The Fabric of Spacetime!

Everything travels at the speed of light through spacetime😲.

Spacetime is something where you can’t not travel! ‘Travel’, in physics, is defined as movement in space as well as in time. If I sit in a place, I will still travel through time. If space around us is considered as 3-Dimensional, time can be thought of as the 4th dimension.

By now we know that time dilates. ‘The faster you go, the slower your clock runs’. Let’s define two times: 1. Proper time: what your clock reads, 2. Coordinate time: what a stationary clock reads. Imagine coordinate time as reference for now. If you are stationary, your proper time matches with coordinate time. If you speed up, your proper time is slower than coordinate time. If you speed up to ‘c’, your proper time stops (=0 seconds).

Mathematically, $t_p = t_c\sqrt{1-v^2/c^2}$, where $t_p$ is proper time and $t_c$ is coordinate time, $v$ is your speed.

Our speed through spacetime is constant, and is equal to the speed of light. So, the faster you travel through the space-axes, the slower you travel through the time-axis. Stay with me. Time and space have different units (seconds and metres), so how do we add a ‘seconds’ dimension to a ‘metres’ dimension? We convert time into equivalent ‘metres’ by multiplying it with ‘c’.

To simplify everything, let’s think of space as 1D, and let’s add time to our 1D space as the 2nd dimension. Let’s now try to get comfortable with our new time which is measured in ‘metres’. 1 second of time corresponds to ‘c’ metres of the new time (1s = ‘c’ m). That is, if you sit in a place for 1s, your clock ticked once, and you travelled ‘c’ metres on the time axis of spacetime, without doing anything. Your speed is the distance travelled/coordinate time, so your speed is 0m/s in this case. Hence, for example, if you travel with 0.6c m/s in the 1D space for 1s of coordinate time (as per a stationary clock), then you have travelled 0.6c metres in space and 0.8c metres in proper time (that is 0.8 seconds in proper time). The 0.8c proper time arrives from the fact that you have to travel ‘c’ metres in spacetime in 1s of coordinate time! ($\sqrt{(0.6c)^2+(0.8c)^2}$)

That’s a whopping ‘c’ m/s of speed! Essentially, you are lightning fast in spacetime⚡!

Note that proper time cannot be negative. That is the arrows in the above spacetime cannot point leftwards.

💡Fun Fact – One step of ‘c’ metres in this spacetime corresponds to 1s of coordinate time. One has to keep hopping ‘c’ metres per second in this spacetime!