Exploring the Concept of Time as a Dimension in Physics

[tempwonderer]

I've often heard that time was considered a dimension, but I don't understand how this is possible as it invalidates the idea of motion. Take a simple number line for example. This is considered the first dimension. A point can be at any place on said number line. Moving on up to the second dimension, we have two number lines criss-crossing. The third dimension is to be expected - three lines intersecting. Any person, object, molecule, etc... can be expected to reside in a set of points. Then time is said to be the fourth dimension. If one is willing to go so far as to extrapolate that the fourth dimension is four lines intersecting, then one can imagine time to be a line where each point holds the entirety of the infinite spectrum of the first three dimensions. However, once I get this far, I get stuck. I cannot figure out how motion can come into play. In order to move, one progresses both through time and through space. However, if one were to move along the number line of time, it would not necessitate the movement of any of the particles of the previous three dimensions. Not only that, saying that time is a dimension would mean that everything is pre-ordained: the points that you will occupy, and the neurons that will fire in your brain have already been decided, and we merely move along in pre-determined manner. This is due to the fact that in each point in time, the universe is in a different place than it was before. If one looks at time as a number line, then, assuming zero is the present, there are both points forward and backwards that have the entirety of the previous three dimensions in slightly altered positions. Thus, the points that you are going to occupy can be seen if you are able to jump to that point in time. I have heard theories that we exist in between the dimensions three and four, and that time is a ray rather than a line, but I still come up against problem of how the objects inside of time are capable of movement. And one can't simply say that time is relative because it isn't, at least not unless you're going at different speeds. Therefore, time must be something beyond a dimension. I'm sorry for making this so large, but I wanted to put everything I could down.

 

[tempwonderer]

Also, when considered with other aspects of relativity, wouldn't time more easily be understood as a perception of the infiniteness of space (for example, as one goes faster, the points separate [meaning that moving objects gain mass, or points] and the distance between places in the universe decreases (fewer points in between) because the time of the universe is slower than the time of the traveler [Note: this would fit in with time dilation, at least as I understand it]). I'm really sorry for asking such convoluted questions and I hope that you all can answer them. Please forgive me if I sound somewhat like a novice: I am.

 

[Fredrik]

You should start by considering one dimension of time along with one dimension of space, since you'll be able to visualize that. You can draw a diagram with the time coordinate t increasing in the up direction and the spatial coordinate x increasing in the right direction. Motion is represented by curves in this diagram. A point particle is a system such that its motion can be represented by only one curve. Since we're usually interested only in how different objects are moving relative to each other, rather than how the component parts of a single object are moving relative to each other, you can draw the motion of any object as if it was a point particle without losing anything important.

The motion of an object that's stationary at a fixed spatial coordinate is represented by a straight line parallel to the t axis. The motion of an object with constant coordinate velocity v is represented by a straight line with slope 1/v. The motion of an object that's accelerating is represented by a curve that isn't straight.

Nothing I have said so far has anything to do with relativity. This is a valid way to visualize motion in pre-relativistic physics too. Relativity enters the picture when you start thinking about what the fact that the speed of light is the same for all observers implies about what coordinates another observer would assign to the points in your diagram.

 

[tempwonderer]

The motion of an object that's stationary at a fixed spatial coordinate is represented by a straight line parallel to the t axis. The motion of an object with constant coordinate velocity v is represented by a straight line with slope 1/v. The motion of an object that's accelerating is represented by a curve that isn't straight.

Thanks. So you just apply the same theory to the time line. I guess that that works. One other question: if time is a flexible dimension (based on relativity), why aren't the other three dimensions flexible as well?

 

[Dale]

Hi tempwonderer, welcome to PF! I completely "second" Fredrik's response. Basically, the 4th dimension idea simply means that a "point" particle is a line in 4-dimensions.

Not only that, saying that time is a dimension would mean that everything is pre-ordained: the points that you will occupy, and the neurons that will fire in your brain have already been decided, and we merely move along in pre-determined manner.

This is already a feature of Newtonian mechanics, and is not due to relativity using time as a 4th dimension.

Thanks. So you just apply the same theory to the time line. I guess that that works. One other question: if time is a flexible dimension (based on relativity), why aren't the other three dimensions flexible as well?

They are. It's called time dilation for time and length contraction for the spatial dimensions.

 

[tempwonderer]

They are. It's called time dilation for time and length contraction for the spatial dimensions.

If spatial dimensions are flexible, then how do they vary when considering the first three dimensions alone? Isn't it only when time enters into the picture that length, width, and depth start to change? If so, then that would indicate that time was the variable rather than the spatial dimensions. Or am I totally misperceiving the point here?

 

[Dale]

I'm not really sure what you are asking. Time and space are related to each other via the Lorentz transform.