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The informational paradox of rectilinear motion

  1. Feb 11, 2016 #1
    If the torsion of the straight line is undefined what happens with the information about the torsion?

    It is known (https://en.wikipedia.org/wiki/Quantum_no-deleting_theorem, http://van.physics.illinois.edu/qa/listing.php?id=24045) that the information conserved in a system can be nor created, neither destroyed.

    Therefore, if a body is heading on a certain pathway, the information about the pathway’s curvature and torsion should remain unchanged, no matter the modifications the body is suffering.

    Let’s assume then, in the beginning, that, under the influence of some forces, a body is firstly heading on a pathway that has its curvature and its torsion non-zero and well defined - a state we call “initial state”.

    Then, following a certain process (for example, releasing the body), the body starts moving rectilineal, more exactly, on a straight line - a state we can call “final state”. The straight line has zero curvature, and the vanishing of the curvature could be informationally correlated with the intensity of the forces that lead to the initial state.

    However, the problem is THE TORSION. The straight line’s torsion is impossible to be defined (https://en.wikipedia.org/wiki/Frenet–Serret_formulas#Special_cases). Therefore, the information about the initial state’s torsion is irrecoverable lost in the final state! But this data is contradictory with the principle of information's conservation.

    Of course, the problem can be also reversed. It can be assumed that in the initial state, the body is moving rectilineal and then, in the final state, it starts moving on a curve with the torsion well defined. In this case, the information would be created out of nowhere, data that is again contradictory with the principle of information's conservation.

    How can we solve this problem?
     
  2. jcsd
  3. Feb 16, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Feb 17, 2016 #3
    I believe the paradox can be solved if we add the following postulate in Physics:

    - Every body in the Universe is moving on trajectories having the curvature and torsion well defined. In particular, free bodies are moving on trajectories having the curvature and torsion constant.

    This postulate includes the current principle of inertia as a particular case. More exactly, the body's rest state corresponds to an infinite curvature, while a rectilinear
    motion corresponds to a null curvature."

    If something is unclear please let me know and I'll try to rephrase - I'm not a native English speaker so it might be that some paragraphs are not correctly expressed.
     
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