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That is because when you want to guide a particle to a precise position, then you need to give it high momentum, so it has enough leeway to spread out in momentum. (Where the trade-off between precision in position and spread in momentum is of course due to HUP.)

But the probing particle has high momentum only in one direction, the direction in which it is accelerated. From that would follow that we can only guide the probing particle in one space direction. The other two directions can't be controlled, since in those there is only little leeway in momentum.

So the question, what happens to the other two space-momentum uncertainty relations in high-energy experiments? (The two relations where space and momentum is orthogonal to the moving direction of the accelerated probing particle.)

thanks in advanced