On 7/24/2011 12:05 AM, Jesse Mazer wrote:

On Sat, Jul 23, 2011 at 11:24 PM, Stephen P. King <stephe...@charter.net <mailto:stephe...@charter.net>> wrote:

    On 7/23/2011 9:45 PM, Jason Resch wrote:
    If you want to formulate block time without reifying spacetime,
    then just consider block time a collection of events separated by
    certain distances and directions from eachother.  You may be
    right that ultimately this is all related to a theory of
    observation, and I think I can understand what you mean by
    relativity explaining the organization of these
    events/observations.  In any case, a block universe seems to be a
    simpler theory than that of one in which objects become real and
    become unreal continuously, and it is consistent with
    observations.  There is no scientific justification for
    presentism that I am aware of.

    Hi Jason,

        But can't you see that I am arguing against any form of
    spacetime substantivalism, this includes block spacetime, block
    time, presentism
    (http://en.wikipedia.org/wiki/Eternalism_%28philosophy_of_time%29), etc.
    The idea that events exist with specific properties attached
    independent of specification of measurement - of which observation
    by humans is a special case - is what I am arguing against. See:
    http://plato.stanford.edu/entries/spacetime-holearg/ for the full
    details. Substantivalism just a hold over of Aether theories.
    http://en.wikipedia.org/wiki/Aether_theories and I argue that it
    is an unnecessary hypothesis.
        One specific observation that for me nails substantivalism is
    the observation of no delay or polarization difference between
    ultra high gamma photons and gamma photons of lower energies from
    the same gamma ray buster event. Spacetime is show to be smooth at
    all energy scales, this is contra all theories that treat
    spacetime as some kind of substance.

Substantivalism doesn't treat spacetime as a "substance" in the sense of necessarily being made up of discrete grainy bits (which is all that the gamma ray prediction was meant to test, see http://www.sciencedaily.com/releases/2011/06/110630111540.htm ), it just says that spacetime has physical properties of its own, like the notion of the different curvature at different points in spacetime which is present in general relativity. See also the discussion of "sophisticated substantivalism" on p. 9 of http://www.st-andrews.ac.uk/~kjh5/OnlinePapers/MetaphysicsandRelativity.pdf <http://www.st-andrews.ac.uk/%7Ekjh5/OnlinePapers/MetaphysicsandRelativity.pdf> and also at http://users.ox.ac.uk/~ball0402/papers/sheffield.pdf <http://users.ox.ac.uk/%7Eball0402/papers/sheffield.pdf> (the author also apparently wrote a thesis about this and is in the process of writing a book, see the bottom of the page at http://users.ox.ac.uk/~ball0402/research/ <http://users.ox.ac.uk/%7Eball0402/research/> )

Hi Jesse,

To support my possition. From http://www.sciencedaily.com/releases/2011/06/110630111540.htm : "Some theories suggest that the quantum nature of space should manifest itself at the 'Planck scale': the minuscule 10^-35 of a metre, where a millimetre is 10^-3 m. However, Integral's observations are about 10 000 times more accurate than any previous and show that any quantum graininess must be at a level of 10^-48 m or smaller." That pretty much blows up the idea of Plank scale graininess!

From http://www.st-andrews.ac.uk/~kjh5/OnlinePapers/MetaphysicsandRelativity.pdf <http://www.st-andrews.ac.uk/%7Ekjh5/OnlinePapers/MetaphysicsandRelativity.pdf> we read:

"2.2 Substantivalism and Relationalism
Metaphysicians have long argued about whether space and time are entities in their own right, or whether they are mere abstractions from concrete objects and events. Could there be space and time if there were no objects and nothing ever happened? There is consensus that, given relativity, we can no longer talk about three- dimensional space and one-dimensional time, and must instead talk about four-
dimensional spacetime.  But there is no consensus about whether GR favours
substantivalism, the view that spacetime is a genuine entity, or relationalism, the view that spacetime is nothing over and above the events occurring in it. (cross-ref chapter
on space)

As we have just seen, GR invokes the shape of spacetime itself to explain why objects move as they do, why the apple falls, why we can walk around on the surface of the Earth. Spacetime is no longer just an inert, neutral backdrop against which objects and forces interact, it is an element in that interaction. In this way, GR points towards
substantivalism about spacetime.

Yet, as we shall shortly see, the 'hole argument' points in the opposite direction, indicating that substantivalists are committed to the existence of physical facts which go beyond anything required by GR. (In this respect, the hole argument is like the argument against presentism from the relativity of simultaneity, according to which presentists are committed to facts which go beyond anything required by SR.)

Suppose you had to describe the room you're in right now. You could describe the various objects in the room, and then describe how they are related to each other ('there's a monkey and a toy car, and the monkey is sitting in the car'). Asked to describe the whole universe, we could say 'there's a bunch of spacetime points, they
have such-and-such spatiotemporal arrangement, and matter and energy are
distributed amongst them thus-and-so'. The bunch of points is the 'manifold', their spatiotemporal arrangement is the 'metric', and the distribution is the 'matter field'. GR tells us how the metric is related to the matter-field, how the shape of spacetime is
related to the distribution of objects.

Now, how does the traditional substantivalism-relationalism debate translate into these terms? What do substantivalists affirm and relationalists deny? Perhaps substantivalists should claim that the manifold of points exists independently of the
events happening at those points, whereas relationalists should deny this.

If substantivalists rashly accept this characterisation of their position, then relationalists can pounce. Suppose we have the manifold of points, arranged with their metric and their matter-field. Would things have been different if the points had been reshuffled, keeping the metric and the matter field constant? If the points are independently-existing entities, as substantivalists think, then presumably any
reshuffle makes a difference.  But GR tells us that many reshuffles make no
detectable difference at all. The points themselves don't seem to differ in their intrinsic properties: they don't have tiny labels that would enable us to keep track of them if they were switched around. So substantivalists are committed to facts in
addition to those recognized by GR -- facts about which points are where.

(This criticism of substantivalism is known as the 'hole argument' because, as a special case, the points in a given region -- known as the 'hole' -- could be reshuffled
without affecting what happens before, after or around that region.)

/Substantivalists need to reconsider what they are substantivalists about. If they take spacetime to be just the manifold, the bare collection of points, they will be committed to undetectable facts, but they may be on safer ground if they take spacetime to be the manifold together with the metric, i.e., the collection of points together with the way in which they are arranged with respect to one another. If this more complex entity is replaced by an alternative manifold-plus-metric, this would
certainly make an empirical difference. /

What sort of entity is a manifold-plus-metric?  Different 'sophisticated
substantivalists' have developed this idea in different ways, but one option is to think of each spacetime point as having its relations to other points essentially, so that the
points exist together in a web of mutual dependence.  It seems clear that
substantivalists can escape the hole argument in this way.

What's not so clear is whether sophisticated substantivalism is really distinct from relationalism. /The more that GR gives a quasi-causal, dynamical role to the manifold-plus-metric, the more difficult it is to draw a line between material things (which relationalists accept) and spacetime itself. What's so special about the spatiotemporal properties of a point, in contrast to its other properties, like those
which fix how much mass or charge is there?  Why think the spatiotemporal
properties of a point are essential to it, whilst its other properties are not? /"

(the italics are mine to highlight important sections)

I agree with this argument completely but go further! In my thinking a manifold and metric do not have specific properties independent of observers in the same way that physical objects do not have specific properties independent of observers. Please correct the following if I am wrong. Crudely sketched: A manifold is made up of a patch work of "charts" or coordinate systems sewn together by mapping functions that identify certain points of one with certain points of the other. Forgive me if I use the wiki articles for brevity sake. See: http://en.wikipedia.org/wiki/Manifold, http://en.wikipedia.org/wiki/Metric_tensor and http://en.wikipedia.org/wiki/Tangent_space .

What if we can define the charts in terms of the particular position and duration observables that some large collection of QM systems have?

A metric defines a notion of distance on the manifold and is derived by how a set of orthogonal vectors changes or remains the same along points of a curve on the manifold. To be precise, let me quote the wiki article on metrics: "In differential geometry <http://en.wikipedia.org/wiki/Differential_geometry>, one considers metric tensors <http://en.wikipedia.org/wiki/Metric_tensor>, which can be thought of as "infinitesimal" metric functions. They are defined as inner products <http://en.wikipedia.org/wiki/Inner_product> on the tangent space <http://en.wikipedia.org/wiki/Tangent_space> with an appropriate differentiability <http://en.wikipedia.org/wiki/Differentiability> requirement. While these are not metric functions as defined in this article, they induce metric functions by integration <http://en.wikipedia.org/wiki/Antiderivative>."

The key is the tangent space. "In differential geometry <http://en.wikipedia.org/wiki/Differential_geometry>, one can attach to every point /x/ of a differentiable manifold <http://en.wikipedia.org/wiki/Differentiable_manifold> a *tangent space*, a real vector space <http://en.wikipedia.org/wiki/Vector_space> which intuitively contains the possible "directions" in which one can tangentially pass through /x/. The elements of the tangent space are called *tangent vectors* at /x/."

We can think of a tangent space as a set of possible directions that a vector located at each point of a chart. In that sense tangent vectors seem to be similar to momentum if their length are allowed to vary as d/dx. My thought is that the relationship that we see in canonical conjugates, say position and momentum is the same as points on a chart and the vectors on the tangent spaces of that chart. The same would hold for energy and duration (not time!) How this works for spin is beyond my ability to put words together in English...

The idea here is that the observables of QM map to the building block of GR so that the relationship between the two theories is a duality; one cannot be defined without the other. Similarly, observations cannot be defined without observers, so the idea that spacetime is a substance that is a 'bearer of properties" fails. Presentism fails as it is a form of solipsism. Endurantism fails because it treats time and space as separate and independent. OTOH, we can rehabilitate all three so long as we consider QM system as observers. Each QM system has a set of observables that are uniquely "real" to it (ala solipsism) and those observables are integrated with those of other QM systems via requirements of mutual consistency of observations; which is just another way of saying that the laws of physics are the same for all.

From http://users.ox.ac.uk/~ball0402/papers/sheffield.pdf <http://users.ox.ac.uk/%7Eball0402/papers/sheffield.pdf> we find:
"Substantivalists understand the existence of
spacetime in terms of the existence of
its pointlike parts, and gloss spatiotemporal
relations between material events in terms of
the spatiotemporal relations between points
at which they occur. Relationists will deny
that spacetime points enjoy this robust sort
of existence, and will accept spatiotemporal
relations between events as primitive.
(Belot and Earman, forthcoming)"

Here I disagree with both substantivalist and relationists! Neither spacetime points nor spatiotemporal relations are taken as "primitive" but instead are emergent from a continuous interplay between QM systems. I see QM systems as equivalent to Leibnizian Monads including the property that they are "windowless" - they cannot 'exchange substances with each other. All appearances of interactions flow via residuations as explained by Vaughan Pratt here: http://boole.stanford.edu/pub/ratmech.pdf The basic idea of residuation works from a dynamic, as opposed to static, interpretation of the Stone duality between logical algebras and topological spaces.



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