Time spaced out & Space times in: My impressions

1. According to the singularity theorems of Prof. Roger Penrose and Stephen Hawking, any stellar body of a mass more than that of two suns collapses to a singularity - unless it manages to throw off enough mass in a supernova explosion that its mass falls below that of the cut off limit of two solar masses.

2. Although the General theory of Relativity deals with structures on the very big scale and Quantum Mechanics consider things in the scale of very tiny and these two great theories do not reconcile in any normally occurring body or structure of the universe;

3. The singularity theorems underline the fact that matter can be squeezed to dimensions where their Quantum Mechanical properties cannot be ignored.

4. In fact, in a way, the high curvature of space-time produced by highly compressed matter, brought about by gravitational collapse brings the quantum mechanical properties of all that matter out to the fore so much so that it overshadows space-time and ends the histories of all particles in real time.

5. As formulated in the theories and principles of quantum mechanics beneath a certain length- which is lower than the wavelength of light e.g. gamma rays, it is difficult or rather impossible to determine both the position and velocity of a particle with any arbitrary accuracy.

6. Time dimension is a derivative of the space dimensions: time is measured by diurnal motion of the earth, annual motion of the earth around the sun, motion of the sun as round the galactic centre or the oscillations of a cesium atom in an atomic clock i.e. different kinds o periodic motion
7. When matter gets highly condensed on account of gravitational collapse- say in a black hole or in baby universe as was during the one second after the ‘big bang’, its position becomes highly certain but even the velocity of a photon may a fluctuate wildly in a quantum mechanical way, off the known velocity of light.

8. In such circumstances, it would be very difficult to measure with arbitrary accuracy the periodic motion of any particle in condensed mass clutter in a singularity. In other words, it would be very difficult to say with certainty the positions of a particle whose periodic motion so long rendered a time- keeping service. Chronology of particle positions would become meaningless, as it would be impossible to fix with any arbitrary accuracy, positions of a time keeping particle for labeling their position as past, present and future, if the velocities are very certain for such particles. Time, as we understand, ceases to exist in such a situation.

9. Anybody trying to correlate spatial positions of a time keeping particle -i.e. its chronological positions within a periodic motion- with the spatial positions of any other particle (without a recurring motion) will find the task practically impossible;

10. here will be no past or present against which the chronology of other particles’ positions may be labelled, it would be only positions correlated with positions without any consideration of chronology.

11. This above situation may be called “time getting spaced out” in black - hole condensation or if the reverse process of inflationary expansion after big bang is concerned, “space timing in” –where getting free from the quantum mechanical prison of indetermination, one can detect and measure stellar periodic motion.

12. When the histories/ world line of a particle(s) ends in real-time after entering the event horizon of a black hole, it is still possible for an observer outside that singularity to compute the histories of the particles converging into the black hole in real or imaginary time as the situation permits.

13. However, when an universe comes out of a worm hole or ends up in it (call it big bang or big crunch) nobody can measure the histories/ world lines of its constituent mass of particles proximate to either of the boundaries (i.e. big bang or big crunch) be it real - time or imaginary time.

14. From it comes out the further question: is it possible for an observer in another universe to calculate the sum over histories of our universe in imaginary time or for us to do the same for another universe?

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

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)