the many worlds interpretation does not work (yet)

I posted a comment on the Shtetl blog, rejecting (once again) the many worlds interpretation (mwi); it is supposed to solve the "measurement problem" of quantum theory, so let us first consider a simple experiment with 2 possible outcomes.
The main mwi assumption is that after the measurement both outcomes are realized and subsequently two macroscopically different configurations M1 and M2 exist in some (decohered) superposition.

However, we can make the differences between M1 and M2 arbitrarily large and therefore gravitation cannot be ignored. M1 and M2 will in general be associated with two different space-time geometries and so far we do not have a consistent framework to deal with such a superposition (*); should we e.g. use 2 different time parameters t₁, t₂ - one for each observer in each space-time?
In a few cases it has been tried to describe such an evolution but the conclusions are not in favor of mwi.
And how would the branching of space-time(s) work if the measurement is spread out over spacelike events, e.g. in an EPR-type experiment?

This gets worse if one considers a realistic experiment with a continuum of possible outcomes, e.g. the radioactive decay of a Pu atom, which can happen at any point of the continuous time parameter t. Assuming that this decay gets amplified with a Geiger counter to different macroscopic configurations, how would one describe the superposition of the associated continuum of space-time geometries?

The Copenhagen interpretation does not have this problem, because it only deals with one outcome and in general one can "reduce" the wave function before a superposition of spacetime geometries needs to be considered.

A mwi proponent may argue that this issue can be postponed until we have a consistent theory of quantum gravity and simply assume a Newtonian fixed background (or a flat Minkowski background). But if one (implicitly) allows the existence of Newtonian clocks, then why not the classical observer of Copenhagen?

In addition one has to face the well known problem of the Born probabilities (x), the preferred basis problem, the question of what it takes to be a world, the puzzling fact that nothing ever happens and other problems, discussed previously on this blog.

In other words, the mwi so far creates more problems than it solves.


(*) In technical terms: The semi-classical approximation of quantum field theories plus gravitation is ultimately inconsistent and we do not yet have a fully consistent quantum theory of gravitation to describe such a measurement situation.

(x) See also this opinion, which is a variant of the argument I made previously here and here.

my derivation of the Born rule

I just read (parts of) Sean Carroll's derivation of the Born rule, but I do not find it very convincing, because there is a much simpler, straightforward derivation available to resolve this problem of "self-locating uncertainty".

1) We shall use a "hardcore" many worlds interpretation, assuming that the world splits into a quasi-infinite number of branches at any time, which realizes all possible outcomes of quantum theory. We assume that those branches are all equally real and a simple counting argument shows that the Born rule does not hold for almost all of those branches. It follows that we do not live in one of those generic branches, which solves the first part of our self-location problem.

2) It is reasonable to assume that some of those infinitely many branches contain at least one quantum computer capable of simulating human life. Those computers will have to simulate quantum theory, but we can further assume that they will only keep one branch at a time in order to save resources. It is straightforward to assume that they are programmed to use the Born rule to select this branch randomly.

3) We observe the Born rule to great precision and it follows that we are the human beings simulated in one of those quantum computers. This finally resolves the self-location problem.

I would add that (some of) the simulated human beings will use the Copenhagen interpretation to explain what they experience; i.e. an interpretation which emphasizes the importance of the observer and her 'conscious experience'. Obviously, the simulated human beings are unaware that their 'conscious experience' is indeed a side effect of the procedure which selects the simulated branch randomly.

preferred basis

I did write some comments on Scott's blog which might be interesting to those bothered by the 'preferred basis problem'. It begins here and references are made to this answer at physics.stackexchange by Jess Riedel and this paper by Dowker and Kent.

While I'm at it, I should also link to this paper about 'entanglement relativity' and a (claimed) inconsistency of the Everett interpretation. I am not sure if the argument is correct (decoherence might appear different for two different decompositions, but does this really prove anything?) and would appreciate any input.

added later: The back and forth in the comment thread ended (for now) with a homework exercise for mwi proponents.

added later: Btw another interesting paper from an Austrian team about decoherence due to classical, weak gravitation (i.e. on Earth).

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Btw this unrelated comment Scott made about the "arrow of time" was a bit shallow imho. My own view of the problem begins with this thought experiment.

the strange result(s) of Frank Tipler

I met Prof. Tipler in 1992 during a seminar in Vienna about relativity and cosmology, he was a visiting professor for a year and I remember very 'normal' discussions e.g. of the Reissner-Kerr solution.
Two years later he wrote about The Physics of Immortality and I thought that his book was quite interesting, although I disagreed with his conclusion(s) and I remember that I felt uneasy about the certainty with which he expressed his unconventional views.
He jumped the shark with his next book about The Physics of Christianity and I am not sure in which Lalaland he found himself after this jump ...

But he continues to write papers about quantum physics as a proponent of a 'hardcore' many worlds interpretation (m.w.i.) and this post is about one of his conclusions:
His interpretation is actually based on the Bohm interpretation, assuming a deterministic Hamilton-Jacobi evolution of a distribution of hidden variables. While the original Bohm interpretation considers particle positions, in the Tipler interpretation the different possible universes are the hidden variables. He understands the Bohr probabilities as Bayesian probabilities obtained by the many real observers in the multi-verse of all those universes. I think at this point his views are still compatible with m.w.i. a la Everett and he argues that the Heisenberg uncertainty principle follows from his proposal arising "from the interference of the other universes of the multiverse, not from some intrinsic indeterminism in nature". So far so good ...

But then he claims to have a test of his interpretation by measuring pattern convergence rates: Frequencies of events measured in real experiments with sample size N will converge as 1/N to the Born frequencies. And I think this has to be wrong.
He even notices that in classical statistics the frequencies of events following e.g. a Gauss distribution converge slower, i.e. 1/sqrt(N), and I wonder why this does not bother him. After all, it is not difficult to set up a simple quantum physics experiment which reproduces classical convergence. Consider a (weakly) radioactive source which triggers a Geiger counter with 50% probability in a certain time interval. Now we let the Geiger counter tick along and we can be quite sure that the sequence 100101011111000010101000... that we will obtain obeys the well known laws of conventional statistics.
What am I missing?
Can one use Tipler's result as (another) example that m.w.i. does not reproduce the properties of Born probabilities correctly?


Btw if you wonder why I wrote this post now ... I saw Tipler's name on this diagram and remembered that I always wanted to write something about his strange result.

many Turing machines

We randomly implement a Turing machine Tm with N states, using a Geiger counter plus radioactive material as 'quantum coin'. We proceed as follows: First we use the 'quantum coin' to determine (with probability 1/2) if the Tm has N=2 (head) or N>2 (tail) states. If we got tail, we use the 'quantum coin' again to see if N=3 or N>3 and so on and so forth.
Once we have determined N in that way, we then construct the transition table(s) of the Tm, using the 'quantum coin' again and again, so that all (8N)^N possible transition tables could be realized.
Once this construction is finished, we start the Tm on a tape with a few 1s sprinkled on it and then watch what happens.

This experiment is easy to understand if we follow the Copenhagen interpretation. The Tm we will build is most likely quite simple, because the probability for a complex N-state Tm decreases rapidly as 1/2^N-1. Once the Tm is put together, its evolution is not even a quantum mechanics problem any more. If we want, the transition table(s) of this particular Tm can be inspected before it runs, to determine if it will halt.

But this experiment is much more difficult to understand within a many worlds interpretation: Every use of the 'quantum coin' splits the world and thus we are dealing with a wave function of the universe which contains every possible Tm in one of its branches. The amplitudes assigned to worlds with N-state machines are quite small if N is large, but all the worlds are equally real.
Unfortunately, due to the Halteproblem, the evolution of this wave function is uncomputable. In other words, the wave function of the universe does not have a mathematical description at all.

The best part of this experiment is that I do not even have to do it myself. Somewhere in the universal wavefunction there is already a branch where somebody, somewhere in the universe, has decided to do this experiment (*). This means that the amplitude of my branch is already uncomputable (x).


(*) This also takes care of the counter argument that on Earth resources are finite and thus the experiment has to terminate at a certain (large) N₀. Since we have to consider the wave function of the multiverse (of infinite size), this argument is not convincing, because we cannot know N₀.

(x) Notice that the overlap between different branches of the wave function is very small, due to decoherence, but in general non-zero.

the many urs interpretation

Recently I read the biography of Erwin Schrödinger by John Gribbin, who points out that E.S. proposed a many worlds interpretation of quantum theory several years before Everett. This got me thinking how to make sense of m.w.i. after all.

As I have pointed out several times on this blog [1, 2, 3], a major problem of the many worlds interpretation is the derivation of the Born rule.
But I think there is a way out: If qubits are the fundamental building blocks of our world, then every event could eventually be reduced to a series of yes-no alternatives of equal probability (an ur alternative) - and in this case the m.w.i. gives the correct probability.
I think this would also take care of the 'preferred basis' problem, because if the world is fundamentally discrete, the 'preferred basis' would assign two unit vectors in Hilbert space to each qubit.

C.F.v. Weizsäcker proposed his ur-theory many years before the term 'qubit' was invented and if one is serious about m.w.i. then it would be a strong reason to consider ur-theory or something similar (*).
Much later the idea that our world is a large quantum computer has been investigated e.g. by Seth Lloyd (but I don't know if it would work with urs).
In this case the task to derive the Born rule would be equivalent to derive QFT as we know it together with general relativity from ur-theory and/or from the behavior of large quantum computers.


(*) C.F.v. Weizsäcker himself was a believer in the Copenhagen interpretation and rejected m.w.i. explicitly in his book.

many simulated worlds

I think it makes sense to combine Nick Bostrom's simulation argument with the many worlds interpretation.

While Copenhagen tells us that some outcomes are very unlikely, the m.w.i. assures us that every possible world actually exists. So we can be sure that there are worlds which contain the necessary equipment to simulate your conscious experience - and since there are (infinitely) many different ways to simulate the same experience, we can follow Bostrum's argument to finally conclude that it is almost certain that you are experiencing The Matrix right now (*).



If you believe the m.w.i. then you must believe that your experience is just a fake (x).




(*) There are N ways how your experience can be simulated and only 1 how it would be real, since you cannot distinguish them they have equal probability and for (infinitely) large N the conclusion follows.





(x) Of course, my argument will probably not convince you, which is just what The Matrix does to you ...

too many worlds

This is the story told in many books: Initially Erwin and his cat are in some initial state |I> and then they develop into a superposition |F> = |H> + |N> with H indicating a happy cat and N a not so happy one (*). Due to decoherence the overlap <H|N> is very small - but not exactly zero. The interpretation is that |H> and |N> are associated with two different worlds, there is no 'collapse' (real or subjective) of the wave function which would eliminate one of the two.



But there is one issue I have with this story, not often told in those books: If there is no 'collapse' then how did we get the initial state |I> ? We have to assume that before his experiment with the cat Erwin made a decision to use his cat and not a dog, so really we have something like |I> + |d>. But before that he made a decision to do the experiment or not at all and before then a committee made a decision if he gets funding and before then ...

So really the initial state was something like |I> + |x1> + |x2> + |x3> + ...

and therefore the following state looked something like |F> = |H> + |N> + |x1> + |x2> + |x3> + ... .



If there is never a 'collapse' then quantum theory is like a programming language without garbage collection and we have to assume that the number of branches of the wave function is infinite - at least from our branch we cannot determine how many other branches there are. (Also we do not know the amplitude of our branch relative to all the others; We could exist due to a freak event in the past for all we know.)



But this is a real problem, because the overlap between different branches is very small but not zero.

So if we calculate <H|F> we get <H|H> + <H|N> + <H|x1> + <H|x2> + <H|x3> + ... and although every <H|x> is very small due to decoherence, there is a priori no reason for the infinite sum over all branches to converge (**); I have never seen a good argument why this (infinite) sum should remain small compared to the terms we are interested in.



Of course one can try to save the appearances by making the assumption that somehow the sum only has a finite (but certainly very large) number of terms, e.g. the universe is finite and time is discrete. However, it would mean that we try to save quantum theory by making assumptions about cosmology and I don't think this is very convincing.





(*) Notice that I omit normalization factors (like 1/sqrt(2)) in this text to keep the ascii math readable.

(**) Notice that the point of this post is that it is actually a problem to determine those normalization factors (like 1/sqrt(2)) so that the total sums to 1.