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To me Mach's principle can be summarised as acceleration being every bit as relative as velocity. It don't won't this to turn into an argument or get hijacked by relativity deniers, this thread assumes (with good reason) that relativity is valid.

 

The simplest way to start is to ask if a lone object could accelerate. How could acceleration be defined without using a coordinate system that includes non-accelerating objects?

 

One way is to use tidal force to show that the one object can objectively measure their own acceleration but then you can break that object down into a connected series of smaller objects with the tidal force created by the difference in acceleration between them.

 

Would a uniformally accelerating object feel tidal force?

 

You can view inerial motion as a straight path through spacetime while accelerating motion creates a curved path through spacetime, are those arbitrary if the coordinate system contains no other objects?

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