Ps Audio recently posted on this very topic. Perhaps the answers you seek are contained within Paul’s posts. 

@wturkey while it is possible for Paul to provide an answer, I have nmot seen it happen for me so far. But a link is easier to click on.

Back to the reality of the thread..
the OP says/asks:

 

Has anyone been able to define well or measure differences between vinyl and digital?

Is there a synopsis of the measurements?
(I know you are kind of asking it as a question, and the thread has strayed into subjective places.)

But do we have an agreed description or agreed measurements of the differences between vinyl and digital?

Yes… Do we have an idea of what to consider and what to look at?

Hi there.

I’d like to ask @fair & @thespeakerdude to disengage from your conversation with each other. You have reached an impasse where no greater value is being added either to my original questions or each other’s position.

Again I want say thanks to both for your energy and effort to address the technical aspects of these questions.

But honestly, I learned somethings from each of you, and I respect you for maintaining civility. I ask that you and we need to move on. Please.

Id like to hear more diversity of thoughts and experiences here.

fair

... A mathematical theorem is like a part of a legal contract: its words have precise meaning, often unexpectedly different from their everyday meaning; and it has small print ...

A math theorem is a principle that can be proven with math. The Fourier Transform is a theorem. It has been proven by both math and in actual implementation - it's the basis of both digital and analog audio. Your alternative paradigms aren't consistent with Fourier. You're probably having fun with your fanciful imaginings but that's all they are. If you want to make actual progress you'll have to accept the math. Anything else is futile and more than a bit silly.

@johnread57 , I was out a few messages ago.

I'm telling you that the errors are signal dependent, you are quoting this, and then are asking me to tell you exactly how big the errors are? 

You know, serious people run long simulations to answer this question for specific digitization schemes and sets of representative signals.

To quote @cleeds these are fanciful imaginings, not serious discussion points. Serious discussion points would come with serious analysis or serious links showing that analysis. 

@cleeds

A math theorem is a principle that can be proven with math. The Fourier Transform is a theorem. It has been proven by both math and in actual implementation - it's the basis of both digital and analog audio. Your alternative paradigms aren't consistent with Fourier. You're probably having fun with your fanciful imaginings but that's all they are. If you want to make actual progress you'll have to accept the math. Anything else is futile and more than a bit silly.

Let's make it more interesting. Shall we?

You likely know who Bob Stuart is:

Despite his lifelong achievements and indisputable expert status, audiophile community met MQA format he co-created with significant controversy, e.g. 

I propose reading a peer-reviewed paper he co-authored:

And then telling us what Tidal did wrong to further stir up the MQA controversy. And perhaps what Tidal and others can do in the future to improve the MQA situation. You may think it can't be improved, and this would be interesting to hear too. 

I hope the ensuing discussion would be very relevant to topic at hand, because Tidal and other "Ultra HD" music streaming services hasn't yet made a dent in LP sales, but I believe they may do so in the near future.