Try to think about this question and when all your knowledge has been used, search wiki. for this experiment and read Bohr's remark to this experiment.

Imagine a particle A to be a rest hence the center of mass is at rest and the velocity of center of mass and hence the momentum is 0. The particle A decomposes to two particles B and C which move at 180degree angle.What you do is that you make the uncertainity of position of B as small as possible and let the momentum have a huge uncertainity -who cares.And then you measure the momentum of C very carefully neglecting the position of C.

The uncertainity of position of B is z then minimum uncertainity in momentum is of order h/z. But momentum of B=momentum of C hence as we can measure the momentum of C with an uncertainity smaller than h/z we can in a way defy uncertainity principle but which is true........so where lies the fallacy?

To tackle this intriguing question, we need to delve into the principles of quantum mechanics, particularly the Heisenberg Uncertainty Principle. This principle states that there is a fundamental limit to the precision with which certain pairs of physical properties, like position and momentum, can be known simultaneously. In your scenario, we have a particle A at rest that decays into two particles, B and C, moving in opposite directions. Let's break this down step by step to identify where the misunderstanding might lie.

Understanding the Setup

Initially, particle A is at rest, meaning its momentum is zero. When it decays into particles B and C, these particles move apart at a 180-degree angle. According to the conservation of momentum, the momentum of B must equal the momentum of C but in opposite directions. Thus, if we denote the momentum of B as \( p_B \) and that of C as \( p_C \), we have:

• \( p_B + p_C = 0 \)
• \( p_C = -p_B \)

Uncertainty in Measurements

Now, you propose to minimize the uncertainty in the position of particle B while allowing its momentum to have a large uncertainty. According to the Heisenberg Uncertainty Principle, the relationship can be expressed as:

Δx * Δp ≥ ħ/2

Here, Δx is the uncertainty in position, Δp is the uncertainty in momentum, and ħ (h-bar) is the reduced Planck's constant. If you make Δx (the uncertainty in position of B) very small, then Δp (the uncertainty in momentum of B) must become correspondingly large to satisfy this inequality.

Measuring Momentum of Particle C

When you measure the momentum of particle C with high precision, you are essentially determining its momentum with a small uncertainty. However, the key point is that the uncertainty in the momentum of particle B cannot be ignored. Since the momenta of B and C are related through conservation laws, the uncertainty in the momentum of B directly affects the uncertainty in the momentum of C.

Identifying the Fallacy

The fallacy in your reasoning arises from the assumption that you can independently measure the momentum of C with a precision that defies the uncertainty principle. While it is true that you can measure the momentum of C with high accuracy, the uncertainty in the momentum of B must still be accounted for. If you have a large uncertainty in the momentum of B, it translates to a corresponding uncertainty in the momentum of C due to their conservation relationship.

Conclusion

In essence, while you can minimize the uncertainty in the position of B, the momentum of C cannot be measured with arbitrary precision without considering the uncertainty in B's momentum. The Heisenberg Uncertainty Principle remains intact, as the uncertainties are interconnected through the conservation of momentum. This illustrates the profound nature of quantum mechanics, where measurements are not just isolated events but are deeply interwoven with the properties of the entire system.