Mass Equation in SR: Determining Rest Mass of Moving Objects

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Discussion Overview

The discussion revolves around the concept of rest mass in the context of special relativity (SR), specifically how to determine the rest mass of an object that is in motion, such as one on Earth. Participants explore the implications of motion on mass measurement and the definitions involved in special relativity.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant questions how to determine the rest mass of an object that is in motion, suggesting that an object on Earth, which is also in motion, may not have its mass accurately represented as its rest mass.
  • Another participant asserts that to measure rest mass directly, one must not be in motion relative to the object being measured, regardless of the motion relative to other bodies, such as the sun.
  • A formula for deriving rest mass from total energy and momentum is mentioned: (E^2 - (pc)^2)/c^2, along with an alternative method involving speed and momentum.
  • A participant emphasizes that the definition of rest mass is based on measurements made by an observer for whom the object is at rest, highlighting the relativity of motion and the importance of the observer's frame of reference.

Areas of Agreement / Disagreement

Participants express differing views on the implications of motion for measuring rest mass, with some clarifying the conditions under which rest mass can be measured, while others question the definitions and the relativity of motion. The discussion remains unresolved regarding the broader implications of these concepts.

Contextual Notes

There are limitations in the discussion regarding the assumptions about motion and reference frames, as well as the dependence on definitions of rest mass and measurement conditions. Some mathematical steps and their implications are not fully explored.

Arsenic&Lace
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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!
 
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Arsenic&Lace said:
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.
 
PAllen said:
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?
 
Arsenic&Lace said:
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.
 
Last edited:
Aah okay, thanks a bunch!
 

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