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New Theories / Re: How does Hamdani explain the twins paradox?
« Last post by hamdani yusuf on 02/05/2024 14:07:43 »I searched and found this formula in quora.What if there is another twin travel to the opposite direction with the same speed? And another one in perpendicular direction?The formula for perpendicular velocity addition is:
https://en.wikipedia.org/wiki/Velocity-addition_formula
In our case, vx=vy=0.866c.
For convenience, I used spreadsheet to calculate.
putting the number to the left formula gives 0.247c
putting the number to the right formula gives 1.732c
Either result doesn't seem to be correct. It shouldn't be slower than the individual velocity. It shouldn't be higher than c either. Can someone show where the error is?
Quote
...Plugging in the value, where vx=vy=0.866c, v is 0.968c.
This messy matrix is not a Lorentz boost. It is, in fact, a combination of a Lorentz boost (corresponding to some velocity in the x−y plane) and a spatial rotation (again in the x−y plane.)
However, at least we can get the magnitude of the resulting velocity from this matrix, as the upper left component of the matrix is not affected by the spatial rotation. It is determined purely by the Lorentz boost. A little bit of trivial algebra tells you the magnitude:
v=√(vx^2 + vy^2 - vx^2.vy^2/c^2)
The gamma factor is then around 3.98. For simplicity, I'll just round it up to 4.