Space & Time Axes Coinciding: Consequences Explored

[Avi Nandi]

Let's consider two inertial frame S and S'. S' moves with speed v w.r.t S along x-axis towards the right. Now we can draw the two co-ordinates system.

The t' axes will make an angle arctan(v/c) with t axes rotated towards x-axis and similarly the x' axis will be tilted towards the t axes making the same angle with x axis. Now for a inertial frame moving with a velocity tending towards c , the t' and the x' axes will tend to coincide with each other.

What will be its physical consequence if they coincide?

 

[Dale]

There is no physical consequence whatsoever to using any coordinate transform.

The mathematical consequence however is that you no longer have a valid coordinate system. All coordinate charts must be a 1 to 1 mapping between events and points in R4.

 

[Ibix]

You can't describe a frame traveling at the speed of light. So such axes do not exist.

 

[robphy]

Indeed, while there might a sequence of Lorentz transformations that approach the suggested result,
there is no such Lorentz transformation that obtains that result...
...since Lorentz transformations are invertible,
...since Lorentz transformations preserve the causal character of the timelike axis and of the spacelike axis.

In other words, no matter how close one gets to the suggested result,
there is a reference frame where those axes are back in the standard configuration.

So, as stated above by others, it can't happen.. those axes cannot coincide.