is the sound of vinyl due to the physical process of the turntable?

Same here and by giving up and going vinyl I will not have the answer which I believe will be found by stepping outside the box + I believe that new remastered vinyl is fake vinyl and to my ears does not have that stereos I hear from 1st press vinyl. This is a conspiracy to destroy the healing effects of real audio and the Hypersonic effect

is the sound of vinyl due to the physical process of the turntable?

@guitarsam - not due to, in spite of. From a noise perspective, turntables only contribute to the noise floor. What a better (but not necessarily expensive) turntable provides is less background noise.

The sound of vinyl is due to the process of the stylus being dragged through the grooves and mechanical energy being transferred to low-level electrical energy. The cartridge/tonearm/wiring/phono stage/preamp  symbiosis AND turntable noise floor is responsible for our tail wagging response. All other things being equal

I think another aspect is that, as I understand it, digital and vinyl are mastered differently, so of course they will sound different.

The mathematician in me can understand the theory of digital, and some of the higher sampling rates should theoretically continue to come closer and closer to vinyl, but the emotion in me understands that it just isn't the same.

One other often overlooked difference, with vinyl people would usually listen to an entire side of a record, with digital they are skipping only between "great songs," yet to me they're still missing out on the "esoteric-ness" of what vinyl is. 

It is very simple for laymen playing records From cereal boxes. Records provide a continuous signal. Any digital source, even if “oversampled” still is not continuous- it has individual bits of information. Remastered records are usually better because the original tapes are typically half speed mastered so it can be cleaned up. Also they are usually made on better vinyl and pressed better. 45s are even better Because you’re getting the information delivered at even higher rates and since they take up less space on the record, the tone arm sits closer to tangent to the record and spends less time at a reduced angle.

The records on the cereal boxes and most importantly inside MAD Magazines ("She Got a Nose Job" and "It's a Gas" were 2 childhood favorites may find them on YouTube) are thin flexible vinyl (PVC). They are made by Eva-Tone Corp. in Illinois and now also FL.  I was at the factory in the 70's. Had them stamp clear Fresnel lenses (similar to record grooves- we furnished the stamping masters) in continuous rolls then cut into squares on same production line as the records. We used them in our Psychedelic/Disco color organ sound to light boxes, made for folks like Spencer Gifts, Radio Shack, etc.  Stayin' Alive in the good old days.