Spacetime, Time Travel and Dilation, Relativity

What is Spacetime? How is it different from the normal time on earth? What is time dilation, and how can we use it to time travel to the future, and how can we achieve it? What does the general theory of relativity state?

So.. earlier, it was all going good... The people then thought that time was flat, as it passes evenly through a place. But then the world came across a guy called Albert Einstein, who ruined it all. He said that the time was curved...
He said that time was relative. He called this the theory of relativity, which established a connection between space and time. He thought of an idea in which fabric permeates the whole universe...The Space Time.
Space time is curved, not flat, and it can be bent and twisted out of it's form by matter and energy, and that's where this picture comes in.

Notice the grid below the planet(or whatever that is). Well, that is time.The force of gravity and the matter of the planet bends the time around it.
GRAVITATIONAL TIME DILATION
As in the figure above, gravity interferes with time. It stretches or slows down the time. This is called gravitational time dilation. Here's what we can use for time travel.
We can somehow manage to build a spacecraft to go to some extremely massive planet(say, the black hole). Once we reach there, we have started time travelling. The time there runs slow, very much slower than it runs on the earth. So, let's say I spent few days near black hole. Assume that you are on earth that same time period. But, for you years would have passed away. When I return earth, I would be a lot younger than you as compared to the same when I was bidding you goodbye and getting into the space-ship(or rather, the black-hole ship). This is not experimentally proven yet, as nothing comes out of black hole or anything of such huge mass.

Below is a famous statement showing the effect of gravity on spacetime.

"Imagine the Earth as if it were immersed in honey," Gravity Probe B's principal investigator Francis Everitt, of Stanford University, said in a statement.

"As the planet rotates, the honey around it would swirl, and it's the same with space and time. GP-B confirmed two of the most profound predictions of Einstein's universe, having far-reaching implications across astrophysics research."

The 'honey' here is the spacetime. 

I'll now mention that the exact same prediction was made by Albert Einstein. Great he was, wasn't he?

Einstein indeed changed our point of view towards gravity. 

As a matter of fact, relativity is explains the source of gravity.

You can see the matter of the earth bending the spacetime blue and white in color. This pulls our moon towards the earth, proving gravity.
In case of Black Hole, the hole is deeper, and wider and hence more gravity. So, the theory of relativity and the spacetime explain gravity 

VELOCITY TIME DILATION
According to this, if I travel extremely fast, let's say somewhere near the speed of light, then I have time-traveled to the future, much the same way as in the previous paragraph. The things move slow when they are moving at the speed of light. This is done by nature to check that nothing goes faster than light, not even time. This has even been proved experimentally. The proof is below:
The scientists had sent an atom clock(a clock which measures super-accurate time, works on atomic principles) to the international space station( it travels at 5 miles per second, not even close to speed of light, but still quite fast), and meanwhile kept another atom clock back here on earth. When the space atom clock was brought down back to the earth, It had 'time traveled' by 0.1 seconds.
Hence Proved.
This is the reason the NASA-people say that the astronauts had aged less than us who stayed back on earth.
Yes, they indeed did time travel.
Now, you might be thinking WHY time slows down for objects travelling very fast.
The answer is 'the Theory of Relativity'

The Theory Of Relativity

Yeah, the theory for which Einstein got really famous.
In 1905, Albert Einstein determined that the laws of physics are the same for all non-accelerating observers, and that the speed of light in a vacuum was independent of the motion of all observers. This was the theory of special relativity. It introduced a new framework for all of physics and proposed new concepts of space and time. This means that nature slows down time for things moving at high speed.
Now think of it this way,
If you're travelling at a speed of 2 x 10^8 m/s, then the speed of light with respect to you should be just 10^8 m/s. But, the nature wants that the speed of light according to you should be 3 x 10^8 m/s.
Now how will nature do that?
Answer: By slowing down time for you.
A high speed moving watch runs slowly as compared to a relatively stationary watch.

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