Magnitude of Vectors in Special Relativity

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In special relativity, the magnitude of a velocity vector must adhere to the constraint that it cannot exceed the speed of light (c). The standard formula for magnitude, v=√(vx²+vy²+vz²), can yield results greater than c, which indicates that such velocities are not physically possible. Instead, velocities in special relativity should be treated as 4-dimensional vectors, where the appropriate magnitude calculation involves 4D vector methods. The discussion highlights the importance of understanding these 4-vectors to correctly interpret velocities in the context of relativity. Overall, the conversation emphasizes the need to apply the correct framework when dealing with relativistic velocities.
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So for finding the magnitude of a vector, velocity for example, we use v=√(vx2+vy2+vz2), but in special relativity, velocities can not exceed c. Is their a different formula for magnitude in SR, or could a velocity like(in natural units) v=(.9,.9,.9) not exist, since the magnitude comes out to be about 1.5588c, which obviously exceeds c?
 
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That vector could not be a velocity. Velocity is limited by v_x^2+v_y^2+v_z^2<1.
 
Ok, thanks I get it now.
 
In special relativity, all vectors should really be regarded as 4 dimensional. UltrafastPED's reference give the method for how to get the magnitude of a 4D vector.

Chet
 
How much about 4-vectors do you already know?
 

Thread 'EPR revisited'

In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
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