Why is time = ct and not t in special relativty?

[rgtr]

Homework Statement

Why is time = ct and not t in special relativty?

Relevant Equations

Why is time = ct and not t in special relativty?

Why is time = ct and not t in special relativity?

I just started reading the book I was recommended. Maybe I missed it but as stated in the title why is time = ct and not t in special relativity?
I understand they want distance/space = time. Just how do they go about doing that mathematically and conceptually.

Link to the book.

Spacetime Physics
https://www.eftaylor.com/download.html#special_relativity

 

[mfb]

c is just a conversion factor to account that we use different units for time and space in everyday life. We can drop it (and we routinely do in particle physics) if we use the same units for both. That means a meter is 3.3 nanoseconds "long", or alternatively a nanosecond is 30 centimeters. If you want to use different units then you need c as conversion factor because you can't add a second to a meter directly.

 

[rgtr]

Thanks that makes sense.

 

[PeroK]

Homework Statement:: Why is time = ct and not t in special relativty?
Relevant Equations:: Why is time = ct and not t in special relativty?

Why is time = ct and not t in special relativity?

I wouldn't say that $ct$ is "time". Either $ct$ or $t$ can be taken as the zeroth coordinate for an event in spacetime. There are, however, some good reasons for using $(ct, x, y, z)$

1) This establishes dimensional consistency of the position vector, as $ct$ is measured in units of distance.

2) The invariant spacetime interval is $c^2\Delta t^2 - \Delta x^2 - \Delta y^2 - \Delta z^2$

3) It makes the Lorentz Transformation more symmetrical:
$$ct' = \gamma(ct - \frac v c x), \ x' = \gamma(x - \frac v c (ct))$$