Space and Time

Space and Time. I think these are the terms we use the most in our everyday life, but we understand the least what it actually means. We, generally, think that space indicates the location or place of the events or incidents, and that time represents the changes in events. Our perception of space and time is absolute, independent and linear. In reality, both space and time are relative, interdependent and non-linear. In order to understand this, let us go back in history.

In Aristotelian physics, there is a notion of Euclidean 3-Space E^3 to represent physical space. In fact, this three dimensional physical space provides the absolute universal space within which events and incidents take place. Here we mean by the absolute universal space is that the space is static. For example, point (1,0,1) at one moment will represent the same point at another moment. Therefore, the space is independent of the time. In Aristotelian scheme, the absolute time is also represented by 1 dimensional Space E, which is independent of the space. With this framework, it is appropriate to think of space-time as the product of A = E (time) x E^3 (space). In fact, Aristotelian notion agrees with our common sense, although it does not reflect the reality.

However, Galileo did not accept the notion of absolute space. He argued that although the Earth seems relatively static to us, it is, in fact, in motion. Therefore, one point on the surface of the Earth at one moment is totally different from the same point at another moment. In addition, he argued that we cannot define the absolute point in space since everything is in motion. For example, the location of the Earth in the Solar System is relative to the Sun, the location of which is in fact relative to our Milky Way Galaxy. Although Galileo did not accept the notion of absolute space, he still agreed with the notion of absolute time. Therefore, in Galilean physics, the space is changing according to the absolute time. In order words, the space is the function of time:

G = E^3 (E)

It was Newton who extended the ideas of Galileo. He once stated, "If I have seen further it is by standing on the shoulders of giants," whom he meant by Galileo and Kepler. In fact, Newton's notion of space and time is very much similar to that of Galileo. By his first law, Newton introduced the notion of inertial frame of reference. Before elaborating on the Newton's first law, let us think about how we perceive motions of objects in the space in motion. In fact, Newton solved this problem by introducing the notion of uniform motion. Regardless of the space in motion, when an object is in uniform motion, it has an inertial frame of reference (the absolute space) on its own.

For example, let us imagine ourselves inside a big box, which is in uniform motion. We cannot see or know what is going on outside the box. As long as the box is in uniform motion, it will provide us the absolute space on its own.

Newton's second law explains what happen when the object are not in uniform motion. When an object is not uniform motion, its inertial frame of reference (the absolute space) will be distorted in accordance with its acceleration.

In fact, Newton's notion of space and time is the same as Galileo's notion of space and time. The only difference is Newton used the bottom-up notion of space and time. He defined the space locally, instead of defining the global picture of everything in motion. In Newtonian physics, the space is absolute when it is in uniform motion, but it is relative when it is not. However, like Galileo, Newton still accepted the notion of absolute time.

In addition to his famous Universal Law of Gravitation, Newton's another major contribution is the Calculus. In fact, calculus provides the systematic study of the rate of change, which later affects the meaning of time (the absolute time). The only reason why the rate of change is so important is because everything is changing.

In reality, we cannot perceive the time. What we can perceive is the change. We can only discerns how fast or how slow the things change. So, if there were no change at all, we would not perceive the time at all.

Rate of change is essential because it relates the space and time by a very simple equation:

Rate of Change = Change in Space / Change in Time.

Although very simple, rate of change is , in fact, very difficult to understand. (I think whoever took the Calculus course will agree with me :P ).

With absolute time notion, rate of change is very simple to understand. Faster rate means, bigger changes in space and slower rate means smaller changes in space as change in time is always equal. But what if the change in time is not equal?

Actually, we held the notion of absolute time, until we encountered the speed of light. The speed of light in fact gave a lot of headache to the physicists. Before discussing about the speed of light, let us think about two frames of references which are relative in motion.

Let us imagine we are inside a big glass box in uniform motion. Since it is the glass box, we can see what is going on outside the box. There is another glass box which is also in uniform motion with different velocity. Inside that box, a tennis ball is moving up and down and a person is standing and watching the ball. For that person, the trajectory of the tennis ball is straight as the ball is moving vertically up and down. Regardless of the velocity of the glass box, the person will say that the ball is moving in a straight line.

However, for us, who are in different inertial frame of reference with different velocity, we will not see that the tennis ball is moving in a straight line. The trajectory of the tennis ball, in fact, is a curve (more precisely a parabola) to us. It is because there is a relative motion between two frame of references. When we look at the events, which are in different inertial frame of reference, the space is distorted in accordance with the relative velocity between inertial frames. In fact, it is very obvious. When someone drops a stone from the moving car, we will see the stone does not fall in a straight line.

However, the speed of light is different. Observers from different inertial frame of references will measure the same speed of light even though there is a relative motion between different frame of references. The relative velocity does not affect the speed of light.

It was Einstein who first stated that the speed of light and the laws of physics will be the same in different inertial frames of reference. From this postulate, he developed the special theory of relativity. In fact, the special theory relativity reshape our perceptions of space and time.

Also, the speed of light defines the universal maximum constant rate of change. There are different rates of change in the universe, but none can exceed the rate of change of light.

c = rate of change of light = change in space / change in time = universal constant

When we look at the equation, we will see that for different change is space, the change in time has to be different in order to keep ratio constant. From this, we realize that there is no such thing as absolute time.

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