Dear Michael, thanks for your reply. Once you introduce torsion, there is this critical uncertainty about what the "minimal coupling" means. The coupling that decouples the torsion altogether always has to be allowed - and it's probably the right one. There are various other fundamental problems - that it's not really clear what the theory should be to describe the real world. Even if you want to couple Einstein-Cartan theory to ordinary electromagnetism, there exists no candidate for a "minimal coupling". Moreover, the newer, more well-defined versions of the Einstein-Cartan theory, e.g. due to Stelle and West (involving non-commutativity as a justification), actually predict big enough phenomena and can be falsified. For both claims, see e.g. the 2009 paper by Gibbons et al.  (the falsification is described in the comment about 1,000 seconds; Gibbons is a senior guy who wrote important papers with Hawking and others). I think it's valid to say that any concrete enough version of the theory - including couplings to known types of matter - can be falsified and has been falsified. So the concept is only surviving as a vague one, with a wishful thinking that there could still exist a viable version of it. But no such version is known - at least not a natural one. What's really missing is the motivation. In string theory, one can see that there's no torsion, perhaps except for the H-field (a 3-form) but the H-field doesn't have the usual normal properties of the Einstein-Cartan torsion field. In fact, in 4D, the H-field may be Hodge dualized to a scalar, the universal axion, and such fields are naturally massive - otherwise new long-range forces would have to exist but they don't. If they were not massive, you would really modify the GR even at long distances, and created new polarizations of gravitational waves, altered the prediction for gravitational lensing, and other things. All these things are absent according to observations as well as string theory. Moreover, the very idea about the "minimality" of the couplings has been changed in the 1970s by the insights of the renormalization group. We no longer prefer "simple" couplings because they look aesthetically and subjectively simple but because we can technically prove that these couplings - and low-derivative terms - prevail at long distances. This modern kind of reasoning leaves no natural room for torsion. So  all the motivation is just historical in character and can't be reconciled with the modern way of organizing fields and terms in field theory, and the people who defend it don't understand the last 60 years in theoretical physics.