Question

Why 'time' is a dimension?

Answer 1

Because it is not along any of the other dimensions

Answer 2

technically, AFAIK, a dimension is something that is required in order to locate a position in a given space. you know, things like (x,y) or (r, Ø) in 2-D space. you can have (x,y,z) in 3d, or latitude, longitude, elevation as we specify locations on the surface of and above the earth.

in that sense, i am not sure that time would have counted as a dimension under the old understanding. time was originally understood to be immutable - time marched on constantly at the same rate wherever you might be located and whatever you might be doing.

on the other hand, it had been understood that the x,y,z dimensions were purely relative - ever since Galileo, we have realised that there is no real absolute position and hence things like velocity are relative too

however, special relativity changed all that. now we have the idea that s^2 = x^2 + y^2 + z^2 - (ct)^2.

the time side of things in this equation is effectively an imaginary number - and so ct is somewhat different in nature from the other 'dimensions' in spacetime - but it is still part of maths used to define an event. so i think that, in this sense, time is now very much a displacement idea and a dimension.

one of the really important new ideas is that time is not absolute. it seems that time is tied into the second law of thermodynamics, inasmuch as that is what seems to make time 'pass'. when the universe finally achieves total entropy, time will stop but i suppose the x,y,z will live on.

i've done my best to share what little i know about this. thanks for a great question and i hope some others chime in with their views. e.g. @Jemurray3

Answer 3

Yep, that's the idea. The only things I'd add are

1) the imaginary time formalism, which would explain the minus sign in the s^2 that you wrote above, has largely been discarded in favor of the explanation that spacetime is simply not Euclidean and therefore does not obey the Pythagorean theorem. This is a technical point but is more reflective of our current understanding of things.

2) Entropy is not necessarily the "driver" behind the movement of time. One could create a system in which the entropy never changes and yet an idealized clock of some kind would still tick forward. The connection between time and entropy is that entropy can distinguish past from future. That is to say, if you played a movie backward and forward, the only physical law that will have been violated in the reverse movie is that the entropy of the universe will decrease rather than increase. Beyond that, it's still an interesting and unresolved question.

Answer 4

Thanks friends, that were all very helpful.