An Explanation for Time Dilation

I. Introductions and Stuff.

A friend of mine posed a question to me: Why is it that at high velocities, time is affected? This is a phenomenon called Time Dilation, a very important component in the Theory of Relativity. So this got me thinking, and I believe I have arrived at a plausible explanation to this. Note that this phenomenon may have already been explained, but at the moment of writing, I am not aware of any such explanation, so I give my own.

Anyway, to all those who aren't too confident about their grasp of physics and/or mathematics, please don't let the topic scare you. I will try to explain my idea in the simplest way I can, so that everyone (hopefully) can understand.

The phenomenon of time dilation, simply put, is that when you travel inside a vehicle at very high speeds (presumably close to the speed of light), time slows down outside your vehicle (while time is normal to you inside your vehicle). Essentially, events occur much more slowly than they would if you were stationary.

The first idea that came to my mind to explain this phenomenon (I honestly hadn't thought about why time dilates. I've always just thought it was a given.) is what i call the highway analogy.

Imagine, if you will, a man walking on the sidewalk of a busy road. Cars zoom past him, all at the same speed. Naturally, you'd imagine that the cars coming towards him from ahead (i.e. backwards, assuming that the man is walking forward) would, to him, appear to be moving faster than the cars coming towards him from behind (i.e. forward in the same direction as the man). The faster the man walks, the cars moving backwards and forwards would appear to be moving even faster or more slowly, respectively.

If you apply this analogy in terms of photons (particles of light) moving, you sort of get the picture that whatever visual information coming from behind you would reach you much more slowly than whatever's coming from ahead, in a sort of vague version of the doppler effect.

But this model has a very glaring problem. If this model were correct, it'd mean that theoretically, at very high speeds, time would only slow down behind you, and speed up in front of you. Experimentally, this is incorrect. At high speeds, time slows down regardless of the direction relative to the moving observer.



II. Preliminary Explanations.

I believe I have found a way to sufficiently explain this phenomenon by modifying the highway analogy model. Thing is, it requires a 5th dimension to exist. I know it's hard to swallow, and I know it's tough on the imagination, but please bear with me.

For those of you who haven't read my entry about the big bang, I will explain again how dimensions work.

-Suppose you have a dot. It has zero dimensions. If you translate (move) it, you form a line, which has 1 dimension.
-Now suppose you translate the line. You end up with a two dimensional square.
-Translate the square, and you end up with a three dimensional cube.
-Translate the cube, and you come up with a moving cube, essentially a solid object in motion. Given that time (denoted by "t") is a component in the 4th dimension, you can say that any moving object is a 4 dimensional object. When we want to find the rate at which this object moves, we use the formula v = d/t, where v is velocity, d is the distance traveled, and t being the time elapsed. Because we're talking about 3d space, d is a function of the x, y, and z axes. Thus, we have a situation which involves x, y, z, and t. 4 dimensions.

Here is where it gets a little tricky, so we need to "simplify" a few things.

Let's call the "moving object" an Event. The rotation of a cube is an event. My fingers typing on this keyboard is an event. Anything involving an object moving is an event.

Now suppose we translate this Event. And so we have a fifth dimension, the axis of which I will denote as "w". To illustrate, we go back to the 4th dimension. As a translated cube is a moving cube, a translated event is an occurring event. The former can be described as the rate at which a cube moves, and the latter can be described as the rate at which an event occurs. (I hope this clarifies my choice of the word "occurring") Let's assume that the equation for finding this rate is R = e/w, where R is the rate at which the event happens, e is the event itself with x, y, z, and t components (in much the same way that d is made up of x, y, and z components) and w, being the 5th axis.

As a side-note, you can also say that the first dimension is contained within the second, and that the second is contained within the third, so on and so forth. The fourth dimension is contained within the fifth.

This may seem a bit confusing at first, but slow down and read again if you must. It isn't complicated at all.



III. Discussion Proper.

Let's go back to the highway analogy. Because the cars and the man are moving linearly in one direction, we can simplify things by assuming that they're moving solely along the x axis. This leaves the y and z axes "unoccupied", and thus unaffected by the "relativity" affecting the walking man. To the man, anything moving along the x axis is subject to relativity, because of the sole fact that he's moving. Anything moving in the same direction will be moving at an altered speed with respect to the walking man. This brings us back to the original flaw of this analogy.

If we use the 5-dimensional model, however, we solve this problem. Instead of using cars, we use events. In the highway analogy, we have a 4 dimensional scene where the 3 dimensional objects are moving along one axis at a rate determined by time (or spacetime), the dimension in which the entire scene is contained. In the 5-dimensional model, we have a 5 dimensional scene where 4 dimensional events are occurring along one axis at a rate determined by w. If we let the axis in which the events occur to be time, then we "free" up the other three dimensions defined by x, y, and z. This means that very high "speeds", time slows down regardless of the spatial direction.

Returning to the phenomenon wherein the high velocity of a moving observer slows down time (because the relationship between the moving observer and the 5-dimensional model is still a bit disconnected): I believe that this relationship is best described mathematically. (don't worry, nothing overly complex).

Let
v = d/t or the rate at which the object moves
R = e/w or the rate at which an event occurs
d contains x,y,z components
e contains x,y,z,t components

Given that d remains constant, at very high v's, t becomes very small.
Because e contains x,y,z and t components, a smaller t indicates a smaller value for e.
Given that w remains constant, at low values of e, R becomes small.

Therefore, R, the rate at which an event occurs, decreases.

And so, we arrive at the conclusion that the higher the velocity, the slower the rate at which events occur, and so the slower time will appear relative to the observer moving at said velocity.