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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?

Harish Chandra Rajpoot
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user6760
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1 Answers1

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  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.

Qmechanic
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