Simple spacetime interval question

[Eric_meyers]

Homework Statement

on a spacetime plot (y-axis) = t (x-axis) = x find the spacetime interval between points (0,0) and (300,700)

Homework Equations

Interval = (c^2(del t)^2 - (del r)^2)^1/2

The Attempt at a Solution

So I can see clearly my del t is 700 (700 - 0 = 700 ) but for the change in r I'm sort of confused about, I'm taking r to be ((700-0)^2 + (300-0)^2)1/2 = 761.577 and thus my spacetime interval number comes out to be 2.1 * 10^11 but I'm unsure if I did the change in r correctly and I'm also not sure what the unit of this number is if it has a unit?

 

[vela]

The variable r is the spatial distance between the two events, so in this problem, it's equal to x.

 

[Eric_meyers]

The unit works out to be in meters but my axis's are both in seconds.. I don't quite understand how this can be resolved or what this interval is even telling me.

 

[vela]

You're not using the regular SI units. If you did, time would be measured in seconds, and ct would be in meters, as would be r, so the interval would also be in meters. But it's often convenient to use units where c=1. In this system, time and distance have the same units, usually meters, but you seem to have converted everything to seconds. Think of c as a conversion factor. It tells you 1 second is equal to $3.0\times 10^8$ meters.

The interval is essentially the distance between two points in spacetime. It's an invariant, meaning that all inertial observers will calculate the same value for the interval between two events, regardless of their relative velocities.

 

[Eric_meyers]

oh so my spacetime interval would then be (700^2-300^2)^1/2 = 632.455 seconds, taking c = 1

Thanks.