B Time & Speed of Light: Not a Universal Constant

[Shubh Goel]

TL;DR Summary

Assumption travelling at speed of light is possible.
1. We are in empty space. I am travelling backwards(I am facing the direction opposite to my direction of motion) at half the speed of light. My other friend is travelling in opposite direction with the same speed being backward. If i look in the direction of my friend, i will see him getting slower and slower as we move apart even though relative velocity between us is still the same.

Time as we perceive is not a universal constant. It depends on the speed of the bodies and the distance between them.

 

[Ibix]

Assumption traveling at speed of light is possible.

It isn't - it's prohibited by the postulates of relativity.

I am traveling backwards(I am facing the direction opposite to my direction of motion) at half the speed of light. My other friend is traveling in opposite direction with the same speed being backward.

Travelling at those speeds with respect to what? In what follows I'm assuming that you are specifying both speeds with respect to some common reference.

If i look in the direction of my friend, i will see him getting slower and slower as we move apart even though relative velocity between us is still the same.

No - you will always see him moving at constant velocity, 80% of the speed of light (in relativity velocities do not add the same way as they do in Newtonian physics). You will see his clocks ticking at a constant rate, albeit slower than your own.

Time as we perceive is not a universal constant. It depends on the speed of the bodies and the distance between them.

This depends a lot on what you mean by "time as we perceive it". Your own wristwatch, for example, will always tick at the same rate whatever your state of motion. Other people's watches may well tick at different rates as measured by you, but they would have the opposite opinion about whose watch is ticking normally and whose is ticking slowly.

Clock rates do not depend on distance, though. I suspect you have misunderstood something around the relativistic Doppler effect. It's fairly easy to show that you will see your friend's watch ticking at a constant rate of once every three seconds. The general formula for someone receding from you at speed $v$ is that their clock ticks once every $$\sqrt{\frac{c+v}{c-v}}$$seconds. If you correct for the increasing light travel time, you will calculate a tick rate of once every $(1-v^2/c^2)^{-1/2}$ seconds, which turns out to be once for every 1.67 ticks of your watch in your scenario. Neither of these formulae depend on the distance between you.

 

[PeterDonis]

The OP is based on a misunderstanding of relativity, which has been explained. Thread closed.