Consistent Histories inability to combine Frameworks

[jbergman]

TL;DR

The single framework rule in CH makes it hard to accept conclusions drawn from a framework as ontic without additional rules for selecting frameworks.

Suppose you have a 2 step Stern Gerlach where you measure spin in the z-direction and then in the the x-direction.

I can have two incompatible frameworks for the two time steps. Not sure on the correct notation here.

For Framework 1 we have the projectors at $t_1$ $[z^+]$, $[z^-]$ and $[x^+]$,$[x^-]$ at $t_2$.

For Framework 2 we have the projectors at $t_1$ $[x^+]$, $[x^-]$ and $[x^+]$,$[x^-]$ at $t_2$.

We then measure spin up, $z^+$, and spin right $x^+$.

As I understand it in the first framework that would give the history of $[z^+]\odot [x^+]$ a probability of 1.

And in the second framework $[x^+]\odot [x^+]$.

So according to CH, in one framework the history was definitely spin up and spin right and in a different framework it was spin right at both timesteps.

The inability to conclude that the particle was $x^+$ and $z^+$ at $t_1$ is hard for me to reconcile. Doesn't that fundamentally mean that CH is not a true description of reality without additional rules for determining which frameworks are valid?

 

[gentzen]

TL;DR: The single framework rule in CH makes it hard to accept conclusions drawn from a framework as ontic without additional rules for selecting frameworks.

You want additional rules for selecting frameworks? Like one might want additional rules for selecting the initial state in MWI? Or if you have an elliptic PDE additional rules for selecting boundary conditions?

And without such rules, you believe it would be hard to accept conclusions drawn as ontic?

Wait, I might be starting to see why people have more issues with framework selection than with the initial state: You want to have a state given at some point in time, and then an unambiguous rule how it propagates into the future, just like in Bohmian mechanics. The freedom to select frameworks is annoying, because it means information is constantly flowing into the system "from the sides".

For an experiment in a laboratory, you may know and control that information influx. But if you want to apply CH (or decoherent histories) to the entire universe (like MWI), things stop working. So CH is not better than Copenhagen in this respect, that it breaks down in such scenarios.

I am willing to accept this as a limitation of CH, just like Bohmians are willing to accept non-locality as a limitation of BM.

 

[Morbert]

The inability to conclude that the particle was $x^+$ and $z^+$ at $t_1$ is hard for me to reconcile. Doesn't that fundamentally mean that CH is not a true description of reality without additional rules for determining which frameworks are valid?

Roland Omnes, another founder of CH, takes an alternative approach. He would say this unease of yours is because neither framework makes true statements about the particle. Frameworks do not provide truth. They instead provide reliability for predicting what data you will collect in your experiments.

 

[jbergman]

Roland Omnes, another founder of CH, takes an alternative approach. He would say this unease of yours is because neither framework makes true statements about the particle. Frameworks do not provide truth. They instead provide reliability for predicting what data you will collect in your experiments.

Yeah. What really bothers me is in the second framework where we say that the particle has spin $x+$ with 100% probability.

If we had a rule to the effect that at time steps where measurements have been made, frameworks are preferred that commute with the measurement result so you don't get non-sensical statements that are not compatible with measured outcomes.

 

[Morbert]

Yeah. What really bothers me is in the second framework where we say that the particle has spin $x+$ with 100% probability.

What bothers you about it?

 

[gentzen]

Yeah. What really bothers me is in the second framework where we say that the particle has spin x+ with 100% probability.

I once quoted from “Quantum Philosophy” by Roland Omnès parts of the replies to such objections:

Some of them will lead to the same conclusions and they are just as good. Others will be useless, not necessarily wrong but only idle talk of no consequence. Why bother? Asking questions about the existence of useless histories amounts to performing calculations that are of no help in solving a problem. They belong in the waste-paper basket.

 

[jbergman]

What bothers you about it?

I mean at $t_1$, we have only measured the z-spin, so I would consider the x spin not known. But if we choose the projectors I described in framework 2 we are forced to conclude that the electron had spin $x^+$ at $t_1$.

 

[Morbert]

I mean at $t_1$, we have only measured the z-spin, so I would consider the x spin not known. But if we choose the projectors I described in framework 2 we are forced to conclude that the electron had spin $x^+$ at $t_1$.

Note that the conclusion of $x^+$ at $t_1$ follows because at $t_2$, the apparatus registers $x^+$. This is the intuitive everyday notion we have of measurement at some time revealing a pre-existing property.