- #1
SamRoss
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Does anyone know of a derivation of the energy-momentum relation that does not make use of relativistic mass? In other words, a derivation that only uses invariant mass.
Derivation of Energy-Momentum Relation WITHOUT using relativistic mass?
- Thread starter SamRoss
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In summary, there is a discussion about a derivation of the energy-momentum relation that does not involve the concept of relativistic mass. There is also a mention of the confusion and misunderstanding caused by the use of this concept in special relativity. A suggested resource for further understanding is also provided.
- #2
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http://www.lightandmatter.com/html_books/genrel/ch04/ch04.html#Section4.2
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- #3
bobc2
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Check out post #3 of earlier today in the following Special Relativity thread:
https://www.physicsforums.com/showthread.php?t=457318
Mass is introduced as a scalar nonrelativistic quantity. The mass energy is seen to correspond to the 4th component of 4-dimensional momentum from the vantage point of one observing the moving mass.
https://www.physicsforums.com/showthread.php?t=457318
Mass is introduced as a scalar nonrelativistic quantity. The mass energy is seen to correspond to the 4th component of 4-dimensional momentum from the vantage point of one observing the moving mass.
- #4
jtbell
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SamRoss said:
Do you mean the equation [itex]E^2 = (pc)^2 + (m_0 c^2)^2[/itex]? What derivation of it uses relativistic mass, seeing as it contains the invariant mass to begin with?
- #5
torquil
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I wish "relativistic mass" had never been defined! 
It seems to be a source of confusion for newbies in SR.
It seems to be a source of confusion for newbies in SR.
- #6
SamRoss
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torquil said:I wish "relativistic mass" had never been defined!
It seems to be a source of confusion for newbies in SR.
I couldn't agree more
1. What is the energy-momentum relation?
The energy-momentum relation is a fundamental equation in physics that describes the relationship between energy and momentum in a system. It states that the energy of a particle is equal to its mass times the speed of light squared (E=mc²), and its momentum is equal to its mass times its velocity (p=mv).
2. Why is it important to derive the energy-momentum relation without using relativistic mass?
Deriving the energy-momentum relation without using relativistic mass is important because it provides a more accurate and fundamental understanding of the relationship between energy and momentum. Relativistic mass is a concept that is used to simplify calculations in special relativity, but it can be misleading and cause confusion.
3. How can the energy-momentum relation be derived without using relativistic mass?
The energy-momentum relation can be derived using the principles of special relativity, specifically the Lorentz transformations and the equation for total energy in a system. By combining these equations and making the necessary substitutions, the classic form of the energy-momentum relation (E²=p²c²+m²c⁴) can be derived without the use of relativistic mass.
4. What are the implications of deriving the energy-momentum relation without relativistic mass?
Deriving the energy-momentum relation without relativistic mass reinforces the idea that mass is a constant property of a particle, and that it does not change with velocity. This can help to clarify misconceptions about relativistic mass and lead to a better understanding of the relationship between energy and momentum.
5. Is the derivation of the energy-momentum relation without relativistic mass widely accepted?
Yes, the derivation of the energy-momentum relation without relativistic mass is widely accepted and is the standard approach in modern physics. It is based on the principles of special relativity and has been experimentally verified numerous times. However, the concept of relativistic mass is still used in some contexts for convenience and simplicity, but it is not considered a fundamental property of particles.
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