Re: Why must time be related to space?

Lee

A full answer to this requires a small book so I hope I will loose nothing by being brief. To help understand why time and space are related it helps to understand the history behind the concepts.

In our every day experience space is a simple three dimensional thing with height, width and depth (x,y,z) in cartesian coordinates. Time, t, is an abstract notion to explain when things happen. Essentially time is a seperate entity that just keeps going forward regardless of what we do and is unaffected by us. This is called, Absolute Time, and it assumes that Time is the same for all people, regardless of where they are or what they are doing (their frame of reference). Essentially Newtonian Physics is based on the notion of Absolute Time as it matches our everyday experiences. In the mid to late 1800's people started investigating light and asking silly questions like, what is Gravity, what is light. The end result of part of this was the discovery that the speed of light is constant for all observors, it is said to be invariant. To put another way, if you are travelling at the speed of light and measure something else travelling at the speed of light you would expect to measure its speed to be twice the speed of light. What you actually measure though is just the speed of light. This does not match our everyday experience and had to be explained.

A chap by the name Lorentz put forward a new idea that mathematically described why light speed is invariant. In this mathematics you have to assume that time can be measured differently for different observors. What matters is the speed, properly velocity, you are going at. This is done by assuming that Time is just another dimension like (x,y,z). So to actually measure something and describe what it is doing you have to write its coordinates as (x,y,z,gamma*ct), where c is the speed of light and t is time. Gamma is called the Lorentz Transform and has the following formulae,

gamma = sqrt (1-v²/c²)

When v is very near c gamma becomes large and starts affecting things. When v is much less than c gamma is small and can be ignored for all practical purposes. It is this idea that Einstein took and messed around with in Special Relativity. What he found was that how things look when travelling near light speeds will be different to observors not travelling at light speed. For example, the faster you move the slower time ticks as observed by an outsider. The length contracts and your mass increases, as measured by some one who is stationary. Light itself is unaffected by this as it has no mass and as such carries information about events happening. In a way light carries information about time.

Life though gets even more complicated when you start considering what happens when things start accelerating and take into account Gravity. In Einsteins General Theory of Relativity it is assumed that you can not tell the difference between acceleration and gravity. This leads to the idea that mass `bends' space which is the cause of Gravity. You can then fiddle with some maths and look at what happens to light passing through a Gravitional field. It is found that the path of a light ray is also bent by Gravity. Basically light always travels in straight lines but gravity bends the straight line, properly called a geodesic. The stronger the gravity the more pronounced the effect. If gravity is strong enough the Lorentz transform starts becoming important again.

So, what we see here is that time can be different for observors. Space can be affected by a mass which in turn affects light. As light carries information about time, space itself is affecting how we see time move for something. Put all this together and I hope you see that Space and Time are closely interlinked to each other. If you wish to know more I would recommend a good general book on Relativity. There are plenty about and should be stocked by your local Library. I can not really recommend any one over another, they all explain things slightly differently. A good online source on the basics can be found here.

These are very strange ideas and initially no one believed them. It contradicts everyday experience and common sense. A number of tests have been done that show that space-time is indeed as described by Einstein.