I am just wondering what's the difference between the two. I would say that there is something different, but honestly I can't define what it is exactly. What do you think?
Logical modalities: possibility and necessity that is regined solely by conventions of logic that hold true in every possible world, to use possible-world semantics.
Physical modalities: possibilites and necessities which are a direct result of contingent laws of nature.
it is possible that I have a six fingers. Which, in turn means there is a world acessible to the actual world in which I have six fingers.
It is necessary that I have five fingers. Which, in turn means I have five fingers in the actual world, and also every possible world acessible to the actual world. (This proposition is obviously false, since there is a possible world in which I can have more, or less, than five fingers [refer to polydactyly].
It is necessary that a square has four sides, this is a true modal statement, since there is no world acessible to the actual world in which a square has greater than, or less than, four sides, because, then by definition it will not be a square.
As you can see, the only constraint on logical modality is the logical frame-work we are working in.
Physical Modalities (Newtonian):
it is possible that something has zero air resistance (yes in a vaccum)
A mass can accelerate iff there is an external force acting on it. [Refer to newton's second law: F=dp/dt]. This is true in so far as we are working within newtonian physics. However, this general uncertainty within physical modalities is not something contingent, but necessary [Refer to Problem of Induction].
In summary: logical and physical modalities are two seperate things, they are only similar because of the use of the same operators: "necessary" and "possibly." Finally, logical modalities are certain by definition, while physical modalities are not.
Keep in mind logical modalities are not like laws of physics, they are merely operators used within a framework to evaluate modal arguments [Refer to https://plato.stanford.edu/entries/logic-modal/ ]
Forms of logical modalities:
1.Necesssary and possibly
2.Obligatory and Permissible
3.It has always been and It will be the case that
[Hint: compare the above mentioned operators with the oft used Universal and Existential operators]
In essence, logical and physcial modalities are same solely because they use the same operators (necessary and possible); however, they are different because they are used in vastly different contexts:
Physical Modalities are particular; where as, logical modalities are universal (they hold in every possible world, given we suppose now that the possible world is the actual world). [I am ssuming here the modality is proven sound and valid]
Logical modalities are usually expressed through relational semantics for modal logic developed by Saul Kripke and André Joyal in the late 1950s and early 1960s.
In this semantics, formulas are assigned truth values relative to a possible world. A formula's truth value at one possible world can depend on the truth values of other formulas at other accessible possible worlds. In particular, possibility amounts to truth at some accessible possible world while necessity amounts to truth at every accessible possible world.
While what you mean by your own non-confidently defined "physical modalities" must be those modalities related to our physical world alone imho. Logical possible worlds imagined by logicians above are by no means physically possible, since by now science hasn't proved definitely whether there's another universe different from ours, not to say all infinitely possible worlds employed in logical modalities. So strictly speaking, "logical modalities" using relational semantics above cannot apply to your "physical modalities", but it still may help physics philosophically...
I wonder if you are referring to the kind of thinking of Wheeler's 'It From Bit' doctrine, which suggests logic is the fundamental substance, something like a string of yes & no answers.
VonNeumann proposed the extension of universal Turing machines, to a 'universal constructor'. Superficially, it seems there isn't an ontological difference, but topologically it seems there is, one that is involved in Turing machines being unable to reproduce themselves. This suggests there is a difference between logic as we have conceived of it, and matter.
Deutsch & Chiara have been developing a research paradigm, that looks to universal constructors to bridge between quantum fields & gravity: https://www.quantamagazine.org/with-constructor-theory-chiara-marletto-invokes-the-impossible-20210429/ It seems very promising.
The notion that there are straightforwardly something like "physical modalities", say "possibilities" of the state of a thing, has been largely assumed to be a kind of naivete or an offense agst reason since the 19th century. Strictly speaking there are no "possibilities", there is "sense data" gathered by observation. The great emphasis on so-called "epistemology", which is in truth a post-Kantian conception, and its projection back into the history of philosophy, has to do with the radical excoriation of all things "anthropomorphic" including mere "folk sense" and its "possibilities", and correspondingly the philosophic treatment of the conception of possibilities which goes back to Aristotle, and is itself based on something like a primitive common sense view. In order to affirm physical modalities one would have to deny the claim of a cardinal distinction between sensation, e.g., seeing stuff, and ideas, for instance memories which are available to transforming in imaginative processes. Once something like that is presupposed, one can not talk of the so-called raw "sense data", and "possibility" is not something seen or touched (something "physical").