
Computability: The Greatest Law of Physics - theaeolist
http://researchblogs.cs.bham.ac.uk/thelablunch/2015/11/computability-the-greatest-law-of-physics/
======
chriswarbo
Reminds me of [http://arxiv.org/abs/quant-
ph/0502072](http://arxiv.org/abs/quant-ph/0502072)

Also, as a Physicist and Computer Scientist, it explains my uneasiness when
existence claims are made regarding infinite objects.

For example, we can _describe_ the trajectory of a particle using Feynman path
integrals, which involve infinite sums over all possible paths. That's fine.

Some will then treat this as a _mechanism_ , i.e. claim that the _reason_
particles have the trajectories they do, is because they _literally are_
taking every possible path at once. This kind of reasoning sets my off my CS
alarm bells, and articles like this provide justification for that.

To see why this leap of reasoning is flawed, consider the fact that _we_ don't
solve integrals by summing up an infinite number of infinitesimal quantities.
To say that a human writing out a sequence of symbolic manipulations on a page
_literally is_ performing an infinite amount of computation is clearly false.

I think Computer Scientists are much more comfortable than Physicists with
considering the role of calculation in a theory; i.e. in Physics, the
calculations we perform _about_ a system are utterly distinct from that
system: whether those calculations are easy or hard says nothing about what
the system is doing (e.g. we can easily calculate path integrals, which
particles "solve" using an infinite amount of brute-force); the only
physically-relevant details are the values. In CS, we _focus on_ the
performance of calculations; we cannot claim that a system behaves over time
in some way unless we can show that _calculating_ that behaviour can be done
in that time.

~~~
hn9780470248775
A classical particle can't literally "take every path at once." But
fundamental particles - electronics, photons, etc - are governed by quantum
mechanics, in which they really consist of a wave of probability amplitude.
These really do "explore all possible paths".

------
liamzebedee
Ooooo this topic has been intellectually tingling me for two weeks now -
ontologies, knowledge, how we construct the line between abstract
(mathematical objects) and reality (all the way down to elementary particles),
and at its core the nature of information. If you're further interested in
this area, some very interesting lines of inquiry to go down is the the
mathematical universe hypothesis [1], bit-string physics [2] (the theory of
everything that explains the universe as a binary string), digital physics [3]
and of course the Stanford Encylopedia of Philosophy article on information
[4].

[1]
[https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...](https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)

[2]
[http://www.osti.gov/scitech/servlets/purl/28404/](http://www.osti.gov/scitech/servlets/purl/28404/)

[3]
[https://en.wikipedia.org/wiki/Digital_physics](https://en.wikipedia.org/wiki/Digital_physics)

[4]
[http://plato.stanford.edu/entries/information/](http://plato.stanford.edu/entries/information/)

~~~
chriswarbo
One thing to keep in mind with ideas like the Mathematical Universe Hypothesis
is their predictive power. Once a "theory of everything" describes what _could
have been_ as well as what _is_ , you end up needing _another_ theory to
distinguish between the two [1].

For example, Champernowne's constant contains every number in its decimal
expansion, and hence contains a complete description of our universe, all of
the true laws of Physics and the outcome of every random quantum effect.
However, it's not a very satisfactory "theory of everything", since it makes
no predictions. (Note that I could have used pi instead, but its not yet known
whether pi is a "normal" number [3]). This is the same idea as the Library of
Babel [4].

On the other hand, if you start distinguishing between possible worlds in some
way, then you can do real science. For example, the Boltzmann Brain idea
describes ordered systems (like our Universe) emerging from disordered systems
(like clouds of gas) by pure chance [5]. Such a statistical argument is
useful, since we can reason about probability distributions over possible
Universes. In this case, small pockets of order are vastly more likely to
arise spontaneously than large ones (since we can consider a large pocket to
be a contiguous collection of smaller pockets), hence we obtain predictions
for all kinds of experiments: namely that we'll probably see a cloud of gas,
rather than any ordered structure. Since we tend to see ordered structure, we
can prove the hypothesis wrong experimentally.

A related idea, which is also relevant for this article, is that the Universe
could be generated by a random _computer program_ [7]. If we apply the same
reasoning as with Boltzmann Brains, we would expect _short_ programs to be
vastly more likely than _long_ programs. Since the length of a program
determines how "random" its result is (in the Kolmogorov sense [8]), short
programs would produce more ordered structure than long programs, hence this
hypothesis make the _opposite_ prediction to the Boltzmann Brain: i.e. that
when we observe new places, we will tend to see the same kind of order as we
have already observed elsewhere. So far, these predictions seem to hold ;)

[1] [http://arxiv.org/abs/0912.5434](http://arxiv.org/abs/0912.5434) [2]
[https://en.wikipedia.org/wiki/Champernowne_constant](https://en.wikipedia.org/wiki/Champernowne_constant)
[3]
[https://en.wikipedia.org/wiki/Normal_number](https://en.wikipedia.org/wiki/Normal_number)
[4]
[https://en.wikipedia.org/wiki/The_Library_of_Babel](https://en.wikipedia.org/wiki/The_Library_of_Babel)
[5]
[https://en.wikipedia.org/wiki/Boltzmann_brain](https://en.wikipedia.org/wiki/Boltzmann_brain)
[6]
[http://www.preposterousuniverse.com/blog/2008/12/29/richard-...](http://www.preposterousuniverse.com/blog/2008/12/29/richard-
feynman-on-boltzmann-brains/) [7] [http://arxiv.org/abs/quant-
ph/0011122](http://arxiv.org/abs/quant-ph/0011122) [8]
[https://en.wikipedia.org/wiki/Kolmogorov_complexity](https://en.wikipedia.org/wiki/Kolmogorov_complexity)

------
dsfsdfd
I suspect that this is all because the universe is mathematics. It is simply
the expression of all possible things.

~~~
Xcelerate
That's always been my view — God created mathematics and the laws of physics
just fell out as a byproduct.

~~~
andyjohnson0
(Putting to one side your reliance on God)

 _" and the laws of physics just fell out as a byproduct"_

Why? Don't you need a theory for why this is?

~~~
Xcelerate
What I mean is that math seems to constrain our universe, and given enough
constraints, the universe might be completely specified. For instance,
consider Noether's theorem. The laws of conservation of energy, momentum,
angular momentum, charge, and particle number all fall out due to continuous
symmetries. Mass indexes the irreducible representations of the Poincaré
group. Spin is simply the result of SU(2) being the double cover of SO(3).
Conservation of probability implies unitary evolution of state vectors. And so
on.

My guess is that once you consider _all_ of the symmetries that could exist
(and there are many which have not yet been found; supersymmetry has long been
posited but remains undiscovered), then our laws of physics are basically the
only laws that _can_ exist in a mathematically consistent way. Of course,
that's just my hypothesis.

There's also the possibility that our universe is _unnatural_ , which some
physicists have recently been considering, but I'm skeptical. ("Unnatural"
means that all of the constants in our universe that cannot be calculated from
first principles are simply the result of random chance — i.e., only those
universes with "finely-tuned" parameters capable of supporting life would have
life in it to observe those parameters.)

~~~
evanb
I'm confused by this 'hypothesis'

>My guess is that once you consider all of the symmetries that could exist
(and there are many which have not yet been found; supersymmetry has long been
posited but remains undiscovered), then our laws of physics are basically the
only laws that can exist in a mathematically consistent way.

If physical evolution is unitary, it may be phrased in terms of an S-matrix,
and the possible symmetries of the S-matrix are well-known by the Coleman-
Mandula theorem[0] and its supersymmetric generalization[1]. So, supersymmetry
is possible, but, as you rightly point out, may or may not exist in the world.
So mathematical consistency (unless what you mean is that quantum gravity
might violate one of the assumptions of those theorems) is a lot less powerful
than you guess.

[0]
[https://en.wikipedia.org/wiki/Coleman%E2%80%93Mandula_theore...](https://en.wikipedia.org/wiki/Coleman%E2%80%93Mandula_theorem)

[1]
[https://en.wikipedia.org/wiki/Haag%E2%80%93Lopuszanski%E2%80...](https://en.wikipedia.org/wiki/Haag%E2%80%93Lopuszanski%E2%80%93Sohnius_theorem)

~~~
Xcelerate
Huh, interesting. I was not aware of this. Thanks for the link!

