Zero lagrangian and induced gravitation

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SUMMARY

The discussion centers on the concept of "induced gravity" and its relationship with systems exhibiting a zero Lagrangian. Participants clarify that a zero Lagrangian implies a constrained system, potentially leading to a zero Hamiltonian. The conversation highlights that in such systems, both kinetic energy (T) and potential energy (V) are equal, resulting in an action of zero, which complicates the application of the Euler-Lagrange equations. This indicates a unique scenario in theoretical physics where conventional equations of motion may not apply.

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  • Understanding of Lagrangian mechanics
  • Familiarity with Hamiltonian systems
  • Basic knowledge of kinetic and potential energy concepts
  • Awareness of Euler-Lagrange equations
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  • Research "induced gravity" in theoretical physics literature
  • Study "Lagrangian mechanics" and its applications
  • Explore "Hamiltonian mechanics" and its constraints
  • Examine "Euler-Lagrange equations" and their derivations
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Sunfire
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Hello,

Does anyone know what "induced gravity" is and where can one read (something not too technical) about it?

I am trying to understand how a system with zero Lagrangian has something to do with gravity.
Could someone explain perhaps?

Thanks
 
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0 Lagrangian ? You might mean 0 Hamiltonian, which is a constrained system.
 
The text I read was brief... it only mentioned "zero Lagrangian (i.e. induced gravity)". I would have imagined this meant a system where T and V are equal. I am unsure what would be special in a such zero-lagrangian system. Then the action is zero too. One can't write the euler -lagrange equations either , because all terms are zero

or am I missing something?
 
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