Pre-theoretically, we notice that objects have some property responsible for their varying dispositions to resist being pushed around in space, or to resist changes in motion given applied forces ("inertia"). So we introduce the term "inertial mass" to apply to the most physically interesting property responsible for such dispositions.(adsbygoogle = window.adsbygoogle || []).push({});

We then, naturally, try to get precise about the exact relationship between this "mass" property, and resulting accelerations given applied forces. Testing at low relative velocities, we quantify the mass / inertia relationship with F=MA.

But then we realise that spacetime is structured so as to prevent particles from accelerating past the speed of light. Consequently, objects have more inertia, more resistance to acceleration, in the direction of their velocity: objects are harder to "push around" in the direction of their velocity. So if we want to keep 'mass' close to inertia (the original rationale for the term's introduction), then it looks like we had better introduce direction relative masses, Transverse mass and Longitudinal mass. Quantifying the mass / inertia relationship then yields F= ##\gamma^3##MA = M_{L}A; and F= ##\gamma##MA= M_{T}A.

That all makes a lot of sense to me. What doesn't make sense to me, is modern SR formalism, which purports to be able to describe this phenomenon, without introducing direction relative quantities.

According to wikipedia's entry on mass in SR, we don't need to distinguish direction relative equations, we just need to give up on F=MA and instead work with F=d(M_{R}V)/dt. I do not understand this suggestion.

I thought the reason that F=MA is no good is because the applied force can alter the mass - mass is not constant in SR. So we had better put 'M' into the time derivative to its right to get F=d(M_{R}V)/dt or F=d(M_{0}##\gamma##V)/dt. But if we work with one of the two latter equations, haven't welostcrucial information about inertial behaviour? Where has thecubed gammagone? How can one derive the phenomenon of direction relative inertia from this equation?

Any suggestions would be most welcome.

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# How does SR quantify the direction relative properties of inertia?

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