Mixed and Pure states in QM

[Alan Grayson]

Doesn't a mixed state satisfy the Ignorance Interpretation by definition? Concerning a pure state, does it negate the Ignorance Interpretation because it's a linear combination of pure state vectors in some Hilbert Space? 

Brent was emphatic, writing "exactly wrong" that a pure state, presumably represented as a linear sum of pure basis states, could be interpreted by the Ignorance Interpretation. But he hasn't proven that, or given a link which does. 

Quentin, OTOH, offered an example to show that a pure state could not be interpreted as satisfying the Ignorance Interpretation, but his example had a typo near the beginning which he hasn't corrected, so I gave up on his example.

So, what is the status of the Ignorance Interpretation for mixed and pure states, and why is that the case. TY, AG

[Alan Grayson]

Concerning pure states which are linear sums of basis vectors, aka a superposiiton, my claim is that a system which is in such a state, is NOT simultaneously in all states of the superposition; rather, as in linear algebra, each basis state just contributes to, but is not equivalent to the summed state. With this interpretation, some of the weird claims of QM go away, such as that a system can be in different locations simultaneously. AG

[Alan Grayson]

On Saturday, November 16, 2024 at 11:03:43 PM UTC-7 Alan Grayson wrote:

Concerning pure states which are linear sums of basis vectors, aka a superposiiton, my claim is that a system which is in such a state, is NOT simultaneously in all states of the superposition; rather, as in linear algebra, each basis state just contributes to, but is not equivalent to the summed state. With this interpretation, some of the weird claims of QM go away, such as that a system can be in different locations simultaneously. AG

Consequently, it's obvious why a pure state cannot be interpreted by the Ignorance Interpretation, because every pure state can be decomposed into a set of basis vectors in some Hilbert Space, even orthogonal basis vectors if so desired. Thus, since each basis vector defining the summed state contributes to, but isn't equivalent to the summed state, it would be incorrect to assert that the summed state is identical to one of those basis vectors, but we just don't know which one. AG 

[Alan Grayson]

On Sunday, November 17, 2024 at 12:36:28 AM UTC-7 Alan Grayson wrote:

On Saturday, November 16, 2024 at 11:03:43 PM UTC-7 Alan Grayson wrote:

Concerning pure states which are linear sums of basis vectors, aka a superposiiton, my claim is that a system which is in such a state, is NOT simultaneously in all states of the superposition; rather, as in linear algebra, each basis state just contributes to, but is not equivalent to the summed state. With this interpretation, some of the weird claims of QM go away, such as that a system can be in different locations simultaneously. AG

Consequently, it's obvious why a pure state cannot be interpreted by the Ignorance Interpretation, because every pure state can be decomposed into a set of basis vectors in some Hilbert Space, even orthogonal basis vectors if so desired. Thus, since each basis vector defining the summed state contributes to, but isn't equivalent to the summed state, it would be incorrect to assert that the summed state is identical to one of those basis vectors, but we just don't know which one. AG

 

However, upon further consideration, it is evident that analyzing pure states which are sums of pure states in terms of basis vectors, a superposition is in all states of its sum simultaneously. So I agree with Brent's original claim, which I just stated, as well as the fact that the Ignorance Interpretation of a superposition cannot be applied. AG