God's truth is in the Numbers?

[bobzills]

that’s the continuum hypothesis.

god alone knows if it’s true (and whoever he might have told).

I thought that Godel proved that the continuum hypothesis could not be disproved using the current axioms of set theory?
In another thread which was just closed, you mentioned that gravity and QFT are incompatible. However, hasn’t gravity been quantized in several different ways already, for example, by the use of spin networks?

 

[john_doran]

I thought that Godel proved that the continuum hypothesis could not be disproved using the current axioms of set theory?

yes, godel showed that it couldn’t be disproved by zermelo-fraenkel set theory along with the axiom of choice; but proving that a hypothesis cannot be shown to be false isn’t the same thing as showing that it is true.

that said, paul cohen has also proved that the continuum hypothesis cannot be proven by those same axioms.

bobzills:

In another thread which was just closed, you mentioned that gravity and QFT are incompatible. However, hasn’t gravity been quantized in several different ways already, for example, by the use of spin networks?

gravity has not been quantized in a way that is mathematically consistent and that is predictively useful or not in contradiction with experiment.

spin networks are simply an approximation of a fully developed theory of quantum gravity, and describe only parts of what such a theory might look like.

here’s a good paper on spin networks by a mathematical physicist named john baez (his website is really good, too):

arxiv.org/PS_cache/gr-qc/pdf/9504/9504036v1.pdf

it’s mathematically pretty dense at times, but if you just gloss over the equations and read the text, he gives some pretty clear descriptions of the ongoing problems of articulating a theory of quantum gravity.

it remains arguably the biggest problem in modern physics.

 

[bobzills]

here’s a good paper on spin networks by a mathematical physicist named john baez (his website is really good, too):

arxiv.org/PS_cache/gr-qc/pdf/9504/9504036v1.pdf

it’s mathematically pretty dense at times, but if you just gloss over the equations and read the text, he gives some pretty clear descriptions of the ongoing problems of articulating a theory of quantum gravity.

Why do you have to have a quantisation of the theory of general relativity in the first place? This type of quantisation with spin foam doesn’t appear to offer any hope for making new predictions.
Further, it looks like it might break unitarity, doesn’t it?

 

[john_doran]

Why do you have to have a quantisation of the theory of general relativity in the first place?

we don’t - we could scrap one or both of GR and QM altogether in favor of a new theory, and that is precisely the alternative that some theorists are pursuing.

but other than that, if GR is right about gravity (as it seems to be), and QM is right about the other two or three forces (as it seems to be), then some reconciliation between the two theories needs to be formulated, whether that’s a quantisation of GR, or a (general) relativization of QM.

bobzills:

This type of quantisation with spin foam doesn’t appear to offer any hope for making new predictions.

not sure - haven’t really looked into it too much. wouldn’t surprise me, though - most of the current theories of quantum gravity are plagued with either or both of a failure to make new predictions or to make untestable predictions.

bobzills:

Further, it looks like it might break unitarity, doesn’t it?

i don’t understand the math of the theory well enough to be able to judge its consistency (and neither, probably, do its proponents).

 

[bobzills]

we don’t i don’t understand the math of the theory well enough to be able to judge its consistency (and neither, probably, do its proponents).

Quantisation of a theory can have more than one meaning. for example, in spin foam there is the underlying assumption that space time is discrete and granular? You can make this assumption, I suppose, but it leads to a violation of very important symmetries in physics. For example:
www.iop.org/EJ/article/1742-6596/24/1/009/jpconf5_24_009.pdf
So I don’t see why you really would need a quantum theory of gravity anyway. It doesn’t lead to any new predictions, does it?

 

[bobzills]

here’s a good paper on spin networks by a mathematical physicist named john baez (his website is really good, too):

arxiv.org/PS_cache/gr-qc/pdf/9504/9504036v1.pdf

it’s mathematically pretty dense at times, but if you just gloss over the equations and read the text, he gives some pretty clear descriptions of the ongoing problems of articulating a theory of quantum gravity.

it remains arguably the biggest problem in modern physics.

It looks like this problem has been solved by a friend of John Baez. Or maybe he is not a friend. But he does mention him in the acknowledgements and also refers to a paper of Baez called “The Octonians” in the references. The author A. Garrett Lisi, claims to have unifed all fields of the standard model and gravity as an E8 principle bundle connection.
According to Lee Smolin this theory is: “One of the most compelling unification models I’ve seen in many, many years.”
David Finkelstein, emeritus professor of the Georgia Institute of Technology said: “Some incredibly beautiful stuff falls out of Lisi’s theory, I think that this must be more than coincidence and he really is touching on something profound.”
and news articles at:
telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/11/21/scisurf121.xml
telegraph.co.uk/earth/main.jhtml?view=DETAILS&grid=&xml=/earth/2007/11/14/scisurf114.xml
For the paper: An Exceptionally Simple Theory of Everything, you may download it at:
arxiv.org/abs/0711.0770

 

[john_doran]

Quantisation of a theory can have more than one meaning. for example, in spin foam there is the underlying assumption that space time is discrete and granular? You can make this assumption, I suppose, but it leads to a violation of very important symmetries in physics. For example:
www.iop.org/EJ/article/1742-6596/24/1/009/jpconf5_24_009.pdf
So I don’t see why you really would need a quantum theory of gravity anyway. It doesn’t lead to any new predictions, does it?

what i mean by “quantisation of gravity” is simply something like “reconciliation of GR and QM”.

and a theory of gravity that’s applicable to the planck scale, for instance, would make new predictions - it would make predictions about gravitational phenomena at those scales.

whether they are now or ever would be testable is another question.

more relevantly, though, we don’t know what predictions a good quantum theory of gravity would make, because that theory hasn’t been articulated yet…we never know what predictions a theory would make before that theory is developed. how could we?

 

[john_doran]

It looks like this problem has been solved by a friend of John Baez. Or maybe he is not a friend. But he does mention him in the acknowledgements and also refers to a paper of Baez called “The Octonians” in the references. The author A. Garrett Lisi, claims to have unifed all fields of the standard model and gravity as an E8 principle bundle connection.
According to Lee Smolin this theory is: “One of the most compelling unification models I’ve seen in many, many years.”
David Finkelstein, emeritus professor of the Georgia Institute of Technology said: “Some incredibly beautiful stuff falls out of Lisi’s theory, I think that this must be more than coincidence and he really is touching on something profound.”
and news articles at:
telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/11/21/scisurf121.xml
telegraph.co.uk/earth/main.jhtml?view=DETAILS&grid=&xml=/earth/2007/11/14/scisurf114.xml
For the paper: An Exceptionally Simple Theory of Everything, you may download it at:
arxiv.org/abs/0711.0770

that’s interesting - thanks a lot for the links.

i like smolin a lot, so i take his opnion on these things very seriously.

 

[john_doran]

…lisi’s model predicts new forces and new particles, as well as proton-decay.

not sure how he proposes to deal with the problem of proton-decay (it’s never been observed), but the LHC ought to give us some insight into the exra particles and fields.

we’ll see, I guess.

 

[bobzills]

that’s interesting - thanks a lot for the links.

i like smolin a lot, so i take his opnion on these things very seriously.

However, that was his first impression. Since then, he has written further on it, Anyway, some people are skeptical since for one thing, the theory runs against the Coleman-Mandula theorem.
cosmicvariance.com/2007/11/16/garrett-lisis-theory-of-everything/#comment-306890