Can two simultaneous independent measurements circumvent uncertainty?

Question

Without understanding the mathematics, I have learned that the uncertainty principle precludes being able to precisely measure the position and velocity of a particle at the same time. So my question is, would two different people be able to measure a particle at the same time, one measuring the velocity and the other the position. And so by sharing their results be able to circumvent the uncertainty principle?

Answer 1

No matter how many people take measures, the object under study is the same for all of them. So you can't avoid the indetermination principle.

Answer 2

I ask that you learn the mathematics. It is not too hard! You don't even need to understand all of the bra/ket formalism or the Schrödinger equation, just the de Broglie relation is enough.

Waves have a size scale at which they interfere, which we call their "wavelength," and de Broglie correctly predicted that for matter this would go inversely as the momentum, $\lambda=h/p$. The whole quantum theory is about matter being made of these probability waves with these sizes. But there is an intrinsic uncertainty between the position of a wave and its wavelength: if you know its position really well then you know it fits into a very small box, say of size $\Delta x$. But if you know its wavelength very well then you must be able to observe it for many wavelengths, and that means it must be spread out over space.

With a bit of reasoning you can come to this idea: that for any waves there should be an intrinsic fractional uncertainty in wavelength $\lambda$ which goes inversely with the count of wavelengths that fit in the box, $\Delta x/\lambda$. We would write this as $$ \Delta\lambda/\lambda \ge \alpha \lambda/\Delta x.$$With some mathematics due to a man named Fourier we can determine what this constant $\alpha$ must be, and with some mathematics due to a man named Leibniz we can see this pattern of uncertainty $\Delta \lambda/\lambda^2$ as an uncertainty in the reciprocal $\Delta(1/\lambda),$ which de Broglie's relation tells us is $h^{-1}~\Delta p$ because $h$ is a constant.

So to answer your question whether two people can measure both simultaneously: No, they will get in each other's way because one is trying to see if the particle is in a small box, and the other is trying to measure the number of wavelengths that fit into that box, but as they want to measure precisely enough to violate the uncertainty principle, the first researcher has a maximum size constraint while the second has a minimum size constraint for the same box.

Answer 3

When you measure something, a limit in the uncertainty you have is how well defined is the quantity you want to measure. Example: the position of a table with 1 meter of width, will have a inevitable error of 1 meter in the direction of it's width, because the table isn't a point with infinitelly well defined position. Well, when two variables don't conmute and heissemberg's uncertainity tell's you that the product of the error of both quantities is, at least, a given magnitude, tour trouble with the inevitable error on the measurement is in the object itself (the table width), not in the way you are trying to measure. If you smash the table and you cut it in tiny pieces, you will have a smaller error with the position of every bit of what ago was a table, but you aren't trying anymore to measure the table's position, because it doesn't exist anymore. Also, if you are trying to measure the position of a part of the table when it isn't broken, that's a different measurement, it isn't the table position.

Good look.