Historical origin of energy momentum equation?

In summary, the energy relation E2=m2c4+p2c2 is a consequence of the relativist energy and momentum, and was first discussed by Einstein in his first papers. The modern view is that m² = E² - p² corresponds to the first Casimir of the Poincare group, but Einstein would hate that! So the only (historically correct) way to derive the relation is to deal with the "relativistic mass" which Einstein didn't like, either.
  • #1
SamRoss
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Does anyone know who first posed the energy relation E2=m2c4+p2c2 and where its original appearance can be found?
 
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  • #3
You should check

http://www-itp.particle.uni-karlsruhe.de/~schreck/general_relativity_seminar/Zur_Elektrodynamik_bewegter_Koerper.pdf [Broken]
http://www-itp.particle.uni-karlsruhe.de/~schreck/general_relativity_seminar/Ist_die_Traegheit_eines_Koerpers_von_seinem_Energieinhalt_abhaengig.pdf [Broken]

Of course this relation follows immediately from the relativistiv energy and momentum - and these have been discussed by Einstein in his first papers - but I don't know whether he explicitly wrote down the relation you are asking for.
 
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  • #4
tom.stoer said:
You should check

http://www-itp.particle.uni-karlsruhe.de/~schreck/general_relativity_seminar/Zur_Elektrodynamik_bewegter_Koerper.pdf [Broken]
http://www-itp.particle.uni-karlsruhe.de/~schreck/general_relativity_seminar/Ist_die_Traegheit_eines_Koerpers_von_seinem_Energieinhalt_abhaengig.pdf [Broken]

Of course this relation follows immediately from the relativistiv energy and momentum - and these have been discussed by Einstein in his first papers - but I don't know whether he explicitly wrote down the relation you are asking for.

I've read those papers (in English). Relativistic energy is in there although I don't think relativistic momentum is. In any case, do you know a proof that utilizes the two quantities? Most of the proofs that I see depend on the ambiguous relativistic mass.
 
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  • #5
The modern view is that m² = E² - p² corresponds to the first Casimir of the Poincare group - but Einstein would hate that! So I guess the only (historically correct) way is to deal with the "relativistic mass" which Einstein didn't like, too, as you can see from some remarks like the following one from a 1948 letter to Lincoln Barnett:

"It is not good to introduce the concept of the mass M = m/(1-v²/c²)½ of a body for which no clear definition can be given. It is better to introduce no other mass than 'the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."
 
  • #6
tom.stoer said:
The modern view is that m² = E² - p² corresponds to the first Casimir of the Poincare group - but Einstein would hate that! So I guess the only (historically correct) way is to deal with the "relativistic mass" which Einstein didn't like, too, as you can see from some remarks like the following one from a 1948 letter to Lincoln Barnett:

"It is not good to introduce the concept of the mass M = m/(1-v²/c²)½ of a body for which no clear definition can be given. It is better to introduce no other mass than 'the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."

What do you think Einstein would have said the correct proof was?
 
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  • #7
Einstein observed that introducing velocity dependend xyz-masses always leads to confusion. Just look at p(v) = mv /(1-v²/c²)½; introducing M(v) = m /(1-v²/c²)½ one can write p(v) = M(v)*v which looks rather familiar; it seems that one can save the Newtonian equation for the momentum p.

But what about E(v); neither the total nor the kinetic energy can be re-written using the same trick. E(v) = M(v)*v^2 / 2 is nonsense, and E = M(v)*c² is correct but does not correspond to any Newtonian formula. So all equations Einstein derived are correct, but using new terms for new, velocity dependend entities does not help.
 
  • #8
SamRoss said:
In any case, do you know a proof that utilizes the two quantities? Most of the proofs that I see depend on the ambiguous relativistic mass.

[tex]E = \frac{m_0 c^2} {\sqrt{1 - v^2/c^2}}[/tex]

[tex]p = \frac{m_0 v} {\sqrt{1 - v^2/c^2}}[/tex]

Use algebra to eliminate v between these two equations. Sheldon Cooper would say, "Easy-peasy." :wink:
 

1. What is the historical origin of the energy momentum equation?

The energy momentum equation was first developed by Isaac Newton in his famous publication "Philosophiae Naturalis Principia Mathematica" in 1687. This equation is a fundamental law of classical mechanics and describes the relationship between an object's mass, velocity, and momentum.

2. Who contributed to the development of the energy momentum equation?

In addition to Isaac Newton, other scientists such as Gottfried Leibniz, Pierre-Simon Laplace, and Joseph Louis Lagrange also made significant contributions to the development of the energy momentum equation. These scientists built upon Newton's work and helped refine the equation to its current form.

3. How does the energy momentum equation relate to the laws of motion?

The energy momentum equation is closely related to Newton's laws of motion. In fact, it can be derived from the second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. The energy momentum equation takes into account an object's mass, velocity, and momentum, and allows us to calculate the effects of forces on an object's motion.

4. Has the energy momentum equation been modified or updated over time?

While the fundamental principles of the energy momentum equation have remained unchanged since its development, it has been modified and extended to apply to different types of systems and scenarios. For example, Einstein's theory of relativity introduced the concept of relativistic mass, which can be incorporated into the energy momentum equation to describe the motion of objects at high speeds.

5. How is the energy momentum equation used in modern science?

The energy momentum equation is a crucial tool in many fields of science and engineering, including mechanics, thermodynamics, and fluid dynamics. It is used to analyze and predict the motion and behavior of various systems, from simple objects like projectiles to complex systems like planets and galaxies. It also plays a key role in the development of technologies such as rocket propulsion and energy generation.

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