Landau's inertial frame logic

  • #1
gionole
281
24
I had an interesting thought.

Let's only look at the free particle scenario.

We derive euler lagrange even without the need to know what exactly ##L## is (whether its a function of kinetic energy or not) - deriving EL still can be done. Though, because in the end, we end up with such EL(##\frac{\partial L}{\partial q} - \frac{d}{dt}\frac{\partial L}{\partial \dot q} = 0##), we see that ##L## couldn't have been a function of ##\dot q## which depends on ##t##, because if ##\dot q## depends on ##t##, euler lagrange couldn't be applied to it as EL derivates ##L## wrt to ##\dot q##.

So at this time, we know ##L## is a function of ##v## in which ##v## doesn't depend on ##t##.

Then Landau tries to come up with what ##L## is. in the ##K'## inertial frame, he shows that ##L' = L(v^2) + \frac{dL}{dv^2}2v\epsilon##. Everything is clear till now, but then he changes ##v## into ##\frac{dr}{dt}##. How can he do that if the initial assumption is that ##v## and ##q## are not a function of ##t## in ##L## ? (I know that adding total time derivative doesn't change EOM, but this question is not about this)
 
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  • #2
I think I figured out the logic in my head.

By that, he doesn't say that ##L'## is a function of ##v, q## which depend on $t$ - he doesn't say this. He just shows that adding total time derivative doesn't change EOM.
 

FAQ: Landau's inertial frame logic

What is Landau's inertial frame logic?

Landau's inertial frame logic is a theoretical framework that extends classical mechanics and special relativity by providing a more rigorous and formalized approach to understanding inertial frames of reference. It builds on the principles laid out by Lev Landau and aims to resolve ambiguities related to motion and reference frames in physics.

How does Landau's inertial frame logic differ from classical mechanics?

While classical mechanics relies on Newton's laws of motion to describe the behavior of objects, Landau's inertial frame logic introduces a more formal structure to the concept of inertial frames. It emphasizes consistency and rigor in defining these frames, ensuring that the laws of physics hold true in a more universally applicable manner.

Why is Landau's inertial frame logic important in modern physics?

Landau's inertial frame logic is important because it helps to bridge gaps between classical mechanics and relativistic physics. By providing a more precise definition and understanding of inertial frames, it allows for more accurate predictions and analyses in both theoretical and experimental physics, enhancing our understanding of the universe.

Can Landau's inertial frame logic be applied to general relativity?

While Landau's inertial frame logic is primarily developed for classical mechanics and special relativity, its principles can be extended to general relativity. In general relativity, the concept of inertial frames becomes more complex due to the curvature of spacetime, but the rigorous approach of Landau's logic can still provide valuable insights and aid in the formulation of more precise models.

What are some practical applications of Landau's inertial frame logic?

Practical applications of Landau's inertial frame logic include improving the accuracy of satellite navigation systems, enhancing the precision of experimental measurements in physics, and providing a more robust framework for simulations in astrophysics and cosmology. Its rigorous approach to defining inertial frames ensures that these applications are based on a solid theoretical foundation.

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