If time has slowed down for one person and if other person who is observing an action done by person for whom time got slowed down then the action Which took place at a particular instant be observed by both observers at that same instant while time for both is not same? If we see things moving then we say that time is passing how far is it correct? If nothing literally nothing in universe is dynamic or moving then will the time exist?
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First, let me make it clear that time, like space is complex. The real component of both is the Galilean spacetime. The imaginary component is proportional to the Proper velocity. Their vector sum is the total magnitude. The ratio of imaginary to real components is the tangent of the phase angle that defines relative velocity, v = c sin(phase). When relative velocity ceases, both time and space return to their normal behaviors, because the cosine of 0 degrees is exactly 1, and 0 velocity IS 0 degrees. But time is a rate, and returning to normal does not change what has already transpired. The rate of time elapsed during motion is less than the rate of time while standing still. So the moving observer ages more slowly than the stationary observer.
Here is a geometric interpretation. While time is 3D symmetric under normal circumstances, it is asymmetric when relativistic velocity is involved. When we talk about amplitudes using the Lorentz Transform, we don't really care how many dimensions are involved. In fact, relativistic effects occur in only 1 direction, the one parallel to the velocity vector. Both the time coordinate and this one space coordinate (assuming we orient the coordinate axes so that the velocity vector is parallel to only 1 dimension) are affected the same way. So, I propose a model in which time is also 1 dimensional. This is an analogy, so it isn't a literal representation. But I think it makes the correct point.
So consider time to be a flux. The rate is constant everywhere. In this flux, we locate a window, starting perpendicular to the flux at zero relative velocity. From this starting position, the window tilts according to the angle defined by v = c sin(angle). The amount of flux that flows through the window is then proportional to the area of the window and the cosine of the tilt angle. At a full 90 degrees of rotation, the window is parallel to the flux, and none of it passes through the area. In our model, this corresponds to relative velocity of c, and the fact that time stops at that speed. The window represents any physical object. If time flux does not pass through it, no aging occurs.
Relative quantities do not care which component is changing, only that the difference between two states is changing. Same with relative rotation. If the window is held fixed in the moving observer's frame, the time stream is rotated away from perpendicular by relative velocity, v = c sin(tilt). In the extreme limit, the perfect suspended animation is possible. Because as we think of it, suspended animation is really just suspended consciousness. The body must still be maintained by the apparatus. In a cavity in which time is frozen electromagnetically (by hypercomplex engineering), there is no need for life support or cryogenic cooling or food or even air. Because when time stops, it freezes ALL physical processes. Nothing can decay, because decay takes time. No bacteria or virus can infect the person, because all chemical processes stop, and even if present, they do not grow. There is no metabolism, no heartbeat, no need for waste removal. And as soon as the switch is turned off, everything starts up exactly where it stopped. Hypothetically, the person inside would come out asking, "When does it start?"
To summarize, time is complex. Its phase angle is determined by relative velocity (at least its special relativity effects). Observers can only measure cosine projections of length. This is a misnomer, because the co-moving observer never detects a change resulting from a passing observer trying to take a measurement, which is always short. Time is exactly the same. Complex time is the same magnitude (rate) as always, but for the moving frame, the phase angle is no longer 0. Their time vector is complex, and they can only measure its real projection.
Here's the best part. Everybody knows that there is a unique Lorentz factor for every relative velocity. Even before they knew why, they had derived an empirical formula from experimental data. γ = 1/√(1-v²/c²). We recognize v/c as the sin(tilt). This means γ = 1/√(1-sin²(tilt)) = 1/cos(tilt) = sec(tilt). So when a moving frame projects an interval of length r onto a stationary frame (the reference observer), it projects r' = r cos(tilt). This is equivalent to r = r' sec(tilt) or r = γ r'. Same relationship is true for time, ct = γ ct'. Keep in mind that these are projections of invariant magnitude radii. Nothing shrinks. Just that we can't measure the imaginary phase. After all, it IS perpendicular to the real component that we can measure, but it cannot contribute anything to it as a result. Now, that's relativity for you!
