Bohmian mechanics has not been well-received in the physics community. Why? And what are the arguments against it?
The why of the rejection is a matter largely for sociologists. For the most part, it seems that thinking in terms of particles with positions at all times was/is something that is flatly rejected by those who support the standard quantum formalism and decide to discuss it. Truth be told, most physicists seem to just not care. They are not seeking an understanding of quantum mechanics. They have accepted that it is not humanly possible to understand physics on that level. After all, what makes us think we can understand a world 10 to 30 orders of magnitude smaller than our own level of reality?
It is sad. We can understand the nanoscopic reality. Bohmian mechanics has shown us how. Those who would like to accept it might have legitimate concerns about how it relates to quantum field theory and quantum gravity. Until the theory at least reaches parity with existing quantum theories, why should one bother with it?
We would argue that it helps with intuition and clears the very bad statements that appear out there. Quantum mechanics had injected black magic into physics and Bohmian mechanics reveals the mechanism of that magic. That alone should be worth it. And, of course, if one does not pursue the theory, then one cannot make the theory reach the next level.
There are other objections which are false. The most prevalent one is that Bell (and others) showed that Bohmian mechanics cannot agree with quantum predictions and is therefore a failed theory. This is false. A counter proposal is that since quantum and Bohmian mechanics gives the same predictions, why bother? It is interesting that both arguments are used. This last one is a matter of debate and theory acceptance as it is based in true facts. Bohmians would argue that quantum mechanics is incoherent and not a valid theory at all. But if one puts this debate on the level of equally valid quantum theories without observers, which certainly exist and can be quite respectable, there is no answer. Learn them all if one can and appreciate the beauty of nature that it allows us to have such varied ways of looking at its majesty.
Other objections are rooted in the fact that Bohmian mechanics does not treat momentum and position on equal footing. This is again something we largely shrug at. The theory defines what is relevant and important. The momentum operator in quantum mechanics can be problematic in various situations. It is not a fundamental part of quantum mechanics. It is a derived object and Bohmian mechanics elucidates its role. It is still there. It is just not part of the assumptions. Even the position operator is derived despite position being the “hidden variable”. Operators encapsulate information about certain physical situations that we call experiments or measurements. It is necessary to understand those experiments/measurements from the viewpoint of the theory. Once that is done, the correspondence to the usual quantum stories becomes clear. This reliance on paying attention to the details of experiments is somehow considered poor form. This is rather surprising since who in their right mind would believe predictions about experiments when the details of the experiments are not considered? But somehow that is the idea. To those people who have this idea that the momentum operator is fundamental, it is doubtful that any result or argument will dissuade them.
There are many more criticisms that one could go through and perhaps they will be added here someday. But the main take away point is that Bohmian mechanics works, is equivalent in predictions to the quantum formalism as long as the latter gives predictions, and that the details of experiments do matter.