Non-separability and solipsism

[Maui]

Are they different and in what way?

 

[Fredrik]

Are they different and in what way?

What do you mean by non-separability? (You posted in the quantum physics forum, and here it means that a topological space doesn't have a countable base. For Hilbert spaces, it can be translated to "doesn't have a countable orthonormal basis").

 

[Maui]

What do you mean by non-separability? (You posted in the quantum physics forum, and here it means that a topological space doesn't have a countable base.

Well yes, consider an entangled state W of a system S - neither subsystem S₁ nor S₂ is, by itself, associated with an individual definite state. If a physical system is described by a state vector assignement of states, then S₁ and S₂ can be said to have no definite states at all, even when S₁ and S₂ are spatially separated. Only the compound system S is in a definite pure state, represented by a state vector. Hence, knowledge of the parts of a system does not allow the possibility of gaining knowledge of its component parts(no state vector for S₁ and S₂ in S), and the separability principle is violated. Nonseparability may be described by saying that there exists only the whole, and not the parts, or the parts lack individuality(S₁ and S₂ can be assumed to have a state, but only after a reference is made to its partner state via the information in S). Without making additional assumptions, the 'parts-whole' nonseparable relation in spatially separated entangled states implies solipsism, doesn't it?

 

[tom.stoer]

You are confusing non-separability in the sense used for Hilbert spaces with non-separability in the sense of non-locality.

To make it clear: an entangled state like
|S> = |a,b> + |b,a>
for particles |1,2> can be formulated in a separable Hilbert space but is "not separable" in two single particle states. But this "separable" is the wrong term; nobody will understand what you mean.

 

[Demystifier]

Without making additional assumptions, the 'parts-whole' nonseparable relation in spatially separated entangled states implies solipsism, doesn't it?

I think that solipsism also cannot be derived from it without making additional assumptions.

 

[jambaugh]

Nonseparability may be described by saying that there exists only the whole, and not the parts,...

Careful here. The parts don't fail to exist, they fail to have a definitive description as parts...until and unless observed. But this is no different from the indefiniteness of any quantum in the absence of a measurement.

Let me say it this way. The obstacle to separation is not physical. One can choose to observe and manipulate the separate subsystems. The obstacle is one of logic, you cannot both assume an entangled system and then ignore the entanglement by making statements about the individual components prior to a corresponding measurement.

Recall that the preparation of the composite in an entangled "state" is itself an act of measurement of the whole. This inseparability is another manifestation of the HUP. Just as you cannot make statements about a quantum's position when one has prepared it with or measured a definite momentum, one cannot make statements about separate component modes when one has assumed the measurement of an entangling correlation.

Just because our quantum by virtue of definiteness of momentum have no definite position doesn't mean the ability to subsequently measure a position ceases to exist. Likewise just because our quantum pair are correlated and have no definite individual sharp modes doesn't mean we have lost any ability to measure individual observables.

It is helpful to speak separately of the existence of a property (that may be observed) and the existence of a value for that property (that has been observed). We, of course, are shaving hairs mighty thin here. In the presence of an incompatible measurement the value ceases to exist even as an unknown value, hence the failure of Bell type inequalities.

 

[Maui]

Careful here. The parts don't fail to exist, they fail to have a definitive description as parts...until and unless observed.

The sentence you quoted parts of finished in: "(S1 and S2 can be assumed to have a state, but only after a reference is made to its partner state via the information in S). ", which is essentially the same as what your remark addressed.

But this is no different from the indefiniteness of any quantum in the absence of a measurement.

In the example i gave, not only is there indefiniteness, but a kind of nonseparableness of the states S₁ and S₂. The nonseparability is the key issue that I meant to discuss.

Let me say it this way. The obstacle to separation is not physical. One can choose to observe and manipulate the separate subsystems. The obstacle is one of logic, you cannot both assume an entangled system and then ignore the entanglement by making statements about the individual components prior to a corresponding measurement.

This is a key issue. There is an obvious physical, spatial separation that without making additional assumptions(nonlocal influencing, magic, coincindence, strong determinism, etc.) appears to point to nonseparability(if some mild form of realism is to be retained). If the obstacle to separation is not physical, then there must be some new, unexplored part of physics going on.

 

[Maui]

I think that solipsism also cannot be derived from it without making additional assumptions.

Valid point, solipsism and non-separability aren't different definitions of the same phenomenon, hence my initial question is somewhat wrongly posed. However, peculiarly, they both describe a nonseparable oneness that's hard or impossible to understand in different terms.

 

[jambaugh]

...This is a key issue. There is an obvious physical, spatial separation that without making additional assumptions(nonlocal influencing, magic, coincindence, strong determinism, etc.) appears to point to nonseparability(if some mild form of realism is to be retained). If the obstacle to separation is not physical, then there must be some new, unexplored part of physics going on.

Or the insistence on even a mild form of realism (at a fundamental level) is inconsistent with empirical experience.

I don't think you can moderate (e.g. speak of a mild form) the reality hypothesis except in the way I think should be done namely: Objective Reality is a pragmatic construct we use tentatively for classical scale phenomena. It is in trying to retain reality at the fundamental level that we end up bending over backwards and invoking very unlikely assumptions such as non-local yet unobservable causation.

Stuff happens... and happens in a very consistent way we can codify via physical theory. We construct a classical reality model of interacting objects with objective states and it works great for doing classical physics but this model fails to properly predict quantum phenomena. We see quantum phenomena so why insist on retaining that classical reality model?

It is technically metaphysical solipsism in that I am saying reality is all in our minds but not in the sense usually interpreted. The metaphysical solipsism is integrated into a phenomenological materialism. We can call it actualism. There is an independent actuality of external phenomena (electrons, protons, neutrons and photons buzzing around as phenomena) but their description as classic classical objects is only in our minds.

 

[Pythagorean]

Jambaugh,

just to nitpick, all those electrons, protons , etc aren't just buzzing around is, they're part of us, and they mingle in and out of the boundary between us and our external environment, as fuzzy as that boundary is.