Hypothetically, should a force feel the same as its measured force at relativistic speeds? Obviously a human body would not survive the force of a rotation at say, 0.6 the speed of light, but it’s easier to imagine the problem using large values.

Now, because time runs slower in the body's frame for every completed rotation at 0.6c, the (externally applied) force will be felt for a shorter time per rotation. Will the force therefore be felt more or less intensely- due to “relativistic power”? (I don't know if this makes sense). Perhaps there is no change. Or no answer.

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    $\begingroup$ Note that $\mathbf F\neq m\mathbf a$ in relativity, you need to use $\mathbf F=d\mathbf p/dt$ where $\mathbf p=\gamma(\mathbf v)m_0\mathbf v$. You might interested in this post, as it discusses your situation a little bit. $\endgroup$ – Kyle Kanos Aug 14 '14 at 16:15
  • $\begingroup$ The most intuitive answer can probably be given in the coordinate system of a relativistic rocket, which is always non-relativistic (v=0 from the standpoint of the astronaut). I think math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html might answer your question, by calculating and tabulating the travel time of a relativistic rocket with constant acceleration in the rocket's frame? $\endgroup$ – CuriousOne Aug 14 '14 at 20:32

Assume that 'feeling of a force' is due to a physical activity - like the pressure acting on a surface. I think because there is no way to differentiate between two inertial frames of reference (axioms of SR/GR), even when you go at relativistic speeds, the feel of the force should be the same. In other words, if you had a different feel, for the same force applied, in the 'rest' world vs 'moving' world, you could differentiate between the two worlds - a contradiction.


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