Many-Worlds, Deriving the Born Rule?

[kurros]

I don't like this continually exponentially increasing number of new worlds - its far too extravagant for my tastes.

I agree intuitively with this, but do you really think it is the case? I mean sure, pieces of the wavefunction become distinct at some probably even combinatoric rate, but you don't 'really' create new worlds right? They are all there to begin with, it is just that they start off all the same, and entangled with each other.

 

[bhobba]

I agree intuitively with this, but do you really think it is the case? I mean sure, pieces of the wavefunction become distinct at some probably even combinatoric rate, but you don't 'really' create new worlds right? They are all there to begin with, it is just that they start off all the same, and entangled with each other.

That's all true (they are not entangled but they are there) - but with each 'observation' you get new copies of you and those copies increase at an alarming exponential rate. Its just a bit too weird for me. Its a personal view only.

Here is a link that goes a bit deeper into the issue of these 'new' worlds and exactly what it means as far as the energy needed to create them etc goes - issues not related to this thread regarding the Born rule:
http://www.askamathematician.com/20...y-and-matter-for-the-new-universes-come-from/

Although the energy of each world is 'diluted' in proportion it reduces at an alarming rate - to me that is also bit hard to swallow.

Thanks
Bill

 

[Quantumental]

That's all true (they are not entangled but they are there) - but with each 'observation' you get new copies of you and those copies increase at an alarming exponential rate. Its just a bit too weird for me. Its a personal view only.

Here is a link that goes a bit deeper into the issue of these 'new' worlds and exactly what it means as far as the energy needed to create them etc goes - issues not related to this thread regarding the Born rule:
http://www.askamathematician.com/20...y-and-matter-for-the-new-universes-come-from/

Although the energy of each world is 'diluted' in proportion it reduces at an alarming rate - to me that is also bit hard to swallow.

Thanks
Bill

So what you're saying is that basically you find no problem with MWI in terms of Born Rule, preferred basis or non-locality like most physicists and philosophers, but because it *feels* weird you don't believe it?

That's just denial though if you have no other reasons for rejecting

 

[tom.stoer]

Let's come back to the energy question:

Suppose I have an electron in a double-split experiment. Due to the plane wave and spherical wave ansatz we nearly have energy eigenstates. When measuring the position we measure its momentum and therefore energy, too. For the incoming electron I have energy

$E = \text{tr} H \rho$

For the detected electron I will find nearly the same amount of energy. This energy E is what I prepare in the beam and what I measure in the detector.

Now let's compare collapse and MW interpretation. In the collapse interpretation I find the electron at position x. All the energy E is contained in one "new world" to which the electron state collapsed. In the MW interpretation we have a set of branches, each containing one electron at a certain position. The energy measured in all these branches is nearly identical to the original one. So what an observer in one single branch measures is still

$E = \text{tr} H \rho$

He does not find some thing like

$E^\ast = \text{tr} H P \rho$

where P projects to his branch.

So my conclusion is that energy is conserved over all branches. Each single branch would contain only a small portion. The observer "in one branch" finds an electron position for "his branch", but an amount of energy like "over all branches". So even so other branches become invisible to the observer when it comes to the location of the electron, these other branches are visible when it comes to measurement of energy in one single branch.

This conclusion seems to be weird.

What's wrong with my conclusion?

 

[bhobba]

That's just denial though if you have no other reasons for rejecting

If so I am not the only one (see my next post - I think many simply believe its an unnecessarily confusing complication that can be avoided).

BTW I am not sure most physicists have the issues with it you think they do. For example it was MFB, who is a particle physicist, that changed my view on it as far as Born's rule goes.

Philosophers I can't comment on, but since they generally don't as a group agree on anything I am not sure it carries the same type of weight.

Thanks
Bill

 

[bhobba]

This conclusion seems to be weird. What's wrong with my conclusion?

As far as I can see there is nothing wrong with it. MW is beautiful, elegant, logically coherent, but weird.

We all choose the interpretation we prefer based on our personal criteria and I think many people find MW just a little 'too much'

I know Murray Gell-Mann holds that view, and I am pretty sure he is not alone:
http://olena.tumblr.com/post/25070169127/on-hugh-everetts-many-worlds-theory
'his interpretation is often described in terms of ‘many worlds,’ whereas we believe that 'many alternative histories of the universe' is what is really meant. … the many worlds are described as being 'all equally real,' whereas we believe it is less confusing to speak of ‘many histories, all treated alike by the theory except for their different probabilities.’ To use [this recommended] language is to address the familiar notion that a given system can have different possible histories, each with its own probability; it is not necessary to become queasy trying to conceive of many ‘parallel universes,’ all equally real.”

Its not denial - its just not as confusing. But of course what is confusing to one, isn't necessarily that to another.

Thanks
Bill

 

[Quantumental]

If so I am not the only one (see my next post - I think many simply believe its an unnecessarily confusing complication that can be avoided).

BTW I am not sure most physicists have the issues with it you think they do. For example it was MFB, who is a particle physicist, that changed my view on it as far as Born's rule goes.

Philosophers I can't comment on, but since they generally don't as a group agree on anything I am not sure it carries the same type of weight.

Thanks
Bill

I understand that you find it weird, but is that enough reason to say it's wrong in your opinion? Don't you also find it weird that you are on a rock in the middle of space and that the world is a sphere, but you don't fall off ? I reject it due to the issues I mentioned and because I am sure there is a deeper theory that will involve the holographic principle and things like the amplituhedron. I.E. our current theories are approximations of a deeper underlying theory, which will obviously also be weird, but more classical than QM.
If space time is no longer fundamental then non-locality isn't that hard to swallow anymore and then suddenly determinism is back into play etc. But obviously we are far from close to creating a theory out of these speculations.

As for Gell-Mann, his statements are diffuse, some places he definitely reject the MWI view in some statements. But i don't know him so I won't put words in his mouth.
One person who used to lean toward MWI and now reject it due to Born Rule si Steven Weinberg.As for the open problems, even David Wallace flat out admits that wf onticism in hilbert space simply isn't enough. In his Space Time State realism paper he goes through the problems with that view and propose his own view.
David Deutsch claim that MWI is 100% local in the Einsteinian sense and refers to the Heisenberg picture as justification. David Wallace and Simon Saunders on the other hand accept some non-locality (non-narratability)

Then there is the issue of divergent worlds vs branching worlds.
Some Alastair Wilson and Simon Saunders argue in favour of the worlds being divergent. So you (Bhobba) are forever stuck on this branch and there are infinite other worlds where all other outcomes occur, but you are never in those worlds. I.E. all worlds sprung into existence at once.
Then you have people like Deutsch, Papineau, Greaves etc. who claim the worlds do infact branch.
Wallace holds the view that there are no facts about it and it's all semantics, but that doesn't make sense. Reality has to be this or that way.

Also take for instance the proponents of Many Minds, they claim there is problems with not specifying an observer ( Zeh being one )

Then there are also those who propose Many Bohmian Worlds, physicists like Sebens, Boström, Wiseman all came up with this independently of each other as a response to the basis issue.So there is clear disagreement among the top developers of this modern Many Worlds view and no one seem to be sure of anything yet.
The basis problem and Born Rule is still one of the most debated subjects.

 

[bhobba]

I understand that you find it weird, but is that enough reason to say it's wrong in your opinion?

You misunderstand. No interpretation is wrong since none can be proven or disproven by experiment. Until that is the case all are equally valid. The choice of one over the other is purely based on its appeal to you.

because I am sure there is a deeper theory that will involve the holographic principle and things like the amplituhedron

The above being a prime example.

Actually I believe the amplituhedron is trying to tell us something important - but exactly what is unclear - only time will tell. Opinions are like bums - everyone has one - it doesn't make it correct - even mine - no especially mine.

Thanks
Bill

 

[kith]

So what an observer in one single branch measures is still

$E = \text{tr} H \rho$

He does not find some thing like

$E^\ast = \text{tr} H P \rho$

where P projects to his branch.

I can't follow.

If ρ is an energy eigenstate, there's no branching in an energy measurement and therefore no difference between E and E*.

If ρ is a superposition of energy eigenstates, the measurement outcome will be one of the corresponding eigenvalues. But in gneral, neither E nor E* is equal to such an eigenvalue.

 

[kith]

I reject it due to the issues I mentioned and because I am sure there is a deeper theory that will involve the holographic principle and things like the amplituhedron. I.E. our current theories are approximations of a deeper underlying theory, which will obviously also be weird, but more classical than QM. If space time is no longer fundamental then non-locality isn't that hard to swallow anymore and then suddenly determinism is back into play etc.

To me, this doesn't sound much different from the MWI. The MWI is deterministic and the cause of non-locality is that the wavefunction doesn't live in spacetime but in Hilbert space.

Or do you think that determinism may be restored to the experimental realm? If so, I disagree. I don't see anything hinting in this direction.

 

[Dale]

You misunderstand. No interpretation is wrong since none can be proven or disproven by experiment. Until that is the case all are equally valid. The choice of one over the other is purely based on its appeal to you.

I agree completely, and this is a good place to close the discussion. Everyone has had a chance to plug their favorite interpretation, and there is no way to objectively do anything else.