Questions about Adler paper "Why Decoherence has not Solved ...."

[msumm21]

TL;DR Summary

Two questions I have regarding the paper "Why Decoherence has not Solved the Measurement Problem" by S. Adler

On page 8, I don't understand the last paragraph. It says if $|A \rangle = U|0\rangle$ and $|B \rangle = U|0\rangle$ then $\langle A | B \rangle = 1$. Of course $U |0\rangle$ is a unique state ($A$ and $B$ are the same by this definition). So I assumed what he meant was more like $U_t|0\rangle$ and $U_{t'} |0\rangle$ (where $U_t$ is evolution over time $t$ and $t\neq t'$) for $A$ and $B$, but then the conclusion $\langle A | B \rangle = 1$ is not true. Anyone understand this paragraph, or what is meant by $A$ and $B$ here?

The last paragraph (pages 10-11) discusses an alternate "stochastic unitary evolution" which could agree with the predictions of QM for both microscopic and macroscopic systems. This looks interesting at first (at least to a non expert). Has subsequent work falsified or supported such approaches?

 

[PeterDonis]

Summary:: Two questions I have regarding the paper "Why Decoherence has not Solved the Measurement Problem" by S. Adler

Can you provide a link?

 

[Paul Colby]

This seems to be a match.

 

[msumm21]

This seems to be a match.

Yep that's it, sorry I meant to include it in the original post.

 

[PeterDonis]

On page 8, I don't understand the last paragraph. It says if $|A \rangle = U|0\rangle$ and $|B \rangle = U|0\rangle$ then $\langle A | B \rangle = 1$. Of course $U |0\rangle$ is a unique state ($A$ and $B$ are the same by this definition).

Yes, they are. This paragraph is supposed to be justifying the statement that you can't get both of the orthogonal observed outcome states in equations 6a and 6b by unitary evolution from the same initial state; but that should already be obvious from the fact (which you are in effect pointing out) that unitary evolution is deterministic and one-to-one, so from any given initial state you will always get just one final state; you can't possibly get sometimes one state and sometimes another. I'm not sure why the author didn't just make that (stronger and more obvious) observation in words, since that is effectively what the math he gives shows.

The last paragraph (pages 10-11) discusses an alternate "stochastic unitary evolution" which could agree with the predictions of QM for both microscopic and macroscopic systems. This looks interesting at first (at least to a non expert). Has subsequent work falsified or supported such approaches?

AFAIK this alternative is still consistent with experiments to date, but it has theoretical issues when trying to explain correlations that violate the Bell inequalities. I believe there have been some previous PF threads on this.

 

[gentzen]

They meant exactly what they wrote in that paragraph on page 8. The point is that two orthogonal states A and B cannot have evolved from the same initial state by unitary evolution, since if they did, they would be parallel instead of orthogonal.

 

[PeterDonis]

The point is that two orthogonal states A and B cannot have evolved from the same initial state by unitary evolution, since if they did, they would be parallel instead of orthogonal.

No, they wouldn't just be parallel, they would be the same state. Unitary evolution is deterministic and one-to-one. If you start from the same initial state and apply the same unitary operator, you will always get exactly the same final state. Not just one of a set of parallel states--the exact same state.

 

[gentzen]

No, they wouldn't just be parallel, they would be the same state. ... Not just one of a set of parallel states--the exact same state.

Yes, we all know that. What we don't know is how to help msumm21 accept that S. Adler had his reasons for writing that paragraph like he did.

I'm not sure why the author didn't just make that (stronger and more obvious) observation in words, ...

Neither do I, but I tried to come up with a reasonable explanation to make sense of that paragraph.

 

[PeterDonis]

What we don't know is how to help msumm21 accept that S. Adler had his reasons for writing that paragraph like he did.

Maybe he doesn't need to accept such a thing. Maybe there wasn't a good reason for that paragraph being written like it was written.

Yes, we all know that. What we don't know is how to help msumm21 accept that S. Adler had his reasons for writing that paragraph like he did.

Neither do I, but I tried to come up with a reasonable explanation to make sense of that paragraph.

Maybe there isn't one. There is no requirement that everything in a paper must make sense when read by someone other than the author.