Derek Zeng

Loneliness is the gift of life

A brief history of time - my understanding of spacetime

I've been thinking about this for quite some time.

The very meaning of stopping time is to stop the movement of everything. Thus, the definition of time has to be relative to the positions of things. If you want to slow down the time, really all you need is just to slow down the speed things move. The "things" here refers is every single particle that constitutes the space. The particle specifically refers to the tiniest building block of matters. The space can be anything like a city or entire universe.

This idea sounds simple and logical. But there is one big problem, stopping everything requires "impractical amount of energy" that is out of human's imagination. So it just stays as my naive idea of time.

I didn't realize my naive idea is actually quite right until I read the book "a brief history of time" by Stephen Hawking.

Einstein's initial assertion is that the speed of light is constant, no matter where you measure it. It's the speed limit that anything in the universe must obey. The implication is subtle however.

First, added speed is bound by light speed too. Intuitively if you are walking in a train towards the locomotive. Your speed is faster than the train's speed as seen by a person outside of the train. But, the added speed may not be exactly the speed you feel because the added speed has a limit.

Second, if you shine light from the train. The light should form a sphere and spread out uniformly outwards. This is to obey the rule that no matter where you measure it, the speed of light should be the same. That is the distance travelled by any thread of photon per time unit must be the same. However, in the perspective of the person standing outside the train, the photons shot towards the back must leave the light source faster than those shot towards the front. This seems to be a contradiction. How can some photons leave the source faster while still maintaining the same speed of light?

You must marvel how imaginative Einstein was when he came up with the general theory of relativity. In the theory, he propose, the space is distorted/warped/folded in the front of the moving train. So that while the speed is the same for all directions, the spatial distance travelled for the photons towards back is actually longer than that travelled by photons toward front.

So Einstein thinks the space can be folded. The folding of the space depends on the mass of the object. The more mass it has, the more space is folded. His famous e=mc2 indicates that, when object moves, it gains mass. The faster it travels, the more mass it gains. The closer to speed of light, the closer of the mass to the infinity.

When the theory is applied to the cosmology, the stars has the ability to stretch the space. In the diagram above, the grid is initially uniform. Let's say it's a grid of squares with length 1. When the yellow star is put in the grid, the squares' length becomes more than 1 (curved and stretched). The closer the square to the star, the more stretched it becomes. The square is the space. Since the area is larger, it'll take more time to travel across the stretched squares than the non-stretched. This is consistent to the real life where the time past in space is slower than the time past in earth. So when the space is warped this way, it might be possible to jump across space of great distance.

It worths to note that, the speed of light is still constant no matter which square it is measured in. And since the light travels in space, the path can be affected by the curvature of spacetime.

Einstein showed that, there is no such thing called gravitational force. The gravity is manifestation of curvature of spacetime. The movement of planets is simply a straight line in the spacetime dimensions. We see them moving around a star because that's the shortest path it can move from a point to another.

The very meaning of relativity is that the time and space is relative to each other. The time measured in different space/location is thus different. If we have built a light-speed spaceship that travels to alpha centauri. We on earth have to wait for 4 years for it to reach there. However in the perspective of the pilot on the ship, he would think it's just a few seconds. But I think such spaceship is not possible, because human cannot withstand the acceleration to the light speed (think of huge amount gravity). Also the space will be squashed when it reaches light speed (mass would be close to infinity, so as the gravity), any massive things will be crashed into a singular object like blackhole.

When travelling at light speed, the time literally stops in the perspective of the traveller because all other thing is considered stopped (they are either slower or equally fast).

Knowing all this now clears a lot of doubts I had before.

We always talk about time travel. There is actually no 'time travel'. All we talked about is just go to a space with slower time in the perspective of human on earth, then come back after some short time, by then, maybe a few years had past on earth. Clearly this cannot be reversed.

(End of article)