interpretations, part 4/4
I recommend that you read the first part of this series first.
"If the facts don't fit the theory, change the facts." Albert Einstein
If you assume that nothing is wrong with the wave function W and you dislike
the interpretations of the previous part 3, then you have to conclude that
something is wrong with (your perception of) the reality R.
So, one way out of the interpretation problem, as posed in the first part of this series, is to simply assume that actually both detectors clicked; You are just somehow confused about it.
The many-worlds interpretation and its variants (consistent histories, many minds, etc.) are increasingly popular and solve the interpretation problem by pointing out that the wave function W = |1> + |2> continues to evolve into |1>|D1> + |2>|D2> and finally |1>|D1>|Y1> + |2>|D2>|Y2> , where Y1 indicates you, puzzled why click 1 has been observed but not click 2.
But, as I have argued previously, the full meaning of a many-worlds interpretation can only
be appreciated if one goes 'backwards in time', trying to find the origin of W (which
cannot evolve from a 'collapsed' wave function). In the words of Matthew J. Donald:
"Each time we pass back (through the appearance of a collapse) we get a better approximation to W.
Eventually, we arrive back at the big bang. ...
The quantum state of the universe coming out of the big bang looks - at least in its non-gravitational
aspects - very like a thermal equilibrium state. In the Hamiltonian time propagation of that state,
the stars and planets which we see now do not exist as definite objects, and certainly neither does any particular
measuring device now being used by us on one of those planets. W seems to be a complete mess.
However, it does have a great deal of hidden structure, and it is the job of a no collapse interpretation to explain
how that hidden structure comes to be seen." (*)
You may think that we have only replaced the original interpretation problem with a much more complicated one.
But the beauty of it is that this allows us to continue to think about the meaning of life, the universe and everything... (x)
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(*) While I agree with the overall conclusion, I disagree with the details.
i) Nowadays the multiverse landscape seems very popular (especially among string theorists) and it is not clear at all that we arrive back at one big bang.
ii) In general, I doubt that one could really reconstruct W as suggested or otherwise determine the wave function of the universe, unless
there is a new general principle which limits the possibilities (notice that we only know about one branch out of an infinity of possible branches.)
iii) If one assumes that W may contain an infinite number of branches and since those branches (assuming decoherence) are only almost-orthogonal to each other this poses a real problem, If one wants to use W to calculate anything.
(x) As far as I know, Frank Tipler was the first who realized that the many-worlds interpretation opens the door to theological interpretations of quantum theory. If one wants to follow this path (and don't we all want to believe?), then I would use a previous result to conclude that the wave function of the universe is not only invisible but necessarily pink.
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6 comments:
That reminds me, I have another beef with ensembles: how is proper grouping done? It's easy if you made it easy, in a case where there's a consistent distribution (say, 50/50 H and V pol. light.) But what if the distribution changes over time? What if, the shots start out mostly H and then there are more and more V added? What is the true "average" or "density matrix" then, when the result depends on where you make the fence to gather the examples?
I think, you can't even pretend the average can be explicit if it changes too, since it isn't clear - w/o a big ensemble - just what the average is "at a point." (Unless you had pre-knowledge of the chances, and just used that.)
I don't think we can rationally solve the collapse problem. If you think the WF is "real", then what happens later is absurd per collapse. If you try to "solve" it by cheating, well that is cheating. That is what many DI advocates do. Some, like Zurek (not Chad, I acknowledge) say that decoherence solves the MP. I know, I see their statements. But they use a circular argument, in which the very same probabilities caused by collapse (whatever it is) are inserted into the DM along with the classical type chances of the WF being present.
Then, the way the statistics from the DM occur after decoherence is claimed to show why the result is a mixture. Well, it's a circular fallacy as Penrose notes obliquely: if they hadn't put in the quantum probabilities at the outset, those statistics wouldn't be available (in any form - coherent or incoherent) at the output. What gets the quantum statistics in there *in the first place*?
BTW BO's humbleness is refreshing. I'm not so humble (look at my blog title!), so here's my pitch for possible significance: Google search "quantum measurement paradox." (in quotes) My post/s come up in top five, FWIW ;-)
>> that is a choice about which way to go, and if we had detectors right outside BS1 (instead of BS2) then it would be a "selection" or collapse at that level.
I am not a MWI proponent, but I think the answer would go like this.
After the first beam-splitter the worlds do not 'split' unless you place macroscopic detectors there.
But placing such macroscopic detectors (or not) makes for two completely different observational situations.
A many minds proponent may also insist that the 'split' into several worlds really happens when the state of your mind ends up in two different branches which are very unlikely to interfere with each other.
>> I don't think talking about the whole universe or its origin is highly relevant.
My point is that it is *necessary* if you accept the MWI.
(Of course, H.D.Zeh, one of the first to examine decoherence, made this point already long before I made it.)
Without 'collapse' we have to talk about the 'wave function of the universe', due to the entanglement of macroscopic systems with the environment.
After the first beam-splitter the worlds do not 'split' unless you place macroscopic detectors there.
Maybe (heh, who knows.) But like I said, MWI and DI are supposed to allow transcending of the specialness of "measuring devices". Hence, it shouldn't matter whether or where you put "macroscopic detectors." Again, I go by advocates' own words.
There is still also the "shifting ensemble" problem.
Neil B.,
may I ask. What is *your* favorite solution to the interpretation problem?
Well, I don't think there is a "solution." I think the Universe just cheats us out of it being comprehensible. If you really believe in wave functions, their later behavior doesn't make sense. If you cheat as per previous, it's wrong. If you don't have WFs at all, how to explain later interference etc?
There may be some clever angles (transactional, by Cramer?) but nothing really works or makes sense in the way most people seek. I do think my DI proposal empirically rules out that way of thinking, aside from DI's logical flaws.
We have ways to find out what will statistically happen, but don't understand what's under it. Maybe a Kantian idea of a world of relations is better, with some way of representing that isn't like having distributions of independent specific quantities (e.g. amplitudes) in common space and time. Perhaps a programmer will invent a representation of items and connections that can't be "pictured", that is more like how QM things work.
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