That sentiment is due to many people who cannot really visualize QM

in the same way they understand Classical Physics, so they make a lot of noise about this limitation.

However QM has good recipies to follow to get the correct results.

Thus Feyman sais "shut up and calculate".

Quantum mechanics is a weird field. From its very birth, at the 1927 Solvay conference, a very unexpected consensus was achieved on its mathematical formalism, difficult as it was, and an almost as unexpected polemic raised on the interpretation of this formalism (namely, on the physical sense of the quantum wavefunction).

For decades, while some older physicists tended to dwell on these metaphysical rather that physical aspects of the theory, the injunction to the young PhD students was to work on the physics — hence, to "calculate", for the theoricists.

Note that the deal has changed with the so-called "second quantum revolution, in the 1990s: while the question of interpretation remains mostly open, physicists tend to have a more casual relation to the quantum objects, and to use more freely the common language to discuss them, where the so-called Copenhaguen school insisted that mathematics was the only legitimate language to describe the quantum world.

“What does the modern quantum mechanical command "Shut up and calculate" mean?”

- really "Shut up and calculate" in mainstream physics isn’t a “command” that relates to only QM, that relates to whole physics for a rather long time and till now, and really now in the mainstream that isn’t a “command”, that is a mainstream “commandment”.

That happens in the mainstream since yet in first 1900ties physics reached the level, when really fundamental problems were really studied – i.e. that relate to fundamental phenomena/notions first of all in this case “Matter”, “Consciousness”, “Space”, “Time”, “Energy”, “Information”, which were – and are till now fundamentally completely transcendent/uncertain/irrational in mainstream philosophy and sciences, including physics,

- which yeah, earlier were some “metaphysical” subjects for study by only philosophy. However yet in those times that really have became Meta-physical problems; and so, say, it has became principally necessary to define clearly and quantitatively these phenomena in physics.

Firstly that was made relating to “Space” and “Time”, when in physics the standard now Minkowski theory [now “SR”] was developed, where the author, having only completely transcendent imagination about what are “space” and “time” “discovered” by ad hoc postulating, the really his transcendent illusory interpretations of existent experimental data; further was development of the equally transcendent GR, etc.,

- however in those romantic times these perfect mathematical constructions, in which really “metaphysical” problems were seems completely truly solved, the theories were well adequate to the reality, and so yeah, when the initial QM versions were developed,

“…For decades, while some older physicists tended to dwell on these metaphysical rather that physical aspects of the theory…”

- i.e. the QM fathers indeed attempted to find metaphysical interpretations of this new theory, what resulted in the first, and really utmost rational, till now “metaphysical” Copenhagen interpretation of QM.

Further the development of physical theories proceeded really only in obtaining of next and next mathematical constructions, which were well adequate to the experimental reality, while the really fundamental points remained completely transcendent and rationally rather evidently insurmountable,

- while mathematics, again for some mystic reason and by some mystic way, was again extremely effective at description and analysis of what exists and happens in Matter.

What created rather strong illusion of omnipowerful mathematics, and so, yeah, that

“….Note that the deal has changed with the so-called "second quantum revolution, in the 1990s: while the question of interpretation remains mostly open, physicists tend to have a more casual relation to the quantum objects, and to use more freely the common language to discuss them…”

- indeed quite correctly describes what happened/happens in mainstream physics, with a correction, though - in 1990s in computers a number of word soft programs appeared, and writing of any complex equations has became a rather easy job, what resulted in innumerous nicely mathematically written publications, which were/are really nothing else than some senseless LaTeX exercises; and to be an “outstanding” physicist there is now no necessity to be a real physicist, it is enough to study LaTeX.

So completely logically inevitably despite that, say, Phys.Rev. every month publishes a few fudamentalest breakthroughs in physics, really physics-2023 is the same as physics 1980, and on 90% as physics 1935;

- though again with a correction, yeah, that

“… Copenhaguen school insisted that mathematics was the only legitimate language to describe the quantum world.…”

- indeed is practically cancelled in the recent mainstream.

Really any really fundamental development of any science, including physics, is fundamentally possible only after the “metaphysical” problems above are solved, what is possible, and done, only in framework of the 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception, recent version of the basic paper see

https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed

- and the informational physical model, the couple of main papers are

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, and

https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics ,

- where the fundamental phenomena/notions above are rigorously scientifically defined, and so more 30 really fundamental physical problems are either solved or essentially clarified.

The post is rather long already, so more see the links; now.

Cheers

It plainly means there is very little objective correspondence between Quantum-Science and reality as we are to perceive and apperceive it .......

The so called correspondance principle , along others such as linearity

of operators were long used in the development of QM.

Remember, this has not been exactly a "voluntary" theory in Physics, but one forced by empirical facts of nature, notably energy levels of electrons in atoms, Black Body Radiation and electron diffraction experiments. Also after passing through the old QM phase.

Who does not know its prior history since 1900 is at loss today.It is not used because it is "liked", it is used in spite of a prior principles.

About the so called newer reformations, supposed around 1990, these were

very minor; a debate if the wave function is real or not.

However its extensions to new topic such as QED are more important.

Not everything is clear, as many wish, this is true.

Some more advanced studies, like Feyman diagrams, have these famous divergences, thus

renormalization attempts, perhaps faulty math, perhaps not.

The rise and fall of the Mechanical point of view (D´Abro)

FWIW, I believe this article by Mermin is the origin of the "shut up and calculate" remark about the Copenhagen interpretation; but note that he isn't particularly endorsing it; he follows with "But I won't shut up".

Physics Today 42 (4), 9–11 (1989)

Article What's Wrong with this Pillow?

For myself, would suggest that sometimes it is most useful to calculate before making statements or assertions about the outcomes; intuition is not always reliable, and even if you might still want to dispute the physical reasonableness of some quantum mechanical result, it is helpful to know what it would actually be.