About Heisenberg uncertainty principle

Question

What would happen if someone invented a way to measure both position and momentum precisely? If it is impossible why?

Answer 1

I sense that the mathematical derivation of the uncertainty principle may not be a sufficient explanation... :) But if you're interested, look at the answer here: Heisenberg Uncertainty Principle scientific proof

Think about how we look at something in macro space - we shine a light on it, such as with a microscope, and see what reflects back. In the case of a very small particle, this light could be as small as one photon - but one photon has enough momentum to push the object we're examining when they collide. So if we want to know where a particle is in space, we bounce a photon off of it - but this accelerates the particle, so now its momentum is "uncertain" (or changed). Likewise if we want to know what its momentum is - now its position has changed.

Whatever technique is used to measure a quantity (photons are just an example), it necessarily has an impact on the subject of that measurement. Thus it is impossible to measure these quantities simultaneously to a degree of precision which exceeds the uncertainty principle's limitations.

Answer 2

You've probably heard the observational reason for the uncertainty principle which basically states that if you measure either position or momentum very accurately your measurement changes the other. That's a really nice hand-wavy explanation but the uncertainty principle is fundamental to waves and is not about measurement.

Check out the Wikipedia article on this. The second paragraph states:

[...] the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology

The article goes on to spell out in detail why this is so.