Yes, I can see that if the fundemental particles had no invariant mass, the stress energy tensor would not be zero, so we could still have gravitational coupling. But if this were the case, could we really have anything but a thermal bath?The proton and the neutron, for example, don't need the higgs to be massive. And dark matter would probably still be massive, too. So this tells me that the higgs has absolutely no relationship to gravity. That is, gravity still exists if there is no higgs.
yes, that's exactly what I have in mind (taking "length scale" to mean both space and time lengths, of course).Humanino, is that what you are referring to above as well? With no effective masses we'd have true scale invariance, so there would be no "length scale" to any interactions in the universe?
There is no known model without conformal anomaly ?The conformal symmetry is violated by quantum effects, so you couldn't have it, even in principle with or without the Higgs. You'd have to imagine a different universe.