# Falsifiability - another challenge

1. Feb 12, 2009

### Dmitry67

Kerr black holes have 2 horizons: outer (event horizon) and inner (cauchy horizon). I also heard that inner horizon is called a Killing horizon, which is actually funny because it can KILL - literally.

Even it is not proven yet, but it is possible that there is an infinite density of evergy on the second horizon (called a "blue sheet"), so any infalling bserver will be burnt to quark-gluon ashes (9-degree burns :) ) or killed by infinite tidal forces (infinite gravity as a result of infitite density there), or both

So lets assume that it is true. Now my question.

No observer can arrive safe and sound inside the second horizon to see the ring sigularity. In that case, is any theory which describes what happens there falsiable?

2. Mar 10, 2009

### yyttr2

Any thiory is falsifiable...thats what makes it a theroy.

3. Mar 10, 2009

### Tom Mattson

Staff Emeritus
Not if it's tautological it isn't.

It could be if it makes predictions as to what happens away from there. That is, let $P$ be a statement about what happens in the "kill zone". If, using the theory, you can derive from $P$ some statement $Q$ that pertains to the region outside that zone, then you could have a falsifiable theory. That's because $P\Rightarrow Q$ is logically equivalent to $\neg Q\Rightarrow \neg P$.

4. Mar 11, 2009

### Dmitry67

Based on that definition falsifiability is a "local" thing: for 2 spacetime regions L and R separated by a horizion some statements are falisable in L, but not in R, and vice versa.

However, we except the physical laws to be "global" and any statements about the fundamental laws should be equally applicable everywhere, in L as well as in R, do you agree?

Also, do you agree that in our epoque of superstrings the principle of falsifiability has less and less value?

5. Mar 11, 2009

### Tom Mattson

Staff Emeritus
That's not really what I'm saying. I'm saying that if you can derive a statement $Q$ from a statement $P$, where $Q$ is contingent on experimental results, then the theory is falsifiable whether or not $P$ can be verified. That's because if $Q$ is shown to be false then $P$ is shown to be false as well.

Here's an example from QM. If you input a potential and some boundary conditions into the Schrodinger equation, it spits out a set of wavefunctions. Since the wavefunctions are complex valued they aren't measurable. Hence there is no way to verify directly that, say, the ground state of the hydrogen atom is described by $\psi_{100}=R_{10}(r)Y_{00}(\theta,\phi)exp(i\omega t)$. However there are obsrevable quantities that are derivable from this. For instance the eigenvalue that corresponds to this is $E=-13.6eV$, which gives you a prediction of the ionization energy of the atom in its ground state. This is a contingent proposition, which turns out to be true. But what if it weren't true? Then we would know for sure that the complex wavefunction given above isn't the right one to describe the atom. Thus, the theory is falsifiable. This is an issue of logic, not of local vs nonlocal.

Sure.

Perhaps among string theorists. In school I studied plain vanilla particle physics, and I never was exposed to strings.

6. Mar 11, 2009

### Dmitry67

So you are repeating what Max Tegmark had wrote:

And I agree with you and with him. I hope, you prefer Multi-worlds interpretation of QM? But it is difficult to explain it to others. People tend to say "we can observe other 'branches' of our reality, hence it is not falsiable/physical" while MWI is a simplest version of QM (pure QM + decoherence)

It means, that there are 2 versions of falsiasibility:
"strong": all consequences of a theory must be testable.
"weak": some consequences of a theory must be testable.

7. Mar 12, 2009

### Tom Mattson

Staff Emeritus
Yes, I would take the "weak falsifiability" stance. I think that in order to accept for instance (unobservable) wavefunctions as part and parcel of the theory of QM, it is unavoidable to take that view.

As for interpretations of QM, I prefer Feynman's: "shut up and calculate". I never saw the use in the debate of Many Worlds vs Transactional vs Copenhagen, or whatever.

8. Mar 12, 2009

### Dmitry67

So we had agreed on everything.

But do you agree with me that there are double stadards in physics regarding the subject?

In GR there is a buzz regarding the interior solutions of black holes. And nobody talks about it as 'non-physical'

At the same time, people are afraid of naked singularities and try to hide from the problems behind the 'cosmic censorship' hypotesis which is quite artificial and I bet it is false.

If there is something really wrong or weird with a theory inside the BH (like closed time-like loops) then the fact that it is inside the horizon does not resolve that problem.

9. Mar 14, 2009

### Tom Mattson

Staff Emeritus
Dimitry, I'm not enough of a "GR guy" to have anything to say there. I'm a fan of Popper, so when I saw the word "falsifiability" I was drawn to the thread. But I know my limits on GR so rather than stick my foot in my mouth I'll just shut up now.