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

AI Thread Summary
In special relativity, time is expressed as ct rather than t to maintain dimensional consistency, as ct is measured in units of distance. This formulation allows for the invariant spacetime interval, which is crucial for understanding the relationship between time and space. Using ct also enhances the symmetry of the Lorentz Transformation equations, facilitating calculations in relativistic physics. The conversion factor c is essential when different units for time and space are used, ensuring proper addition of measurements. Overall, representing time as ct helps unify the concepts of space and time in the framework of spacetime.
rgtr
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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
 
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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.
 
Thanks that makes sense.
 
rgtr said:
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:
$$ct' = \gamma(ct - \frac v c x), \ x' = \gamma(x - \frac v c (ct))$$
 
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