Hi everybody! Hope you all had a great break, I think it was
my turn to do the blog post (if not then sorry for stealing the moment!)
As the Hoefer paper is quite long and covers a lot I’ve
decided to focus on a particular area (manifold substantivalism vs determinism).
Before beginning I think it’s important to state that (by
his own admission) Hoefer is not a substantivalist. I think it’s important to
reiterate this as it does explain his attitude to some of the articles cited in
his work.
As we have discussed in an earlier blog post, a committed
substantivalist considers spacetime to be a real thing. Hoefer admits that this
is a fairly natural position to take given the past and present success of
Newtonian physics and GTR, which allow for spacetime existing as a separate entity
with its own intrinsic properties. However, according to Hoefer there are too
many different brands of substantivalism for its merits to be properly assessed
against alternative theories. So the question follows, if spacetime is a real
thing in GTR, as a substantivalist would say, then what part of a GTR universe
represents spacetime.
This is probably a good time to through in some definitions
to save everybody checking back to the lecture slides!
Manifold of events: A
set of events with a smooth coordinate system
Metrical structure:
Temporal and spatial distances between events
Matter fields: Where the
stuff is. Distinct lumps of matter like galaxies can be represented by world lines
Manifold Substantivalism –
The manifold seems to closest resemble what a substantivalist
wants spacetime to be. Earman and Norton split energy bearing structures
(physical fields) as being the contents of spacetime which therefore leaves the
manifold to be “the container”. It is not clear why such a seemingly arbitrary decision
is permitted, other than it does seem to resonate with what is implied when substantivalists
‘spacetime’.
Problems emerge with this interpretation of spacetime in GTR
due to Leibniz equivalence. Simple mathematical manipulation can lead to the
creation of multiple models in which the material content and the metric field
is distributed differently. Hence Manifold Substantivalism would seem to allow
for many possible indistinguishable worlds. Leibniz equivalence means that any
model produced is actually a representation of one possible world. This is a
similar argument to that used in the Leibniz shifts and must be dismissed by
any substantivalist true believers!
The hole argument and the breakdown of determinism –
I won’t go into detail regarding the setup of the hole transformation
or about general covariance which allows it but essentially the fields within the boundaries
of the hole have been manipulated (Einstein initial considered the region to be
empty – hence why it’s called the hole). The two setups are indistinguishable because
all the observable features are invariant (they remain the same regardless of
how much you play with the coordinate system as the coordinate system is arbitrary
and doesn’t affect physical laws) This leads to some serious conflict with
determinism. As is clear from the diagram the metric and stress fields within
the hole cannot be determined using information gathered from outside. It is
therefore impossible to link a point within and without, which means you cannot
relate a previous state of affairs to the future state of affairs regardless of
how well you understand the system. There is nothing too controversial about
this in my opinion, it is not a given that the universe is deterministic and
there is no reason to be bound to this worldview. But it is clear that that
determinism and this form of substantivalism are not compatible. Earman and
Norton (also critical of manifold substantivalism) say that it is unacceptable
to promote a substantivalist model which dismisses determinism is insufficient.
This is because the substantivalist properties are less/not essential (I don’t
like my terminology here but I’m trying to put it in simpler terms) so are not
grounds to let go determinism, or at least not sufficient in isolation. Here I
have to agree with Hoefer in that this doesn’t really seem to be a case against
substantivalism but more that manifold substantivalism is perhaps not a
complete enough representation of spacetime. I think this would be a good topic
to start discussion on Monday so I’ll stop here!
RE the separation of the container and contents by Earman and Norton
ReplyDeleteAn argument for why splitting the metric structure from the manifold might be ok goes something like this.
One has to separate container from contents somehow or else the statement of substantivalism becomes trivial---the manifold and metric structure and matter distribution taken are clearly real because the matter is real.
Hence one has to at least separate the matter distribution from the rest in order to have a non-trivial substantivalism doctrine to debate.
Then, however, one can point out similarities between gravitational waves and, for instance, electromagnetic waves---gravitational waves are the analogues of electromagnetic waves but are propagating disturbances in the gravitational field rather than the electromagnetic field.
But the electromagnetic waves are counted in the matter distribution whilst gravity waves are manifested in the metric structure.
Hence if the matter distribution is counted as contents rather than container then the metric structure should also be a part of the container.
This leaves only the manifold left to be the container by itself, as Norton and Earman suggest.
Despite this I don't think it is a very good separation. The Manifold has no properties other than containing points, and the topological relations between those points. Wasn't the point of substantivalism originally (ie from Newton) meant to for relations of distance and place to arise from an underlying substance of space? But the manifold by itself cannot support relations of distance, the metric structure (including any gravitational waves present) is required for this. Hence it seems to me that the metric structure needs to be included in the substance of space-time.