On 9/17/2019 3:49 PM, Bruce Kellett wrote:
On Wed, Sep 18, 2019 at 3:01 AM smitra <smi...@zonnet.nl
<mailto:smi...@zonnet.nl>> wrote:
On 17-09-2019 13:32, Bruce Kellett wrote:
>
> So why do all Everettians have to add so many additional assumptions
> in order to pretend to get out the Born rule?
>
Simply assuming the special case of the Born rule that measuring a
system in an eigenstate of an observable will yield the eigenvalue of
that eigenstate with certainty, is enough.
Where did the concept of an observable as an operator in a Hilbert
space, and the idea that measurements correspond to the action of that
observable on the state, giving a result that is the eigenvalue
corresponding to the projected eigenvector, come from?
The operator should be expressible in terms of the Hamiltonian of the
measuring instrument and its interaction with the system. But nobody
tries to write down the Hamiltonian of the instrument; they just look at
what it's supposed to measure classically and then they write an
abstract operator that does that.
Brent
As I said, you have to build an awful lot into the Schrodinger
equation in order to get out quantum physics. The Born rule is one of
the hardest things to get. And no one has yet produced a convincing
argument that the Born rule can be derived in Everettian QM.
Bruce
You can consider the case of
repeatedly preparing and measuring N copies of a system and then
consider the observable that corresponds to the frequency
distribution
of the individual measurement outcomes in the limit of N to infinity.
The special case of the Born rule applied to observable for the
frequency distribution then implies the general Born rule.
Saibal
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