Born rule derived from pure QM by Max Tegmark

[Dmitry67]

Sorry if this had been already discussed:

http://arxiv.org/abs/1008.1066

So, what I see (assuming that Universe is infinite, this is an important assumption, not proven of course, but if this is true):

1. The 'Interpretation war' is over, amen, the most important weakness of MWI has been resolved (wow!)
2. As a side effect, Max had shown an equivalence between Bayesian and frequentist definitions of probability (wow!).
3. Finally, there is an additional (and strange) equivalence between MWI branches and alternative histories in spacially different locations of an infinite Universe. As these 2 types of 'branching' are mathematically and observationally equivalent, that goes even futher than just MWI. In fact, *ANY* theory compatible with QM (with countable number of states) in infinite universe would have the same properties.

Thoughts?

 

[xts]

Thoughts?

As for me 'infinite universe' is just reformulation of Everett's Many-Worlds in a bit different words.

The only ontological difference is that in MWI the world splits to new ones, while in 'infinite universe' multiple (actually: infinite number) copies of the same world existed previously, but at the momement they split into two parts: those realising one or other of Everett possibilities.
Of course: Everett postulates that Many Worlds exist independently in some mystic space of multiverse, while 'infinite universe' claims they exist in the same "objective" timespace, just separated spatially, somewhere, pretty far, beyond Hubble's horizon.

Is Eden located in Armenia or in immaterial heaven? Doesn't matter, unless we got technical possibilities to visit Armenia and see that it is far from being a heaven... Worlds beyond Hubble's horizon are equally unreal as Everett's Worlds.

 

[Fyzix]

Holy ****...
I made you aware of this paper so you could see that even Max Tegmark has recognized just how flawed the standard MWI is.
For **** sake he is abandoning the splitting model and postulating a completely new model with a infinite universe!

So the "interpretational war" is far from over, most people see this as a defeat on MWI's part, as this is no longer MWI at all and this is the extreme length he has to go to to make any sort of "many separate worlds" view work..

Stop being so painfully religious
You just want MWI to be true, so you are willing to accept ANY unfounded postulate, whether it's God, dualism, many SEPERATE universes etc.

 

[Hurkyl]

2. As a side effect, Max had shown an equivalence between Bayesian and frequentist definitions of probability (wow!).

You're talking section 3 and the limit as N goes to infinity? That's not new news -- I recall deriving the Born rule by computing frequentist probabilities in the exact same way a few years back and I was given the impression it was already old hat then. (aside -- I don't see the letters 'bayes' anywhere in the article)

 

[xts]

you could see that even Max Tegmark has recognized just how flawed the standard MWI is.

Max Tegmark never advocated MWI - just contrary - he published lots of ironical critics on it, e.g. "MANY WORLDS OR MANY WORDS?" (1997) http://arxiv.org/abs/quant-ph/9709032v1, inspired (or rather being surprised) by wide popularity of that idea. So he put some effort to analyze weird theory and take out its even weirder logical implications. Don't take his last papers on infinite universes as advocating for that idea. It is again finding logical consequences of the assumption. Leaving it to your metaphysical taste if weirdness and absurdity of those consequences is sufficient to reject the assumption by reductio at absurdum.

 

[Dmitry67]

Max Tegmark never advocated MWI - just contrary - he published lots of ironical critics on it, e.g. "MANY WORLDS OR MANY WORDS?" (1997) [/QUOTE] He had changed his mind...ly used MWI calling it 'level III multiverse'

 

[Dmitry67]

(aside -- I don't see the letters 'bayes' anywhere in the article)

Well, you're right - he had never used this word. But it is very straightforward, bayesian probabilities (in frogs view) are mapped to frequencies in the infinite universe.

 

[Fredrik]

Max Tegmark never advocated MWI - just contrary - he published lots of ironical critics on it, e.g. "MANY WORLDS OR MANY WORDS?" (1997) http://arxiv.org/abs/quant-ph/9709032v1, inspired (or rather being surprised) by wide popularity of that idea. So he put some effort to analyze weird theory and take out its even weirder logical implications.

Did you read that paper? It's very clearly an endorsement of Everett's MWI. He's mentioning a few arguments against it, but only to dismiss them very quickly. "Many words" isn't a stab at MWI interpretations, it's a stab at arguments against Everett's MWI that he considers bad. At one point, he mentions Adrian Kent's "Against many worlds", an article that explains why several MWI-related ideas can't work. It's the only article on MWI interpretations that I've read that I consider good. He immediately dismisses it with the words "most of its claims were subsequently shown to result from misconceptions", without going into detail or offering any arguments to support his claim. Instead he references an unpublished article that looks like garbage to me.

 

[xts]

Yes, I read it. And I see Tegmark as a guy playing intellectual speculative game of finding consequences of certain ideas. Tegmark analyses the consequences of assumptions about different levels of parallel universes, but never assigns to them any ontological status.

Look at his personal page (http://space.mit.edu/home/tegmark/home.html) - all those papers are labeled by him as 'crazy universes', see also intro to this section.

he had explicitly used MWI calling it 'level III multiverse'

And I, atheist, several times explicitely used the example of heaven. It doesn't mean I advocate its real existence.

 

[Dmitry67]

Tegmark analyses the consequences of assumptions about different levels of parallel universes, but never assigns to them any ontological status.

No, he explicitly assigns them an ontological status:
http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.0646v2.pdf
page 16

Could there really be a fundamental, unexplained ontological asymmetry built into the very heart of reality, splitting mathematical structures into two classes, those with and without physical existence? After all, a mathematical structure is not “created” and doesn’t exist “somewhere”. It just exists.

As a way out of this philosophical conundrum, I have suggested [12]) that complete mathematical democracy holds: that mathematical existence and physical existence
are equivalent, so that all mathematical structures have the same ontological status

 

[Hurkyl]

http://arxiv.org/abs/1008.1066

I confess it isn't clear to me exactly what he's arguing for, or how.


I get^* the idea of interpreting a statistical ensemble as describing a distribution across all of the replicas of your laboratory, and then doing the conversion

The frequencies of the outcomes I would see if I performed hypothetical experiments in my laboratory --> ensemble --> the frequencies observed across the infinite replicas of my laboratory​

I get the idea that the Born rule is rendered redundant, but not why he thinks that has anything to do with his ideas about infinite space.


I don't see how he's collapsing many worlds into one world (or what he actually means by that), or really any of the ideas in his "Interpretations" section.



*: I don't buy the premise it depends upon, though

 

[xts]

Could there really be a fundamental, unexplained ontological asymmetry built into the very heart of reality, splitting mathematical structures into two classes, those with and without physical existence? After all, a mathematical structure is not “created” and doesn’t exist “somewhere”. It just exists.

As a way out of this philosophical conundrum, I have suggested [12]) that complete mathematical democracy holds: that mathematical existence and physical existence
are equivalent, so that all mathematical structures have the same ontological status

If you take it as a postulative comment, rather than irony about ontology, unable to consistently define the word 'existence' - you are putting Tegmark in mental hospital along with all those, who say that flat Earth exist (it is also valid mathematical structure), that flatters (two-dimensional people living in two-dim world) exist, etc.

I understand such his sentences (all mathematical structures have the same ontological status) as: "Many Worlds exist in the same sense as two-dim flatters" - we may think about them and we may have their mathematical model.

 

[Dmitry67]

There is no irony in his article. It is serious.
And it is a main idea behind MUH.
The very reason why he wrote this article.
Definitely, I did not bother reading the article.

you are putting Tegmark in mental hospital

I see. Your only argument is "it sounds too crazy".

 

[xts]

OK - let take it serious. So you may just treat Tegmark as an extreme ontological idealist, who uses the word 'existence' in regard to anything which may by thought of (mathematically modeled).
Just be honest to him, and admit he makes no difference between the meaning of 'existence' of his copies in Many Worlds and the 'existence' of pink elephants with two heads.

 

[Dmitry67]

Just be honest to him, and admit he makes no difference between the meaning of 'existence' of his copies in Many Worlds and the 'existence' of pink elephants with two heads.

Does it make sense to discuss it if you did not read the MUH article?
Check p16.
D. The “anything goes” critique

 

[Fredrik]

If you take it as a postulative comment, rather than irony about ontology, unable to consistently define the word 'existence' - you are putting Tegmark in mental hospital along with all those, who say that flat Earth exist (it is also valid mathematical structure), that flatters (two-dimensional people living in two-dim world) exist, etc.

I don't see how you can interpret the stuff he writes the way you do. You even described the "many words" article as an ironic criticism of the MWI, but what it actually does is to dismiss all criticism as garbage. There's no irony in that article. You are however right that he didn't claim that this is what reality is really like. He was simply arguing (badly IMO) that Everett's MWI is a perfectly reasonable candidate for a description of reality.

Regarding his articles about the "MUH", I think it's clear that he thinks reality is mathematics. The idea that he calls "ERH" (there exists an external physical reality completely independent of us humans) isn't really controversial, and he's claiming that this idea implies the MUH. So if you think that he doesn't mean that the universe really is mathematics, then you are in fact saying that he believes that there's no external reality. That would be much crazier IMO.

 

[xts]

I read it. Frankly - that's not my favourite paper by Tegmark, but I know it.

The MUH and the Level IV multiverse idea does certainly
not imply that all imaginable universes exist. We humans can imagine many things that are mathematically undefined and hence do not correspond to mathematical structures.
- with such restriction everything, which may be described as a consistent mathematical structure, exists. Pink elephants are equally mathematically modellable as gray ones. Two heads can also be described within consistent mathematical model.

 

[xts]

I agree that in "MUH" Tegmark shows that reality is mathematics. He states it as Our external physical reality is a mathematical structure.
It however does not imply that in turn every valid mathematical structure is reality. If such statements appear (like the one cited few posts above) they are either not quite serious, or otherwise - redefining the non-controversial meaning of 'External Reality', laying at the foundation of the whole article.

 

[Dmitry67]

I agree that in "MUH" Tegmark shows that reality is mathematics. He states it as Our external physical reality is a mathematical structure.
It however does not imply that in turn every valid mathematical structure is reality.

It is explicitly stated in his quote:

Could there really be a fundamental, unexplained ontological asymmetry built into the very heart of reality, splitting mathematical structures into two classes, those with and without physical existence? After all, a mathematical structure is not “created” and doesn’t exist “somewhere”. It just exists.

As a way out of this philosophical conundrum, I have suggested [12]) that complete mathematical democracy holds: that mathematical existence and physical existence
are equivalent, so that all mathematical structures have the same ontological status

Of course, it is not a proof, but a proposition. However, if you don't agree with that proposition, you need to create some additional stuff, which "burns fire" into some equations, leaving other equations dead. So you have to invent something new.

MUH, like MWI, does not invent new things, it just denies some extra things.

 

[xts]

I see that as lack of self-consistence in "MUH" paper. Tegmark either invalidates this way his basic assumption about ERH (External Reality Hypothesis), or (which is my interpretation of his words) just goes to far in rethorics, which have no significant consequences however for the rest of his conclusions.

Anyway - don't take me as an advocate of Tegmark, especially in context of MUH paper which I dislike, as I find it totally wrong for yet other reason: the assumption that all baggage may be removed while making theories more and more mathematical. There are two flaws in this assumption:
1. theory always consist of some mathematic model in relation to reality, rather than being pure model;
2. even pure mathematics is not free from human baggage (Hilbert's programme failed on its attempt to remove all baggage and fully de-humanize mathematics)

 

[Fyzix]

xts: Tegmark believes in every multiverse you can imagine, go to his website and you will see his entire level I to level IIII model.
He even said he might commit quantum suicide when he's "old and crazy" to test it out.

However in this paper it seems he is abandonig the splitting view and with the QS.
Something Dmitry67 won't adress

 

[Dmitry67]

No, he just talks about the equivalence of the Everettian branches and spacially-separated branches. If you don't agree, please provide an exact quote where he "abandons" the MWI.