Understanding Mass from Different Observers

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I take it rest mass means relative to the observer. We on Earth are speeding through space so to a different observer that mass is not at rest. Correct? So is there any way to tell when something is at rest and to get one absolute amount of mass? Oops! Do I see it? It's both. The mass is different to each observer and the measurement is correct but different in each case. Wow!
 
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The rest mass is invariant to observers (it does not change based on your frame of reference). The "mass" that DOES depend on observers is the so called "relativistic mass".
 
Tregg Smith said:
I take it rest mass means relative to the observer.
No, it means the object's inertial mass (resistance to acceleration) in the object's own rest frame at any given moment. Unlike with relativistic mass, all observers agree on an object's rest mass.
 
In any inertial reference frame, you can find the "rest mass" (more properly called "inertial mass") by measuring the object's energy E and momentum p, and calculating

m = \frac{1}{c^2} \sqrt {E^2 - (pc)^2}
 
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