Undergrad Is the math for collapse int different than for mwi?

[stevendaryl]

No. The original Everett article talks about branchings and splittings AND maintains the universal wavefunction obeys unitary evolution at all times.

I think that in Everett's original paper, the emphasis was slightly different than the world splitting. Instead, the state of the world is relative to the observer's state. Each observer experiences a slightly different world.

 

[Michael Price]

I think that in Everett's original paper, the emphasis was slightly different than the world splitting. Instead, the state of the world is relative to the observer's state. Each observer experiences a slightly different world.

Seeing a different world is the same as saying the world has split. Everett never called the state relative to an observer a "world", but he used the language of splitting and branching everywhere. It is just a terminology thing.

 

[stevendaryl]

Seeing a different world is the same as saying the world has split. Everett never called the state relative to an observer a "world", but he used the language of splitting and branching everywhere. It is just a terminology thing.

This might be splitting hairs (no pun intended) but to me there is a difference between saying "The world splits every time a measurement is made" and "The state of the universe is relative to the observer". The latter has the consequence that no two observers share exactly the same world.

 

[Michael Price]

Surely the former implies this as well? When the world or timelines splits, each branch is slightly different, since each contains an observer having recorded a different result and the object system in a different state.

 

[stevendaryl]

Surely the former implies this as well? When the world or timelines splits, each branch is slightly different, since each contains an observer having recorded a different result and the object system in a different state.

Let's take a Schrodinger's cat example. With the "branching worlds" interpretation (which isn't Everett), there's a world where the cat is alive afterward, and there is a world in which the cat is dead. But in a relative state interpretation, the cat might be alive for some observers, dead for other observers, in a superposition for yet other observers. (Well, the cat by himself can't be in a superposition, because of decoherence, but the cat + environment can be in a superposition).

 

[Michael Price]

I dispute this "isn't Everett", since the branching worlds view has the same collection of dead cat, alive cat and superposed cat. Branching is a local process which spreads out causally. When you look at the cat you get split or "branched" and the cat is only either dead or alive in anyone branch. If you haven't looked at the cat (directly or indirectly) then the cat is in a superposition, because you haven't split yet - but if you want to you could regard the cat as having decohered into alive and dead, prior to external observation, and the observer being split into identical states. Which is what the relative state formulation is also all about. There really is no difference between Everett and Dewitt. Just some terminology, but the content is the same.

 

[stevendaryl]

I dispute this "isn't Everett", since the branching worlds view has the same collection of dead cat, alive cat and superposed cat. Branching is a local process which spreads out causally.

Yes, that's what Everett says, but that isn't the popular idea of Many-Worlds, which says that the universe splits each time a measurement is performed.

 

[bhobba]

I have posted it many times but those not familiar with MW (I am from reading Wallace - The Emergent Multiverse) I like Murray Gell-Mann's explanation:


From Wallace and some prodding by Peter Donis (who helped me understand this 'rogue' branching thing which had me baffled before - thanks Peter) I have now been able to put my finger on the exact issue with MW IMHO (see page 196 of Wallace). In deriving Born's rule he uses rational agent arguments, but put into axiomatic language - its called decision theory - strictly speaking its an interpretation of probability closely related to the Bayesian view based on the Cox Axioms. It not often explicitly used, but actuaries and such sometimes use it in contingency theory for example. Now the question is why not simply use Gleason's Theorem? The answer is there is an out in Gleason - contextuality. This is avoided in MW because a rational agent would say - there is no reason for a rational agent to prefer some act to exactly the same act in a different description (really - that is debatable - I agree with it - but is it true a-priori - of course not). Its this rational agent stuff that's a bit strange for me. But I also have to say the Bayesian interpretation of probability has exactly the same issue - its not objective - its based on the belief of a rational being. As John Beaz says - a lot of discussions about QM interpretations ends up as a discussion about the meaning of good old probability:
http://math.ucr.edu/home/baez/bayes.html

An no I do not want to argue one way or another - I have said it before - and will say it again - all interpretations, IMHO, are good for is shedding light on the formalism. What this is saying is the formalism is not specific on what probability means and all its associated issues - it leaves it up in the air.

Thanks
Bill