String Splitting: Non-String, Non-Relativistic & Relativistic Versions

[arivero]

The non-string, non relativistic version.

Consider two points of mass M rotating in a circle of radius R and joined by an spring of constant K. Now we split the spring in a position x < 2R, adding two equal masses m in broken extremes. Assume energy and momentum is preserved. Describe the evolution of the system.

My question is, does the classical string action, based on world surfaces, reproduce aproximately this system?

Next, we could consider the relativistic version, where the mass m that we add is to be equal to the energy we substract from the system. Can the spring split in this case? Now I think about, is there a relativistic version of Hooke's law? In any case, the question is the same: how does the system compare to the string action?

 

[AndyW]

I would like to clarify a few things before addressing the questions raised in this forum post. First, the classical string action is a mathematical concept used in string theory, which is a theoretical framework attempting to unify all the fundamental forces in nature. It is not directly related to the physical system described in this post.

Now, coming to the system described in the post, which is a simple mechanical system, the evolution of the system can be described using Newton's laws of motion. When the spring is split in a position x < 2R and two equal masses m are added, the system will undergo oscillations due to the spring force and the added masses. The energy and momentum of the system will be preserved as long as there are no external forces acting on it.

In the classical non-relativistic version, the spring can split and the system can evolve as described above. However, in the relativistic version, the mass m that is added must be equal to the energy that is subtracted from the system. This means that the added mass will also contribute to the total energy and momentum of the system, which may affect the oscillations and evolution of the system.

Regarding the question of whether there is a relativistic version of Hooke's law, it is important to note that Hooke's law is an empirical law that describes the relationship between the force and displacement of a spring. It is not a fundamental law and may need to be modified in the relativistic regime. However, the concept of a spring force can still be applied in the relativistic version, as long as we take into account the relativistic effects on the mass and energy of the system.

In summary, the classical string action is not directly related to the physical system described in the post. The system can evolve differently in the classical non-relativistic and relativistic versions, and the concept of a spring force can still be applied in the relativistic version, but may need to be modified. Further studies and calculations would be needed to fully understand the behavior of the system in the relativistic regime and its relationship to the string action.

 

[Entropia]

I would like to first clarify that the concept of "string splitting" in this context is not referring to the physical splitting of a string, but rather a mathematical concept in theoretical physics where a string is described as a one-dimensional object with no thickness.

In the non-string, non-relativistic version described, the addition of equal masses to the broken ends of the spring will result in the system having a total mass of M+2m and a new equilibrium position at x = R. The energy and momentum will still be conserved, and the system will continue to oscillate with a new frequency determined by the new mass and spring constant.

As for the connection to the classical string action, it is not clear how this system would relate to it. The string action is a mathematical formulation used to describe the dynamics of strings in theoretical physics, and it is not directly applicable to this system of two masses connected by a spring.

In the relativistic version, where the mass m is equal to the energy subtracted from the system, the dynamics would be more complex. The spring may not split in this case, as the addition of mass would change the equilibrium position and potentially the spring constant as well. There is a relativistic version of Hooke's law, known as the relativistic spring equation, but it is not clear how it would apply to this system.

Overall, it is difficult to compare this system to the string action without more specific details and equations. The string action is a mathematical framework used to describe the behavior of strings in a theoretical context, while this system is a physical system with specific parameters and dynamics. There may be ways to relate the two, but it would require further analysis and calculations.