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Special relativity tells that space and time should be seen as a single four dimensional space time. Even the metric for SR has four components, x1, x2, x3, and x4 = ict. The Lorentz transform tells us how to convert these coordinates from this to another providing that we are moving at a constant velocity v in an inertial frame. Therefore, to completely express an event in a coordinate transformed spacetime, we need, not just the current space and time coordinates but also our velocity.

Now, dimensions are also defined as the minimum number of quantities that are required to completely identify a "point" in our manifold. By this definition, shouldn't velocity be counted as a dimension as well?

To put in other terms: Suppose I tell you that I am at x,y,z at time t but don't tell you what my v is - if we are in different frames of reference, then you still cannot compute my exact coordinates. It seems to me that the velocity v is as critical a quantity as the other four and hence should be accorded the title of a dimension.

If my question is clear to you, what are your thoughts? Cheers!

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# Why isn't velocity a dimension in SR?

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