Confusion About Quantum Uncertainty

It is a somewhat contentious issue between two points of view on the Heisenberg Uncertainty Principle
(1) You can't measure both of two conjugate characteristics (e.g. position and momentum) simultaneously with no error in either one
(2) You can measure them but if you create EXACTLY the same starting conditions again, you won't get the same result.

I think #2 is generally agreed on by everyone, so it's the best way to look at it. In any case, it's not a measurement problem, it's a fundamental characteristic of nature. Basically, what #2 says is that nature is not deterministic, it is probabilistic.

The other aspect of what you are asking is, I think, "what is an electron doing when no one is looking", and the answer is "what it is doing is not defined". That is an electron does not HAVE a position unless and until you measure it. It does hang out close to the atom it belongs to but not in any fixed position or orbit.

 

What you hear is one thing and what can be proved is another thing. Quantum theory does not have a formalism for dynamically describing "knowing." So, what you hear is what many people think, but are not able to prove. A proof would require a reliable and accepted unanomously "measurement theory". There is not such a theory yet. Physicists and philosophers can argue, but then others can argue differently. Rely on what has been proven and not on what people think or write.

 

This is only partly true. It is possible to mathematically describe how much information you can possibly obtain about both the position and momentum of a particle. In particular, you can reformulate the uncertainty principle in terms of information and entropy.

In that form the uncertainty principle would be read as:
" No matter what the measurement, the remaining number of bits you would need to uniquely specify the position and momentum of the system you measured at the time of measurement will always be some number greater than zero"
The specific number depends on your experimental setup and the kind of measurement you do.

 

This is only partly true. Quantum theory does not have a dynamical scheme describing the process of "obtaining information".

 

Quantum mechanics experts haven't come to a consensus on resolving the issue of the collapse of the wavefunction, but we can describe the measurement process as an entangling between system and measurement device (i.e., by a coupling Hamiltonian correlating the two), where the possible outcomes of the system become correlated to specific states of the measurement device.

We won't be able to tell which outcome is measured, but it is possible to say how much information is gathered by looking at the duration and the strength of the coupling between system and device.

As a neat example, in weak measurement, the coupling is weak and for a short enough time that the state of the system is negligibly perturbed, while we still learn something about the distribution of outcomes of the observable we weakly measure. The idea is to then strongly measure in another observable so as to get some information, say, about both the position and momentum statistics of a system, or about both the amplitude and phase of a quantum wavefunction.

The limitations of what information can be gathered can be described by information exclusion relations (derived from entropic uncertainty relations). What they say is that the more position information a measurement gathers, the less momentum information it can also gather. The total amount of information is bounded from above by a constant that depends on the particular experiment. These information exclusion relations don't form a dynamical theory of measurement, but the coupling Hamiltonian approach can be thought of as such.

 

This is not a measurement, because it does not result in an "event" that happens in final time. I know that it is hard to admit it, but that's life. The sooner experts realize it and state it clearly and aloud - the better will be chances to solve the measurement problem in quantum mechanics, for instance by taking really seriously alternative approaches.