### Heisenberg uncertainty principle

(uncertainty principle)
(limit on observable position and momentum of an object)

The Heisenberg uncertainty principle is a limit on how precise the position and momentum of an object is defined, specifically a limit on the product of their precise values such that the more precise the momentum is known to be, the less determined the location is. The large mass of everyday items makes this lower limit unnoticeably small for them, but the limit is significant at atomic scale and smaller. A concise statement of the principle:

```σxσp ≥ ℏ/2
```

Since the object's momentum is directly related to its mass, another way of stating the principle is that the definition of the object's speed and position are limited by an amount inversely proportional to the object's mass. The principle is derived from quantum mechanics (QM), essentially a theorem that can be used in QM calculations, and which can be thought of as one of QM's weird aspects. The question of whether the object really has no precise position and momentum versus the notion that we are merely unable to determine both (hit the object with a photon to attempt to locate it and you've pushed it a bit) is under continual discussion, and depends upon interpretation of QM, but whatever the answer, it must be consistent with the established fact that putting a particle near a barrier such that this principle suggests it might be on the other side of the barrier does sometimes result in the particle being there (i.e., resulting in quantum tunneling), which is not merely observed in the lab, but used in everyday technology such as tunnel diodes.

(physics,quantum mechanics)