You leave out the other possibility a particle is nothing more than an illusion and you can no more measure it accurately than you can measure a rainbow, you have assumed particles are infact accepted as real solid things :-)

There are two common views of particles from scientists that fit the above description.

There is a group who would say particles are infact virtual and always have been wave packets. That is there is absolutely nothing solid or fixed about particles ever.

There is a group who would say particles are an illusion reflected into our physical universe they really are the proverbial rainbow.

I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.