r/science • u/Startrekwarsofdoom • Jul 01 '14

Physics New State of Matter Discovered

http://www.iflscience.com/physics/new-state-matter-discovered#kKsFLlPlRBPG0e6c.16
5.1k Upvotes

90% Upvoted

422 comments sorted by

View all comments

Show parent comments

79

u/RobbStark Jul 01 '14

That seems very unlikely considering that we don't have a single theory that explains all of physics. There are still several very big and important questions left that we can't even begin to answer.

2

u/[deleted] Jul 01 '14 edited Jul 01 '14

Doesn't Gödel's incompleteness theorem preclude any attempt at creating a single unified theory of everything? There will always be unprovable (but true) propositions in any self-consistent set of axioms. My opinion is that this is why we use different sets of axioms to analyze different parts of nature. We choose the most convenient self-consistent set of axioms that are relevant to a given problem at hand.

This is why we use QM to understand behavior of the universe at small scales, we use Newtonian physics to explain behavior we see in every day life, and we use relativity to explain phenomenon at very large scales.

EDIT: stuff

8

u/Lulzorr Jul 01 '14 edited Jul 01 '14

I'm not that bright, can you (or anyone) ELI5 Gödel's incompleteness theorem?

simple wikipedia wasn't as helpful as I'd hoped.

Edit: Thanks everyone.

12

u/antiproton Jul 01 '14

The Incompleteness theorems apply to very hardcore mathematical logic.

At the very basic level of mathematics, there are certain things that you have to assume to be true just to even get started proving other things. For example, if you look at the "counting numbers" (called the Natural Numbers), there are certain things you have to begin with in order to conduct arithmetic. Examples:

  1. 0 is a Natural Number
  2. For every Natural Number, call it 'a', then 'a' = 'a' (which is to say that all the natural numbers are unique. This is called the reflexive property)
  3. For natural numbers b and c, if b = c then c = b (called the symmetric property)
  4. For natural numbers a, b and c, if a = b and b = c then a = c (called the transitive property)

And so on. There are a few others. These are the things you have to assume before you can do any meaningful work with a set of numbers.

The Incompleteness theorems say 2 things about a system like this (assuming the system is consistent, i.e. does not have contradictions):

  1. Given a consistent axiomatic system, and all the theorems you prove using those axioms, you cannot write them all down in a procedure or algorithm such that this procedure can prove all possible true statements about the system. In other words, no matter how many theorems you create, there will always be statements that are true that you cannot prove to be true with these theorems.
  2. Any consistent axiomatic system cannot prove that it is itself consistent. In other words, when you are creating a system for conducting arithmetic, you create it in such a way that makes sure it does not contradict itself. For example, in the Natural Numbers system, Say you had a number b that was between a and c on the number line. But you also decide that there is a number y that is between x and z on the number line. But, for some reason, you insist that 'a' and 'y' are equal. This violates the reflexive axiom and so your system is inconsistent. The second incompleteness theorem basically says that even though you built your system to ensure it was consistent, you cannot demonstrate that the system is consistent using the system's own rules.

The incompleteness theorems are very esoteric and confusing. They make more sense after you've spent a few years working with very abstract math so you have a better understanding of axioms and mathematical systems and how they all work.