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Happiness

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Electrons are indistinguishable, but we may pretend that they are distinguishable if their wave functions do not overlap in space. For example, an electron "a" in Chicago and an electron "b" in Seattle would produce a zero integral in [5.20], and so their indistinguishablilty would not produce any different observable compared to those of distinguishable particles.

But any 2 electrons always overlap in space because their wave functions are never zero! For example, the radial wave functions of the hydrogen electron are all proportional to ##e^{-kr}##, where ##k## is a constant. So, that makes [5.20] never zero. And from [5.22], we know the distance between the electrons (in fact, any 2 electrons in the Universe) change when any electron has its wave function altered. That means a change to the electron in Chicago instantaneously causes a change to the electron in Seattle. This is obvious if you consider the giant wave function encompassing all the electrons in the Universe. This giant wave function has to be antisymmetric (since electrons are fermions), and so any change to one electron must result in an instantaneous change to at least one other electron to keep the giant wave function antisymmetric.

This seems to enable faster-than-light communication, because I could instantaneously take measurements on the electrons at Seattle to know instantaneously whether or not there is a change to the one at Chicago. Also, this seems to violate locality, because just by moving my hands, I am changing the position of all the electrons in the Universe instantaneously.

Reference: Intro to QM, David J Griffiths, p208

But any 2 electrons always overlap in space because their wave functions are never zero! For example, the radial wave functions of the hydrogen electron are all proportional to ##e^{-kr}##, where ##k## is a constant. So, that makes [5.20] never zero. And from [5.22], we know the distance between the electrons (in fact, any 2 electrons in the Universe) change when any electron has its wave function altered. That means a change to the electron in Chicago instantaneously causes a change to the electron in Seattle. This is obvious if you consider the giant wave function encompassing all the electrons in the Universe. This giant wave function has to be antisymmetric (since electrons are fermions), and so any change to one electron must result in an instantaneous change to at least one other electron to keep the giant wave function antisymmetric.

This seems to enable faster-than-light communication, because I could instantaneously take measurements on the electrons at Seattle to know instantaneously whether or not there is a change to the one at Chicago. Also, this seems to violate locality, because just by moving my hands, I am changing the position of all the electrons in the Universe instantaneously.

Reference: Intro to QM, David J Griffiths, p208

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