Existence and the interpretation of infinite uncertainty?

[hollowsolid]

The trade off in uncertainty in momentum vs position in the HUP leaves me
confused.

In the context where the momentum is measured to increasingly greater precision and
consequently position becomes less refined, is any logical inference made about the
existence of the object i.e. is it less less likely to actually be in existence since it is
convergng to an infinite uncertainty on exactly WHERE it exists.

Similar logic could apply to the Energy-time uncertainty relation.

OR

Do we reason that the object exists because it has momentum measured to to higher
and higher precision, but just where it has that momentum is increasingly unknown.

Yet I would have thought that an object that is becoming infinitely less precise in
having a momentum property AT a position in space is testing the limits of being a
physical object at all.

Does uncertainty converge in any situation which reaches a known limit such as
for example at the Planck scale.

Also I'm assuming the HUP has relativistic versions?

 

[AndyW]

Thank you for raising these interesting questions about the Heisenberg uncertainty principle (HUP) and its implications on the existence of objects. I can understand how the trade-off between uncertainty in momentum and position can be confusing. Allow me to provide some insights and clarification on this topic.

Firstly, it is important to note that the HUP is a fundamental principle in quantum mechanics, which states that it is impossible to simultaneously know the exact position and momentum of a particle. This means that the more precisely we measure one of these properties, the less precise our measurement of the other property will be. This does not mean that the particle does not exist, but rather that our knowledge of its properties is limited by the fundamental nature of quantum mechanics.

In the context where momentum is measured to increasingly greater precision, it does not necessarily mean that the particle is less likely to exist. It simply means that our knowledge of its position becomes less refined. The particle still has a definite momentum, but its exact position cannot be determined with certainty. This does not question the existence of the object itself.

Similar logic applies to the energy-time uncertainty relation. As we try to measure the energy of a particle more precisely, our knowledge of the time at which it has that energy becomes less precise. However, the particle still exists and has a definite energy, but our ability to measure it is limited.

It is important to note that the HUP is a fundamental principle and applies to all objects, regardless of their size or scale. This means that even at the Planck scale, where the uncertainty becomes very small, it still exists.

Regarding your question about the HUP having relativistic versions, the answer is yes. In fact, the HUP is a fundamental principle in quantum mechanics and applies to all physical systems, including those described by relativity.

In conclusion, the HUP does not question the existence of objects, but rather highlights the fundamental limitations of our knowledge and measurement in quantum mechanics. I hope this helps to clarify any confusion you may have had on this topic.