The development of quantum mechanics in the first decades of the twentieth century came as a shock to many physicists. Today, despite the great successes of quantum mechanics, arguments continue about its meaning, and its future. ...This is a very strange complaint. Obviously he understands perfectly well how probability, measurement, and chaos get into quantum mechanics, because there is wide agreement on how to do the calculations that predict experiments.
Probability enters Newtonian physics only when our knowledge is imperfect, ...
Many physicists came to think that the reaction of Einstein and Feynman and others to the unfamiliar aspects of quantum mechanics had been overblown. This used to be my view. After all, Newton’s theories too had been unpalatable to many of his contemporaries. ...
It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means. The dispute arises chiefly regarding the nature of measurement in quantum mechanics. ...
The introduction of probability into the principles of physics was disturbing to past physicists, but the trouble with quantum mechanics is not that it involves probabilities. We can live with that. The trouble is that in quantum mechanics the way that wave functions change with time is governed by an equation, the Schrödinger equation, that does not involve probabilities. It is just as deterministic as Newton’s equations of motion and gravitation. That is, given the wave function at any moment, the Schrödinger equation will tell you precisely what the wave function will be at any future time. There is not even the possibility of chaos, the extreme sensitivity to initial conditions that is possible in Newtonian mechanics. So if we regard the whole process of measurement as being governed by the equations of quantum mechanics, and these equations are perfectly deterministic, how do probabilities get into quantum mechanics? ...
What then must be done about the shortcomings of quantum mechanics? One reasonable response is contained in the legendary advice to inquiring students: “Shut up and calculate!” There is no argument about how to use quantum mechanics, only how to describe what it means, so perhaps the problem is merely one of words.
So his problem is purely philosophical. If this is a problem, then I think that most theories have problems if you take them too literally and ask too many philosophical questions.
When it comes to well-defined laws governing the evolution of probabilities in time, it's just a plain stupidity to suggest that these laws are "troubling" in any sense. Quantum mechanics doesn't change anything about the meaning of probabilities, their relationship to imperfect knowledge, the existence of well-defined equations by which these probabilities evolve as well as discontinuous Bayesian/collapse changes by which the probabilities jump after an observation. The only thing that is new in quantum mechanics is the uncertainty principle (due to the nonzero commutators) which, among other things, forbids any perspective in which two generic observables are perfectly known at the same moment. The nonzero commutators make it unavoidable to talk about probabilities between 0% and 100% i.e. about imperfect knowledge. But what the "knowledge", "imperfect", "probability" etc. mean is exactly the same as it always was. ...Weinberg's hangup about probabilities is especially strange. He says that probabilities enter classical mechanics "when our knowledge is imperfect", and enters quantum mechanics because "not everything can be simultaneously measured." Okay, I can accept that, but why is it a problem? Our knowledge is always imperfect in the classical case because of observation errors, and always imperfect in the quantum case for the additional reason that it is impossible to predict the measurement of variables that cannot be simultaneously measured. So yes, probabilities are appropriate in either case.
At any rate, I consider Weinberg to be a 100% anti-quantum zealot ... at this point. It's sad.
I can only infer that Weinberg has some conceptual misunderstanding of probability, but I don't see what it is.
He favorably describes the many-worlds interpretation, but does not endorse it.
Physics professor Frank Tipler does endorse the many worlds:
Most physicists, at least most physicists who apply quantum mechanics to cosmology, accept Everett’s argument. So obvious is Everett’s proof for the existence of these parallel universes, that Steve Hawking once told me that he considered the existence of these parallel universes “trivially true.” Everett’s insight is the greatest expansion of reality since Copernicus showed us that our star was just one of many. Yet few people have even heard of the parallel universes, or thought about the philosophical and ethical implications of their existence.Quantum mechanics is a theory of physics on an atomic scale, so only crackpots apply quantum mechanics to cosmology. Maybe most of them believe in many-worlds, I don't know, but I really don't think that most physicists do.