"Bob cannot predict himself, even if he had this unobtainable state. It would require a mechanism to simulate itself faster than real time. Alice of course would just be waiting for Bob’s prediction, at which point Alice will choose the opposite thing. I can make a small mechanical device with only a couple parts that does that, and Bob will fail to predict its behavior. That doesn’t demonstrate that the device has free will, however you might define it."
— noAxioms

It doesn't. But I don't define free will as implying unpredictability (nor predictability as implying its absence), but as choosing what one wants. The point is that there is no outcome that Alice must accept if she doesn't want to. — Andrew M

I agree that your definition is enough to assign responsibility for one's actions. The average argument defines free will differently, but then incorrectly concludes that I should not be held responsible (on Earth) for my actions. "You shouldn't jail me, physics made me do it!". This is bunk. Physics will also toss your sorry posterior in the clink, and by the same argument, is not wrong for doing so.

So the question seems to break down into the nature of self (am I a soul or a physical construct?), and the thing which is holding you responsible for your actions. I think of three primary cases, and the definition of free will seems to apply differently to each of them, making it a mistake to apply one argument to all the cases.

Case 1: Physicalism: Your definition works fine here. Alice definitely can choose as she wills, and held responsible for her actions by physical society. Not completely. Alice wills to fly, and physics prevents that. Alice cannot be held responsible for failing to fly.
Free will is rarely defined your way. The argument typically points out that Alice's will is determined as well, being a causal effect of prior state, which makes it not free. I have no idea why it would be a bad thing for my will to be based on prior state. Example: Alice sees a person cross the road in front of her car. She's more responsible for her actions if she ignores that state? Physics says Alice sees the person and wills to hit the brakes because of that input, but a free willed person will base the decision on something other than the detection of a person crossing in front of her. This makes no sense. Why is that a better thing?

Case 2: Non-physical interactive soul: The analogy here is Tomb Raider. The player is the spirit soul, and Lara is the physical avatar. Lara is not responsible for her mistakes, you are. You are punished (in the spirit realm) for screwing up by not finishing the game.
The soul is not part of the physical system, and can be held responsible by some similar non-physical entity, typically a deity. Most proponents of free will assume biases for case 2, but fail to understand that the logic only applies to case 2.
Alice (spirit soul) again can do what she wants since her soul is supposedly in charge. It means that physics must must include a mechanism for introduction of external change, else the actions of Alice's physical person do indeed come from physics, fully determined or not. I agree, determinism or predictability is irrelevant. It just makes the analysis easier, but doesn't change the answer.
Absurdly, the physical Alice in the case 2 scenario is considered to be free willed precisely because she's not able to choose for herself, but lets her actions be determined via remote control. "You can't jail me you honor, my soul made me do it!".

Case 3: Epiphenomenal soul: This one is dualism with no violation of physics. The analogy this time is Harry Potter being held responsible for wandering the grounds after hours. You are the spirit soul experiencing Harry. Harry can be held responsible by Snape, who is also part of the physics, but you the epiphenomenal experiencer cannot be held responsible for Harry's actions either by Snape nor by your society since you lack the ability to choose. Again, I like your definition. The viewer and Harry are two separate entities, not one with a agent/avatar relationship.

- - -

I may comment on the free will thing separately. Doesn’t belong in this post.
— noAxioms

I disagree. How one views free will is a reflection on how one views the passing of time. And that is central to this issue. — Metaphysician Undercover

That post was not about the passage of time. Neither is this one, but I agree that interpretation of time is relevant to the issue.

The point I wanted to discuss is that IF our universe is such a structure, it need not be instantiated in some larger context to explain empirical experience.
— noAxioms

I agree that it doesn't need to be instantiated in some larger context (since there may be no larger context), but I would argue that it still needs to be concrete, not merely abstract. — Andrew M

Being concrete would be an objective context, the larger context of all things that actually exist, not in relation to anything. I guess I’m trying to argue against your point, that concreteness is necessary.
What do you mean by ‘abstract’? Just not-concrete? The word has connotations of being a mental construct (thought or idea), which is not the direction I’m going. Our universe is not necessarily conceived of by something not part of the structure.

I'd like to highlight this part of Tegmark's (shorter) explanation of the MUH:

“Before discussing whether the mathematical universe hypothesis is correct, however, there is a more urgent question: what does it actually mean? To understand this, it helps to distinguish between two ways of viewing our external physical reality. One is the outside overview of a physicist studying its mathematical structure, like a bird surveying a landscape from high above; the other is the inside view of an observer living in the world described by the structure, like a frog living in the landscape surveyed by the bird.”
— Shut up and calculate - Max Tegmark

So I don't agree that there is a bird's eye view of the universe (i.e., a view from nowhere). We never directly observe numbers or mathematical structures, only concrete things that we can then describe in abstract terms.

Agree. Tegmark is speaking of an objective description of the universe, not a relational one. There is indeed no nowhere from which there is such a view. I find his bird analogy a poor one, since it is only panning back to a larger picture, but not one from outside. Telescopes and microscopes are both still subjective views.

One can consider the universe in objective terms, but it is not an actual ‘view’. At best, the structure can be simulated, and the simulation viewed. The simulation serves no purpose to the thing simulated. It only serves a purpose to the runner of the simulation, allowing examination. The fact that it does not server a purpose to the structure simulated is a primary motivation for realization that the structure being concrete is not a requirement.

Mathematical equations ultimately derive their meaning from those concrete things, they aren't dispensable "human baggage". So a complete mathematical description of the universe would need to be in human-observer terms (i.e., a view from somewhere).

The meaning might be indispensible human baggage, but the structure itself (not necessarily any ‘equation’ that describes it to an observer for whom it means something) seems not to require said observer. OK, ours comes with humans built in, so it seems to be a structure that finds meaning in itself, but that’s an internal relation, not ontology.

We seem to just be asserting opposite views. I don’t see either of us making good justification of our positions. Doing my best. I don’t claim that there is no ontology, just that it is not necessary. To me, that seems to put at least some burden on you to show (not just assert) that it is necessary. The humans in the uninstantiated universe would have the exact same observations and thoughts as the humans in the instantiated universe. Do you disagree? It seems to assume that humans are part of said universe, and not external experiencers of it, so kind of discarding dualist biases, which is hard to do.

The idea that there are pure abstractions or a view from nowhere seem to be claims without an empirical basis.

Not claiming this, so agree. From nowhere, there is no view at all.


I may comment on the free will thing separately. Doesn’t belong in this post.

We seem to be going down an irrelevant tangent.

And if both a line and a number (a point on the line?) can be a universe, does that mean that there are universes within universes? — Andrew M

I think the use of the word 'universe' is about as much loaded human baggage as the term 'physical'. The (our) universe could be a mathematical structure, but to call any mathematical structure a universe is to load it with meaning unintended.
The point I wanted to discuss is that IF our universe is such a structure, it need not be instantiated in some larger context to explain empirical experience. It needs to be instantiated in said larger context only in order for something in that larger context to examine it. I've given examples.

Yes, I was meaning the equation for a line. In this case, would the line have an infinite number of points or would it be discrete? — Andrew M

x=1 then means that for any x, the value is 1. So x can be a continuous line, an infinite series like the integers, or maybe a finite segment, discreet or not. It works for all of them. They’re all valid mathematical structures, and thus can be designated as a universe if you like.

And if both a line and a number (a point on the line?) can be a universe, does that mean that there are universes within universes?

There can be, sure. Our universe might be defined as our own chunk of spacetime as we know it, but inflation theory says that we are but one bubble condensed from inflation stuff, each of which is a non-interacting universe on its own, some as trivial as x=1. That bubble-space might be considered to be a larger universe that contains ours. In that view, our bubble is not a universe, just a bubble among others in this container.

My main objection is that you seem to be making a distinction between things in a universe, which are physical, and the universe itself which is not physical. But aren't the things in the universe themselves mathematical on your view? In which case, isn't the term "physical" merely human "baggage", to use Tegmark's term?

I like the term ‘human baggage’. I’m not calling contained objects ‘physical’, but in the example of CgoL, similarities can be drawn. In other ways, the similarity are thinner. CgoL has no concept of inertia or force for instance. Time has an arrow at the quantum level, not just at the entropy level.
Another mathematical structure example is the set of all valid chess states. This is a finite set (there is a maximum possible chess game of around 5000 moves), and there is time, entropy, and the possibility for the addition of dualism to the universe to allow ‘players’ which designate which of the states are real (in relation to the player) compared to the other states. But sans-player, the states as a universe unto itself is all equally real.

I think it's worth considering something like Rovelli's (and Bitbol's) relational approach here. Bob may be able to secretly predict the outcome of Alice's choice with certainty, per Bob's deterministic theory. But there is no specific outcome that Alice should regard as certain, since she can always reject that outcome and choose differently. — Andrew M

Wanted to comment on this. Where is Bob in relation to Alice? If outside (non-interacting) with closed Alice system, and if hard single-outcome determinism is true and Bob has access to full state and the resources to make the prediction, then yes, Alice, in the deterministic contained system, can be perfectly predicted and has no ‘predicted outcome’ to reject. Bob cannot divulge the prediction to Alice as that would be interacting, making the system not closed.

OK, so if Bob is within the closed system, there are several reasons, determinism or not, that he cannot make such a prediction. 1: State cannot be known, per Heisenberg uncertainty. 2: Bob cannot predict himself, even if he had this unobtainable state. It would require a mechanism to simulate itself faster than real time. Alice of course would just be waiting for Bob’s prediction, at which point Alice will choose the opposite thing. I can make a small mechanical device with only a couple parts that does that, and Bob will fail to predict its behavior. That doesn’t demonstrate that the device has free will, however you might define it.

Sorry! What I was actually drawing attention to in that quote was that observer O' measures particle S with spin-down. But, earlier, observer O had measured particle S with spin-up.

In quantum mechanics, subsequent spin measurements of a particle in the same basis give the same result. So there would seem to be a paradox here, since (in realist terms) the measurements by observer's O and O' contradict each other.

But, per RQM, no comparison can be made until observer's O and O' physically interact and compare results. And when they do, they will find their two spin measurements are in agreement, just as quantum mechanics predicts! So there is no paradox in relational terms.

That should seem a bit fishy. Is there any possible mechanism by which that agreement could come about without bringing in many physical worlds? — Andrew M

There are two states in superposition (in relation to O''). That superposition has always been many worlds. The photon takes both paths and then interferes with itself. The cat is both dead and alive, and does not interfere with itself. The latter macroscopic picture is closer to many-worlds than is the one where interference is still likely.

- - -

Looking for inconsistencies in the view. I really like the view since it removes the need for instantiation, which always seems rationalized, and not actually rational, when I see it explained for other views. Cosmological argument for God is such an example.
— noAxioms

OK, I'll take up the challenge. :-) Are the physical things in the universe also merely formal? Or does your ontology have two kinds of things - the formal structures (the universes) and substantial (physical) things in the universes? — Andrew M

Well, I'd have to say two kinds of ontology: The structures themselves, which have no ontology, and the things in it (galaxies, cups, photons, gliders) which have a relationship to the structure as a whole. That relation is 'is a member of' as best I can articulate it, and is effectively as close as you're going to get to ontology. So 5 exists in the set of integers because it is a member of that set.
This here glider exists in some CGoL block, having perhaps finite duration. It seems appropriate to use 'physical' to describe that since it has analogies to our universe. But other cellular automata don't really have objects or sub-structures like that, and it becomes less appropriate to use the term 'physical' to describe states or movements of 'objects'. At least it is a temporal structure. The universe of the Mandelbrot set has an obvious 'physical' object in it, but it isn't temporal. So is it appropriate to use that term then?

Also is the equation "x = 1" a universe? How about just individual numbers, like the number 1? Or 0?

I think they can be trivial universes on their own. Does x=1 mean anything that just '1' doesn't? What is '1' if the set has no other members? The universes are so trivial that there seems to be no way to have any relations except the identity relation. The universe have no requirement to have meaning, lacking something external to give it that. But we're considering them here, so in the context of this discussion, '1' should have meaning to us I think. Don't think I was out of line to ask it.

Thanks for the replies.

Which is to say, multiple measured outcomes can occur, but this can't be coherently expressed in relational terms since no interactions between the worlds occur. That is, in relational language, the other worlds are not real for observers in this world and neither is our world real to them. — Andrew M

Wow, a lot of context is missing here. Had to go back to the wiki entry to figure out the scenario being described. O' is observing system O and S. One could say that O is the cat, and O' is the guy outside the (initially closed) box.

As you quote, no paradox was described in the scenario when the question is correctly framed. A full description of the interaction between O and O' (with all worlds in superposition) can always be expressed by some outside O'' so long as interaction with O'' does not take place.

OK. So to clarify, you're saying that CGOL (as a formal and non-instantiated structure) nonetheless has its own internal physics. And from inside the structure, gliders are physical but, from their frame of reference, their universe is formal.

And similarly for us, birds, trees and human beings are physical. But our universe is formal. — Andrew M

Yes. Except I'm not sure about the necessity of the frame of reference. Both universes are formal structures from either frame of reference, but each is its own local reality. So CGol structure is not part of my personal reality, and our universe is not part of theirs. Each is not real to the other, but there is no objective (instantiated) reality to any of them.

Looking for inconsistencies in the view. I really like the view since it removes the need for instantiation, which always seems rationalized, and not actually rational, when I see it explained for other views. Cosmological argument for God is such an example.

It would seem so, but I'm not really sure. Per RQM, the quantum state continues to evolve unitarily for an external non-interacting observer (i.e., the superposition is maintained) while at the same time the quantum state reduces to a single definite outcome for the interacting observer (where that outcome is undefined, not merely unknown, for the non-interacting observer). — Andrew M

While at the same time, but not in relation to the same things, so the they cannot be compared like that. To the noninteracting observer (the guy outside the box), no observation has been make and the odds of the outcome of the eventual measurement is still 1. In relation to the more local observation (the geiger counter and the cat it didn't kill), there is only one outcome, not both. RQM seems to never allow multiple outcomes.

Conway game of life is such a structure. Not a physical thing, just formal construct. It does however have physical things in it, with particles that zoom around at varying speeds with casual laws, etc.
— noAxioms

If Conway's Game of Life is instantiated on a computer, then gliders and the like emerge. But without that instantiation, it's just a formal construct where nothing happens at all.

I must disagree. This lack of need for instantiation is critical to the view that the universe is such a structure.
The CGoL needs instantiation (via simulation by us on a computer for instance) only for us (not part of it) to view the structure. But the structure is unaltered by said instantiation. Time is built into the structure (I'm picturing 2d space and a third time dimension, an eternal view), just like it is in this universe. An eternal view is necessary since we are not part of the CGoL and the block has no 'current state' from our point of view. The simulation might, but not the structure itself.
I would agree that instantiation of sorts would be needed to define a 'present', something external that moves that present along. Presentism doesn't fit well with the view, nor does dualism, both involving things external to the structure.

So the ontology of the structure need not exist for the physics of the thing to be there. The gliders and such exist as 'physical' parts of that universe. If the structure was sufficiently complex, thinking beings could be part of it, that deduce the nature of their world and contemplate their ontology. But the instantiation of the structure is unnecessary for any of these thinking-relationships to be part of it, just as surely as 3+5=8 does not require numbers to have Platonic existence in order to be true.

Actually Copenhagen takes an instrumentalist view of the wave function and so denies there is ever more than one photon. — Andrew M

How does Copenhagen describe the cat in the box then? The cat is in superposition, both dead and alive, despite the measurement being taken from the cat POV. I realize that is a relational description, but I've known no other even before I knew the name for it.

Defining reality as a relation only shifts the basic claim. The claim now is whether there is one measured outcome or whether there is a measured outcome for each relative state. Copenhagen and Bohm (and most other interpretations) deny the latter, contrary to MWI.

Relational also denies the latter it seems. The other outcomes don't exist in relation to any observation.

If the physical universe is a mathematical structure, and humans are part of it, and not something separate from it but interacting, then humans are 'in' the structure, just like my engine is in my car. How is that a category mistake?
— noAxioms

A mathematical structure is a formal construct not a physical thing.

Agree. If the universe is a mathematical structure, then yes, it is not a physical thing. Doesn't seem to be one even if not. It contains physical things, but that's just how this structure works.

The analogy is saying that your engine is in an equation.

No, the car is, and it is a bad analogy because a car is thought of as a physical thing in a world of other things. The universe is not such an object.

Conway game of life is such a structure. Not a physical thing, just formal construct. It does however have physical things in it, with particles that zoom around at varying speeds with casual laws, etc.

Everyone has been pointing to the paper on relational quantum mechanics, which I read from the Stamford entry.

[Rovelli] also has co-written with Federico Laudisa the entry on Relational Quantum Mechanics in the Stanford Encyclopedia of Philosophy. — Pierre-Normand

While I actually agree with the paper, it seems to relate measurement event outcomes to observers, and not the more general case of relating is-real as opposed to property of is-real. So to illustrate, take something not part of quantum mechanics: 5 exists in the set of integers (existential quantification). That's a relation, not an ontological assertion. Do the integers exist? Two ways to answer: Existential: Sure, they exist in the set of rational numbers for instance. Ontological: The have (or do not have) platonic reality. I find that a meaningless distinction, lacking a relation. They exist to or in something, but that just defers the ontological question to the something, adding another turtle to the pile. There seems to be no need for there to be a bottom turtle (an objective set of all things that actually are).

As for relational quantum mechanics, they point out something I've always noticed: There is a quantum measurement that triggers the poison release that kills Schrodinger's cat. Surely the cat counts as having measured the sample. If not, put Schrodinger's underpaid lab assistant in the box. The wave function of the measurement collapses to the observer in the box, but not to the observer outside. Doesn't copenhagen interpretation (and any of the others) already say that? And there's always a larger box, so the outside observer peeks in and sees both a dead and live lab assistant. In what way does copenhagen interpretation allow for the cat to be both dead and alive without asserting that it does not count as a measurement?

Hi, I need a clarification. Do you think that our experience is totally illusory? — boundless

No, not at all. I perceive the cup. It is as real as I am probably. If it were an illusion, it would have a different reality-status from me. Can't rule that out, but not where I'm investigating. Just saying that it is a real part of this world in which I'm also a real part. It is a relation of reality to the world. If reality is related to my direct experience, then the cup is real only when experiencing it, and not otherwise. That's idealism of sorts, but still no illusion. The view is not in conflict with the former, just a relation to a different definition of reality. None of it requires objective (relation-independent) ontology. I guess there is still ontology, but only as a relation.

Mmm, do you follow Rovelli's interpretation? — boundless

Have to look it up.
Meta pointed me to MDR (model dependent reality), which I had not seen either. I find no references to Rovelli in it. His work is more on the QM level than just, um..., I guess macroscopic metaphysics.

I'm sometimes pretty slow to respond. Plenty of new things to read are being suggested.

So you assume that 12 and 6 exist. You don't think that this presupposes an ontology? — Metaphysician Undercover

No, I don't think 6 needs to have platonic reality for 12 to be even.

If you can't say what you mean by "6 exists", then how are you using that word "exists"?

I think the term is 'existential quantification'.

Do you recognize that "a relation" requires things which are related? When you say that reality is a relation, don't you think that the things which are related are at least as real as the relation itself? — Metaphysician Undercover

Yes to both questions. The reality of both things is probably the same.

Instead, ask why there is what there is, rather than something else. — Metaphysician Undercover

There are biases in the asking of this. I wanted to get below that. So wrong question.

If it is a description, it relies on an ontology, because the description must claim to describe something. Maybe you're just trying to deny that your description relies on an ontology. — Metaphysician Undercover

Yes, I think I'm denying that. I can describe the even numbers without the necessity of them having an ontology. 12 is even regardless of whether numbers have some sort of Platonic existence. It is even because there exists some other integer (6) that yields 12 when added to itself. That is the sort of existence that we require if the universe is a mathematical structure.

As for MDR (which does not assert this mathematical reality), that is another view that makes reality a relation, not an objective state, known or not. A thing is real to something else. I think perhaps the view denies an objective correct answer as to which model is in fact correct, be it proposed somewhere or not.

I'm, not questioning your view — Metaphysician Undercover

I am. I don't really hold to a specific view. I'm just exploring in this area lately, and looking for inconsistencies.

The quest comes from all the unsatisfactory answers typically offered for the "Why is there something, not nothing?" question. Taking a step back and noticing the biases in the asking of that question sheds a lot of light on a suggested solution.

Unitary QM does. If a quantum state describes a photon being emitted towards a 50/50 beam splitter then, per the Schrodinger equation, this initial quantum state evolves into a superposition of two quantum states with one state describing a transmitted photon and the other state describing a reflected photon.

Other interpretations provide different accounts because they alter or add to unitary QM in some way (e.g., adding collapse). — Andrew M

Wait, how is a collapse-interpretation not unitary? Unitary seems to mean that probabilities of various outcomes of measurements add up to 1. There are apparently some interpretations where this is not so, but I'm not very familiar with them. Granted, they all seem to describe superposition states.
I always wondered how they detect superposition of say macroscopic states. They put some object (a small bar just large enough to see unaided) into a superposition of vibrating and not. I didn't get from the article how they knew this state had been achieved.

There are either two photons emerging from the beam splitter in the scenario I described above (per unitary QM) or just one (per most other interpretations). Aren't they mutually exclusive claims?

The interpretations with which I am familiar say the photons are both there, in superposition, so long as they've not been measured. It is only after measurement where they differ. Mostly talking about collapse or not interpretations. Copenhagen is mutually exclusive with MWI only in its choice of reality against which the state is defined. If reality is a relation, this is no more contradictory than my location being both north-of and south-of something. Just different things.

OK, but the theory still has to be coherent. I think it's a category mistake to talk about "the human in the mathematical structure..." or to presume that humans and numbers have the same ontology.

If the physical universe is a mathematical structure, and humans are part of it, and not something separate from it but interacting, then humans are 'in' the structure, just like my engine is in my car. How is that a category mistake?

- - -

Demonstrate said impossibility please. In particular, which empirical observation would be different (rendering it a scientific falsification), or what inconsistency is there in the logic (rendering it a self-contradictory philosophical stance)?
— noAxioms

It's quite simple. Ontology puts forward the fundamental principles by which we understand reality, it determines how we distinguish true from false [...] because one's ontology (world view) determines how one describes what is observed. — Metaphysician Undercover

Clearly I do not take this assertion as a given. I just said that my description relies not a bit on the ontology of the situation. I do have a description, having just described it.
I think you don't understand the view, in the same way you claim eternalism is false because the empirical experience would be different.

Since doing away with ontology renders this as an impossibility, it is an unacceptable proposal. — Metaphysician Undercover

Demonstrate said impossibility please. In particular, which empirical observation would be different (rendering it a scientific falsification), or what inconsistency is there in the logic (rendering it a self-contradictory philosophical stance)?

No, the model is not the reality. Turns out we don't yet have an accurate model, so I can hardly claim that say the current standard model is our reality.

My proposal of reality being a relation (not actual ontology) is something like model dependent realism, except the realism claimed is more like existential quantification.

To quote fragments from the wiki header:

"Where several models overlap in describing a particular subject, multiple, equally valid, realities exist"
That use of 'exist' is open to interpretation, but I agree, the stance would seem to be contradictory if 'exist' means 'is objectively real'. If used as a relation as I propose, then yes, all of the models (if they are accurate ones) describe existing realities. Idealism even makes sense this way.

"[MDR] claims that it is meaningless to talk about the "true reality" of a model as we can never be absolutely certain of anything. "
This is just acknowledgement of epistemology. Few stances claim that absolute certainty can be known. But does MDR take a stance that despite the inability to know it, there might be (must be???) a true reality?

I will look at it more, and what Hawking has to say about it.

Had to jump in on this. Quoting some of Andrew M comments and boundless's replies to them.

Yes. So what I'm getting at is that a notion of res potentia (i.e., a dualistic substance) does not arise in the Schrodinger equation. As far as the Schrodinger equation is concerned, the quantum state continues to evolve unitarily regardless of observed measurement outcomes, with each state equally physical. — Andrew M

I don't disagree, but this is already stepping into interpretation territory. QM doesn't say what the states actually do.

Ok, with this I agree. In fact the problem arises with the interpretation of the Schroedinger equation. If you accept it as the "reality", then of course all branches are as real as ours. However, if we accept from the beginning that the wave-function is epistemic and not ontic, then the relation between "potential" and "actual" becomes much more relavant. — boundless

Epistemic, not ontic, yes. I find that ontic makes no difference to anything, and ontology itself is perhaps a relation and nothing more than that. It is meaningless to say something exists. It always exists in relation to something else, and there is perhaps no objective base to act as a foundation for relation-independent ontology. This is just a proposal of mine, not an assertion, but it does away with a whole lot of problems.

Neither the Schroedinger equation necessarily motivates one to take the wave-function as "the reality" (except maybe in the "Platonic" realm, if it exists). I admit that "simplicity" is a respectable motivation, but personally I do not see it as a compelling one. IMO QM, among many other things, suggest us that the "model" is not necessarily a "picture" of reality. And to me saying that reality reduces to "one wavefunction which never collapses" seems too reductionist. As I said, it seems a subjective issue. Of course this is not an argument. But IMO "simplicity" is not an argument for the same reasons. :smile:

They can both be correct. The wave function in its simplest form exists in relation to the whole structure of the Schroedinger equation for any closed system, but it exists in collapsed form for any isolated quantum state such as the point of view a human subjective view. These are just different relations, not mutually exclusive interpretations, at least one of which is necessarily wrong.

Not necessarily. MUH is an example of Platonic realism about universals. In his paper, Tegmark says:

Stephen Hawking famously asked "what is it that breathes fire into the equations and makes a universe for them to describe?" In the context of the MUH, there is thus no breathing required, since the point is not that a mathematical structure describes a universe, but that it is a universe. — Max Tegmark - The Mathematical Universe

Yes, it is this unnecessary breathing of fire that I'm talking about. Is such a structure real, in that Platonic sense? Turns out it doesn't matter. The human in the mathematical structure will behave identically, asking the same questions about the same experience, whether or not there is some ontological status to the structure itself. That designation does not in any way alter the structure.

In a way I find myself to be a reverse Platonist. I believed numbers to be real for a while, but now I favor a view that ontic structural realism, where yes, we perhaps share the same ontology as those numbers, not that the numbers must exist, but that the existence of our universe is required much in the same way that numbers don't need it. OSR says we're made of the same stuff, so it presumes the two have the same ontology, but it doesn't presume that shared status must be some kind of objective existence.

Still, the physical duration of processes seem to me not to be perspectival in any one of the two senses distinguished above (i.e. "frame-perspectical" or "agent-perspectival"). — Pierre-Normand

OK, I see that. I was meaning that a worldline (not just one light-cone-laden event along it) is a perspective as a whole, and a person (a localized process) thus has a perspective that includes the duration of that worldline. That's isn't one of the two ways you are using 'perspectival' in your post.

The author displays a parallel misunderstanding of the barn-pole paradox. — Pierre-Normand

I had to look that up, and the flaw in the criticism was trivial. The barn and pole are treated as simultaneous objects instead of events. Using the latter, there is no paradox.

This crude mistake also appears to have led Robbins to a rather confused conception of what it is that it might mean for a duration to be "ontologically real" rather than its being merely perspectival or relative to a reference frame. — Pierre-Normand

Here is perhaps the disconnect between what fdrake has been addressing and what I've been denying, which is the ontological status of duration, or of time. So I think some clarification is needed, because I think the wording you put here is the more standard one.
When people ask me if they think time is real, I don't know how to answer since I don't associate ontologly with my understanding. But apparently it is in contrast to 'prespectival', and no, I don't think it is real in that sense.

The way I have been using it is my sense of presentism, that there exist a subset of events that are in 'the present', that this 'the present' is a boundary between nonexistent past determined events (how could they be determined if they don't exist??), and future undetermined ones. This view seems more ontological to me (only present events are real, the rest are not), but it proposes zero falsification tests (if worded well), and thus is in no way refuted by any empirical theory like relativity or any other.
On the other hand is the assertion that humans experience of duration is unique in experiencing not physical processes like clocks or anything else physical, but of the advancement of this "ontologically real" present. This would elevate it to an empirical claim, and despite being untested, would seem to be complete nonsense. It means that in the twins experiment, the traveling twin at sufficiently high velocity would die (of suffocation perhaps) because his physical processes would occur faster or slower than he could consciously tend to them. The view also tends to put Earth at the center of the universe, but that is not necessary. I find any view that necessitates heliocentrism to be one equating the universe to be all about us.

Sure, logically possible. I ain't believing in it though. — fdrake

Your thread seems to have been trying to demonstrate that relativity renders presentism a contradiction. Sure, I don't believe it either, but I don't consider it to be a proven thing. I just try not to be in the habit of believing in things that add to a model without explaining any of it better.

Sorry, but the equations did not quote properly.

Because this is interesting, let's have some maths for it.

The quantity 'proper time' is invariant between inertial reference frames.

If dτ2>0 between two events occurring at t1 and t2, then the separation between the events is called time-like. This occurs, roughly, when the temporal separation between two events is greater than their spatial separation.

if we wanted to find a frame of reference in which t2 occurred before t1, reversing the inequality here, it would need squared average velocity which can't happen, since it would be higher than c2. So, if two events have a time-like separation, there does not exist an inertial frame which has their ordering reversed. — fdrake

I follow what you wrote and mostly agree. There doesn't exist a valid frame which covers t1 and t2, but Zog is moving (proper distance increasing) by over 4c, which is not a valid velocity, so hence I say Zog doesn't exist in our frame. But it exists in the universe as does its frame, so I hesitate to assert that this frame that is invalid for t1 is nonexistent. Just invalid for t1. Yes, t2 is ordered before t1, and in fact both predate the big bang. This is what happens when you consider an object or frame in the context of an event for which it is invalid.

Another consequence is that all events occur simultaneously for light. The orders can reverse for space like intervals - when dτ2 is negative.

It is meaningless (but not invalid) to reverse the order of simultaneous events. Either way they both happen at once.

Thus, two events can be said to be in causal contact if they are in time-like separation, but not in space-like separation.

Right. And any pair of events in causal contact can be said to be at the same point in space in some frame, and any pair outside causal contact can be said to be simultaneous events in some frames.

From the perspective of light, there is no duration. From other perspectives, there is duration.

Local spacetime collapses to a singularity at light speed. Not sure if it is valid to reference that as a 'perspective'. It is not a valid inertial frame.

A very distant observer moving in a particular way could see our history with some events in a different order. Why should the universe be seen from the perspective of a human, and not a photon or a distant observer (with space-like separation)?

Oooh.... Example please, because this seems totally implausible. What is 'our history'? Sure, if we colonize distant stars, event ordering starts getting ambiguous, but it doesn't take a distant observer to notice that. So presume our history is confined to this planet, and we're not just talking about milisecond differences that it takes for light to traverse the diameter of the planet. Sure, events on opposite sides of the planet within a milisecond of each other have frame dependent ordering, but again, it doesn't take a distant observer to notice that.

This is a fun way to smuggle in an objective ordering without justification. Why would it be contradictory for an event to happen before its cause as viewed from some reference frame? Contained within the series of cause and effect is the universal succession, only this time of equivalence classes of causes occurring before a given ordinate in the series. — fdrake

Had a hard time following this.
One property of relativity is that from any given event X, there is a fixed set of events in its direct past and future causal cones, and this set is frame independent. OK, the frame of Zog puts 2017 in my future, but I don't exist in that frame, so no contradiction.

Ok. What differentiates an objective ordering from one in obtaining in a reference frame in special relativity? — fdrake

It's an ontological assertion. Presentism posits not just a real ordering, but also a real boundary between past and future events. Just the objective ordering is not enough. Presentism adds a boundary that traverses the events in objective order.

SR make no ontological assertions. It just says that physics will be observed to work identically in any frame.

All reference frames have just as good a candidate for universal time. That is to say: they all suck for it. — fdrake

Yes they do. No inertial frame gets near covering the universe, so if there is an objective ordering, it cannot be an inertial frame. SR doesn't say that, but GR does.

Take planet Zog 60 BLY away. We don't exist in its frame and they don't exist in ours. Some other non-inertial ordering of events is needed to cover such places, and it need not even be smooth. Perhaps it advances only over there for a while and later on advances for us, making the the boundary a wobbly thing that makes uneven progress. So long as the boundary doesn't get so advanced one place that events happen before their causes, there's no contradiction. Light cones limit the maximum distortion of the boundary.

That there is a unique ordering of events with respect to time is something that is false because of the special theory of relativity. — fdrake

Totally agree. SR says physics is unchanged in all these different orderings. There is not a unique ordering of my children either. I could order them by height.

What stops the following from being inferred from special relativity: there is no objective ordering of events.

It doesn't follow. What follows is that if it existed, it would be undetectable. There is no premise of its nonexistence. I don't like its existence because it is a needless addition that explains nothing.

Reference frames can be attached to moving particles.

Yes, but any frame can be attached to any particle. It is moving in all but one of them. Yes, some object is typically used as a specification of a frame. There is almost no other way to do it. So we all know what we mean by "frame of the train platform" even though the platform exists just fine in the frame of the train. But I think it is sloppy to say clock C dilates relative to object R. It should more correctly say it dilates in the frame of object R, or even more anal, in the frame in which object R is at rest.

I agree that presentism doesn't imply SR. What I'm saying is that insofar as presentism claims that there is a unique objective ordering of events, it is contradicted by SR.

It says there is a unique objective ordering, not a unique ordering. None of the SR orderings are objective.

What stops the following from being inferred from special relativity: there is no unique objective ordering of events with respect to time. — fdrake

SR doesn't talk about objective orderings, so I don't see how the above can be inferred.

I don't see how these two things can be compatible:
(1) There is a unique order of events induced by the idea of the present in presentism.
(2) Events A and B can be ordered differently depending on the motion of a particle. — fdrake

The first speaks of objective ordering, and the latter means that the observer is free to order events differently, and physics will still work without detectable differences, rendering any potential objective ordering undetectable. The latter is about empirical observation, not about an interpretation of what actually is. And #2 should be "depending on the reference frame", not depending on particle motion. Motion.

I don't understand how you can say 'presentism is independent because it's metaphysics', when one of its implications is negated by how time works in SR.

Presentism doesn't comment about how time works in SR. Presentism was around well over a century ago, and SR was not in any way suggested by it. Not sure when the term was coined, since the interpretation is far older than the name needed to distinguish it from alternative interpretations.

You misrepresent what Everett proposes
— noAxioms

Well, perhaps the Wikipedia entry on the topic needs to be updated, because it begins:

The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternate histories and futures are real, each representing an actual "world" (or "universe"). In layman's terms, the hypothesis states there is a very large—perhaps infinite[2]—number of universes, and everything that could possibly have happened in our past, but did not, has occurred in the past of some other universe or universes.

The quantum-mechanical "Schrödinger's cat" theorem according to the many-worlds interpretation. In this interpretation, every event is a branch point; the cat is both alive and dead, even before the box is opened, but the "alive" and "dead" cats are in different branches of the universe, both of which are equally real, but which do not interact with each other.

So - this is all wrong? — Wayfarer

A lot of it is indeed misrepresented. The people updating the wiki perhaps have not actually read the thesis. The first half of the first sentence is a different wording of what I quoted, that closed systems evolved according to the Schrodinger's equation. The rest is implications of that one presise, not additional premises. Wave function collapse violates the premise, but is not explicitly stated. They put "universe" in quotes there, and that's OK, because they mean 'worlds', which most laymen take for 'planets' instead of the mathematical meaning. There is no implication of actual multiple universes. It is one wavefunction with multiple solutions.

Worlds do not have identity (there is no objective has-split or not state), so the cat being both dead and alive (in superposition) is a relation to something, not an objective state. So while still in the box, it is superposition from the point of view outside the box, but very much not in superposition from the cat point of view. From within the box, the live cat is in a different world from the dead one at all times, despite still being in superposition relative to the external point. Likewise, all worlds are just one universe in superposition from outside the closed system. There is never a new universe.

Not sure how copenhagen interprets the cat thing. Surely the cat observes the quantum event, and if that is denied, put the expendable lab assistant in there instead. Schrodinger's cat exercise has always been MWI of sorts it seems. They have had such boxes a long time, and recently have managed to put a macroscopic object in one, putting a thing visible to the unaided eye, in superposition. Never build a local one that can hold a cat. Trivial if non-local.

Answer number two:
Relativity is a scientific theory born of empirical observations. Presentism is a metaphysical interpretation of time, not a scientific theory at all. It has zero falsification tests, as do all interpretations. If such a test (a difference between 4D block and 3D universe) could be proposed and performed, then it could be elevated beyond interpretation and one or the other could be falsified. Meanwhile, relativity would stand because it works the exact same way in both interpretations.

And you don't think that simultaneity is a frame dependent phenomenon refutes the idea of there being an objectively correct answer to whether A is before B? Why or why not? — fdrake

Your question can be interpreted different was, so I pick this one: Time as used in physics equations is what simultaneity is about, and relativity describes that. The second definition of time is from presentism, which is the rate of advancement of this 'present', which has no units, not even seconds per second since the two are different things. So I will say that presentism posits a different definition of simultaneous altogether, and there is no refutation of any part of the presentism because presentism is irrelevant.

That's the key word: irrelevant. It is an invisible pink unicorn, and not refuted for the same reason.

Do you conclude that relativity thus refutes presentism? — fdrake

Again, no.
Relativity says the math works with or without the existence of magical invisible pink unicorns, but it doesn't refute said unicorns. Presentism is such an addition: Something irrelevant, undetectable, and unrefuted.

There are real trajectories with which the expansion of the universe looks different.

Yes, but I think that from any such trajectory, the universe appears younger than it would if it were a comoving object, and an observer on that trajectory would be aware of the deviation from the local mean.

What problem is the Many Worlds Theory of Hugh Everett a solution to? In other words, why was it necessary for Everett to propose an hypotheses comprising the apparently radical speculation of ‘infinitely branching universes’? — Wayfarer

You misrepresent what Everett proposes. To quote a paper on this point:

• EVERETT POSTULATE:
All isolated systems evolve according to the Schrodinger equation d/dt |ψ> = - H|ψ>
.
Although this postulate sounds rather innocent, it has far-reaching implications:
1. Corollary 1: the entire Universe evolves according to the Schr¨odinger equation, since it is by definition an isolated system.
2. Corollary 2: there can be no definite outcome of quantum measurements (wavefunction collapse), since this would violate the Everett postulate.

• What Everett does NOT postulate:
At certain magic instances, the the world undergoes some sort of metaphysical “split” into two branches that subsequently never interact. This is not only a misrepresentation of the MWI, but also inconsistent with the Everett postulate, since the subsequent time evolution could in principle make the two terms in equation (2) interfere. According to the MWI, there is, was and always will be only one wavefunction, and only decoherence calculations, not postulates, can tell us when it is a good approximation to treat two terms as non-interacting.

No proposal of new universes. It is not an ontological assertion.
I disagree with the author's proposal of quantum suicide to test the theory since other interpretations predict the same results.

I was meaning something like the following: the equivalence principle in SR is essentially that motion is always relative motion - which introduces coordinate transforms - constrained by a cosmic speed limit -which introduces the scaling factors. In GR the equivalence principle is essentially between gravitation and an accelerated (that is curvilinear) coordinate system, and that intrinsic curvature is introduced by mass.

One of the motivating examples for the equivalence principle is the elevator thought experiment. Someone in an elevator could not tell the difference between the elevator moving down with constant acceleration due to a cord and the elevator moving down with constant acceleration due to a gravitational field. If you ignore tidal forces, there's nothing the person in the elevator could do to see if their acceleration is cord based or gravitation based. — fdrake

Right. Tidal forces is effectively a non-local experiment. Make the box big enough and the mass close enough, and tides can be felt. In SR, it doesn't matter if one of the frames is special since that special nature is undetectable, and thus moot just like it doesn't matter to the elevator guy how the force being applied to his box is linear acceleration or bent space. Either way he holds his cup this way to prevent the drink from spilling. That's my point, that the reality behind the experience doesn't matter. It makes no useful predictions either way.

I was trying to say that the undetectability of the difference between the relata in any equivalence principle should not be interpreted as an epistemic property, the equivalence in descriptions should be interpreted to be as real as its consequences - such as the relativity of simultaneity and length contraction. These things really happen and are not mere artefacts of coordinate system choice.

I find myself resisting this. Is my length really contracted if in my frame, it's the length of everything else that's contracted? Seems like an artifact of of choice. On the other hand, the twin really does come back younger, despite the stay-home twin aging slower during both legs of the journey, from the frame of the rocket-twin. No mere arithmetic games can do that.

A foliation of space-time is a lot different from a foliation of time, you were referring solely to the latter?

Don't know what the latter is. Events are points in spacetime, not in time. Not trivial to order them, but it would be trivial to order moments in time.

I don't understand how this is possible, given that in some reference frames event A can happen before B and in some event B can happen before event A - and there can be no strict total order (like <) with this property. How would you construct a foliation to produce a time which obeyed this?

Different frames foliate space differently. That's what frames do. They specify an ordering, but not otherwise a coordinate system or an origin. An actual present would imply an objective foliation instead of a relative one, but SR is all about the physics in relative terms and isn't affected by a possible objective foliation.

One possibility would be to say that if there exist two events A and B, that they occur at the same time if and only if there exists a coordinate system in which they do occur at the same time.

Actually, under relativity, there exists a frame such that any two (reasonably local) events are simultaneous with only spatial separation, are at the same location with only temporal separation, or right on the edge between the two (on the edge of each other's light cone) in which case separation is 0/0 or undefined. From event A, all events outside its light cone are the first sort, all inside are the second sort. There can be no two points that don't meet one of those 3 cases. This is pure relativity, and has nothing to do with 3D space or absolute time.
So as for your comment above, no, A and B are not simultaneous just because some frame exists where they are. They're only simultaneous in that frame, and not in some other frame where they're ordered A first or B first. One can rotate the paper at will to put C above or below B in the time dimension (my events B and C were potentiall simultaneous in my paper example. A and B were inside each other's light cones and B is unambiguously after A).

Or that there exists a coordinate system in which A is before B and B is before A. Of course coordinate systems exist in which B can be said to have occurred any time before A or B by adopting the frame of a particle with a particular motion (you can solve the Lorentz equations for v). But I think that this conception of time inappropriately quantifies over reference frames, and destroys the relativity of simultaneity. That is to say, simultaneity in SR is simultaneity in a reference frame, and the solvability of the Lorentz transform for arbitrary t shows that the ordered pairs of events in any such order are incompatible with a total order; unless time is trivialised in the sense that all events occur at the same time (which isn't presentism or a block universe).

All true. Presentism just says that there is an objective correct answer as to which of A or B happens first. Relativity supplies frame dependent answers, not objective ones.

So, the question is whether an order produced by such a foliation would resemble anything like a universal time. I'm not convinced that there is such an ordering, could you provide some references for where you're getting this from? I think you're losing too much detail when thinking of foliations as an order.

Comoving time is such an ordering. Essentially, for every event in spacetime, the actual time there is the age of the universe in the frame that maximizes that age, or in which the red shift of distant objects (most notably the CMB) is isotropic. Same thing. That age is an objective one, and provides an objective ordering of all events.

So that's the 'frame' referenced when they say our galaxy is moving at about 0.2%c. Our solar system is on the side that cancels out some of that, so we're actually cruising at about 0.12%c. I put 'frame' in quotes because it is not an inertial reference frame, and is different for every point in space due to expansion.

I don't think an undetectable in principle difference should be elevated to a difference in practice. — fdrake

What difference can an undetectable thing make to practice? In what way is the latter 'elevated'?

I'm assuming 'foliates' here means, essentially, 'providing a coordinate system for'.

It is an ordering of events, and not otherwise specifying full coordinates. This event is simultaneous with that one, and prior to that third one over there. A foliation of the universe must order all events, not just local ones like an inertial reference frame does.

And the way in X foliates Y is always done differentiably (my differential geometry-fu isn't particularly strong). So I'm thinking of a foliation as the thing which describes the rate of change of an application of a coordinate system to a locality with respect to infinitesimal shifts in its origin.

Foliation specifies no origin. Just relations, and only temporal relations at that.

So at time t they were in the Hubble volume, and at some time t' they expanded out of it? That's the picture?

Pretty much yes. Time t' would be the event of that thing increasing its proper distance from us at the speed of light. Like from beyond the Hubble Sphere can still reach us by crossing back and eventually getting here. So maybe the image of it we see is one already outside that Sphere. There is an event horizon beyond which objects are undetectable from here even in infinite time.

About t', I speak of proper distance. In reality, time is frozen for it in our frame, and t' is unexpressible in our reference system, so t' represents the local time of both here and there when the contracting Hubble Sphere no longer includes that distant place. Something like that.

What implications do you draw from this? I've said previously that there are still things which can be said about spacetime in general with respect to increasing time - like the expansion of space when the metric tensor is an increasing function of time. I interpret foliations as ways of setting up for questions like this - they will provide a system of coordinates in which the evolution with respect to some variable, probably time in this case, can be indexed.

Well, IF presentism is true, AND the foliation suggested by GR happens to match the geometry of this 'present' boundary, then there is an actual velocity and location of all things. So from what I read, this 4D metric tensor means in part that the distance between two events is path dependent, and none of the paths is straight or obviously the actual separation. In 3D, a lot of that falls away, and two events need to be simultaneous to have a defined spatial separation. Not sure how much I'm addressing your question, or if I'm being accurate here.

I don't think this makes length contraction or time dilation go away, but it does implicate some notion similar to universal time in the pre-theoretic sense. Regardless, how would you think of this time without destroying the relativisation of time/space through motion? I doubt the right answer is through an assertion against the relativisation of simultaneity (which screws with time = the succession of events), or against the way space expands/contracts relative to motion (which screws with its identification with pure extension).

Of course this 3D view still works under relativity. The twin comes back younger because time progresses slower if you move faster. Clocks do not measure time in that view since there is no way to know if it is stationary. So they just measure local process rates. Relativity of simultaneity is an illusion then. As I said, the platform guy is using incorrect data to determine the two events were simultaneous. They're simultaneous in his frame, which is all he cares about. He cares not that his frame is not actually stationary, since that distinction makes zero difference.

Aha, I see what you mean. You're providing a demonstrative example of motion in 1 spatial dimension and 1 temporal dimension, not saying space and time can be thought of as physically 1 space 1 time in general. — fdrake

No, ours is 3+1, but the concepts are the same. The coordinate system (all four axes) can still be oriented any way, so long as they stay perpendicular. Radial systems sometimes work better for the cosmological scale where SR is completely irrelevant.

The rest was just an example of the conservation of proper time.

I don't think this is true. If it were legitimate to axiomatically posit a preferred frame of reference with which to define all motion relative to, it'd be a consequence. I think the absence of a preferred reference frame is an implication of the equivalence principle - what would be the point in stressing the transformability of motion to equivalent forms if the only purpose was to index all motion again to an arbitrary origin point? Why should any one ordering of events be more true than another?

Undetectable is what the equivalence principle states, no?. Just because something is undetectable doesn't mean it isn't there. Hey, I'm not arguing for it, just against this being a proof against it. I personally favor a block view, and no ontology to it at all.

In other words, nothing changes about relativistic computations if there is a preferred reference frame for any given motion, so there being a preferred reference frame is something out-with the influence of the theory. An arbitrary decision about space-time should not structure how we think about it.

Correct. Something undetectable makes no difference to what is an empirical theory.

Your post takes the view that a predicate equivalent to 'is the true reference frame' is something that can be appended to a reference frame, this is something SR and GR prohibit from having any ontological import.

If I've understood you and it, anyway.

No GR prohibitions anyway. SR perhaps not, but it describes a flat massless spacetime that doesn't correspond to reality. I.E. no inertial reference frame foliates the universe, so none can be the correct one. Inertial frames are local, and the universe is not. There are objects that can actually be seen that do not exist in our inertial frame since they are, in our frame, simultaneous with a time before the big bang. Talking about stuff near the edge of the visible universe that "has since" (<-- questionable use of verb tense) passed beyond the Hubble Sphere which confines events even remotely valid in our reference frame. Hence the curved foliation with is not a reference frame at all, but covers all the universe.

Velocity is the slope of the worldline of some object. Relativity works in block or in 3D view, so the ontological difference is interpretation with no empirical difference. Relativity was born of the observation <of fixed light speed>. That fact is not a necessary property of Minkowski spacetime, so block universe is not necessarily relativistic. — noAxioms

So you're saying that a block universe is neither implied by or implies either relativity? I think I agree with this, but I don't understand how you're using four-velocity in the presentation. Can you give me some more words please? — fdrake

Pictures are hard to post. Consider a simple spacetime of 2D, one of space, the other of time. Lots easier to visualize. Twins experiment requires only 1D of space for instance. So it can be done on 2D paper, preferably circular paper so there is no preferred orientation.

Draw a dot A somewhere, and B somewhere else. This represents 2 events, say the start and stop of a journey. Straight line between the two is its worldline, unaccelerated. A curved line denotes acceleration. So now superimpose a vertical axis S (space) and perpendicular horizontal axis T(time), with origin at A. If you orient the paper so the line is at an angle, the vertical space displacement of B is nonzero and the slope is the (positive or negative) velocity. If you assume a different frame and orient the paper so the T axis followsthe worldline, then the space displacement is zero, T is at a maximum value at event B. There is no motion in this frame since spatial displacement remains zero for the length of the worldline. Angle the paper a lot and the space displacement gets large and the T displacement starts to shorten, but regardless, the unitless separation between A and B (called the interval) remains fixed.
If there is a third event C which is directly above B at a certain orientation of the paper, then B and C are simultaneous, but only in that frame. Orient the paper different and the events become ordered differently.

All this is pretty much a description of flat Minkowski spacetime. At no point does something move across the paper, and orienting the paper different does not make any real change to what is drawn on it.

I'd also really like to see an abbreviated form of the post you made on another forum.

Found a bit of it: Context is the train experiment, where two lightning strikes occur, one at each end of the train, leaving a mark on the platform (and train ends) as it strikes. An observer on the platform and on the train each make their assessment of the simultaneity of the two lightning events.
----
Under the 4D model, the platform guy notices the two strikes at the same time, and after measuring the distance from where he was standing to each of the platform strike marks, determines that the two strikes were simultaneous. The train guy detects the strike at the front of the train first, and afterwards the rear strike. He also measures his distance to the two marks on the train, and is equidistant. He thus concludes that the front strike happens before the rear strike. Two frames, two different but valid ordering of events.

3D model, with 3D space and separate absolute time:
Two events are not ambiguously ordered. If one frame orders them differently, that frame is not the preferred one and it orders events incorrectly. Two events simultaneous in that frame are not in fact simultaneous, and thus there are no future events that exists. The frames that put you simultaneous with those future events are simply wrong about their designation of simultaneity.

So in my examples, I always pick the unintuitive stationary guy. So it turns out that the train guy is the one actually stationary. The platform observer is on the moving ground.
Lightning flashes go off, hitting the front of the train first, and the back later.
The train observer is midway between the two events, and records the front strike first. Being equal distant from the two events, the observer knows the front strike happens first.

The ground observer is moving towards the rear of the stationary train, and by the time the light from the two signals meet, he is at the point where they meet, so he measures the two signals as arriving simultaneously, but one has traveled further than the other, so this is expected. His clock also runs slow, but since he didn't use it, nobody cares.

The guy not actually stationary is incorrect in his assessment of two events being simultaneous. So the guy on the platform is basing his simultaneity assessment on the false fact that the two marks on the ground are where the lightning struck. Since the ground is moving, this is clearly not true. The marks are not the point in space where the strikes took place. The endpoints of the train are the actual spot where the strikes took place.

This is a description of the 3D scenario, and I hope is free of inconsistencies.

BTW, I also saved a post describing the twin experiment with only SR rules, no acceleration, and using a tag team. It is more for illustration purposes, and argues no philosophical points.

Well, in block universe, there is no motion, just worldlines, straight (inertial) or otherwise. The dimensions of those worldlines can be different depending on the choice of coordinates, but that change (the separation (interval) of any two events, say the event of some twin's departure and the event of his return) is a fixed value, and not frame dependent. — noAxioms

I think it's strange to say that there's no motion in special relativity, — fdrake

I meant nothing moves through the block of Minkowski Space time. Time is built in. This is about the block view, not SR or GR. Velocity is the slope of the worldline of some object. Relativity works in block or in 3D view, so the ontological difference is interpretation with no empirical difference. Relativity was born of the observation that the worldline of a photon has the same slope regardless of assignment of coordinate system. That fact is not a necessary property of Minkowski spacetime, so block universe is not necessarily relativistic.

A 3D model of the universe works, despite the 4D Minkowski spacetime model that SR suggests. — noAxioms

I really doubt this, since this trivialises space-time curvature. The Einstein and Riemann tensors are 4-tensors, and the metric derivatives and Christoffel Symbols they consist of interact to give 4 tensors., They need to maintain the number of indices they have so that they can be contracted through identification or multiplication by another tensor to derive the Einstein field equations. 4D space-time can't be removed from SR or GR without drastically changing their character.

But, if you have a reference or previous post on this, I'd be happy to read it. — fdrake

My post was using SR case, which admittedly has bunk to do reality except in a local sense, away from significant spacetime curvature. So perhaps the field equations do indeed require 4D spacetime.

The posts I refer to is not in this forum. Took a long time to figure out why I was in read-only mode here. Essentially I ran the train thought experiment in 3D absolute space and ran into no contradictions. At least one observer is simply wrong about his assessment of the simultaneity of certain events.

With regard to the block-universe that this thing seems to imply. The block universe is essentially conceiving of the vector space (x,y,z,t) as a space-time manifold - as if when all components were free to vary along their ranges, we have a continuous set of snapshots of all events. This isn't implied, what is implied is that for a given equation of relativistic motion there is a space-time 'block' corresponding to its trajectory over space through time. It would be odd to consider space time an invariant block when the things within it can distort all of its motions with their particular properties. — fdrake

Well, in block universe, there is no motion, just worldlines, straight (inertial) or otherwise. The dimensions of those worldlines can be different depending on the choice of coordinates, but that change (the separation (interval) of any two events, say the event of some twin's departure and the event of his return) is a fixed value, and not frame dependent.

Actually I don't see any ontological necessity from relativity theory. A 3D model of the universe works, despite the 4D Minkowski spacetime model that SR suggests. I did an advocatus diaboli piece about the universe being 3D, and the train-thought-experiment being considered in that light. It works in either model, and thus I find no ontological implications. One thing that I did find is that no inertial frame can be the correct one because no inertial frame foliates spacetime. So a curved foliation (not an accelerated frame) such as the comoving system may be a description of the ontology. I don't buy that, but I cannot disprove the view. The comoving frame functions locally as an inertial frame.

Well, as I said previously, numbers are in some sense only identity. It's not that they have an identity - '7' can't be anything other than '7'. And '7' says all there is to know about it - you can carve the symbol in stone, draw it, or represent it in binary code, but at the end of all that, 7=7. So perhaps what I meant by 'having an identity' is 'being an individual existent'. But I admit, it's blurry. — Wayfarer

That seems more like identity than anything with this temporal existence for which you are reaching. 7=7 is pretty pure. But OK, you using 'exists' to describe I guess 'objects' within this universe, despite their having questionable identity. A piece breaks off a rock. Is it still the same rock? 7, having a more solid identity, seems more immune to that sort of questioning.

I would say 7 exists, but not in an ontological Platonic sort of way, but rather more like existential quantification. You are using the word differently, that's all.

The domain of natural numbers is real - but where does it exist? Only 'in the mind'? — Wayfarer

The domain of this universe is also real, but similarly has no 'where' to its existence. North of the next universe on God's shelf? (the natural numbers are kept in his box of playing cards)

Have not yet read all the replies to this, but the definition and examples of 'exist' don't seem to match, and I think need to be clarified.

'Exist' is derived as follows: 'ex-' to be apart, apart from, outside (as in external, exile), and '-ist', to stand or to be. So to 'exist' is to be 'this as distinct from that', to have an identity. In my heuristic, the 'domain of existents' is basically the realm of phenomena. 'What exists' are all the billions of compound objects that are composed of parts and have a beginning and end in time. Also, ‘existence’ refers to the human life considered longitudinally through time, 'our life', and the phenomena that we encounter within that context. — Wayfarer

The definition would seem to include numbers: they have identity, being distinct from each other. The example seems to include only temporal objects, of which the definition makes no mention. I think the definition needs rework since you seem to group numbers as real, but not existent.
And wouldn't it be noumena, not phenomena? Do stars on the far side of the galaxy not exist because we can't experience them? That would be an idealistic notion that doesn't seem represented in the definition.
My own investigation keeps pushing me more to idealism when pressed about the nature of an existent thing-in-itself, as opposed to the identity that I give it as a phenomenon. So I'm actually quite open to the example as phenomena, and not as a noumena.

Your example would accept the existence of the universe only if time is put outside the universe, since only then can the universe be a temporal object with a time before which it was not in existence.


Real: I'm fine with your 'real' definition. My own view is that given that the universe is the manifestation of what are 'real' laws, the universe is real. That's just me though. Your definitions of 'exist' and 'real' both seem to lack an ontological statement, with which I can again relate. You seem possibly to reserve that distinction for 'being':

The 'be' of 'be-ing' is of a completely different nature to the existence of objects. This is the distinction basic to ontology.

OK, a possible ontological statement, but it seems to go in a personal direction from there:

But Being is prior to knowing, in the sense that if we were not beings, the cosmos would be nothing to us, we would simply react to stimuli, as animals do.

So we're different than animals, despite the lack of evidence for this? I don't find it offensive to include my species among them. Anyway, it seems to have stopped being an ontological statement, and again been reduced to a relation: Things exist only as phenomena a specific 'being', and are real only as understood by said special 'being'. I'm probably making a strawman of this, but that's how it came across to me.

Our grasp of rational principles, logic, and scientific and natural laws mediates our knowledge of the Cosmos, that comprise the basis of ‘scientia’. However what has become very confused in current culture, is that the mind, which in some sense must precede science, is now believed to be a mere consequence or output of fundamentally physical processes - even though what is ‘fundamentally physical’ is still such an open question.

Why is that stance 'confused'?

Anyway, my primary point was about the 'exists' definition seemingly not matching the examples following it.

— Jonathan AB

First consider gravity to be instant as Newton theorized; then consider it to travel at the velocity of light as Einstein proposed. — Instant Gravity Proof

The problems start right there. Einstein did not propose gravity to propagate at all. Gravity waves, yes, which act as the particle equivalent of excitations in the quantum field, but gravity itself (the sort that attracts two orbiting stars to each other) is just an effect observed by spacetime being curved by the two masses. There are no gravitons involved, and no propagation of anything.

Here is my proof that gravity is instant:
http://www.flight-light-and-spin.com/proof/instant-gravity.htm
(my answer in short)
(ranked #1 at most search engines for 'instant gravity proof') — Jonathan AB

Didn't read it all, but the nature of the proof is pretty obvious in the initial diagram, and yes, it (speed-of-light gravity) would seem to inject energy into a closed system, with action not being balance by an opposite reaction.

The physics of instantaneous gravity seems flawed as well since it requires a simultaneity that is undefined without a frame. So OK, the frame of the mutual center of gravity is used, but that means that in different frames, the force on one object from another is different, which is contradictory. How can object X pull on me in different directions depending on reference frame? It could be measured, and the direction of force be used to determine an absolute reference frame.

Bottom line is I think your physics is off in the SOL example that spirals out, but I cannot yet put my finger on it. Such a simple proof must have been critiqued by the physics community.

You mean the force of gravity. Yes, that is pretty much everywhere. — Rich

No, I mean the force of the "Spaceship engines".