What is the fourth-dimension in time and space?How its existence could be proved?

The answer really depends on whether you are asking from a scientific, metaphysical or spiritual perspective. Though from the way you worded your question, I assume your asking about the 4th dimension in terms of physics.

In that sense, the 4th dimension IS time. It's not the time we see on the clock necessarily, but time itself, in it's natural essence. As far as proving it exists, the only way to do that would be to prove the "theory of mind", which you can do all day for yourself, but you can never do for another person.

If you can prove that theory of mind is correct, then you can prove that the 4th dimension (time) truly exists.

Your answer gets support from Wikipedia,but not by physics. 'Time' as far as I understand,has hardly to do anything.

That is conceived out of definitions of existing three dimensions. I find no conceptual or mathematical relevance between the two. 'Time' is a factor that relegates to a process of aging of a chemical reaction or a like happening.

I suppose,as no proper categorisation has so far been found out to pin down the 'Time' into,hence it is heaped into head of chapter of dimensions, just for literary satisfactions.

A state of things to be categorized as 4th Dimension,must bear a direct relevance of it,to a three D surface,across a perpendicular upon it,enable it to encompass a space out of reach of space cover able by mother surface,a set of things not remaining inconsistent to each other,so that a mathematical resonance and interrelationship could be found out,to establish.

So far as it relates to theories of mind,i would like to submit that.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.