In principle, it is possible to entangle any property of two particles, including speed and momentum. Surely then, this could be used to defy the Uncertainty Principle, which states that the momentum and position of a particle cannot be together measured with accuracy, but the more accurate one gets, the less accurate the other becomes:
$$\Delta x\Delta p=\dfrac{\hbar}{2}.$$
If one was to set up an experiment where two particles are entangled, one could then measure the position of one particle with great accurary at the same time as measuring the momentum of the other particle with great accuracy, which would mean that, as the two particles are entangled, one would then know the momentum of the particle they measured the position of.
Therefore, the Uncertainty Principle would have been defied, as both momentum and position have been measured with a high accuracy.
However, this can't be true, as someone would have thought of this before.
So why wouldn't this work?
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