I've never understood the difference in physics between 'information' and 'data', so I use the latter word.
Information in physics is a mathematical entity, i.e., a quantity. In the most non-technical sense, information is the resolution of (an) uncertainty. See:
https://phys.org/news/2016-07-refutes-famous-physical.html All of the answers there are informative.
In any case, in response to the question in your OP: information definitely does not possess mass.
In fact, a recent study showed that the assumption by which Ralph Landauer asserted that "information is physical"--i.e., is logically irreversible--is false:
The motivation that led Bennet to introduce logical reversible operations was to overcome the minimum energy expenditure introduced earlier by Landauer. Bennet wrote:
"Landauer has posed the question of whether logical irreversibility is an unavoidable feature of useful computers, arguing that it is, and has demonstrated the physical and philosophical importance of this question by showing that whenever a physical computer throws away information about its previous state it must generate a corresponding amount of entropy. Therefore, a computer must dissipate at least kBT ln2 of energy (about 3 X 10-21 Joule at room temperature) for each bit of information it erases or otherwise throws away."
This limit was generally attributed to all the logical irreversible devices, and among them, the traditional logic gates like "OR", "AND" and "NAND." The work of Landauer and Bennet inspired a significant amount of scientific literature opposing or supporting the existence of such a minimum limit. It's no exaggeration to state that for more than 40 years, the topic has been considered highly controversial.
Now, an experiment has settled this controversy. It clearly shows that there is no such minimum energy limit and that a logically irreversible gate can be operated with an arbitrarily small energy expenditure. Simply put, it is not true that logical reversibility implies physical irreversibility, as Landauer wrote.
The results of this experiment by the scientists of NiPS Laboratory at the University of Perugia are published today in
Nature Communications. They measured the amount of energy dissipated during the operation of an "OR" gate (that is clearly a logically irreversible gate) and showed that the logic operation can be performed with an energy toll as small as 5 percent of the expected limit of kBT ln2. The conclusion of the
Nature Communications article is that there is no fundamental limit and reversible logic is not required to operate computers with zero
energy expenditure.
[. . . ]
Though Landauer famously said "information is physical," it turns out that
information is not so physical after all.
Read more at:
https://phys.org/news/2016-07-refutes-famous-physical.html#jCp
We can imagine there's a realm of unknown phenomena all smaller than the Planck length (though Bell's theorem may raise difficulties for such an idea)
I don't know of anything relating to Bell's theorem that raises any difficulty in assuming the existence of phenomena smaller the Planck Length.
As the 2 sources linked to at my above post explain, phenomena smaller than Planck length have no location in spacetime and are inherently unmeasurable.
Fermilab Today notes:
When you scatter a particle of light off another particle -- say an atom -- the atom's gravitational attraction to the light particle causes an intrinsic uncertainty in the atom's location. Mead used the uncertainty principle and the gravitational effect of the photon to show that it is impossible to determine the position of an object to a precision smaller than the Planck length.
According to the explanation at Futurism:
If two particles were separated by the Planck length, or anything less, then it is impossible to actually tell their positions apart. Moreover, any effects of quantum gravity at this scale (if there are any) are entirely unknown as space itself is not properly defined. In a sense, you could say that, even if we were to develop methods of measurements that took us down to these scales, we would never be able to measure anything smaller despite any sort of improvements to our equipment or methods.
Obviously there is no rational reason to impose the requirement of location for the psyche, soul, consciousness, etc., that one cannot impose on phenomena smaller than Planck length.
Indeed, assuming the basic tenet of reductionism, in which causation arises from the smallest or most fundamental "level" of empirical reality, then causes would arise from those phenomena smaller than Planck length.