OK, yes, I'm posing a controversial question, but honestly and with the best of intentions. I recognize that there's no quantification of either medium that will be fair to both formats. That at some point you have to call in a cognitive expert to weigh in on what the ear is capable of hearing and what can be perceived. To even pose such a question is like bringing up politics or religion. Vinyl junkies swear there is a difference: It's the only medium that contains actual music.
Adherents of digital encoding of audio point out all the many benefits and practicalities and the emergence of better and better technologies. Plus, most new vinyl contains music that was processed digitally at some point anyway, so they might say that fans of vinyl are deluding themselves.
But I'd like to put such things aside and ask if there has ever been a study to quantify what is required to reproduce audio digitally what is possible with analog. For that matter, how do either compare to actually being there? Can digital one day exceed vinyl or has it already? What's the bitrate of the human ear?
You seem to understand the issues. Given that understanding, you must know that there is no answer to your question, and that it is likely to ramble on with often-repeated arguments, eventually turn sour, and end with a locked thread. So why not play your hand up front and be done with it? What do you think?
My ears tell me that given exactly the same master of the same recording, the only thing redbook (16/44.1) misses is the noise, distortion and designed limitations of vinyl. The Nyquist-Shannon sampling theorem supports my ears, theoretically (in the scientific, not philosophical sense) , anyway. Others believe that vinyl contains an immeasurable quality that brings it closer to live music than digital ever gets. We all hear what we hear and believe what we believe. As to your other questions:
has (there) ever been a study to quantify what is required to reproduce audio digitally what is possible with analog
There have not only been studies that quantified what is required to reproduce audio digitally, audio has, in fact, been reproduced digitally. What is possible with analog is long-established and has been measured and studied ad-infinitum. It is only what is heard, but cannot be measured, that is controversial. Science will not help you there; blind listening tests won't even be helpful as the differences between digital and vinyl are not subtle, it is the subjective quality of those differences that is in question.
how do either compare to actually being there?
How do they compare to being where? This subject has been beaten pretty hard around here. Is the "there" in question some imagined seat in the hall where a live recording took place? Or is it the very different positions of the various microphones that captured the music in that hall? Is "there" the mixing, processing and remastering after the recording? Or is it the recording itself, which in almost invariably sounds radically different from what human ears would hear from any seat in the hypothetical house? The recording that would reveal what you're hoping to reveal is exceedingly rare, if in existence outside of bad bootlegs, audiophile noodlings and the odd binaural recording. No recording engineer worthy of minimum wage would try to capture a professional live recording with a stereo mic from a single seat in the house. "There" isn't here.
Can digital one day exceed vinyl or has it already?
See all that subjective stuff above.
What's the bitrate of the human ear?
What's the wordlength of the human imagination?
Tim