# The GUT and the Black Hole

1. Jan 27, 2005

### einstein_from_oz

We all know how the black holes form from stars. We also know that there is a region outside the black hole called "event horizon". Beyond such a region, our laws of physics become invalid. (Right?)

We also believe that the universe began with a huge explosion known as the Big Bang.

Now here comes the interesting bit I was wondering. There is a length called "Planck length". I know (from calculation or data) that the Schwarzschild Radius is bigger than the Planck length. Our knowledge about the origin of the universe becomes meaningless if we go back in time and the size of the universe becomes less than the Planck length. So, when we either go into the black hole's singularity, or come out from the singularity of the origin of the universe, our laws of physics is not valid.

So I want someone to tell me what the purpose of the GUT (Grand Unified Theory) is. Or does the Quantum theory allow us to work out the origin or end of the universe?

2. Jan 27, 2005

### JesseM

The Schwarzschild radius depends on the mass of the black hole. As explained here, when the mass of the black hole is set equal to the Planck mass, that's just the point (ignoring some numerical factors like $$2\pi$$) where the Schwarzschild radius becomes equal to the Planck length! This is probably telling us something important about quantum gravity, although I don't know enough about it to say what, exactly.

Last edited: Jan 27, 2005
3. Jan 27, 2005

### vanesch

Staff Emeritus
Strictly speaking, GUTs are not theories of gravity. They are unifications of the strong and the electroweak force (and are also hypothetic in the sense that no discriminative experimental evidence has pointed out in either way).
Historically, the electromagnetic force (quantum electrodynamics) has been unified with the "weak" force (which had a phenomenological description as a quantum field theory by Fermi, but had difficulties on its own) into the Electroweak force. This was the brainchild (in the 60ies) of Weinberg and Salam, and was experimentally confirmed in the 80ies by Carlo Rubia et al.(lots of Nobelprices for this work !) with the discovery of the Z0 particle. LEP has since then carefully measured all kinds of things around this theory and it works very well.
On a completely different side, people were working on the strong force, and during the 70ies, quantum chromodynamics (inspired by the structure of the electroweak theory, but in fact structurally much simpler) was develloped. QCD is a nice theory but gives quite some calculational difficulties (contrary to the Electroweak theory), so it has been harder to get hard numbers out of QCD to compare with experiment, but nevertheless QCD stands as a rather satisfactory theory of the strong interaction.
The "2 for the price of 1" bundle of Electroweak theory and QCD is called the Standard Model, but it is not a *unification* of both theories, in the sense of having a common origin, and 2 aspects of the same thing. They are just two different theories, which can coexist without any great difficulty, in the same bag.

So people got ambitious, and tried to find a "master" theory that would lead to both theories in a natural way, and these proposals are called Grand Unifying Theories (GUTs). Several proposals got out and a lot of them died, because most of them predict a decay of the proton. It is not clear if this GUT way is the way to go. But in all of this, we haven't touched upon gravity.

Another, much more ambitious plan is to unify gravity and the standard model. We have also a classical theory of gravity, namely General Relativity, but contrary to the peaceful coexistance of the Electroweak theory and QCD in the standard model, GR is INCOMPATIBLE with the standard model. Much more profound changes have to take place in order to make them fit into one bag ; one such tentative approach is superstring theory. And the questions you ask are related to issues in THIS kind of theory (which are usually called TOE - Theories of Everything).

cheers,
Patrick.

4. Jan 27, 2005

### trosten

general relativity is still valid inside the event horizon, there are some other coordinates that are valid inside finkelstein (or something). it all breaksdown at the real singularity in the center of the blackhole.

5. Jan 27, 2005

### marlon

Vanesch explained already the meaning of TOE's and all...I will just add that General relativity is still valid inside the Schwardzschild radius but NOT "inside" the singularity. The thing is that inside this radius, space-time is "severly" curved and the main result predicted by GTR is that the time-coordinate becomes space-like and the spatial coordinates become timelike. This implies that you WILL move toward the singularity and you can't do anuthing about it. A timelike spatial coordinate means that your "position moves like time. Here on earth, you can't prevent the fact that seven days from now it will be again thirsday, you see ?

Inside the singularity, all of our physical laws break down and are invalid. Why ? Well, this is a region of very great density (described by GTR) and it is very small in dimension (QM-description is required). However, like vanesch said, we cannot come both QM and GTR at the same time. These two models contradict each other because of superposition in QM and Heisenberg uncertainty in QM and curvature of spacetime in GTR

regards
marlon

6. Jan 27, 2005

### dextercioby

There are some inexactities here:
1.By the time the first article on the unification of EW interactions came out,the weak interactions had a rather satisfactory description done in 1958 by Murray Gell-Mann & Richard P.Feynman.So the part with Fermi (1933) is completely decieving.

2.Actually i never understood why the 3 (sic) physicists got the Nobel Prize...I haven't read the article by Sheldon Glashow (Nuclear Physics 22(1961),579) and neither the ones by Steven Weinberg & Abdus Salam (1967),but i think the latter came with an improvement to the work done by Glashow 6 years before.
So i think it's unfair to disregard the pioneering work by S.Glashow... :yuck: After all,the money from the Nobel Prize got split equally...

Daniel.

7. Jan 27, 2005

### vanesch

Staff Emeritus
Ah, I wasn't aware of that! I thought that the theory with the "contact" interaction was all there was to weak interactions before Weinberg (and as you know, it is non-renormalizable).

cheers,
patrick.

8. Jan 27, 2005

### dextercioby

9. Jan 27, 2005

### vanesch

Staff Emeritus
One is never too old to learn (well, sometimes one is, but then one is dead )

I had a look at the paper but this was the theory I was talking about: the contact interaction with the four dirac fields in it. I remember my professor present it as Fermi's theory of weak interaction...
(and the problem is of course that by dimensional analysis, it cannot be a renormalizable theory). Maybe it was the QFT-style reformulation that is due to Feynman and Gell-Mann ?

cheers,
Patrick.

10. Jan 27, 2005

### dextercioby

Well,the theory due to Fermi is OLD,since he had no idea about violation of parity in weak interaction and that was solved in an elegant manner by Gell-Mann & Feynman by the so-called "V-A interaction"...Oof course they were aware of the "trend" in QFT,since they both were among the ones that built it...

Daniel.

11. Jan 27, 2005

### vanesch

Staff Emeritus
I see now. Indeed, what I thought was Fermi's theory was indeed the V-A interaction, and this couldn't have been invented before the Wu experiment, showing parity violation! Right...
So I never knew what was Fermi's theory in the first place.

thanks!
cheers,
Patrick.

12. Jan 27, 2005

### DrChinese

Vanesch,

I am splitting semantic hairs here, so please forgive me...

When you say that GR and the standard model (SM) are "incompatible"... I usually see this as relating more to boundary conditions, often in the very early universe. In our day to day universe, how are they incompatible? I think of the 2 theories as otherwise useful within their domains of application.

13. Jan 28, 2005

### vanesch

Staff Emeritus
You are quite right that for most thinkable experimental setups in the near future, you are OR in the GR application domain, OR in the SM-QM application domain. But you could possibly think of situations, such as black holes, where you need both, and that's where they are mathematically incompatible. If you use classical GR, you screw up the superposition principle, and if you try to quantize GR, you hit all kinds of mathematical problems too.
It is the theoretical fact that you can think of situations where this clash occurs that makes theorists unhappy. But it is the factual situation you mention which makes experimental inquiry in that domain difficult :-)

cheers,
Patrick.