LizR wrote:
On 6 June 2015 at 11:26, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
LizR wrote:
This is true if events have an existence apart from maths.
However, that is still being debated. Tegmark's "mathematical
universe hypothesis" suggests that time and events are emergent
from an underlying timeless mathematical structure.
To take something that is (hopefully) less contentious, the
block universe of special relativity already suggests something
similar to this. In relativity, all chains of events are
embedded in a space-time manifold, and hence causation comes
down to how world-lines are arranged within this structure.
This is not true. Causality is still a fundamental consideration in
SR, and that carries over into the basic structure of quantum field
theory. Even within the block universe model, the light cone
structure of spacetime is fundamental. The light cone encapsulates
the fundamental insight of SR that causal influences cannot
propagate faster than the speed of light -- the light cone is the
limiting extent of causal structure. The laws of physics consistent
with this structure in SR and beyond are have a (local) Lorentz
symmetry, which preserves the causal structure between different
Lorentz frames. The distinction between time-like and space-like
separations of events is aa fundamental tenet of physical law.
None of this contradicts what I said. All I am concerned with is that SR
indicates that events are embedded in a 4D continuum. Describing how
they're embedded doesn't change that.
You started with Tegmark's idea that time and events are emergent from
an underlying timeless mathematical structure. My point was that in
order for time to emerge from a block universe certain structure was
necessary -- we need a 4-dim manifold with a local Lorentzian metric,
and physical events must be arranged with a particular structure on this
manifold -- they cannot just be arranged at haphazard. So the way events
are embedded is in fact crucial.
The question is then whether this 4 dimensional manifold with a local
Lorentzian metric exists in arithmetic? If not, there is no possibility
for a time variable in arithmetic per se, and consequently nothing can
'emerge' from arithmetic, since emergence is a temporal concept. Note
that it is important to distinguish between structures that can be
described mathematically and the structure of arithmetic or mathematics
themselves.
Bruce
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