Doubt in time travel?

A rocket cannot travel at the speed of light! At the speed of light, time passage stops for matter. In contrast, the mass of the rocket becomes infinite at the speed of light, and it cannot be accelerated. The rocket is smaller than the Earth and the Universe, so what do you think is true? Your question concerns impossibilities, so there is no real answer.

Note: Since anything with mass can't move "at light speed", I'll be assuming "near light speed" instead.

"So, how can we be sure which one happens??"

Actually, both happen!

To understand why this isn't self-contradictory, you need to consider the following fact:

Two events that happen simultaneously to one observer, may not happen simultaneously to another observer. (See source)

Let's use your rocket as an example:

Someone on Earth notices that 10 hours after the rocket leaves Earth, the following events happen at the same time:

A) 10 hours have passed on Earth.

B) 1 hour has passed in the rocket.

However, to someone in the rocket, those event do not occur at the same time. While event B occurs after 1 hour, event A doesn't occur until 100 hours have passed in the rocket.

So the fact that both clocks run slower than the other (depending on the observer), isn't self-contradictory if you also consider the relativity of simultaneity.

Let's put some numbers to this.

Let us say the rocket travels to a point 50 ly away. Let us say we want this to take about 1 year ship time, round trip (discounting exploring while there).

So I get a speed of 0.999955634c.

So the ship arrives 50 ly away, having traveled (with measurements made while moving) just under 1/2 light year in 1/2 year ship's time. Signals from Earth are just now arriving from about a day after departure. It looks like the Earth's clocks ran slower. (At least until the return trip, when 100 years appear to pass, 50 enroute to the destination anyway, plus the other ~50 years travel time as measured on Earth's clock. Note that the Earth sees the ship depart the distant point about 0.8 days before it shows up here.)

"So, how can we be sure which one happens??"

Which one had the whole Universe moving for the duration of the trip, and which one had just the ship moving? That is how you know "what really happens". Detecting acceleration is nice, but not really required to show time dilation.

The reference point is where the observer is. But the observer in the rocket feels the acceleration and knows she or he is moving.

Time dilation is real... it was demonstrated around 1960 by some HP (now Agilent) engineers who took an atomic clock around the world on a 707 (Pan Am had "around the world" flights back then). The clock that flew "lost time" or was slow compared the the one that stayed in the lab in Palo Alto back then. The same effect has to be compensated in the GPS satellite navigation system as well.

It's not actually the speed that makes time slow down and mass increase for the ship. It's the acceleration that was put into it to get it to that speed. A spaceship traveling fast enough that time runs at 1/2 the normal rate as measure by an outside observer who's standing still also has twice the mass. That mass comes from the energy imparted to the ship by the acceleration needed to get it to that speed.

Well bring this problem into real life. Suppose two people are standing next to each other. suddenly one of them runs away from the other. now what would you say has happened. only an idiot would say that one of them has magically slided away from the other (who has assumed a running position).

This is the simple line between perception and action.

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Interesting point but in your example the earth didn't move at light speed, whereas the rocket did and thus brought into equation the issue of time. Your point is irrelevant.

It is maths tells about photons for future! It is just information! Accelerators can do it.