Division by zero is a violation of the axiomatic system of real numbers. This easily follows from the associative and distributive properties. For example 10/5 = 2 and 2*5 always = 10. If we allowed 1/0 to be defined such that 0(1/0)=1 then we would have to assume that since x/b = y and b*y=x then if we let b = 0 then x = 0(y) even if x were some number other than zero. The number system does not have a rule for this operation, if you use the existing rules it results in a contradiction.
Now, it is not really physically impossible nor is it physically possible to divide by zero. It is simply meaningless. The real number system, which is the environment where actual operations are performed, is an abstraction that does not exist anywhere except in our minds in the same way that there is no such thing as a “dog”, that is a set of three letters composed of two constants separated by a vowel which has learned tricks and eats dog food. There are no actual three letters that do tricks and eat dog food, only combinations of letters that we use to convey to one another a representation of such a creature. So it is the same way with the real number system. If we count two apples and one orange we are aware of three fruit, It does not matter how we choose to divide these fruit, there are still two apples and one orange.
Therefore a Division by zero in the real number system is simply an absurdity according to how our system for processing numbers has been defined and division by zero in physical reality is also meaningless because we do not perform any mathematical operations on the material world anyway.
You may be thinking, I perform mathematical operations, I count beans, if I miscount the beans then I must either add beans or subtract beans until the count is correct. OK then, you count beans, you add beans, you subtract beans. But the beans don’t care. If you count the beans wrong, then count them wrong again, and keep counting them wrong, the beans are unaffected. The number of beans that are out there does not change as a result of your count. You could get fired from your bean counting job and the beans won’t miss you. If they can’t find a new bean counter to replace you, the beans will still be beans and are not affected by whether they get counted or not.
Even if you correctly guess the spin of a photon, it doesn’t mean you cannot correctly guess the position of the photon. You knowing the angular velocity and the position of the photon are not physically mutually exclusive. Your measurement of its position screwed up your ability to know its velocity because your system of measurement is inadequate. You are not changing the photon by cognate recognition but rather by physical scale limitations. This is no major revelation and the same could be said of performing any mathematical operation in the physical universe. Not only is division by 0 physically meaningless but so is multiplication and division by 10.