
The Trouble with Theories of Everything - dnetesn
http://nautil.us/issue/29/scaling/the-trouble-with-theories-of-everything
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eridius
With the idea that different theories hold at different scales, I've always
wondered what happens as you transition between the scales? Saying "Oh, this
theory holds at macro scales, and that one at micro scales" doesn't explain
what happens as you slowly build up the micro. At which point does it become
macro? What happens on the boundary?

~~~
abdullahkhalids
There doesn't have to be clear boundary. You can continue using the micro
theory at the cost of computational resources and (often) loss of analytical
analysibility. Or you can use a mix of both theories. Remember the map is not
the territory; the theory/ies not the actual system.

This is typically apparent to people working in numerical simulations of
systems that don't fall cleanly in one bucket. For example, someone in my
department does simulations of biological molecules. They simulate only the
part of the system they are interested in (a few atoms) using quantum
mechanics. For the rest they use classical physics. The accuracy is much
better than what experiment can achieve.

~~~
eridius
So you _can_ keep using the micro theory? That's good to know. Especially
given the claims of this article that different scales will always want
different theories, I got the impression that micro theories simply don't work
anymore at macro scales. I can quite readily believe that the computational
resources necessary to evaluate a micro theory at macro levels may be
completely infeasible, but as long as the theory still actually holds true
(even if you can't compute it), that makes a lot more sense.

So I guess the real claim here about the nonexistence of a Theory Of
Everything is really about there not being a _computable_ theory that holds
true at all scales?

It also seems like there's a bit of a confusion going on here between a theory
that describes all forces, and a theory that works at all scales. The article
here is making the argument that there won't be a Theory Of Everything because
you really do want to use different theories at all scales, rather than
finding one grand theory that works everywhere. But previous discussion of a
"Theory of Everything" (or "Grand Unifying Theory") that I've seen were
concerned with finding a theory that describes all the forces, not one that
works at all scales. The article did talk a bit about that, and mentioned
string theory and superstring theory, but it seemed like more of an aside. My
impression is that if we do find a Grand Unifying Theory that describes all
the forces at the smallest scale we know of, that still wouldn't be a Theory
Of Everything according to this article because it wouldn't be usable at macro
levels.

~~~
abdullahkhalids
You are essentially correct in the third paragraph. Let me elucidate and be
more correct. Bear with me.

We have found four field theories (electromagnetism, weak theory, strong
theory, gravitation)[1]. Each of theories have a domain of applicability in
which, in principle, all the results of all experiments can be predicted using
that one theory. Domain of applicability includes length scale, time scale,
energies involved etc. This is not a satisfying situation because it is
extremely common for systems to not respect this human-imposed domain.
Therefore, we want a single theory whose domain is the union of the domains of
all of these theories. Call this goal the goal of unification. This has been
partly been achieved (electroweak theory), and work continues.

Then there is another goal. To find a theory that has a even larger domain of
applicability than before. This is the problem of scale. The article claims
that the problem of scale is never ending because finite experimental data
(and philosophical claims not discussed in the article). String theory is an
attempt at the unification goal but it comes with a larger domain of
applicability as a bonus. I think this makes the two separate issues discussed
in the article clear.

I make a third point that you asked about. I make the following observations.
General relativity under reasonable restrictions reduces to Newton's law of
gravity. The correspondence principle claims that quantum mechanics
(typically) reduces to classical mechanics if your system has a large number
of particles. Special relativity reduces to classical mechanics for low
speeds. These are three pairs of micro-macro theories. In all of these cases
the micro theory also works at the scale of the macro theory if you choose to
use it: In other words the domain of applicability of the macro theory is a
strict subset of the domain of applicability of the micro theory.

This subset business does not work so nicely for field theories. Or when
looking at general relativity and quantum theories at the same time. There are
overlapping domains but no nice strict subset. In that case there is not
simple notion of micro-macro theory. However, returning to your original
question you can sometimes use multiple theories at the same time to make
predictions. Eg. particle physics experiments at CERN do this (multiple field
theories), or that blackhole physics that keeps making headlines (quantum and
gravity). This situation is of course far from satisfactory and work towards
the goal of unification continues.

[1] All of these theories of fields assume quantum mechanics which is a theory
of particles. Our universe is made up of particles and fields, as far as we
know.

~~~
eridius
Thanks, that explanation made a lot of sense.

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erik_landerholm
Point by point rebuttal. [http://motls.blogspot.com.es/2015/10/the-trouble-
with-krauss...](http://motls.blogspot.com.es/2015/10/the-trouble-with-krauss-
criticism-of-toe.html)

I'm not knowledgable enough to comment, but he takes a lot of exceptions to
the author's characterization of string theory.

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agumonkey
Krauss talks are entertaining
[https://www.youtube.com/watch?v=7ImvlS8PLIo](https://www.youtube.com/watch?v=7ImvlS8PLIo)

I'm not knowledgeable enough to criticize it though.

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Florin_Andrei
Gödel's Incompleteness Theorem seems to suggest the same conclusion. Yes, it's
not the same thing. Yes, it's an overworked analogy. But the fact remains, we
rely on axiomatic systems for all of science, and axiomatic systems are shown
by that theorem to have fundamental limitations when you try to extend them to
"everything".

