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Quick question about Lorentz symmetry. From the wiki page

the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space.

I'm slightly confused. Obviously four-momentum is not Lorentz invariant. It's value depends on our frame of reference. But it is an observable, so shouldn't we be able to measure it in an experiment and thus find different values in different frames?

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Absolute four-momentum is not an observable. Relative four-momentum is. We cannot find the four-momentum of the lab itself, but we can (and do, regularly) measure the four-momentum of particles relative to a given lab, which then allows us to calculate the four-momentum of said particles relative to any frame you care to name. Whoever said that wasn't measurable?

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  • $\begingroup$ Ah okay I see. I understand what you're saying. My only confusion now is how four-momentum relative to a lab is related to the four-vector $p^\mu$ we use in relativistic mechanics. $\endgroup$ – Okazaki Aug 7 '15 at 19:53
  • $\begingroup$ They're identical. In relativistic mechanics you fix a frame and you talk about momentum relative to the frame. In the lab you measure momentum relative to the frame of the lab. Easy. $\endgroup$ – Emilio Pisanty Aug 7 '15 at 19:56

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