Mass the same for two reference frames

In summary, the problem involves two particles with different rest masses and velocities in the S frame. Another frame, denoted as S0, is introduced with a velocity v in the direction of increasing x. The goal is to show that the invariant mass of the system of two particles remains the same in both the S and S0 frames, indicating that it is invariant under a Lorentz transformation. The equations used in this problem are not explicitly stated, but the concepts of energy and momentum are mentioned in relation to the S frame. The author is unsure of how to begin and is seeking tips to help them progress.
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chris_0101
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Homework Statement



There are two particles with rest masses m1 and m2. In the S frame they have velocities u1 and u2. Consider another frame, which we usually denote as the S0 frame, which has a velocity v in the S frame in the direction of increasing x (i.e., it is going to the right in the S frame). Show that the invariant (or rest or proper) mass of the system of two particles has the same value in the S and S0 frames (i.e., it is invariant under a Lorentz transformation). Recall that the system in the S frame has E = E1 + E2 and p = p1 + p2.


Homework Equations



Really not too sure, I was thinking the Lorentz transformation for mass, but I am uncertain how to begin this question. Any tips to how I can begin, that would be greatly appreciated.

Thanks.
 
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The Attempt at a SolutionI really am not sure how to begin this question, so I am stuck. Any tips to where I can start would be greatly appreciated. Thanks.
 

1. What is meant by "mass is the same for two reference frames"?

Mass is a fundamental property of matter that measures the amount of matter in an object. It is a scalar quantity, meaning it has magnitude but no direction. When we say that mass is the same for two reference frames, it means that the mass of an object will remain constant regardless of its position or velocity in those frames of reference.

2. Why is it important to understand the concept of mass being the same for two reference frames?

Understanding this concept is crucial in the field of physics because it helps us make accurate predictions and calculations about the behavior of objects in different frames of reference. It also allows us to apply the laws of physics consistently, regardless of the observer's perspective.

3. Can the mass of an object change in different reference frames?

No, the mass of an object is an intrinsic property that does not change with the observer's perspective. It will always remain the same, regardless of the frame of reference used to measure it.

4. How does the concept of mass being the same for two reference frames relate to Einstein's theory of relativity?

Einstein's theory of relativity states that the laws of physics are the same for all observers in uniform motion. This includes the concept of mass being the same for two reference frames, as mass is a fundamental property of matter that is unaffected by the observer's perspective.

5. Are there any exceptions to the principle of mass being the same for two reference frames?

In classical mechanics, the principle of mass being the same for two reference frames holds true. However, in the realm of quantum mechanics, the concept of mass can become more complicated and may not remain constant in certain situations. Additionally, in extreme conditions such as near the speed of light or near a black hole, the laws of physics may behave differently, and the concept of mass may not apply in the same way as in classical mechanics.

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