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How generic can be derivation of energy?

In a system with gravity and masses – it is potential energy and kinetic energy.

What if a constraint would be specified that no mass and velocity should be allowed (or possible) to use? For example, suppose there is a system of massless particles. Is there a way to define and use energy in such system? If yes, then how?

In general, I am dealing with abstract systems, where no typical gravity and mass occur. So it is hard for me to use potential and kinetic energy. Yet, I think it is possible to define an energy in such system, a kind of intensity of a process. Is there such thing defined in physics? What are most abstract derivations of energy?

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You put the "Hamiltonian-mechanics" tag, so you know the answer. If your equations of motion are derived from an Hamiltonian, then the Hamiltonian can be considered as an "energy", –  yohBS Feb 10 '12 at 15:40
    
Suggestion to the question(v1): Replace the phrase derivation of energy with definition of energy. –  Qmechanic Mar 11 '12 at 17:58
    
Lagrange/Hamiltonian work well when there is motion and conversion between Kinetic and Potential energy. The question is nice (and I feel that something is missing in the canonical viewpoints). –  Helder Velez Mar 12 '12 at 0:30
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1 Answer

For example, suppose there is a system of massless particles. Is there a way to define and use energy in such system? If yes, then how?

Photons have zero mass, their energy is defined as h*nu ( where nu is the frequency of the wave that also describes them). The microwave background in the cosmos is a good example of such a photon "system", left over from the big bang.

In fact, the dominant theory of particle physics and astrophysics has all particles mass-less up to a certain evolution of the cosmos from a Big Bang, when symmetries are broken and masses are acquired by the particles, avidly sought in particle physics experiments as presently in the LHC at CERN.

Physics has progressed from just measuring kinetic and potential energies.

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It would be great if the abstract energy could be derived as intensity of a generic process.. For example the frequency is a kind of intensity of wave oscillations..? –  Jupan Feb 18 '12 at 0:19
    
In a sense, energy is not derivative, it is defined. The concept starts from everyday expectations, goes to observations which gave the classical kinetic and potential definitions. These led to mathematical systems ( lagrangians and hamiltonians) that obviously described the observations. When quantum mechanics and relativity and general relativity came along the definitions were expanded to confirm to new experimental evidence. If you are happy to define energy as an intensity in a self consistent manner that gives the same experimental results, there should be no problem. –  anna v Feb 18 '12 at 5:33
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