I cannot prove that nothing exist by physical means. Mostly because your Existence is not physical either. This can only be done by conceptual means. That is to say that Existence is a conceptual entity.We can not say that nothing exists due to semantics and logic. To exist, there must be something to exist and obviously something is not nothing.
It is space-time, which is no more than a form of nothing. It is an extension of what we call mass, and that mass is also no more than a form of nothing.There is being and not-being. Being is the state of existing and having properties. Even empty space, a vacuum as empty as it can be made still has properties and energy and is, therefore, something and can be said to exist.
It is the form of nothing that exist, which gives rise to space-time."Nothing" cannot have any properties or energies, is not something, is a state of non-being rather than being, therefore cannot be said to exist.
I repeat - This is not a physical entity, but a conceptual ONE - ONE being the tree trunk of logic.
There is a necessary contradiction here. Suffice to say - I Exist because I don't Exist as the the absolute tool. Existence is no more than a geometric. It's sum total in the infinite sense is a complete definition of nothing. Not to say the definition is complete, but that the process will never be complete. Your Existence is ongoing, which is to be expected in space-time."Nothing" is; "nothing" is real; but, "nothing" does not, can not exist or be said to exist