In this Stanford University lecture on Relativity, it is stated: Likewise, objects in spacetime all move at constant speed c in spacetime but if you change its direction, say by moving at speed v in the x direction, then spatial speed will change and so will the speed along the ct direction. Again, its total speed will still be c through spacetime.
http://web.stanford.edu/~oas/SI/SRGR/notes/SRGRLect6_2007.pdf
Brian Green of Columbia University also says the same thing, as do many others. Are they right?
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