Marcus,
thanks for the very first sentence of you post :-)
Of course I will try to respond carefully. First of all I was trying to go beyond a purely physical (positivistic) concept of a theory. If we restrict the meaning of ToE to "it predicts experimental results accurately" the all you comments are right - or the other way round - my comments a) to d) are somehow irrelevant.
What I was trying to do is to enlarge the concept of a ToE towards an ontology. That does not mean that we must decsribe nature in terms of things, objects and so an, but at least in terms of structures, laws, relations etc. So w/o knowing in detail what a quantum object "really is", we have a gut feeling, that there is some underlying "quantum ontology".
However quantum mechanics does not tell us what this really is and why it is as it is.
The only theory that tries to go into that direction is string theory. It provides a rather large (and rather un-explored) theoretical framework, which allows one to restrict its application due to certain consistency conditions. Of course there is still a long way to go - and to be honest I doubt that string theory will do the job - but is is definately the first theory that at least tries to answer such questions.
Regarding the details:
marcus said:
... Weinberg was using a very pragmatic idea of a ToE when he referred to "how nature is". Talking about a predictive theory that appears good to arbitrary high energy.
OK; here Weinberg restricts himself more than I would prefer; Of course he is right in terms of a scientific program, but I would not call the result a "ToE".
marcus said:
And he was saying that string may be irrelevant. String may not turn out to be "how nature is". ...
Therefore I think your references to string theory (ST) in your quote may be irrelevant and distracting.
see above
marcus said:
d) is right of course ... but ToE does not have to address it.
OK; let's drop d) as it may be too metaphysical and focus on a) - c)
marcus said:
c) does not have to worry us. There can be alternative equivalent formulations of the regularities in nature. Sometimes we eventually find that one is better. Sometimes we find a more general mathematics that comprehends both. It is OK. There can still be a ToE even if it comes in several equivalent formulations.
That's not the point. In terms of purely physical applications you are right, but not in terms of a more fundamental ontology. Look at Maxwells equations: let us assume for a moment that the 4D Minkowski formulation is not known. Then assume that somebody explores the 4D formulation together with Lorentz symmetry, fieldstrength tensor, 4-potentials and gauge symmetry. I would call that a step towards the knowledge what "nature really is".
marcus said:
b) pragmatically, I do not see why any physical theory has to explain why it is an adequate theory. If something works and acts like a ToE then it is a ToE.
It does not have to contain a "theory of theories".
See above; it's especially here where my comments regarding ST apply. As another example I could use Bell's theorem; it is negative in the sense that it tells was what "nature not is". But it reveales some deeper knowledge about the classical and the quantum world and excludes a huge set of "theoretical approaches".
marcus said:
a) What you say here is absolutely right, except that we do not know in advance the ultimate limit that we can probe empirically.
Here we have to be rather careful. If we believe in a theory to be the ToE just because of its support from the LHC, than our belief goes beyond the experimental knowledge.
Assume for a moment that we do not know that GR + QFT are incompatible. Then we could call GR + SM a ToE, simply because all experimental predictions are correct (the problem with 3 generations, Higgs etc. does not apply in the context of argument a). Nevertheless it is no ToE, because:
- we will find inconsistencies at higher energies (argument a)
- it does not explain the particle content, symmetry etc. (arguments b - c)
Of course the LHC could provide mechanisms to test the theory beyond the LHC's energy scale, e.g. due to loop effects that already allowed us to restrict the allowed mass range of the Higgs even if this range is not covered my already operating accelerators. That is not my point.
Predictive out to arbitrarily high energies is a very good starting point. For such a theory I would agree to call it a ToE (of course still with some limitations from b - c). So I think we can agree on a common understanding of a ToE restricted to a pragmatic perspective.
Nevertheless I would like to go beyond that perspective. I know that this is a fundamental clash within the community.
A) we all "agree" that we should use the QM / QFT framework in a pragmatic way - and must not / cannot try to describe nature "as it really is"; photons "are" not the lines within Feynman diagrams, ...
B) All researches trying to understand (e.g.) how QCD works are true believers that quarks, gluons etc. are "real physical entities" - whatever that means - and I am sure sure they would deny that these entities are only mathematical tools to describe scattering cross sections w/o any underlying realistic interpretation.
Of course nobody as of today knows what these "quantum entities / quantum ontology really is", but nevertheless all major research programs are driven by the idea to "understand more about their existence / being".