Mass Equation in SR: Determining Rest Mass of Moving Objects

[Arsenic&Lace]

Here's my stupid question: In the mass equation from SR, we have the m0 term for rest mass; but how would you determine the rest mass of an object? Isn't an object on the earth, which is in motion, also in motion? So wouldn't the mass of an object on Earth not actually be its mass at rest?

Thanks in advance!

 

[PAllen]

Here's my stupid question: In the mass equation from SR, we have the m0 term for rest mass; but how would you determine the rest mass of an object? Isn't an object on the earth, which is in motion, also in motion? So wouldn't the mass of an object on Earth not actually be its mass at rest?

Thanks in advance!

All you need to measure rest mass directly is to not be in motion relative to the object you are measuring. It doesn't matter at all that you and the object are moving relative to something else (e.g. the sun).

Further, if you are measuring an object moving relative to you, there is a simple formula for deriving its rest mass from its total energy and momentum (E^2 - (pc)^2)/c^2 . Alternatively, if you measure its speed and momentum, you can calculate its rest mass.

 

[Arsenic&Lace]

All you need to measure rest mass directly is to not be in motion relative to the object you are measuring. It doesn't matter at all that you and the object are moving relative to something else (e.g. the sun).

Thanks! If you don't mind, another question: why is this the case?

 

[PAllen]

Thanks! If you don't mind, another question: why is this the case?

Well, the whole point of relativity is there is no way to know 'who is at rest', so a definition of rest mass that could never be computed would be pretty useless.

So it's just a definition: rest mass = mass measured by an observer for whom the body is at rest. Shorthand: mass measured in the body's own frame of reference.

 

[Arsenic&Lace]

Aah okay, thanks a bunch!