Air molecule has $6$ degrees of freedoms: it can move up & down, left & right, front & back, rotate along $x$-axis, $y$-axis, $z$-axis. But I heard about graviton, a hypothetical particle can have up to anywhere from $2$ to $10$ degree of freedom.

How and why do certain particles be restricted to less than $6$ degree of freedom and also even exceeded the limit?

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    $\begingroup$ you have to give a link reference for your "heard", it is all a matter of context, particularly for hypothetical particles. $\endgroup$
    – anna v
    Aug 2, 2020 at 5:40
  • $\begingroup$ please keep in mnd that when one talks of photons electrons etc, one is talking quatnum mechanics and the standard model where all elemetnary particles are assumed axiomatically to be point particles. gravitons will enter that table, once gravity is quantized definitively. at the moment it is only effective quantizations that are used in cosmological models. $\endgroup$
    – anna v
    Aug 3, 2020 at 3:44
  • $\begingroup$ @annav: oh that's why earlier you said context matters so it is depending on which model is used. $\endgroup$
    – user6760
    Aug 3, 2020 at 4:23

1 Answer 1

  1. In classical point mechanics, (on-shell) degrees of freedom (DOF) typically are the number of initial conditions needed divided by 2, cf. e.g. this Phys.SE post.

    Example: A rigid body has 6 DOF, cf. e.g. this Phys.SE post.

  2. Using the point mechanical definition of DOF a field (such as the gravitational field) has infinitely many degrees of freedom. For this reason the DOF of fields in field theory is counted in a different way. Additional complications arise if the field has several components and gauge symmetry. See e.g. this Phys.SE post.

    Example: In GR in 3+1D the metric tensor field $g_{\mu\nu}$ has 10 components, 6 off-shell DOF & 2 on-shell DOF, cf. e.g. this Phys.SE post.


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