one of those, noAx no more can feel warmth than can the thermostat. I refuse to be placed in a privileged category over it, unearned.

I tend to think [thermostats] are incapable of feeling warmth, although I wouldn't rule some form of panpsychism completely out.

Oooh, magic sauce!

I simply don't believe you when you claim skepticism about feeling warmth just because you can't say the same for thermostats in this discussion.

I'm merely skeptical of this immaterial experiencer/possessor, or of the magic sauce, or however it's presented. Surely I'm not the first person on these forums skeptical of dualism.

Of course they are. This is why they tend to say we have these properties, but these things over here, they don't. — InPitzotl

Don't or can't? This seems awfully begging to me.

if you had your name scratched onto the toaster when I stole it, it will tend to still be scratched on there unless I scratched it off.

Would it make it not the same toaster if the name got scratched off, or was never there in the first place? Despite my calling it a 'legal identity' (an old habit), I'm not talking about being able to prove the fact to a court of law. I'm talking about it actually being the toaster in question or not.
Perhaps 'pragmatic identity' fits better.

We might could even say certain arrangements of physical objects have privileged status, raising them above other arrangements.

That's not the story being pushed:

A zombie is physically identical to a normal human being, but completely lacks conscious experience.
— consc.net/zombies-on-the-web — InPitzotl

Per this assertion, the lack of privilege does not come from a defect or other difference in the physical arrangement.

The "I" I accused you of having is simply a unit of theory of mind as it applies to the linguistic aspect of your posts.

Not how I'm using it when I make a distinction. The "I" refers to the non-physical experiencer, the thing that gives the privilege.

You, OTOH, meet the requirements to apply theory of mind to as humans above the age of five regularly do.

Age of five eh? Does that imply you were a zombie until some sufficient age? What do you experience before then?

A computer can't tell you it's conscious? — frank

Only if someone conscious programs it to. — Janus

While there are plenty of computers running fixed algorithms that just play pre-recorded messages (a typical phone tree for instance), a true AI isn't programmed to say any specific words. It learns them, same as you do. Its programming may have been done by another computer, probably better than would have said 'conscious programer'. Your assertions are rapidly going to be demonstrated false as capabilties improve.

The "I" on the other hand refers to the experiencer of a conscious thing, something which gives it a true identity that doesn't supervene on the physical.
— noAxioms
I cry foul here. Imagine a believer of the classical elements telling you that he just fetched a pail of water from the well. When you ask the guy what water is, he explains that it is the element that is cold and wet. Analogously, you object... there is no "water"; for "water" refers to an element that is cold and wet, and we don't have such things. The problem is, the guy did in fact fetch the stuff from the well. This I believe is your error. — InPitzotl

This comment would perhaps at least make sense to me had it been attached to a comment of mine about pain and "data which could be interpreted as pain", but you've chosen to reference a comment about different kinds of identity for two very different things (a car and its driver say).
The only way I can parse it, it is the followers of Chalmers that are making the error you point out, where a human is privileged in being allowed to call something water/cold/wet, but anything else (a sump pump moving the stuff) doing the exact same thing is not allowed to use such privileged language (the pump moves a substance which could be interpreted as water). A mechanical device with damage sensors to which it reacts lacks the privilege to say it feels pain. I didn't make those privilege rules, so cry foul to the ones that make those rules. I decline to use the word because I don't consider myself to be in the privileged class.

Slightly more analytical, the guy has a bad theory of water. When asked to describe what water is, the guy would give you an intensional definition of water that is based on the bad theory. It's proper to correct the guy and to say that there is no such thing as he described in this case; however, the guy is also ostensively using the term... the stuff in the well is an example of what he means by water.

Bad analogy. In the case in question, nobody is ostensively using a term. You can't point to your subjective feeling of warmth and assert the toaster with thermostat doesn't feel anything analogous. Sure, it's a different mechanism, but not demonstrably fundamentally different.

So the guy is in a sense wrong about what water is, but is not wrong to have the concept of water.

No, wrong to have the concept of water since the term 'water' is not in fact being ostensively used. Perhaps not wrong, since there may be water in his well, but I detect none in mine and he cannot show me the water in his.

You're objecting to an intensional definition of "I".

I think so.

No, that's the legal 'me' doing that. Any toaster has one of those. Any automaton can type a similar response in a thread such as this.
— noAxioms
I've no idea what you mean by legal me

Legal identtiy: There is a rock placed at X, and you move it to a new location Y. Is it the same rock, or merely a different arrangement of matter in the universe with only language suggesting a binding between the prior arrangement and the later one? Is that toaster under your arm the same toaster as was stolen from me a moment ago, or a different one to which I have no claim? I shake a rope sending a wave down its length. Is the wave I created the same wave that reaches the other end despite not involving motion of a single bit of the original perturbed material? That's what I call legal identity, and has nothing to do specifically with life forms. It seems mostly language based, not based on anything physical, and it doesn't always work. A cell divides by mitosis. Which is the original cell? Language has no obvious answer and physics doesn't care.

but the ostensive I to which humans refer is not something a toaster has.

This seems to be an example of the privileged language mentioned above. What I see as the 'bad theory' asserts privileged status to humans, raising them above a mere physical arrangement of matter, and assigns language reserved only for objects with this privileged status. I'm denying the status, and thus sit in the group with the toaster, forbidden to use the sacred language. My son has one of those 'hey google' devices sitting on its table, and it might reply to a query with "I cannot find that song" or some such. But such usage seems to refer to the legal identity (something I don't deny) and not to "I, the experiencer of the device" which neither the toaster nor the physical arrangement of matter referred to as 'noAxioms'.

How far does you skepticism go? Do you think there's a strong possibility you're the only mind in existence? — RogueAI

I don't consider my position on this to be abnormally skeptical. I simply deny the non-physical experiencer, which is a fairly standard monist position. I differ from the mainstream position in that I'm willing for others to have the dual relationship (and hence all the talk about it), thus forcing me to use alternate terms to describe how I work. Most monists probably believe that every mind supervenes on the physical, not just some of them. My position explains why the zombies talk about pain when they don't actually 'feel' (privileged definition) it. They are not lying, merely drawing from the limited vocabulary available to them.

I any case, I'm confident you do feel pain, and trying to argue that you don't via some objective comparison or description doesn't change the fact that you do in fact feel pain. — Marchesk

Not if a mechanical device is forbidden from using the word. If a thermostat doesn't feel warmth, then neither do I. I admit to pain being a rare one, with few devices having sensors to provide it.

If the zombie can think it is conscious (which itself is an act of consciousness) , and this thinking is the result of brain activity, then why would consciousnesses not also be a result of brain activity? — Janus

:up:
Or not even necessarily brain activity, but any information-processing activity.

Thanks for all the feedback everyone. I actually appreciate it.

My brain hurts now. I'll admit to having difficulties with the p-zombie argument when it comes time for the zombies to talk about consciousness.
— Marchesk
Yeah, that's the real problem here. If qualia are epiphenomenal, how can we talk about them? — InPitzotl

Indeed, if one with qualia can talk about it, it isn't epiphenomenal. Those of us without the qualia might talk about it because we hear the rest of you talking about it and know no better.

Are you pretending for the thread, or do you actually think you're a p-zombie? — RogueAI

Well, not pretending anything. Chalmers claims a conscious experience that does not supervene logically on the physical. I don't have that since what I do isn't a logical contradiction like that. So I can only presume Chalmers (and the rest of you non-zombies) has a conscious experience that is fundamentally different than me just "receiving data that could be interpreted as pain", as it was put in T2. I might use the word pain, not because I (like the other zombies) am lying, but because we've been provided with no other vocabulary to describe it.

So you don't feel pain? — Marchesk

'Pain' seems to be a word reserved to describe the experience of had by the experiencer of a human. It would be a lie to say that I feel pain, in the context of this topic, so lacking an experiencer, I cannot by definition feel pain any more than can a robot with damage sensors. Again, I may use the word in casual conversation (outside the context of this topic) not because I'm lying, but because I lack alternative vocabulary to describe what the pure physical automaton does, something which by your definition cannot feel pain since it lacks this experiencer of it.

There's no 'I' (a thing with an identity say) that's being me.
— noAxioms
This phrase sounds suspicious. There's a me, but there's no I being me? — InPitzotl

This is a better question. The 'me' is like the robot, the thermostat', the automaton. These things, in common language, have a sort of legal identity, but not an identity which holds up to close scrutiny such as Parfit demonstrates. The "I" on the other hand refers to the experiencer of a conscious thing, something which gives it a true identity that doesn't supervene on the physical. My 'me' doesn't appear to have that. It seems inconsistent that something with an identity can be paired with something without one. The bijunction between the two doesn't work without a series of premises which I find totally implausible.

Also, there's definitely an "I" there. Something typed an entire grammatically correct, if not coherent, response in this thread with a unified theme conveying some particular form of skepticism to zombies.

No, that's the legal 'me' doing that. Any toaster has one of those. Any automaton can type a similar response in a thread such as this.

A self-driving car can't feel pain. I assume you can. — RogueAI

I don't feel pain. I'm a zombie, remember? I merely process the data received from my nerve endings and make the appropriate facial expressions and such.

Some cars don't have damage sensors. They're still awfully primitive. Ones that do have the sensors process the data, which can be interpreted as pain or not depending on your choice to characterize it with such language or not, a choice which doesn't alter what's actually going on one way or the other. But I assert there is no evidence of any fundamental difference between myself and the car. Our mutual refusal to use the word pain to describe the respective systems isn't evidence of anything.

What's that like? — Marchesk

To what? There isn't anything to which it is like something. That's the thing I deny. There's no 'I' (a thing with an identity say) that's being me.

So you see zombie colors, hear zombie sounds, think zombie thoughts, dream zombie dreams? — Marchesk

No, I see colors, hear sounds, think thoughts, and dream dreams, but I do it the zombie way without help from the outside, just like the self-driving car does. OK, the car probably doesn't dream, but it does the other things, however reluctant you might be to ascribe such terms to such a device.

There's nothing it's like to be a zombie. — Marchesk

I sort of agree, but see bold below. I have no evidence that anything is being me. But that doesn't mean that the zombie cannot function, perceive, etc. like any other automaton.

So for us humans switching places

I didn't really have in mind 'switching places' since lacking something being me, there's nothing to switch. Perhaps the zombie (Phil) can be possessed by something (Bob) being it for a short while. But this only lets Bob know what its like to be Phil (who is for a short while not a zombie), but Phil might not necessarily be aware of it.

the same thing experientially as being unconscious.

I think I follow this, but disagree. A self-driving car, with driver in it, has something 'being' it and the car is 'conscious'. The car is an extension (an avatar) of the driver. Not sure how you're using 'experience' here. A self-driving car is capable of being aware of its surroundings and function on its own. That's 'experience' in my book, as distinct from 'conscious' which is the experience and control of the driver. If you use the word differently, then I need one to describe what a mechanical device does to measure the world.

Point is, the car can cede control to a conscious entity (driver) and become a car/driver system, and if you ask the system if it has phenomenal experience, it would be the driver that answers 'yes'. Perhaps the car still has its own experience and notes that it would have done that lane change better, but it's not in control.
If the same car is driving itself with the same person now acting epiphenomenally as passenger, then there's still something 'being' it, but it's the car in control, and thus the car that answers when asked if it has phenomenal experience. The car is unaware of the passenger, so it truthfully answers yes since it is quite aware of the vehicles around it and such and has no driver-phenomenal experience with which to compare.
There may be no passenger at all, and thus nothing 'being' the system, and the experience of the car is the same. So as long as it is in control, the car is going to answer the same way. If it's under control of an external driver agent, then it is the agent that answers, not the car, and the car cannot convey what that experience is like.

I claim to be the zombie car, not the driver/car system because i have no evidence to the contrary and it seems more plausible than the physics-defying system otherwise posited.

a liar, ill educated, or mad person. — bert1

I am neither mad nor ill-educated.
Neither party is lying. For it to be a lie, each being (the zombie using nothing but physics, and the 'human', as y'all put it) need to spend a moment in each other's shoes to compare. This is what the one is like, and this is the other. Now given that, one can select which most closely matches his experience (or choose to lie about it and claim the other). Until then, there's no lie about it since both have only one experience to compare, and each has learned the vocabulary to describe it from places like this forum. I certainly would never have used the word 'qualia' for instance had I not heard it from others.
So in the interest of not lying, I assert that the experience that I have is just the result of doing it the same way as would any physical device with sensory input and an information processor to make sense of it. There's nothing seemingly inexplicable about it, and hence I conclude that I'm one of the zombies and that I'm missing out on the full inexplicable-by-physics experience.

Generically different entities have different evolutionary histories — InPitzotl

But at some point, there'd be a common ancestor, which means that a non-conscious entity bred a conscious one with this new relationship with the external entity.
In other words, what had functioned just fine in the parent (a mind that was self-contained and fit despite the lack of relationship with the 2nd entity) gave birth to one where all those advantages were cast aside, letting the choices be made by the external entity rather than itself as has been done by its parent.

This is probably unfair, since it paints a picture of a very binary, abrupt transition from one way of doing things to a complete new one. The child simply wasn't evolved to take advantage of the external entity, at least not in full, and so I imagine the process to take many generations, with a slow ceding of control to the external choices which for some reason made the phenomenal being more fit.

To me, this sounds like slow possession by a demon, however benevolent.

This also leaves the price paid by the parent (the extra metabolism to support an exceptionally large brain) still being paid by the child despite all the function of that expensive brain having been contracted out to a 3rd party. If the 3rd party is doing all the work, why still cart around a brain whose function can obviously be accomplished by one a 10th the metabolism as is done by other creatures our size.

If a machine with a ghost thinks it is not a machine with no ghost, it is correct. — bongo fury

In that case, it's probably the ghost thinking it's not a machine with no ghost, and the ghost is correct. The opinion of the machine is not given.

But anyone who takes this view will likely be an eliminativist — Pantagruel

Well, I've pretty much eliminated the immaterial mind as described by Chalmers, but the stanford page on eliminative materialism describes a 'radical position' which basic monism is not. I think my mental states supervene on physics, making me sort of materialist of sorts, hardly a radical position to take.
Functionalist about consciousness seems closer to the mark, but they don't call themselves zombies, and neither do I except in the context of discussions such as this one.

If one accepts that our immediate evidence does not rule out the possibility that we are zombies, then one should embrace the conclusion that we are zombies

The OP says they're functionally identical, so by definition, immediate evidence does not rule out the possibility.

But the reason there is a problem about consciousness is that our immediate evidence does rule out that possibility.

How is that a problem? It simply leaves it open to interpretation (as does any position without empirical differences).

If zombie-consciousness is devoid of phenomenality, what possible set of conditions could give rise to the zombie asserting phenomenality? — Pantagruel

I've always claimed to be the zombie, without lying about it. I don't think I'm conscious, at least not by Chalmers' definition, so no, they don't necessarily lie about it. Sure, I can detect red, but so can the simple mechanical device.

Sorry, I lack clarification here. I meant belief as in your belief of validity. Function as in, to invalidate another belief by using some evidence provided. — FlaccidDoor

OK, I see what you're saying. Some used to believe that light moved at a fixed speed through a medium, just as does sound. That was eventually shown to be false by experiment, so the theory was no longer valid, and thus any belief in it was not valid, at least not without some serious modifications.

It isn't? You have an example of something that contradicts neither itself nor empirical evidence that is nevertheless invalid?
— noAxioms

Let me start by clarifying that I don't intend to criticize your beliefs in particular at all.

Have you? I didn't really post to much of my actual beliefs, and I detected no criticism.

My example was to describe a scenario in which a person lives in a logically righteous world because they do not have the same strenuous validation process as you might. They can invalidate other beliefs because validation requires the belief to be his own. All other beliefs are invalid inherently according to this belief.

I didn't understand those last lines. How is the other person's belief (presumably in contradiction with the first person's) invalidated? What does "validation requires the belief to be his own" mean? I just don't see how my own beliefs can have any effect at all on the validity of somebody else's differing beliefs. I might believe they are wrong, but that belief doesn't invalidate theirs.

What do you think it means for a statement to be valid? I gave my definition above, but you seem to have a non-standard definition going on here.

I suspect that the reason you say this specific belief is invalid is because you are working on the belief that validation requires non-self-contradiction and supporting empirical evidence. While many people here will agree with you, including me, the unreasonable individual, as in the example given above, believes otherwise.

Umm.... What specific belief? Does this specific belief (perhaps by said unreasonable person) fail to meet my criteria?

Sorry, but maybe if I figured out what those phrases meant above, I'd figure out what you're trying to get at here.

the basis for invalidating a belief for you is that the belief must be self contradictory. — FlaccidDoor

or falsified by empirical evidence.

Additionally and also as you said, this belief has a weakness in that it needs evidence in order for it to function.

A belief seems not to require evidence, but evidence nevertheless helps.

I believe that is a reason why you struggle now. You believe that a non-self-contradicting perspective is a valid one.

It isn't? You have an example of something that contradicts neither itself nor empirical evidence that is nevertheless invalid?

A belief that invalidates all other beliefs inherently allows for a logically sound environment in which that person can reject all other beliefs without lying to themselves, regardless of whether that belief is based on truth or falsehoods.

I don't see how any belief can invalidate a different belief. I spelled out what does invalidate it, and alternate beliefs are not on the list.

I agree with your reasoning but there's a simple solution to it. That your belief includes believing that other beliefs are invalid. — FlaccidDoor

Doesn't follow. Say I believe in eternalism (block universe, time is a dimension) which is opposed to presentism (that there is a preferred moment in time). I have no reason to believe that the presentist stance is invalid. It is only invalid if it is self inconsistent or inconsistent with actual measurements somewhere, which it isn't (although I might choose to argue otherwise).
Maybe your point is that I have no grounds for my eternalist belief because I have no evidence that alternate views are unsound, but all beliefs are of that nature.

I do hold some beliefs (including some that I'm fairly certain are falsehoods), but I as far as I can manage, I don't claim these beliefs to be true knowledge since there seems to be no access to such knowledge.

Why is believing in falsehoods not the equivalent of interpreting it as truths? If you believe it is real, convince yourself it is real, then to that person it is as if that is a truth. — FlaccidDoor

Truth seems to not be something relative to a person or a belief, so despite the fact that I hold what I would label as 'beliefs', I'm not so naive to assert that those beliefs correspond to truth.

In my case, the things probably closest to truth are probably what I'd label as 'suspicions' rather than beliefs, and my strongest beliefs probably correspond to falsehoods. I find those beliefs useful to me. They make me fit for instance.

Maybe you define truth differently:

truth is a statement or idea describing reality as is.

With this definition, would there be falsehoods that are more useful than truths? — FlaccidDoor

What about belief in specific god X? There's a lot of mutually contradictory X's from which to choose, and some of them must be falsehoods, yet belief in them leads the believer into leading a better life (sometimes) and leads them to fit better into their local community, which is definitely beneficial.

Think of all the people with contradictory philosophies who are nevertheless completely convinced that they're the ones in the right, with everybody else being wrong. They're all lying to themselves, and believing the lies. Not lying that their view is the correct one, but lying that it must be the correct one. — noAxioms

Wouldn't lying necessitate that you "know" something else is true? — FlaccidDoor

You use the word 'know' like 'believe' here. One can believe something (be certain about it even, which is the lying to which I refer), but true knowledge is seemingly out of reach because there is not enough data. The existence of alternate valid interpretations of things means there is no way to know which interpretation (if any) is the true one. No, such lying is due not to knowing something else is true, but to realizing that something else could be true.

I can relate pretty heavily to that. My family is Christian and growing up I could never swallow the ideas they threw at me ...

Oh I swallowed it completely at first, and was put in a Christian school that taught that science (evolution in particular) didn't contradict the teachings of the church. But then other churches began to deny science and force a choice, so I looked at both as objectively as I could, and the choice was pretty obvious to me. I've been on a search ever since to identify the biases I never thought to question and it has led to some less than mainstream conclusions, but not conclusions so strong that I'll make the mistake of asserting them as truth. Just higher on the probability scale (fewest unanswerd problems) than any other interpretation I've considered.

I've come to terms with it recently with pragmatism, in that believing in those Christian things have usefulness to them.

My example above, yes. I wrote that before seeing this.
My first answer was more controversial and I abandoned it for this simpler case.

Aren't there believable lies and unbelievable truths? I guess my question is: can we know that we aren't believing in falsehoods? Can the liars you mention, be believing in falsehoods that they misinterpret as truths? — FlaccidDoor

Yes to all of these. Much of human nature (and certainly not limited to humans) is the preference to rationalize the truth we find convenient rather than rationally seek actual truth. Think of all the people with contradictory philosophies who are nevertheless completely convinced that they're the ones in the right, with everybody else being wrong. They're all lying to themselves, and believing the lies. Not lying that their view is the correct one, but lying that it must be the correct one.

I personally hold contradictory beliefs. I thus know that some of my beliefs cannot be correct, but one cannot simply will ones self to unbelieve something.

As for lies I tell others, I've never told my Mother that I've abandoned belief in God the way I was raised. What's the purpose in telling her that? She just doesn't need to worry that her child is going to hell, although I admit to having been at several funerals of vocal atheists where the mourners (and even the pastor) still comfort each other with words like "he's in a better place now", which is exactly a lie told for a purpose.

Can I then prove that I know this? — Cidat

Prove to who/what? Would not you need to know that I exist in order to prove your knowledge of something to me?

Sorry for long delay. I guess I sometimes go for quite some time without visiting the site.

What would the phrases, "living under a rock", or "living in a bubble" mean for an anti-realist? — Harry Hindu

Not claiming to be one, so I'll let them answer that. I make no claims of the unreality of anything.

Are there other minds, or other bodies?

I favor a relational stance (Rovelli), so I'd say that other people exist to me, and I to them. We measure each other, so each exists relative to the other. This has nothing at all to do with people, mind, consciousness or epistemology. I exist relative to my keyboard because it measures me (I have a causal effect on it). I do not exist relative to the current state of Betelgeuse since that 'system' has not measured me. I suppose I exist to some future state of Betelgeuse, but not necessarily any future state.

Per Rovelli, I do not exist relative to myself, which makes sense, and is essentially why Schrodinger's cat, perfectly capable of sensing its various parts, cannot collapse its own wave function relative to the outside of the closed box.

I favor such a view because it seems to avoid the general paradox of realism which is its inability to explain the reality of whatever the realist considers to be real.

so anti-realism defeats itself by rejecting it's own existence as a belief? A non-existent nihilist? :lol: — Harry Hindu

That's their claim it seems. They give meaning to the property of existence, but claim nothing has that property. I see little point in positing a property that nothing has, but other than that (and your wonderfully worded argument from incredulity aside), I see no contradiction in the stance, even if it isn't my stance.

What do you mean by, "'existence of an objective reality" to say that it is meaningless?

No relation specified, so the statement is meaningless in my view. For something to exist objectively, it would have to exist in relation to, what?... something more encompassing than the universe at least. The proverbial view from nowhere it seems. Is a member of the set of all that exists, except the set cannot list itself for the reason given above.

I am curious as to how the current density would have any influence on either the physical possibility of expansion, or the degree to which it occurs. In what way then are these two factors correlated, in particular? — Vessuvius

It goes a bit beyond my expertise, but density affects overall gravitational effect to the extent that sufficient density suffices to overcome the effects of dark energy. The gravitational epoch epoch ended some billions of years ago and the expansion reached a minimum. The average density is now low enough that dark energy has the greater effect. The Hubble 'constant' will eventually settle on an actual constant of about 57 km/sec/mpc which corresponds to exponential expansion as opposed to the nearly linear expansion of the last several billion years.

Good thought. Add to that, if you would; What does the vision of "multiple" contractions and expansions do if we focus on the velocity of (light in space) during these periods. — Don Wade

You mean a cyclic model? I'm not familiar with any such model that matches empirical evidence at the level of the accepted FLRW tunings. So I think you can make up any rules you want about what properties are preserved from one bang to the next.

Then the question of; how far does the universe contract before it starts to expand. Lots and lots of questions about the model.

I've never heard of a model that posits contraction that doesn't accelerate to some kind of crunch singularity. Doesn't mean such a model doesn't exist, but I've never heard of it.

unsatisfied in the case of a mass subject to an arbitrarily high-degree of compression — Vessuvius

Unsatisfied in the case of uniform distribution everywhere. The level of compression has nothing to do with it. The current density of the universe (about 6 protons per cubic meter) is enough to prevent expansion if it was that mass expanding into empty space. None of the material would have sufficient recession speed to exceed the escape velocity of the bounded mass that comprised the occupied part of the universe.

I do have one example against a 'bang from a location in otherwise empty space' which is that if such a thing occurred, all the mass of the universe would be compressed into a small space and would form a black hole, preventing any explosion (and shock wave) into said empty space.

On the other hand, an expansion of arbitrarily high compression of mass/energy (as posited by the BBT) would still involve a reasonably uniform distribution of mass and energy over all of spacetime, not at all meeting the stress energy tensor conditions of a black hole.

but as seen from the perspective of a fixed observer, relative to some far off point which is of so large a scale as to make the effects of such expansion dominate, for all intents and purposes it does appear to the observer as though a superluminal velocity is attained. — Vessuvius

The rate of increase in proper separation of a sufficiently distant (and visible) galaxy does indeed increase at a rate greater than c, but this still isn't superluminal since the light emitted by that galaxy in a direction away from us is moving away from us even faster. Nothing is outrunning any local light as you know.
The speeds expressed are relative to a non-inertial coordinate system and relativity theory doesn't forbid object or light from moving at speeds above c relative to a different kind of coordinate system, so none of this is particularly contradictory with anything.

Minkowski spacetime does contradict the geometry of the universe. Given Minkowski spacetime, light will eventually get from any location to any other. There are no event horizons. Not so with our universe, so Minkowski spacetime (typically assumed by any naive description of bang happening at a location and filling pre-existing empty space) cannot describe our universe.

Do notice how I qualified my statement with likening its chosen object only as appearance, rather than an absolute.

I did, but there's not much appearance to it. We see redshift and brightness, both of which approach infinity and zero respecitively with subluminal local motion, and from that glean the speed. If we wait long enough, we see the object get smaller over time, but not so much that it appears to move super fast. Take GN-z11 which at redshift z=11 is the most distant galaxy know. Yet it subtends an angle that places it only about 3 billion light years away, making it appear to move quite slowly actually. Speed from appearances is a calculation relative to a model and a coordinate system, not something that can be directly measured just by looking at it.
I think that under a Minkowski inertial frame, the most distant object visible would appear almost 7 billion light years away. I mapped the universe to such a coordinate system as best I could once. It almost works if expansion is uniform and not accelerating, but there's simply no way to work dark energy into it.

As my argument certainly wasn't that this reference frame is somehow privileged, or the only one of merit.

Good grief, I never caught a suggestion of that in your posts.

The purpose for which I cited it was instead to highlight how ideas of causality are meaningless in these cases because the light-cone of the observer is forever prevented from accessing the image of such distant point-sources, and nothing more.

You're talking about objects outside the visible universe? A few will become visible as that radius expands, but most never will. As a non-realist, I cannot say that any of those objects specifically exist relative to us, but someone positing an objective state of the entire universe would say that these distant objects do exist, any one of which is receding from us at an arbitrarily high rate.

Under all circumstances then, and unless the rate of expansion slows considerably enough to no longer appear superluminal — Vessuvius

Again, the expansion rate is expressed in different units and thus is not a speed and cannot be meaningfully compared using a word like 'superluminal'.

Then what is the universe? That is, something other than it started with a big bang. — Don Wade

A reasonable definition, but still dependent on serveral assumptions such as your chosen interpretation of QM. An MWI guy for instance might say that the universe is the one universal wave function. Any follower of a realist interpretation (MWI being one of them) might say that the universe is all that is. I learn towards the RQM side, but I'm hesitant to say the universe is all that I measure since that confines it to the visible universe, and it needs to be meaningful to talk about more distant things, however much those things don't relate to us.

Does the universe exist in space

No model supports that. It is a naive interpretation that is quickly falsified.

or does space exist in the universe?

Time as well since it is the same thing. Few can get their heads around time being part of the universe rather than the universe existing in time, which reduces its ontology to that of a mere object.

Which came first, space, or the universe?

Great example of trying to think of the universe as being contained by time. The universe is not an object. Spacetime is part of the structure that is the universe.

To the OP

If we first assume the universe started with a Big Bang, then there should have been a shock-wave extending out from the center. — Don Wade

The big bang theory does not posit an explosion into space from some point in that space. Any simple description on the web will tell you this. The expansion of the universe is not a speed, and is measured in different units. Pfhorrest seems to know the physics.

Science tells us that the shock-wave could not move faster than the speed of light. Did it?

Science says no such thing. It makes no mention of a shock wave, which is something you get from say a star exploding in space. The universe isn't an object in space like a star.

the diameter of the universe is about 90 billion light years — T Clark

The diameter of the visible part of the universe is about that. That volume includes all the material that can possibly ever have had a causal effect on us today. It doesn't mean we can see that far. Any light that has ever reached Earth up until the present has never been further from us than a proper distance of under 6 billion light years. Measured that way, the size of the visible universe is under a 6 BLY radius. We can only see these really distant galaxies because they were much closer than that distance back when they emitted the light that we're seeing now.

The title question assumes there is something. While I don't assume the opposite, I don't take it as an axiom that there is something. Thus I don't have to explain it, at least not first. Seems a question for realists. How do you explain the reality of whatever it is you consider real? Not my problem. Not a realist.

Been too busy to deal with this fairly unproductive line of discussion.

The Rindler horizon's similarity to the event horizon is only insofar as any light travelling from the negative x direction cannot reach the x=0 worldline. That seems to be the entire basis for your argument that the space the photon travels in does not exist in the Rindler frame. — Kenosha Kid

What light can or cannot do is irrelevant to my point. It is similar in other ways, which is why I brought it up. My arguments have not been based on light signals.

This is exactly the same as saying the car behind does not exist in the frame of the car in front because it can never reach it. It's the same argument.

Either car can say what the other is doing 'now', whether they can reach each other or not, so it is not the same at all. You continue to either not get my point, or you're deliberately evading it because its implications make you uncomfortable. So address the question I asked and not another:

A clock is dropped at Rindler event T=0 X=1. What are the Rindler coordinates of that clock when it reads T=1? When it reads T=2?

That's the question. There's no mention of light in it. I claim a lack of coherent answer, and conclude that Rindler coordinates are inadequate to the task of foliating all of spacetime. Similarly, inertial coordinates cannot foliate spacetime containing a black hole, and no coordinate system can foliate spacetime containing multiple black holes.

[At location x=0 in the ARF,] Time is infinitely dilated, and there is no light cone if there is zero time for light to get anywhere.
...
Nothing can ever get closer to it in its own proper frame. That's what I've been repeating in the last several posts.
— noAxioms

Yes, I know. And this is why your argument is incorrect. You seem to think that somehow, in the accelerating observer's frame, the distance from x=0 to x>0 is infinite in the proper frame because nothing from x<0 can reach x=0 — Kenosha Kid

I do not think this any more than I think the distance to a black hole EH is infinite because light from it will never reach an orbiting object. Pilot at x=1, RH at x=0. That's a constant finite distance of 1 (as I've said above), not an infinite distance as you suggest here.

akin to saying that if two cars were travelling in the same direction at the same speed, the car behind can't be represented in the rest frame of the car in front because it cannot reach it.

I never said one car cannot be represented in the frame of the other. That's partly because they're the same car, the front and rear bumper, moving by definition at the same speed in the rigid car's own frame. But the rear bumper must accelerate harder than the front one. The car on the other side of the RH is what cannot be represented in the Rindler frame of the accelerating car. It cannot be keeping up with the accelerating (but stationary) car in the ARF. (Please tell me if any of these acronyms are confusing. I tire of typing the full words).

For all finite accelerations within finite times, there is no infinite time dilation, no infinite length contraction, and any light approaching from the negative x-direction is getting closer, even if it cannot intersect the accelerating body's worldline in finite time. None of this is new: you can do all of the math in standard SR.

Yes, and the math says the acceleration cannot be finite at the RH, and which is why I said the length of my object extended almost 1 to the rear, but not all the way, because I wanted to avoid the infinite acceleration required there, with yes, infinite time dilation, just like at the EH of a black hole.

Do you accept that the accelerating object is always stationary in its own frame?
— noAxioms
If you'd read me carefully, I not only accept it, I asserted it.

Good. I wasn't sure given your posts.

This is all x=0 is in the rest frame of the moving body: a coordinate of the origin of that frame. It is not a singularity by any definition.

In the Minkowski frame, we know where the x=0 point is at t=0. It is at X=0, T=0, right? Think wiki picture if you don't know what I mean. Our object extends from X=2 back to X=0. It is effectively a long meter-stick in a rail gun, with a clock at each end and in the middle.

t is what's on the middle clock at the accelerating object at x=1. So at t=2, that clock is off the right side of the picture, but not far. Suppose we stop accelerating the entire object simultaneously (in the object frame) when that clock reads t=2. Where is x=0 in the object's frame? I contend that despite infinite acceleration there, it has gone nowhere and is still at X=0, T=0 (in the original Minkowski coordinates, which is not the object's frame) and not anywhere else on that picture. The clock at the rear of the object still reads zero. Do you agree with any of this? If not, where (in the original Minkowski diagram) is the left end of the object (simultaneous with, in the object's new frame, the cessation of acceleration at t=2 on the middle clock?

The problem is you don't understand the framework you're trying to use to make your point, so don't understand why your point is invalid.

You continue to make erroneous assumptions about what I'm saying, so of course you think I'm getting something wrong. No, I never claim a pair of cars following each other are not in each other's reference frames. You totally don't get my point if that's your take.

You have to do the legwork, not just try and jump to the crazy conclusions of some impossible edge cases and mistake that for the theory as a whole.

I'm asking you to do some legwork in the example above, to compute which event corresponds to the cessation of acceleration at the rear of the object, and where that event falls in the original Minkowski diagram. I can do the same mathematics if you like, but the picture already shows the event in question.
You seem to have been claiming that the RH somehow approaches the x=1 point in the ARF as the object accelerates, but in the object's ARF, the object is always stationary, so that can't be happening. It must remain a constant distance from x=1.

If the above is indeed your source, I hope this convinces you that it is the entire x=0 (or t=infinity) line that is the Rindler horizon, not the X=x=0 point. — Kenosha Kid

That's the same as the wiki picture, but with far less detail. Yes, in an arbitrary inertial reference frame as depicted in all these drawings, that entire line is the Rindler horizon. Under Rindler coordinate time (not shown in this new picture), the horizon is a coordinate singularity and is not comprised of a line like that. Time is infinitely dilated, and there is no light cone if there is zero time for light to get anywhere.

Of course, this is not the same as a black hole’s event horizon in two very important respects. Firstly, it’s always possible to stop the spaceship accelerating

Similarly, you can accelerate away from Earth to push the distant event horizon further away in the coordinate space of the thing accelerating away, but that just pushes it off. You can't turn off the acceleration of expansion like you can turn off the ship engine. Yes, I agree, the Rindler horizon exists for a continuously accelerating thing, and it ceases to exist when that condition goes away.

Secondly, there is nothing corresponding to a black hole’s singularity to do any actual damage to anything passing through the horizon.

Nothing is inherently damaged by free-falling through a black hole event horizon. Are you under the impression otherwise? As I said, a small black hole will 'damage' you before you even get to the event horizon, but that's not the event horizon doing it to you. Orbit close enough to a neutron star and you're dead, no event horizon needed at all.

This is not a real event horizon like the boundary of the universe or that of a black hole.

I was unaware of there being a boundary of the universe. In the ship case, yes, you have the option of turning off the acceleration. In the dark energy case, you do not, so no matter what you choose to do, there are points in space in no significant gravity well from which light can never reach you. This is not true in Minkowski spacetime.

It is an artificial horizon based on the decision of the ship to constantly accelerate away from everything else. Things effectively cannot reach it (cannot reach x=0) because it moves away from them. However, things can get closer to it (move toward x=0) in its own proper frame.

No. My bold. This is where you're wrong. Nothing can ever get closer to it in its own proper frame. That's what I've been repeating in the last several posts.

Maybe you could address my points instead of just repeating your own. The wiki picture shows the proper frames of the accelerating object, and since the picture is a different frame, it actually shows the distance increasing, but in the Rindler coordinates, the distance is constant over time. If it wasn't, there would be a test for absolute rest: when the distance to the rear of the ship is at a maximum. That would be a direct violation of Galilean relativity, the first of the SR postulates.

Because lightspeed is not observer-independent in non-intertial frames

No argument.

It is equivalent, in inertial motion, to saying that an object that is following me with the same speed as me doesn't reach me. Or, in my rest frame, an object to my left is not occupying the same space as me.

Do you accept that the accelerating object is always stationary in its own frame? I know it's not an inertial frame, but if you take any event on the ship (say the pilot at x=1 at time t=2, his clock), and you reference the one inertial frame in which the pilot is momentarily stationary at that event, then every location along the ship is simultaneously (relative to that IRF) stationary. In that frame, the Rindler horizon is still a distance of 1 behind the pilot, regardless of the time that has passed.
I typically imagine a ship of length almost 2 with the pilot in the middle and the rear just shy of the Rindler horizon, and the front at x=2.

The photon is still in the moving observer's coordinate system

Not the one at the rear. Time is stopped there in that coordinate system, and the photon makes no better progress than one at a black hole horizon trying to get out. A photon anywhere forward of that does indeed make progress and will eventually reach any part of the ship.

Follow that worldline to the edge of the diagram. Now, tell me, is it closer to the horizon or further away? — Kenosha Kid

The accelerating observer goes off the right side at about t=1.25, where proper distance to the horizon is still exactly x=1 behind him, unchanged. In another frame, the ship is moving, so of course the distance is length contracted, which would be true if the thing was accelerating or not. As I said, you don't need to wait for it's speed to change. Just do a Lorentz transform to a different arbitrary frame and you can contract that distance as much as you like, even at T=0.

Yes, the worldline is bending to the right (increasing X). But the horizon is always moving to the right more quickly

Only in a frame different than the ship frame. That frame is thus arbitrary, and irrelevant to our observer's measure of the distance to the event horizon.
Yes, I acknowledge that in a different frame, that distance is contracted. This seems to be your point,.

The Rindler horizon is not X=0. X=0 lies on the horizon at T=0.

It is a singularity, so this does not follow. Suppose the ship extends all the way back to the horizon. Where is the rear of the ship at t=1 (as measured by our observer at x=1)? Follow the t=1 line-of-simultaneity back to x=0 in the diagram. Where does it go? It goes to the same event where it was at t=0, the left-most event in the picture. That shows which event is approached as you move backwards in the accelerating frame. The actual event there is a singularity, with undefined time, so asking which horizon event is simultaneous with our observer at t=1.25 is meaningless, but I can point to the event in your arbitrary Minkowski frame that is approached.

So what you mean is that we choose a frame of reference where the acceleration is not simultaneous

Unclear what you mean by this. Acceleration is continuous, not something that is 'simultaneous'. At all times in ship frame, all parts of the ship are moving at the exact same speed, and thus the entire ship is always stationary in its own accelerating frame. The ship is said to be Born-rigid.
This implies that in a different frame (such as the Minkowski one in the pic), the various parts of the ship are not moving at the same speed. If they did, length contraction would contradict it, as shown by Bell's 'paradox'.

Your interpretation is still erroneous though, because you still think the Rindler horizon is a spatial horizon.

I don't 'think' that. It is a coordinate singularity, just like the one 16 billion light years away, and just like the event horizon of a black hole. The center of a black hole on the other hand is an example of a physical singularity. A coordinate singularity only exists in certain coordinate systems, and there's nothing actually physically weird going on at them. Hence people can drop into a sufficiently large black hole without really noticing any obvious immediate change, not even if they're looking out of the window. A small one of course will kill you before you get there.

The length of the ship may for all intents and purposes be infinite in the origin's rest frame.

Only to the right in this case, not the left. Can't go past x=0. For the same reason, I cannot have a rigid rod much longer than about 27BLY with us stationary at the midpoint. It is an interesting exercise to figure out how to position a rod of twice that length without strain. It can be done. I digress.

As you move to more rapid parts of the ship through one part's frame of reference, you approach but never reach the rapidity of photon emission

I assume 'more rapid' means higher acceleration (and associated rate of change in rapidity) and not high-speed since the ship is always stationary along its entire length in its own frame (the frame in which rapidity is meaningful), so there is no different frame of reference between one part and another. There is a variable rapidity change rate that is dependent on the different parts of the ship. Over at x=1, acceleration is 1, so the rapidity there is a function of how long it's been doing that between two times as measured by a clock there. At higher acceleration parts of the ship, the same time interval results in a greater rapidity change over the same interval on again a local clock. The rapidity of light is infinite, but I don't know what 'rapidity of photon emission' means.

You cannot map out an entire Minkowski space from the light cone of one event. That's fine because that's not what a Minkowski space is: it is a frame of reference containing all events, not just one.

It contains all events in the Minkowski frame, but in real spacetime, light should be able to get here from far away given enough time, but it doesn't in reality, so the Minkowski model fails to describe the large-scale structure of our universe. It is, and always has been, a model of local spacetime.

You cannot, by definition, "accelerate away from the Rindler horizon". — Kenosha Kid

Nonsense. Show me the definition that says this.

That horizon is an acceleration limit.

It is not. It, like any other event horizon, is a boundary in spacetime separating events that can have a causal effect on a given worldline and those events that cannot. So there is an event horizon currently about 16 billion light years distant beyond which no event can ever have a causal effect on Earth (the worldline in question here). This is due to the acceleration of Earth away from locations more distant than that. The only reason that is technically not a Rindler horizon is that Earth's acceleration is not constant, but is instead increasing.

Lemme dig out a pic to explain.

And you choose a picture correctly showing the worldline of our observer at X=1 (assuming we choose units where α is 1), curving to the right (positive acceleration AWAY from the Rindler horizon to the left at X=0. The text accurately says "If the observer is located at time T = 0 at position X = 1/α (with α as the constant proper acceleration measured by a comoving accelerometer), then the hyperbolic coordinates are often called Rindler coordinates with the corresponding Rindler metric."
X = 1/α (a positive location). α is positive, so acceleration is away from location X=0 where the Rindler horizon is. Your post contradicts your own assertions.

X here is position, T time in a Minkowski frame. The hyperbola are worldlines of bodies undergoing constant proper acceleration. t here is the proper time of the accelerating body.

The picture depicts the Rindler coordinates of one body, one worldline. Yes, other bodies to the left and right, at different accelerations, would trace those other worldlines, but their times would not correspond to the times plotted for the one object at X = proper distance of 1. The t= values are for that body and are not shown for any of the other worldlines.

As the body is accelerated for longer and longer, T and t increase. At infinity, they converge at the event horizon

After any amount of time, the proper distance between our accelerating body and the Rindler horizon remains 1. It is a constant. Sure, if you choose an inertial frame where this whole setup is moving fast, you can length contract it down to any size you like, but you don't need to wait a long time for that. Just choose a different frame. From the perspective of our constantly accelerating observer, the horizon remains at a fixed distance behind him (in the direction opposite his acceleration vector).

So it's difficult to make sense of what you're saying. I get that you're trying to simulate gravity here. If you have a long ship pointed radially outward from a black hole, the bottom undergoes more acceleration than the top. I can't envisage, in the absence of gravity, how you can make a single object do the same.

You are unaware of acceleration not being constant along the length of an accelerating rigid object? This is a simple consequence of special relativity. Read up on Bell's paradox (the two ships accelerating while attached by string). It illustrates most of the concepts involved.

Perhaps a fleet of ships would be better. Non-rigid bodies were among the original hypothetical objects of the equivalence principle for this very reason.

And connect them with string, yes. Unfortunately, the clock of only one of those ships will correspond to the times depicted in the picture above.

in the latter it is the coordinate approached by an accelerating body as t goes to infinity. — Kenosha Kid

What?? The body is accelerating away from the Rindler horizon. It's not approaching it. That's why I call the direction of it 'down'.

Thus I don't know what you mean by the wording here:

All accelerations lead to the horizon at eternity.

You have links where this wording is used? I'm trying to make sense of it.

The Rindler horizon can be reached one of two ways. As the worldline of a body undergoing acceleration, it is reached as that acceleration becomes infinite. — Kenosha Kid

Not sure what worldlines have to do with this. Yes, the (constant) proper distance to the Rindler horizon of a small object undergoing continuous proper acceleration is a function of the magnitude of that acceleration. An extended object such as I described doesn't have a worldline so much as a 'world-swath' of sorts (the accelerated coordinate system of which I spoke) since each part of the object traces different worldlines, none of which intersect the worldlines of other parts.

This is the light-line (e.g. photon creation).

Sorry, I'm unfamiliar with that term. Google was no help.

Why is your apparently infinitely long ship accelerating more the further away from x=0 you go?

Acceleration must be greater further 'down'. Less in the 'up' direction, so the 'ship' can be as long in that direction as required to serve its purpose as a coordinate system for an accelerated reference frame. It is somewhat equivalent to my weight being greater on the ground floor of a building than it is at a higher floor. Clocks run faster in the higher low-acceleration portions of the object than the clocks in higher-acceleration locations further down.

And why do you think it is infinitely accelerating one LY from x=0?

The product of the distance to the horizon and the inverse acceleration will equal c^2. So c^2 / 9.8m/sec^2 = ~9.2e15 meters which is not quite a light year.

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 hoel the fall takes forever - or more.

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

Let me put it this way:

P1 Time is absolute. There is an absolute ordering of all events in all of spacetime.
C1: For any event in spacetime and a given (time-like, or at least not space-like) worldline, that event is simultaneous with exactly one event on the given worldline.
C2: If, from the perspective of any particular observer, the simultaneity of two events does not correspond to C1, then that perspective does not correspond with reality. It is merely an abstract perspective.

Notice that it isn't necessary for any observer to be aware of this absolute time. We're just supposing there is one, not that it can be known for sure. Problem is, no coordinate system I can think of meets the requirement of C1, and the lack of the existence of such a coordinate system contradicts P1.

My choice of the first event is the falling clock when it reads 1 second beyond what it did as it crossed the event horizon. The first worldline is the clock hovering near that black hole, and a second worldline is a different clock falling into a different black hole.
How might one assign a time that is simultaneous with that first event on each of those two worldlines. The coordinate transformations you speak of seem not to exist, and at best they only transform between an abstract relation to the one actual one. I don't see the purpose of considering the abstract one at all.

We can remove GR from consideration by application of the equivalence principle to remove all mass and gravity from consideration, and then use this to illustrate the lack of transformation from one coordinate system to another.

So acceleration is equivalent to gravity, so our space station hovering at 1g outside the black hole can be equivalent to the Rindler scenario where there is only acceleration and no significant mass/gravity anywhere in flat Minkowski spacetime, which can be described using SR rules.

So consider a coordinate system of a long rigid spaceship with meter markings on the sides that acts as our coordinate system. At the origin (the place marked zero), it is accelerating at a continuous 1g. Does this ship's coordinate system map all of spacetime? No, it does not. Acceleration of the ship is greater the further 'down' the length you go, until a limit is reached (about a lightyear from the origin in this case) at the event horizon (called the Rindler horizon).The ship cannot extend further back than this, but in can extend indefinitely in the 'up' direction. A clock dropped from the origin will fall past the ship and appear to freeze as it approaches that event horizon in the coordinate space of the ship. Light from events beyond this horizon can never reach any part of the ship, which means that while I accelerate at 1g, light from about a light year away will never reach me.

The events beyond that horizon do not exist (cannot be meaningfully ordered) in the coordinate space of the ship, and thus there exists no transform between them. Events there cannot be meaningfully placed on the timeline of the ship.

Of course, in the frame of the dropped clock, the rear of the ship passes it by without notice and the clock ticks on. Now from the perspective of the clock beyond the ship's event horizon, there is no event horizon at all. It is merely a coordinate singularity and not a physical singularity. Similarly, a black hole event horizon is a coordinate singularity. That means that from the perspective of beyond the horizon (the falling clock), the space on either side of the horizon can be mapped in a coherent coordinate system (that of the falling clock in this case). So there does exist a mapping between 'inside' and 'outside' so to speak, at least in the Rindler case, but only relative to an inertial (falling) reference. There is no physical singularity in the acceleration scenario, and there is one in the black hole case, and also there's the fact that no object can be falling into more than one black hole, so there seems to be no coordinate system that maps more than one of them.