Is speed of time c, atleast for someone travelling at speed of light?

[aaryan0077]

Okay, I know there are many threads about this and I checked some
like
https://www.physicsforums.com/showthread.php?t=38157" and some more, but I don't found what I was looking for.
Okay, let say we have a light cone http://img7.yfrog.com/img7/6463/lightcone3.jpg
Where Vertical and horizontal axis representing time and space respectively
and L1, L2 & L3 represent path allowed for massive bodies, light and path not allowed respectively.
We travel at a speed that relates to path L1.
If we are stationary we'll just go through time, but no space.
Now, let's say we start to increase speed and time starts to dilates.
The more speed the more dilation.
At speed of light (which I know to reach is not possible atleast until we have much more advance technology) time ceases.
Why?
Because equations shows it.
But what if we look at it in a different way? Time ceases because we are traveling at the rate at which time changes..
So, as we are also changing at the same rate, the time doesn't change according to our perspective.
Does this means that time travels at speed of light?

 

[malawi_glenn]

define "speed of time"

 

[aaryan0077]

define "speed of time"

Sorry, you replied too early, and it's not your fault but mine.
I pressed enter just after typing first line, (and you thought it's the whole question).
I had to edit the post. Now, look its a bit different from what you'd seen earlier.

 

[A.T.]

At speed of light (which I know to reach is not possible atleast until we have much more advance technology) time ceases.
Why?
Because equations shows it.
But what if we look at it in a different way? Time ceases because we are traveling at the rate at which time changes...

That is the idea that everything advances trough space-(proper)time at c. And the speed in space and in proper-time(aging) are just the projections of that advancement. Visualized here:
http://www.adamtoons.de/physics/relativity.swf

So, as we are also changing at the same rate, the time doesn't change according to our perspective.

No, according to our perspective, we are never moving and time always runs normally. You are very confusing by using "we" as the observer and the moving object. And you never say which time you mean: clock stationary to observer(coordinate time) or moving with the observed object (objects proper time). But I guess you mean the above mentioned geometrical interpretation of the relationship:

(delta_coordinate_time * c)² = (delta_proper_time * c )² + delta_space²