I Uncertainty of momentum and position

[manojr]

I was reading a book which had some comments on EPR paper (Einstein, Podolsky, Rosen - 1935) like following:
In Newton's physics, when two identical billiard balls hit each other head-on, bouncing off in opposite direction, knowing one ball's position and speed will also indicate other ball's position and speed. However, in quantum physics, when two particles A and B collide, you can either measure A's momentum which let's you infer B' momentum or you can measure A' position instead to infer B's position.

Now, is it possible to measure A's momentum and B' position there by inferring other attributes of each other? I suspect not, but can someone help to explain why not?

Thank you.

 

[PeroK]

I was reading a book which had some comments on EPR paper (Einstein, Podolsky, Rosen - 1935) like following:
In Newton's physics, when two identical billiard balls hit each other head-on, bouncing off in opposite direction, knowing one ball's position and speed will also indicate other ball's position and speed. However, in quantum physics, when two particles A and B collide, you can either measure A's momentum which let's you infer B' momentum or you can measure A' position instead to infer B's position.

Now, is it possible to measure A's momentum and B' position there by inferring other attributes of each other? I suspect not, but can someone help to explain why not?

Thank you.

One fundamental difference is that in QM particles don't have defined dynamic quantities until you measure them. And, in particular, particles do not have well-defined classical trajectories. You can measure what you want, but you can't infer a classical trajectory for either particle.

Also, the Heisenberg Uncertainty Principle (HUP), which you are alluding to is not about what you can measure but about the range of measurement values that you might get.

To take an example: suppose you have an experiment where a particle emerges and, at some time, you measure its momentum. QM says that there must be a range of possible values that you could get. This is not connected with any margin for error in your experimental setup (although you have to take that into account as well). But, if you repeat the identical experiment many times you will get a range of momenta.

If, instead, you measure the position of the particle, you will also get a range of values.

What the HUP says is that there is a relationship between these two ranges: the smaller the range in momenta, the larger the range in position, and vice versa. The HUP does not have anything to say about any individual measurements.

So, even if you make a measurement of momentum on your particle and infer its position from another measurement, the HUP isn't violated. What would violate the HUP is if you got a very small range of momentum measurements and a very small range of inferred position measurements. That would essentially be a violation of the HUP for your two-particle system.

What you would expect, therefore, is that if the range of momentum measurements of one particle was very small (i.e. almost always the same momentum), then the corresponding measurements of position of the other particle would have a larger range (in accordance with the HUP). And, hence, your inferred position measurements would also have a larger range of values.