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Norman
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Anyone know what quantity is conserved if the Hamiltonian (classical) is invariant under a Galilean boost? Also how would I prove that it is this quantity that is conserved?
Cheers,
Norm
Cheers,
Norm
HallsofIvy said:A Galilean "boost"? If you mean a Galilean transformation, since the Hamiltonian of a system is its total energy, invariant Hamiltonian means unchanging energy- that's conservation of energy.
Conservation laws for Galilean boosts are fundamental principles in classical mechanics that state that certain physical quantities, such as mass, energy, and momentum, remain constant in a closed system, regardless of any changes in its position or orientation.
Proving conservation laws for Galilean boosts is important because they provide a fundamental understanding of how physical systems behave and help us make accurate predictions about their behavior. They also serve as a cornerstone for more complex principles in physics, such as the laws of thermodynamics.
These conservation laws can be proven using mathematical equations and rigorous logical reasoning. This involves showing that certain physical quantities remain unchanged in a closed system, using the principles of conservation of mass, energy, and momentum.
The implications of these conservation laws are far-reaching and have applications in many areas of science and engineering. They help us understand the behavior of objects in motion, the transfer of energy and momentum, and the stability of physical systems. They also provide the foundation for many technological advancements, such as the development of efficient engines and transportation systems.
While these conservation laws are applicable in most classical mechanics situations, they may not hold true in extreme conditions, such as at the quantum level or in the presence of strong gravitational forces. In these cases, more complex conservation laws, such as those based on the principles of relativity, may be necessary.