- #1
martyf
- 42
- 0
Is the 4-velocity always a space-tipe 4-vector?
martyf said:Ok, so if I have a given 4-velocity how can I show in terms of mathematics that it is time-like ?
WHY a 4-velocity that travel slower than light satisfies t² - x² - y² - z² = 1 ?!
martyf said:([tex]\frac{v_{x}}{c\sqrt{1-\beta^{2}}}[/tex] , [tex]\frac{v_{y}}{c\sqrt{1-\beta^{2}}}[/tex] , [tex]\frac{v_{z}}{c\sqrt{1-\beta^{2}}}[/tex] , [tex]\frac{i}{\sqrt{1-\beta^{2}}}[/tex] )
Yes, the 4-velocity is always a space-type 4-vector. This means that its components are purely spatial and have no time component.
A space-type 4-vector has components that represent spatial quantities, such as position or velocity, and do not have any time component.
No, the 4-velocity cannot have a time component. This is because it represents the velocity of an object in 4-dimensional spacetime, where the time component is already accounted for in the time axis.
The 4-velocity is different from regular velocity in that it takes into account the effects of time dilation and length contraction in special relativity. It is also a 4-dimensional vector, while regular velocity is a 3-dimensional vector.
Yes, the 4-velocity is conserved in all inertial frames. This is because it is a Lorentz invariant quantity, meaning its magnitude and direction remain the same in all inertial frames.