What's the modern view on ur theory? (Is there one?)

[S.Daedalus]

No, that wasn't a lapse into lolcatese -- ur theory was CF von Weizsäcker's attempt to explain the apparent unity of physics by basing it on the abstract quantum theory of what he called ur-alternatives -- which are essentially equivalent to the more modern notion of qubits. Starting from general philosophical considerations on abstract information, he (and his collaborators) attempted to essentially reconstruct physics from first principles, reasoning that two-level quantum systems are the most fundamental ones in quantum theory, and that any quantum system can be embedded in the tensor product of such two level systems.

The idea has some interesting implications and applications -- for instance, three-dimensional position space is derived from the urs' symmetry group, there are arguments for deriving Bekenstein-Hawking entropy and a positive cosmological constant of roughly the right order, special relativity, particles, etc. Somewhat more weirdly, ur theory appears to predict the number of nucleons in the universe ($$10^80$$, which I'm told is in line with current observation), as well as the baryon/photon ratio.

However, work on this theory seems to be mainly concentrated on a small 'in-group', and today, almost nobody seems to pursue this line of research anymore; add to that the impression that I have that some of the arguments are a bit on the hand-wavy side, and I wonder if there's actually anything to it, or if it's just one more chimera conjured up by bold assumptions and great hopes...

If you're interested, but unfamiliar with the subject, you can find a paper giving a short introduction to ur theory here: http://arxiv.org/abs/quant-ph/9611048; I'd appreciate hearing anybody's reactions/opinions, and perhaps, if anybody's familiar with it, a bit on how the theory has been/is viewed in the larger research community.

 

[weburbia]

I think that only his own students studied ur-theory as CFvW formualted it, at least in recent times. Therefore the subject has effecively died with his own death a few years ago. However, I think you are right to connect his ideas with qubits and in that sense it lives on. His theory of Multiple Quantization has also been considered in other forms and may have some mileage left in it, but his own particular version is not in line with modern particle physics

 

[S.Daedalus]

Thanks for your answer. Could you elaborate a bit on what you meant regarding multiple quantization? In particular, in what sense is it not in line with modern particle physics?

Also, I'm especially interested in the argument directed towards deriving 3D position space. As given in the paper I've referenced above (the link to which seems to be be broken -- http://arxiv.org/abs/quant-ph/9611048" ), it's basically:

In ur theory the three-dimensional position space is derived as a consequence of these mathematical conditions. This can be explained by analyzing the concept of space. In most cases the spatial distance between objects can be understood as the parameter for the interaction between these objects. On the other hand, the definition of a physical object (e.g., a massive elementary particle) depends on the separation of its typical spatial range. Supposing that all objects consist of urs, the total state of the universe should remain unchanged by transforming all urs with the same element from the symmetry group of the ur, which is essentially SU(2). Thus the interaction between all objects should be invariant and therefore the position space as a parameter space for the strength of interaction should have the same structure as the symmetric space of the symmetry group of the ur. In ur theory therefore the assumption is made that the position space has to be identified with the homogeneous space S3 of the group SU(2).

I can't decide if I consider this too hand waving, or if there's something to it. There's preciously few frameworks in which 3D space is not an input, but rather can be derived, so that's appealing to me. But as I said, I'm not sure whether to trust the argument. Any ideas?

 

[fzero]

I can't decide if I consider this too hand waving, or if there's something to it. There's preciously few frameworks in which 3D space is not an input, but rather can be derived, so that's appealing to me. But as I said, I'm not sure whether to trust the argument. Any ideas?

There's no validity to the argument. This SU(2) he's talking about acts on the space of urs, not on the space that the urs are defined on. To see why the conclusion doesn't follow, we can consider a scalar field theory. The fields are $$\phi^i(x)$$ and we can consider them to be maps from spacetime $$X$$ to a vector space $$V$$, $$\phi^i: X\rightarrow V$$. In the ur theory $$V=\mathbb{C}^2$$. The vector space $$V$$ has a group of linear transformations (matrices) $$GL(V)$$ that acts on it. The global symmetries of the interaction between the $$\phi^i$$s will form some subgroup $$G\subset GL(V)$$ (presumably for urs this is the group $$Q$$). As global symmetries, they are the same at every point in $$X$$ and act only on $$V$$. So the fact that the interactions are invariant under $$G$$ tells us nothing at all about $$X$$. We can associate the space $$V$$ and group $$G$$ for any sufficiently nice $$X$$ (differentiable manifold). This structure is known as a fiber bundle, and has been well-explored in pure mathematics and in physical applications.

Incidentally, the kind of logic that appears in the statement that you quoted is one of the reasons that this work has been ignored. The probability that any novel useful ideas are present is miniscule if the author is so ignorant of well-known mathematical structures.

 

[weburbia]

To say that the SU(2) structure acts on S3 just means that the ur-object is identified with a spin half system. If I remember rightly he does another quantization and gets a larger representation that corresponds to the Lorentz group. Weizsacker certainly understood the group theory very well. This aspect of his ideas ties in well with newer ideas such as Penroses spin networks and twistors, but Weizsacker became isolated after his work on the German atomic bomb and did not work with many people outside Germany accept a few such as David Finkelstein.

The part which seems less modern is the large number correspondence. This may have seemed interesting in the days of Eddington and Dirac but now we know much more about cosmology and it does not really make any sense.

 

[S.Daedalus]

There's no validity to the argument. This SU(2) he's talking about acts on the space of urs, not on the space that the urs are defined on. To see why the conclusion doesn't follow, we can consider a scalar field theory. The fields are $$\phi^i(x)$$ and we can consider them to be maps from spacetime $$X$$ to a vector space $$V$$, $$\phi^i: X\rightarrow V$$. In the ur theory $$V=\mathbb{C}^2$$. The vector space $$V$$ has a group of linear transformations (matrices) $$GL(V)$$ that acts on it. The global symmetries of the interaction between the $$\phi^i$$s will form some subgroup $$G\subset GL(V)$$ (presumably for urs this is the group $$Q$$). As global symmetries, they are the same at every point in $$X$$ and act only on $$V$$. So the fact that the interactions are invariant under $$G$$ tells us nothing at all about $$X$$. We can associate the space $$V$$ and group $$G$$ for any sufficiently nice $$X$$ (differentiable manifold). This structure is known as a fiber bundle, and has been well-explored in pure mathematics and in physical applications.

This is the kind of thing I'm looking for, thanks. However, I think the idea is that there is no spacetime $$X$$ over which there is any fiber, but rather, that there's only the ur-Hilbert space $$\mathbb{C}^2$$ -- the urs themselves are completely nonlocal entities, who don't yet know the difference between particle physics and cosmology, so to speak. But the relation between distinct parts of anything composed of urs is three dimensional.

It's just always seemed very suggestive to me that any two-level quantum system can decide one of three mutually complementary propositions, represented by three measurements along orthogonal axes.

The part which seems less modern is the large number correspondence. This may have seemed interesting in the days of Eddington and Dirac but now we know much more about cosmology and it does not really make any sense.

I agree, that whole thing is kinda weird, and from a modern perspective, perhaps the whole framework seems somewhat low tech, which perhaps makes some arguments seem less convincing. But that doesn't mean there's nothing to it, which is why I'd like to get some discussion on these ideas going.