[quote]LIFTICVSMAXIMVS wrote:
pat36 wrote:
Interesting! Good stuff. I am learning something new. Do the lines intersect and at what point do that intersect? I want to understand the problem from the physics point of view. The fact that both are equally divisible, does one cancel the other out. I don’t know that I am understanding it completely.
Its not that they cancel each other out specifically, but imagine that when going from A to B in space you are also traveling from A’ to B’ in time as well. When you pass the half-way mark in space, you have also passed the half way mark in time.
Constraints of travel tell you that at a certain point the mid-points of both segments will be smaller than the velocity of travel, thus you have arrived at your destination.
Another paradox that arises is when do you know you have arrived at your destination? If we define that location as point B what does that imply? A point is no more an accurate description of space than a line. A point is dimensionless so where in space is it?
Imagine flying home from some location. When can you say you have arrived home; when the plane touches down, when it stops, or when you walk through the door of your house? You see, location is a very abstract description.
Another way of looking at it: Think of space and time as a continuum–which it is. The simplest way I can describe it is in a 2-dimensional coordinate plane. On this plane we can draw a continuous curve (“curve” is just a generic term to mean any line). As long as the curve remains defined–that is, continuous and differentiable, we have a representation of motion.
If the curve is straight we have unaccelerated motion. If the line is horizontal it represents 0 velocity and hence no motion yet time continues to pass (assuming time is represented by the horizontal axis). If the line is vertical it is undefined and represents infinite velocity. This is not allowed because the speed of light is the fastest any particle can travel.
This vertical line is what Xeno’s paradox is represented by–infinite, instantaneous motion. If time does not pass how can one travel from point A to B?
BTW, velocity would be represented by the slope of the first time derivative with respect to x.
So, to answer your question, yes, time and space do intersect but in a very abstract way…since space is 3-dimensional how do we represent the 4th dimension, time, orthogonally to the x, y, z axes? You can see why people have a hard time contemplating the nature of space-time.
Physicists who study elementary particles, like me, do not differentiate between the two because it allows us to describe systems using momentum and energy.
Here is a wiki link to a space-time description which probably does a better job explaining it that I can:
http://en.wikipedia.org/wiki/Spacetime[/quote]
Thanks for the info. I will futhur investigate it, but not right now. I am beat and half hammered right now, and after a difficult past 6 months, I may just take a break. But I do want to understand it as you do, so I will pursue it. Maybe tommorow maybe the next day, who knows. But I may ask you more questions, if you don’t mind.