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Temporal Flow and Quantum Gravity

Wuthrich writes "the presentist maintains that the sum total of existence can be understood as consisting of a three-dimensional manifold of spatially distinct but temporally equally present, and thus simultaneous, events or objects."

That's wrong: it's possible to have a model in which each ontologically existing thing experiences an ontologically independent temporal flow, while simultaneously keeping other temporal correlations. The upshot is there is no single notion of present at which everything obtains in the same R3 space. For two particles, a state is not given in the manifold {t}crossR3, where {t} is the set of all times of a given reference frame. A state is given by two points on ({tparticle1}crossR3)cross({tparticle2}crossR3).

Consider an astronaut that accelerates away from the earth, goes to Alpha Centaui, turns around, comes back, and stops. Because of the astronaut's acceleration, when we compare clocks the astronaut's clock will show a smaller difference in leaving-to-returning duration than our clocks on earth. (Of course, this assumes the astronaut makes the trip in a frame that accelerates a lot compared to the earth's acceleration around the sun et. al.). Nevertheless, throughout the entire journey the astronaut observed, of himself, that clocks in his reference frame evolve at a rate of 1 second per qualitative second.

Vallicella on "the dog barked"

Bill Vallicella at Maverick Philosopher writes "The past-tense proposition that the dog barked... is in dire need of a truthmaker. There is need of an ontological ground of its truth."

The validity of "the dog barked", for the Presentist, could come from the present mathematical model that's an extrapolation of present causation. 

Reference: [maverickphilosopher] William F. Vallicella: Presentism and Causation: A Question for Alan Rhoda at http://lists.powerblogs.com/pipermail/maverickphilosopher/2005-December/000901.html.

After reading A Defence of Presentism by Ned Markosian I've got some questions.

After reading A Defence of Presentism by Ned Markosian I've got some questions.

1) what does it mean to "grab the thing that is now the referent of ‘Socrates’, and then to go back to see whether there is some past time at which that thing is a philosopher."? (p. 26) A Presentist can't "go back" into the past (if that's what it means).

2) what, for a Presentist, is the relationship between a mathematical object and the present?

What a Presentist could do is refer to a different location on his coordinated map, a "history", in the present. The map is such that the meaning of "Schubert started his Symphony No. 8 in 1822" presently refers to a map that is also present, but the map, a "history of sublime music", is ordered by our (present) notion of causality.

This allows us to suppose the mathematical object (... 1821, 1822, 1823, ...) "timelessly" coordinatizes history, in the present. The sense of 'time' in which the map is independent of change is precisely the map's own notion of time.

Reference: A Defence of Presentism by Ned Markosian, Western Washington University, on the web at http://myweb.facstaff.wwu.edu/nmarkos/Papers/Defpres.pdf, also a version appears in Zimmerman, Dean W. (ed.) Oxford Studies in Metaphysics, Volume 1 (Oxford: Oxford University Press, 2004), pp. 47-82.

Qualia and Ontological Ineffability

I can't resist putting up some stuff about qualia. Once again, things hinge on ontological ineffability.

1. qualia are inter-subjectively ineffable.

2. qualia are ontologically subjective and epistemologically objective.

Therefore, there are ontologically ineffable things. I take it qualia ontologically exist, the way some philosophers take numbers to ontologically exist. The question is how do we model ontologically ineffable qualia?

In the picture below, b1 and b2 are physical people, or at least their brains (or, more generally, they are physical information bearers). g1 is the quale green as experienced by b1, and similarly g2 is b2's experience of green. 'g1' is the name/concept/interface b1 has given to it's experience g1. b2 has a name for g1 also, namely, 'g1'. Strictly speaking these should be 'g1'_b1, and 'g1'_b2, but my point is that while g1 and g2 are ineffable, the names 'g1'_b1, and 'g1'_b2 are "effable"--independent of who's word they are, so we can refer to them as just 'g1'. Similarly, 'g2', 'b1', and 'b2' are names for their respective things.

Notice b1 has access to g1 and the names 'g1' and 'g2', but it does not have access to g2. This is equivalent to the common idea that I know the green that I see when I look at a tree, but I can't know for sure that when you look at the tree your green is qualitatively the same as mine, in this model. The green I see is g1 and the green you see is g2. However, we still have names for these experiences: 'g1' and 'g2'. Your name for my green should be interchangeable with my name for my green (in both cases they are "my green"), so we let 'g1'_b1 = 'g1'_b2 = 'g1'. Similarly for "your green", 'g2'.

Here's the point. We agree on all truths/propositions/concepts/instantaneous interactions (TPCI) that are given in terms of the names 'x', 'y', ... But b1 has the further resources of using g1 as a term, but not g2. Similarly b2 has the further resources of using g2 as a term, but not g1. In this universe information is instantiated information, so there are no TPCI in terms of both g1 and g2 simultaneously. There is no brain/mind that encompasses both g1 and g2 simultaneously. All of the facts of this universe are exhausted by the functions

(1) f_b1(g1, 'x', 'y', ...), g_b2(g2, 'x', 'y', ...)

There are also each bearers' functions restricted to the words 'x', 'y', ..., i.e., h_b1('x', 'y', ...), j_b2('x', 'y', ...). h and j are the "effable" parts of the ontology, so we'll assume h = j and, usually, these are even independent of there being any information bearers in the universe, so to the functions in (1) we add

(2) k('x', 'y', ...)

In particular, there is no function l(g1, g2, ...) because there is no ontological fact of the matter involving the simultaneous apprehension of both g1 and g2.

Some Examples

Consider the proposition

(3) Bubbles the cat weighs 20 lbs.

There is nothing particularly ineffable about (3). The word "Bubbles" refers to a particular cat, and "weighs 20 lbs." may, for our purposes, be taken to be a word that refers to a comparison between Bubbles and a standardized unit of weight. So the idea is

(4) k('Bubbles', 'weighs in lbs.') = 20

and this is independent of b1 and b2.

Now consider

(5) my green is █

This is an ontologically different question for every ontologically distinct subject that understands it, necessarily. (5) is not independent of its instantiations. If I read (5) it means one thing, and if you read it it means something different. (5) would be analyzed as

(6) f_b1(g1, 'g1') = what 'g1' refers to is g1

and

(7) f_b2(g2, 'g2') = what 'g2' refers to is g2

Both (6) and (7) are true, maybe tautologously so. The statement that b2's green is qualitatively the same as b1's green is, from b1's perspective,

(8) f_b1(g1, 'g2') = what 'g2' refers to is g1

This is false whenever b1 and b2's greens are qualitatively different. (4) as a logical function takes as input only names of things: its not necessary to do any physical lifting to assert (4). So (4) is usually understood to be independent of its instantiations. (5) can't be. The assertions 'g2' = 'g1' and 'g2' = g1 make sense whether true or not, but g2 = g1 is not even defined.

The cluster of (hard) mind-body problems is given by instances such as

(9) why is my green █?

I have to confess I find the materialist answer to this question incomprehensible, since any answer necessarily involves g1 itself, and not merely 'g1'.

Existence isn't 1^st-order

The above seems to confirm existence isn't a 1^st-order property. Suppose b1 is a person (who exists) and b2 is a unicorn (who doesn't exist). Suppose also that existence is ineffable, and call b1's existential "property" e1. Then b1's name for it's own existence is 'e1', and the name for b2's existence is 'e2'. But, while there is a class of relationships between 'e1' and e1, there is a strictly smaller class of relationships between 'e2' and e2. We can imagine the unicorn as existing, so we can suppose there is an e2. But the unicorn can't connect its name for existence 'e2' with its own existence e2. There is nothing to do the connecting. So if we imagine b2 to exist we are really only using another word (in this case "b2's existence"), which is really just another 'e2'. b1 cannot use b2's actual existence in b1's assertion of b2's existence any more than we can use the actual weight of Bubbles in asserting he/she weighs 20 lbs.

Ineffable Category

What's the form of mathematical theories that have ineffable objects in their ontologies? It's not that you have two functions that agree on a subdomain. The key is that the theories must themselves be instantiated in some way in their ontologies.

It's possible to make sense of 1 second per second

It's possible to make sense of "1 second per second".

This just means a clock-hand shows a difference of 1 second, through '1 second' of qualitative/absolute temporal flow. They are two different things. Thus, it makes sense to say, of a second clock, that it evolves at 1/2 second per second, if its relatively moving or in a gravitational gradient. It is *also* possible to say the second clock evolves at 1/2 second per second and mean you're only comparing the moving clock's hand positions with a local stationary clock's hand positions. That's all relativity does.

But in the previous sense, of things evolving in qualitative/absolute temporal flow, the local stationary clock evolves at a rate of 1 second per qualitative second, or q-second. The moving clock, similarly, evolves at a rate of 1 second per *its* q-second. Its q-seconds are not ontologically comparable to the local stationary q-seconds. The qualitative/absolute time is ontologically ineffable, as argued for previously. The ontologically "effable" part of time is given by the relativistic correlations. There is no fact of the matter, or ontologically possible comparison, between different q-seconds.

A Many-Timelines Interpretation of Quantum Mechanics

A Many-Timelines Interpretation of Quantum Mechanics

What can be called the "Many-Timelines" (MT) interpretation of quantum mechanics is given by the following:

(1) all the information about the universe is given by ontologically existing information-bearers

(2) to the extent an object (information-bearer) is ontologically distinct, it evolves according to its own ontologically distinct timeline

Normally the timelines will be correlated, but distinct. Unlike other interpretations of quantum mechanics, MT is inspired by philosophical considerations that are prior to quantum mechanics itself. I collect a few arguments in favor of (2).

The first argument is the odd behavior of mathematical theories of time. Let b₁ and b₂ be ontologically existing information-bearers... [cf. previous post] ...I conclude there is an aspect of time that is ineffable (incommunicable). I stress this argument is not intended to speak to the presentism/eternalism debate, nor the A-series/B-series debate, only ineffability.

The second is another under-appreciated fact. Alpha Centauri is about 4 lightyears away. It's physically impossible to communicate to aliens who live on Alpha Centauri what it's like to exist now on Earth, because for all we know Alpha Centauri exploded 3 years ago, and we won't even know it for another year.

The third is the often noted fact that temporal flow has a qualitative character, and qualia are ineffable.

The fourth is that things exist at particular times, and existence is supposed to be a 2^nd-order phenomenon.

By (1), there is an aspect of time that is ontologically ineffable.

Different things evolving on different timelines has radical implications. If b₂ evolves on it's own ontologically distinct timeline, then, for b₁, there is never "a time" at which b₂ has a particular state. b₁ and b₂ evolve independently in their respective timelines. By (1) there is no objective time, or objective fact of the matter, about the state of both b₁ and b₂. As a result, at any given b₁-time, the maximum amount of information (i.e. all the possible states of interaction of b₁ with the rest of the universe) is a function of b₂ along all its b₂-times, and vice versa. They evolve in a correlated but ontologically independent way until they physically interact, become one ontological system, and thereby evolve according to one and the same time-parameter. Only then can one talk about "the state" of b₁ and b₂.

Suppose b₁, b₂, and b₃ are three systems that feel a force from the other two systems. There are six relational values of the force R_bibj. Classicaly, the three systems carve out a worldline in the 7-dimensional manifold {t}cross{R_bibj}, with a single state for everything at time t. If they evolve in a universe where time has ineffable aspects, they each have a timeline, t_bi. There is no fact of the matter about the forces R_bibj at a single objective time. Instead one has the three 3-dimensional manifolds {t_bi}cross{R_bibj}, j ≠ i. If they are part of the same universe (ontology), there will be 2^nd-order relations among the t_bi, for a total of 12 dimensions. At any given b_i-moment t_bi all the information that there is in the universe, for b_i, is given by the collection of possible states of b_j at times t_bj, and the possible states of b_k at times t_bk, i ≠ j ≠ k. The upshot is that, for b_i(t_bi), the system (b_j, b_k) doesn't evolve in {b_j}sum{b_j} but instead {b_j}cross{b_j}. The obvious conjecture is

(3) systems that evolve in their own timelines behave quantum mechanically with respect to each other, and otherwise they behave in terms of a classical theory such as General Relativity 

Time is Partly Ontologically Ineffable

I start with a trivial-sounding argument.

Suppose x denotes the position of a particle through time, x = x(t). The worldline of the particle can be plotted on a spacetime diagram. Now I want to highlight a trivial-sounding observation that many have made,

(1)  it's possible to imagine (epistemologically) a point moving along the worldline

The (philosophical) problem is that the worldline was supposed to represent the particle moving "through time" in the first place. But the worldline is a mathematical object that's timeless/eternal/ static/etc., in the way all mathematical objects are, so there's really no chance it could account for the behavior of the point in (1). But then what kind of space-'time' diagram would be appropriate if it's going to account for everything we know about time?

One can model a person performing (1) in/along his own worldline through spacetime. The problem now takes the form that the person (call him p1) moving in/along his world line imagines that his spacetime diagram is independent of his own temporal experience. That's not the case if both of the following are true:

(2)  what's true of the universe is what's true in the universe

(3)  what's true in the universe is the information carried by it's extant "information-bearers" 

The information-bearers are the objects that exist in the ontology. The each bearer's information can be thought of as the maximum amount of information each can have about the universe at that (bearer's) time.

One way to proceed is to say that it's inconsistent to suppose the particle's behavior has been completely specified by the spacetime diagram in the ontology of the spacetime diagram. In support of this is that, by (2) and (3), temporal flow is itself a prerequisite for any theory or information purporting to model the universe through time. But we know these facts. 1. the person p1 experiences a temporal flow. So, 2. If the particle is not ontologically distinct, it's a part of person p1, so is equally associated with p1's temporal flow. This suggests the hypothesis 

(4)  each ontologically distinct element of a theory that satisfies the above conditions evolves in it's own ontologically distinct dimension of time

of course these dimensions are closely correlated. But the point is there does not exist "a time" at which there is a fact as to the state of both objects p1 and particle p2. Suppose we pick a p1-time at which things could be true of p2. But p2's evolution (history) is temporally independent of p1. So there is no p1-time at which p2 exists in a particular state, until they recombine (and vice versa).

Imagine two particles in R³. Put a unit sphere around each. All that's true is the information carried by each particle in it's own timeline. Since each has no information about "what time" the other finds itself to be in, they have to take into account all possible timelines until they actually interact. Moreover, there is only the information about p2's location relative to p1, i.e., p2's location projected onto p1's sphere (and vice versa). There is no objective location for both of them in R³. And along the two timelines there are the possibilities for the other particle's state at it's different possible time values projected to the sphere surrounding each.

Instead of the combined system s = (p1, p2) evolving according to an objective time parameter t in tcrossR³, there is

(t_p1crossS²)cross(t_p2crossS²).

and a particular state is given by values of the two time parameters. Form the space R³-minus-spheres, etc.

More philosophically, what's going on looks like: part of what we mean by "time" is ontologically ineffable. We can't communicate to someone on Alpha Centuri what it's like to exist in the present temporal flow, because for all we know Alpha Centuri was destroyed 3 years ago, in terms of our present, even though it'll be another year before our region of the universe receives the information. 

Moving Point

I want to start with a trivial-sounding argument.

Suppose x denotes the position of a particle through time, x = x(t). The worldline of the particle can be plotted on a spacetime diagram. Now I want to highlight a trivial-sounding observation that many have made,

(1)  it's possible to imagine (epistemologically) a point moving along the worldline

The (philosophical) problem is that the worldline was supposed to represent the particle moving "through time" in the first place. But the worldline is a mathematical object that's timeless/eternal/ static/etc., in the way all mathematical objects are, so there's really no chance it could account for the behavior of the point in (1). But then what kind of space-'time' diagram would be appropriate if it's going to account for everything we know about time?

One can model a person performing (1) in/along his own worldline through spacetime. The problem now takes the form that the person (call him p1) moving in/along his world line imagines that his spacetime diagram is independent of his own temporal experience. That's not the case if both of the following are true:

(2)  what's true of the universe is what's true in the universe

(3)  what's true in the universe is the information carried by it's "information-bearers" 

The information-bearers are the objects that exist in the ontology. The each barer's information can be thought of as the maximum amount of information each ontologically distinct barer can have about the universe at that time.

One way to proceed is to say that it's inconsistent to suppose the particle's behavior has been completely specified by the spacetime diagram in the ontology of the spacetime diagram. In support of this is that, by (2) and (3), temporal flow is itself a prerequisite for any theory or information purporting to model the universe through time. But we know these facts. 1. the person p1 experiences a temporal flow. So, 2. If the particle is not ontologically distinct, it's a part of person p1, so is equally associated with p1's temporal flow. This suggests to the hypothesis 

(4)  each ontologically distinct element of a theory that satisfies the above conditions evolves in it's own ontologically distinct dimension of time

of course these dimensions are closely correlated. But the point is there does not exist "a time" at which there is a fact as to the state of both objects p1 and p2. Suppose we pick a p1-time at which these things could be true of p2. But p2's evolution (history) is temporally independent of p1. So there is no p1-time at which p2 exists in a particular state, until they recombine (and vice versa).

Imagine two particles in R³. Put a unit sphere around each. All that's true is the information carried by each in it's own timeline. Since each has no information about "what time" the other finds itself to be in, they have to take into account all possible timelines until interaction. Moreover, there is only the information about p2's location relative to p1, i.e., p2's location projected on p1's sphere (and vice versa). There is no objective location for both of them in R³. And along the two timelines there are the possibilities for the other particle's time values projected to the sphere surrounding each.

Instead of the combined system s = (p1, p2) evolving according to an objective time parameter t in tcrossR³, there is

(t_p1crossS²)cross(t_p2crossS²).

and a particular state given by the two time parameters. Form the space R³-minus-spheres etc.