On 12 Apr 2016, at 03:17, Jonathan Day wrote:
John Clark: Or maybe nothing tells the quantum foam how to behave;
after all, why does every event have to have a cause?
This is one of the key questions in physics. Causality forbids
effects without causes and physicists are extremely keen on
causality. Singularities also have the potential for causality
violations and I needn't say how many brain cells have been
sacrificed, burned out beyond recognition, by the greatest minds
trying to prevent things like the information paradox arising.
I tend to assume, therefore, that causality must apply absolutely
everywhere, that if violations of the conservation of information
can't arise behind an event horizon, then it can't arise in quantum
foam either.
I tend to agree with this. non causality in physics is not
interesting: its evocation is like using a god-of-the-gap. Non
causality can make mathematical sense, but I don't think it makes
physical sense. It would also demolish the idea that the physical is
explanation-closed (which is not a big problem for a computationalist
which use the much explanation-closed structure provided by the
partial recursive function or arithmetic.
However, one could argue that the sum total information in quantum
foam over classical scales of space and time will always come out at
zero. If the sum is zero, then perhaps no violation is possible no
matter what.
Now, your other point about real numbers is also important. The idea
I was toying with pre-supposes that most real numbers don't exist,
that there are universal constants that can be generated at
arbitrary precision but that all else is subject to the precision of
one Planck unit of spacetime.
(This creates an interesting problem. If the fundamental scale of
the universe is the Planck distance, then is the universe made of
bubbles? You can't tessalate spheres, so are the spaces inside the
universe or outside?)
The idea is to circumvent the problem of precision. A universe with
finite accuracy loses accuracy. I don't see any way to avoid that
unless there's something that effectively goes beyond the minimum
physical scale.
This feeds back round to computer simulation. A computer simulation
cannot handle genuinely real numbers of any kind. So if arbitrary
real values exist, then the universe is not a simulation. It's an
interesting test.
We have explained often this: if "I am digitally emulable", then the
apparent physical universe is not digitally emulable.
Now if the physical universe was digitally emulable, I would be too,
but then the physical universe cannot be emulable.
So in all case, the (apparent) physical reality is NOT digitally
emulable. (nor is any stable form of consciousness also).
To understand this you need to be familiar with the computationalist
first person indeterminacy (FPI). Are you? See this list or my papers
for more on this. Eventually physics is entirely determined by the
logic of self-reference of Gödel-Löb-Solovay and its modal nuances. It
has not provable aspect, and not knowable and not observable aspects
also.
If the universe is an emergent phenomenon resulting from pure
mathematics, then real numbers of all kinds can genuinely exist at
infinite precision even if the physics is quantized.
Why? Some real number might exist, but you don't need to have that all
real numbers are existing. We can be realist on the arithmetical
(digital) reality without being realist on analysis, real numbers,
sets, etc.
At some point, on the fundamental question, it helps to put all
hypotheses on the table, including which logic is used, what
mathematics is used, etc. What you say might make sense in some
intuitionist form of computationalism, but such computationalism is
contradictory with the classical computationalism usually discussed
here.
If the universe does not have a mathematical or computational
substrate, then there should be a recursive phenomenon with short
enough cycles where the loss of precision would be measurable. This
set of experiments would classify what sort of universe we have.
The universe appearance has a mathematical (in fact theological)
explanation (the machine theology emerges itself from arithmetic), but
the physical cannot be digitally emulable, nor is consciousness,
except in some local sense. The mind-brain identity is not correct
once we assume to be Turing emulable. We can associate a mind to a
brain, but a mind cannot associate itself to one brain, but only to an
infinity of brains representation (which are emulated (in the purely
mathematical sense of Church and Turing) in the arithmetical reality.
Bruno
http://iridia.ulb.ac.be/~marchal/
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