This is a really basic question, but...(adsbygoogle = window.adsbygoogle || []).push({});

Say I have a massive scalar field obeying the Klein-Gordon equation linearized about flat space,

[itex]\partial_t^2 \phi + (k^2 + m^2)\phi = 0.[/itex]

This has solutions

[itex]\phi \sim e^{\pm \sqrt{k^2 + m^2}t}[/itex]

and the sound speed should be

[itex]\omega_k/k = \sqrt{1 + m^2/k^2} \geq 1.[/itex]

in which case perturbations of the scalar field propagate superluminally at all scales. This is clearly wrong, but why?

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# Why don't scalar fields propagate superluminally?

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