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Yes it is correct. I derived and used the same expression in http://vixra.org/abs/1008.0051 page 5 (with one extra term to account for space-time transformations that is not needed for internal symmetries). The dependence on the derivatives $\partial_{\nu}\Delta\phi_{i}$ is necessary and not a problem.


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Posting another view on the already nice answers. Conservation of (mass-)energy is a principle in physics. Feynman used to say, (Feynman lectures on physics) that when various processes are studied, one finds that energy is not conserved, but then looks under the carpet or in waste bin and finds another form of energy which when taken into account makes the ...


1

It would appear evident that its KE has been drained out by g and definitely destroyed. Is this correct? This is from a different perspective than the other answers and is not so much an answer as an extended comment on the above quoted question. It occurs to me that creation and destruction are, in some sense, absolute. In your thought experiment, ...


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Consider the case in which we shoot an electron up in the stratosphere, it travels up to a certain height and then it stops when its KE = 0. We say, according to that principle, that lost energy is stored as PE. This has been experimentally verified of course, as in falling back it gains the kinetic energy it lost going up. The concept of potential ...


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The KE is converted to PE. The photon-planet system still has potential energy since there is gravitational red shift.


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(5 downvotes ... oops sorry ... 6 downvotes :) and not a single comment why? None dared to formulate counter-arguments? All one gets on a scientific forum are just NOs? Why I am not surprised? :) Again - as the subject is fundamental - all meaningful comments are heartily welcome) bobie, notice one thing. Gravitation as such is energy from nothing. Where ...


11

The idea of partitioning energy into different forms like "mechanical energy" or "chemical energy" and such is actually arbitrary. More or less by definition, energy is that which is conserved unter time translations by Noether's theorem. If what you call "mechanical energy" has changed, then there is another term in the Noetherian energy that has changed ...


1

It is unclear what you mean by transformation involving space-time, well, at least, I found two possibilities. The mentioned transformations are not gauge, since $\Lambda$ does not depend on space-time. So one way to make it involve space-time is to set $\Lambda \rightarrow \Lambda(x)$. The given Lagrangian is not invariant under these gauge ...


1

In canonical quantization one constructs the Hamiltonian formalism. Energy conservation is therefore manifest (since Hamiltonian is time-independent and commutes with itself). Quantum-mechanically, the Hamiltonian of the system can be expressed via particle creation-annihilation operators. So, the total energy of the field is also the total energy of all ...



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