The HUP says that the more precision with which you measure position, the less precisely can you know momentum, and visa-versa. What if you're not measuring either? What can be said of a particle's position and momentum in that case? Are they both equally (and highly) uncertain?

 

Well, of course they are - if you don't measure either, how can you know either? - but aren't quantum physicists in the habit of taking epistemological statements and treating them as interchangeable with ontological ones? I mean, wouldn't a hardnosed positivist say that if you don't know either the particle's position or its momentum, then it actually has neither to any precision? And if that's so, doesn't this pose as an exception to the HUP as it is mathematically expressed (i.e. as an indirect proportionality)?

How is not knowing either a violation of the inequality?

It's not. What's a violation is when you have:

 

delta x * delta y = constant

 

but allowing delta x and delta y to both be very large.

Right, but since it's an inequality, there isn't a problem.

Right, but since it's an inequality, there isn't a problem.

 

Oh, it's an inequality - that explains it.