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I have a silly confusion about the statement written in the link Einstein and Locality

''external influence on A has no direct influence on B; this is known as the Principle of Local Action.'' Since GTR and Electromagnetism obey principle of locality. And in both cases change in A position affect the B and vice versa. Then why this contradiction come. Please correct me.

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    $\begingroup$ I think electromagnetism and the GTR are both constrained by the speed of light, whereas the quantum mechanical case that does not obey the principle of locality is not (spin states change instantaneously, hence 'spooky action at a distance') $\endgroup$ Jun 6 '14 at 12:59
  • $\begingroup$ Did you mean that direct influence is the instantaneous effect $c\rightarrow\infty$. $\endgroup$ Jun 6 '14 at 13:10
  • $\begingroup$ Read about the EPR paradox.(en.wikipedia.org/wiki/EPR_paradox) I think the resolution to the paradox is during entanglement there is no information transfer or a "physical effect", and hence locality can be violated. Causality is much more fundamental than locality. $\endgroup$
    – user7757
    Jun 11 '14 at 6:17
  • $\begingroup$ @ramanujan_dirac I am clear about EPR paradox and entanglement but i am concerned about the EM force and gravitational force what about them, $\endgroup$ Jun 11 '14 at 7:32
  • $\begingroup$ Quantum mechanics is local physics.stackexchange.com/q/114657. $\endgroup$
    – alanf
    Jun 11 '14 at 15:28
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EM and GR don't actually say that "particles exert forces on each other". What they actually say is that particles produce electromagnetic and gravitational fields, and that these fields then interact with other particles. Significantly these theories describe these fields using differential equations, which means that the field at some point in space is completely defined by the field in its immediate neighbourhood. If a charged or massive particle accelerates, this causes a change in the local field around the particle, which creates a disturbance that propagates outwards as the field reconfigures itself. This disturbance propagates at the speed of light (in fact in the EM case it is light) so there is no violation of locality.

It is important to realise that the principle of locality requires that these fields are in some sense "physically real" (whatever that means) and are more than just a clever bit of maths. In the case of GR we have a nice picture of the field in terms of the bending of space time, while trying to understand what an EM field is leads to QFT.

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  • $\begingroup$ Your explanation is right but can u elaborate the quoted statement in my question more clearly. $\endgroup$ Jun 11 '14 at 16:06
  • $\begingroup$ An influence at A does not directly influence B. Instead there is a direct influence on the local field at A. This in turn exerts an influences on the field at nearby points, which influence points close to them, and so on. This leads to an indirect influence at B which is mediated by a series of local interactions. $\endgroup$ Jun 11 '14 at 16:48
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I'm no expert in quantum mechaincs, but as @polyphant said, Einstein termed this phenomenon as "spooky action at a distance". In quantum mechanics, it is believed that there has to be a certain way in which quantum information(quantum bits) can travel from one place to another without moving the physical matter to which the information is attached. This phenomenon is called as "entanglement"-particles separated by light years can still appear 'connected' to other particles, with the state of one particle instanteneously(yes, speed of light is no longer the limiting speed) affecting the state of other. (most generally, while studying this topic, the information is spin states). Indeed, it is one of the contradictions between relativity and quantum mechanics. (personally, I believe relativity should win..:))

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