Why isn't time a vector quantity since it always moves forward (according to a common man)? can we consider time as a dimension or even extrapolate it as the 4th dimension?
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To talk about time.
When we draw a space graph and mark a point on it as (x,y), the co-ordinates x and y are scalar here as they just indicate numbers. Similarly, in space time when we write the co-ordinates as (t,x,y,z) time is just a coordinate and thus can be called a scalar.
Sometime in relativistic mechanics, the word "scalar" is used as a shorthand for Lorentz scalar, these are quantities which do not change under Lorentz transformation. Time changes and hence it isn't a scalar in this sense.
Although proper time (time measured between two events in space time as measured by an observer who passes through both events) is a Lorentz scalar.
Time per se doesn't have magnitude and direction. A four-vector in spacetime has magnitude and direction of a four-dimensional sort, and some such four-vectors are "timelike". But a time-like four-vector isn't time - time is the projection of the four-vector onto another time-like four-vector that you've anointed as the time axis for your measurement frame. Thus it's the 4D dot product of two four-vectors.
When we draw a space graph and mark a point on it as (x,y), the co-ordinates x and y are scalar here as they just indicate numbers. Similarly, in space time when we write the co-ordinates as (t,x,y,z) time is just a coordinate and thus can be called a scalar.
Sometime in relativistic mechanics, the word "scalar" is used as a shorthand for Lorentz scalar, these are quantities which do not change under Lorentz transformation. Time changes and hence it isn't a scalar in this sense.
Although proper time (time measured between two events in space time as measured by an observer who passes through both events) is a Lorentz scalar.
Time per se doesn't have magnitude and direction. A four-vector in spacetime has magnitude and direction of a four-dimensional sort, and some such four-vectors are "timelike". But a time-like four-vector isn't time - time is the projection of the four-vector onto another time-like four-vector that you've anointed as the time axis for your measurement frame. Thus it's the 4D dot product of two four-vectors.
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