Derek Zeng

A programmer

A brief history of time - my understanding of spacetime

I've been thinking this for a long 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 in a space we are interested in. 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 reasonable. 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, prior to reading the book "a brief history of time" by Stephen Hawking.

After I read the book, I happily realize that my naive idea is actually at least partially correct.

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, since you are standing on a moving 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 front photons is actually greater than that when the train is stationary.

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 in 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 actually 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.

Knowing all this now clears a lot of doubts I had before. We always talk about time travel. Theoretically, we can travel to the future by taking a rocket flying at speed close to light. But there are some problems.

  1. our body won't be able to withstand the space distortion brought by the high-speed spaceship.
  2. we won't be able to travel to the past.

When we can solve the first problem, we can expect to travel farther to the deep space by leveraging on space warping, just like the Enterprise spaceship in the Star Trek.

(End of article)