On 7/24/2011 12:05 AM, Jesse Mazer wrote:
On Sat, Jul 23, 2011 at 11:24 PM, Stephen P. King
<[email protected] <mailto:[email protected]>> 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.
Jason
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/Presentism_%28philosophy_of_time%29),
eternalism
(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.
Onward!
Stephen
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