Loophole-free test of local realism via Hardy's violation

[Morbert]

I'm ignorant on the following question in this interpretation (sorry if it's off topic for this thread): Let's say I run a stern-gerlach experiment and get the result of spin up. Does your interpretation allow observables that commute with spin to take on values even though they aren't directly observed?

Just to emphasize the subtlety in minimalist interpretations: Observables represent macroscopic tests, and a quantum system is "a useful abstraction that does not exist in nature, and defined by its preparation" (A. Peres) What a pair of commuting observables imply is a quantum system can be prepared such that the outcome of the joint/both tests represented by the pair of observables can be known with effective certainty. So when a minimalist defines a system by, say, $|\vec{p}_1,1/2\rangle$, they are not asserting that the quantum system now has values for spin and momentum. They are asserting the outcome of a joint spin-momentum test (or either individual test) can be predicted for this quantum system.

 

[vanhees71]

If you could prepare a silver atom in the state $|\vec{p}_1,1/2 \rangle$ then the momentum of this atom has the determined value $\vec{p}_1$ and the spin-$z$ component as the determined value $\hbar/2$. Of course in reality you cannot prepare such a state, because it's not normalizable to 1, i.e., the momentum must have some uncertainty, which can be made as small as you like but never made 0. That's because the momentum operator has a continuous spectrum. Despite this qualification, if a system is prepared in an eigenstate of an operator that represents an observable, then this observable takes the corresponding determined value, i.e., the eigenvalue of this operator.

 

[Morbert]

If you could prepare a silver atom in the state $|\vec{p}_1,1/2 \rangle$ then the momentum of this atom has the determined value $\vec{p}_1$ and the spin-$z$ component as the determined value $\hbar/2$. Of course in reality you cannot prepare such a state, because it's not normalizable to 1, i.e., the momentum must have some uncertainty, which can be made as small as you like but never made 0. That's because the momentum operator has a continuous spectrum. Despite this qualification, if a system is prepared in an eigenstate of an operator that represents an observable, then this observable takes the corresponding determined value, i.e., the eigenvalue of this operator.

Yes the usual caveats about momentum applies. I have a bit more to say but since we are already quite far from the thread topic I will start a new one.

 

[haushofer]

-It wasn't that simple. -Yes, it was. The heliocentric model was not accepted when it was first proposed (by Copernicus), because it did not match observations as well as the geocentric model. It was not until Kepler developed a better heliocentric model using elliptical orbits and based on Tycho Brahe's data that the heliocentric model made more accurate predictions--and then it became accepted. (To be fair, there was also religious dogma involved, which made it harder for the heliocentric model to become accepted even after it made more accurate predictions. But if it hadn't made more accurate predictions to begin with, nobody would have even tried to get it accepted in the face of religious dogma.)

- I'm not claiming "it was simple"; I'm claiming that observations weren't the only input, and afaik it wasn't Einstein's main reason to find an alternative for Newton's theory of gravity.

- I'm refering to the fact that people could add arbitrary amounts of epicycles to the geocentric model to "explain observations".

But nevermind, this is off-topic here,

 

[vanhees71]

Of course, the development of theories is not simply to take some observations and put them in a mathematical scheme. It's a complicated interrelation between theory and experiment. E.g., the motiviation for Einstein to devlop GR was of course that after the electromagnetic interactions (Einstein 1905) and classical mechanics (Planck 1906) has been successfully "translated" to the relativistic spacetime model, also the gravitational interaction had to be somehow incorporated into relativity. Characteristically for Einstein in his younger years he immediately found out the one specific empirical fact about the gravitational interaction was the equivalence principle, i.e., that in small enough regions of space and for sufficiently small time intervals the gravitational interaction is equivalent to choosing a (local) non-inertial frame of reference. What this really mathematically means in the context of relativistic spacetime took him then 10 years and finally lead to GR.

 

[Twodogs]

This is a wide ranging and incisive discussion that prompts a question.
There is a YouTube video in which a physics post-doc uses the Schrödinger equations to calculate the energetics of “a speck of dust in a light breeze”. He determined that such a speck of dust was outside the quantum realm by 20 orders of magnitude.
Is there such a clear demarcation between a quantum realm wherein the low energetics produce uncertainty and non-local phenomenon and a more classical realm wherein events seem to be more clearly determined? I guess that here measurement is still problematic, the keenness of its blade.
Perhaps this is an off topic question or I am simply out of my depth here.

 

[vanhees71]

There is no clear "demarcation" between a quantum and classical realm. The latter is an approximation of the former. Whether or not you can observe quantum properties on macroscopic objects is a question of the ability of preparation as well as accuracy in measuring. A macroscopic object consists of a huge number of microscopic degrees of freedom, which usually you cannot resolve, i.e., you describe the system by some "relevant" macroscopic degrees of freedom. Usually it is very difficult to prevent decoherence concerning these macroscopic degrees of freedom due to their coupling to the many microscopic ones. The decoherence makes the behavior of the macroscopic degrees of freedom classical.

 

[Twodogs]

Thank you. So, while there is no clear demarcation between quantum and classical realms, there is a limit to the ability of an experimentalist to mathematically model more complex systems. There is no clear demarcation, but rather a sharply attenuated segue between realms. As the mass/energy of the system increases, there is a commensurate increase in the certainty of whether things will go one way or another in the work-a-day world. One can reliably set the shopping bag on the counter.