Relative acceleration between intertial reference frames?

[Uhtred]

Does special relativity hold between two inertial reference frames that are undergoing relative acceleration?

For example, consider two spaceships traveling toward each other on parallel (but not collinear) trajectories. They would pass each other at some non-zero distance, and thus their relative velocity would be constantly changing.

The concept of "inertial reference frame" is all about being unable to detect accelerations via a local accelerometer, correct? And if so, then special relativity would hold between the two inertial reference frames I described above.

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Sorry for posting in the wrong forum. This should probably have gone under relativity, but I suppose most of this question still applies to classical physics...

 

[kuruman]

Does special relativity hold between two inertial reference frames that are undergoing relative acceleration?

Say you have two inertial frames A and B. This means that relative to a third inertial frame C, their velocities are constant, namely $V_{AC}=const.$ and $V_{AC}=const.$ Relativistic addition of velocities says that the velocity of B relative to A is $$V_{AB} =\frac{V_{AC}-V_{BC}}{1-\frac{V_{AC}V_{BC}}{c^2}}.$$The right hand side is constant, so the relative velocity $V_{AB}$ is also constant. What makes you think there is relative acceleration?