What provoked “imaginary time”?

[Prof Stephen Hawking - his imaginary time in Prof. Richard Feynman’s sum over histories - quantum Mechanics & definite measurements]

i. Smearing of position (impossibility of pinpointing space coordinates) when mass contracts beyond the quantum mechanical level into the dimensions of a singularity.

ii. Richard Feynman’s sum over histories for a particle - the world line of particles present insurmountable difficulties when summation is done over real-time. However, such summation is possible it is done over imaginary time.

iii. What is there in the probability distribution in the sum over histories or the world line of a particle that it makes it possible to do the sum over in “imaginary time” ?

iv. Was there anything in the equations of sum over histories that itself suggested to Prof. Stephen Hawking and Jim Hartle to have the idea of imaginary time?

v. How did they do the exercise of sum over histories using imaginary time particularly when all the particles under examination are squeezed into a position of near infinite density?

vi. Is it nor possible in quantum mechanics to create two identical experiments where in one case, attention is focused on the position of a particle rather than the velocity and in the other the velocity of the particle rather than the position? Thereby, if this suggestion is feasible, if not in the same situation, at least for two identical situations of the same kind of particle, say of an electron, you can get definite measurements of the position and velocity of the particle - or to be precise similar particles in identical situations if not most desirably the in same situation.

vii. If Real-time (time as we normally understand plus that which is connoted in the General Theory of Relativity) may be associated with periodic and/ or oscillatory motion, what kind of motion imaginary time may be associated with? Does any such association really exist? Is imaginary time only a mathematical trick coming with diagrammatic representation using imaginary numbers ?

(Ack: Ms. Dimple Tyagi in typing out, editing and formatting; responsibility of errors are however mine)