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Hi. I'm reading David Tong's notes (Causality at page 36: http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf ) on QFT and I'm currently trying to understand the causality requirement that

[tex][O_1(x), O_2(y)] = 0 \ \ \forall \ \ (x-y)^2 < 0.[/tex]

For two operators O1 and O2. He then states that this ensures that a measurement at x can not affect a measurement at y when x and y are not causally connected.

I know that in classical relativity, a spacelike separation between events, imply that the event at the first location could not have been the cause of the event at the second location because it would require a signal to go faster than the speed of light.

However exactly how this statement is related to measurements and operators in QFT is not clear to me. Could someone enlighten me?

[tex][O_1(x), O_2(y)] = 0 \ \ \forall \ \ (x-y)^2 < 0.[/tex]

For two operators O1 and O2. He then states that this ensures that a measurement at x can not affect a measurement at y when x and y are not causally connected.

I know that in classical relativity, a spacelike separation between events, imply that the event at the first location could not have been the cause of the event at the second location because it would require a signal to go faster than the speed of light.

However exactly how this statement is related to measurements and operators in QFT is not clear to me. Could someone enlighten me?

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