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## Main Question or Discussion Point

Is this proven that wave functions extend to infinity, or is it just a theory? What makes them assume that it extends to infinity?

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Is this proven that wave functions extend to infinity, or is it just a theory? What makes them assume that it extends to infinity?

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atyy

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However, it is mathematically convenient, and matches experiments to have models in which the wave function extends to infinity, or in which the results are observed "from infinity". Even in classical physics, a small conducting sheet can be treated as infinitely large for many purposes.

At a more formal level, one has to remember that the wave function is not a field on spacetime, but something in Hilbert space, so it does not "extend to infinity" in the usual spacetime sense.

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So your saying, mathematically the wave function extends to infinity. But physically it cannot extend to infinity, correct?

However, it is mathematically convenient, and matches experiments to have models in which the wave function extends to infinity, or in which the results are observed "from infinity". Even in classical physics, a small conducting sheet can be treated as infinitely large for many purposes.

At a more formal level, one has to remember that the wave function is not a field on spacetime, but something in Hilbert space, so it does not "extend to infinity" in the usual spacetime sense.

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atyy

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Yes.So your saying, mathematically the wave function extends to infinity. But physically it cannot extend to infinity, correct?

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atyy

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Nugatory

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We assume that it extends to infinity because:Is this proven that wave functions extend to infinity, or is it just a theory? What makes them assume that it extends to infinity?

- The wave function is a solution to Schrodinger's equation, and it can be proven (by math) that many solutions of that equation never quite go to zero no matter how far away you go.

- Experiments show that, to the limits of experimental accuracy, these solutions accurately describe the real world everywhere that can and have checked - we can't check at arbitrary distances from earth, nor can we tell the difference between "wave function is zero" and "wave function is so small that the difference between it and zero is less than the limits of experimental accuracy".

There's nothing special about quantum mechanics here. Classical mechanics has its famous inverse-square laws that you will have learned in high school: Newton's law of gravity ##F=Gm_1m_2/r^2##; and Coulomb's electrostatic law ##F=CQ_1Q_2/r^2##. Not only do both of these suggest that the field extends out to infinity, but the inverse square fields fall off with distance much less than than the declining exponentials of the solutions to Schrodinger's equation.

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Sorry if I might be asking repetitive questions. But in all Ψ ontic interpretations of qm where the wave function is real( MWI, de brig lie, penrose, etc), they physicallyYes.

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Nugatory

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OK, this thread is done.Sorry if I might be asking repetitive questions. But in all Ψ ontic interpretations of qm where the wave function is real( MWI, de brig lie, penrose, etc), they physicallydo notextend to infinity?

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