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From: Hal Finney <hal.domain.name.hidden>

Date: Fri, 12 Jul 2002 14:23:37 -0700

One of the criticisms of no-collapse theories has always bothered me.

Some people say that the mystery of non-determinism in conventional

interpretations of QM is replaced by an equally baffling mystery in

no-collapse theories: why do I end up in *this* branch rather than

some other?

The critics understand, I presume, that observers end up in all branches

asking themselves this question. But they still seem to think there is

some mystery about the process, something that needs to be explained.

I don't see what the mystery is. We have often considered thought

experiments involving duplicating machines, which show the same

phenomenon. A man walks into a duplicating machine and two men walk out,

each having equal claim to being the original. Both ask this question:

"Why did I end up as *this* person instead of the other one?"

Is that a question which needs an answer? A question to which there

can be any answer? I don't see it. Each copy is guaranteed in advance

to be a continuation of the original. There is no mystery, nothing

which needs to be explained, in the fact that each copy exists and has

separate consciousness.

Traditionally, no-collapse models were also criticized on two other

grounds. (I will ignore the complaint that the theory is inparsimonious

in its creation of multiple universes, because IMO this is more than

made up for by the simplicity of the theory. Algorithmic complexity

theory teaches us that it is the size of the program that counts, not

the size of the data, and that is the measure we have used on this list.)

One complaint is the non-uniqueness of the basis vectors for the

decomposition. I think it is generally agreed today that this is solved

because in practice only one basis will give the vanishing of off-diagonal

elements in the density matrix, which corresponds to causally independent

worlds. Ultimately this is due to the unexplained fact that the laws

of physics have a built-in concept of positional locality. Locality

manifests itself in the dynamics of QM in such a way that natural basis

vectors correspond to well defined positions of macroscopic objects.

I think the paper of Tegmark's we discussed last month developed this

idea in more detail.

The other critique is that the measure and probability functions are

introduced on a somewhat ad hoc basis. I think this is still a valid

criticism. We need to find some way to explain the MWI measure in similar

terms to how Schmidhuber explains it in the multiverse model. He uses

the universal measure (sometimes), which can naturally be interpreted

as being proportional to the fraction of all countably-infinite size

programs which create the universe in question. That is a very natural

and powerful explanation for measure, but nothing similar exists for the

MWI. If there were an explanation for the MWI branch measures in terms

of a similar argument then I think this problem would be solved as well.

Hal

Received on Fri Jul 12 2002 - 14:37:43 PDT

Date: Fri, 12 Jul 2002 14:23:37 -0700

One of the criticisms of no-collapse theories has always bothered me.

Some people say that the mystery of non-determinism in conventional

interpretations of QM is replaced by an equally baffling mystery in

no-collapse theories: why do I end up in *this* branch rather than

some other?

The critics understand, I presume, that observers end up in all branches

asking themselves this question. But they still seem to think there is

some mystery about the process, something that needs to be explained.

I don't see what the mystery is. We have often considered thought

experiments involving duplicating machines, which show the same

phenomenon. A man walks into a duplicating machine and two men walk out,

each having equal claim to being the original. Both ask this question:

"Why did I end up as *this* person instead of the other one?"

Is that a question which needs an answer? A question to which there

can be any answer? I don't see it. Each copy is guaranteed in advance

to be a continuation of the original. There is no mystery, nothing

which needs to be explained, in the fact that each copy exists and has

separate consciousness.

Traditionally, no-collapse models were also criticized on two other

grounds. (I will ignore the complaint that the theory is inparsimonious

in its creation of multiple universes, because IMO this is more than

made up for by the simplicity of the theory. Algorithmic complexity

theory teaches us that it is the size of the program that counts, not

the size of the data, and that is the measure we have used on this list.)

One complaint is the non-uniqueness of the basis vectors for the

decomposition. I think it is generally agreed today that this is solved

because in practice only one basis will give the vanishing of off-diagonal

elements in the density matrix, which corresponds to causally independent

worlds. Ultimately this is due to the unexplained fact that the laws

of physics have a built-in concept of positional locality. Locality

manifests itself in the dynamics of QM in such a way that natural basis

vectors correspond to well defined positions of macroscopic objects.

I think the paper of Tegmark's we discussed last month developed this

idea in more detail.

The other critique is that the measure and probability functions are

introduced on a somewhat ad hoc basis. I think this is still a valid

criticism. We need to find some way to explain the MWI measure in similar

terms to how Schmidhuber explains it in the multiverse model. He uses

the universal measure (sometimes), which can naturally be interpreted

as being proportional to the fraction of all countably-infinite size

programs which create the universe in question. That is a very natural

and powerful explanation for measure, but nothing similar exists for the

MWI. If there were an explanation for the MWI branch measures in terms

of a similar argument then I think this problem would be solved as well.

Hal

Received on Fri Jul 12 2002 - 14:37:43 PDT

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