I Does the Compton wavelength put a limitation on position measurements?

I have read on Wikipedia (https://en.wikipedia.org/wiki/Compton_wavelength) that we cannot measure the position of a particle more precise than half of its Compton wavelength, since the photon we would need will be so energetic to produce electron-positron pairs.

How does the creation of electron-positron pairs lead to uncertainty? Does this this fundamentally and in principle limit our possible knowledge of a particle's position?
 
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we cannot measure the position of a particle more precise than half of its Compton wavelength, since the photon we would need will be so energetic to produce electron-positron pairs.
Not electron-positron pairs, but particle-antiparticle pairs of the same type as the particle you are trying to measure.

Does this this fundamentally and in principle limit our possible knowledge of a particle's position?
It limits our ability to measure the particle's position, because if a pair is created, there is no way to know whether the position that just got measured applies to the original particle or the particle of the pair that got created (since the two are indistinguishable).
 
Not electron-positron pairs, but particle-antiparticle pairs of the same type as the particle you are trying to measure.



It limits our ability to measure the particle's position, because if a pair is created, there is no way to know whether the position that just got measured applies to the original particle or the particle of the pair that got created (since the two are indistinguishable).
could you explain why they are not indistinguishable? How does the measurement work when we shoot a photon toward the particle?
 
They are indistinguishable.
My question was, how does the position measuring process using a photon works, and why it can't distinguish between the two particles. Do you mean that we get a result which is correct with a probability of %50?
 
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how does the position measuring process using a photon works
You shoot a photon at the area where you think the particle is, and watch what happens to it.

why it can't distinguish between the two particles
Nothing can distinguish between two quantum particles of the same type (such as electrons). That's a basic fact of QM.

Do you mean that we get a result which is correct with a probability of %50?
No, I mean that if a particle-antiparticle pair is created, there are now two particles present of the same type (the original particle, and one of the pair), and there is no way of telling which of the two particles of the same type caused the photon to do whatever you saw it do.
 

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