## New Directions in the Foundations of Physics 2014

This is the last post about the conference because the remaining
of the talks gradually drifted outside of my domain of expertise. Next time I’ll
resume the geometry series. For today I want to talk a bit about the Many Worlds Interpretation (MWI) which was showcased in its talk by David Wallace http://arxiv.org/abs/1111.2187v1 and about Causal Sets (presented by Rafael Sorkin and David Rideout).

Since I am working in an approach different than MWI which also
contends that quantum evolution is pure unitary I am very critical of MWI
claims. I talked in the past about MWI but I want to clearly present why I
believe MWI is fundamentally misguided.

When I was first introduced to quantum mechanics in college,
the lessons followed the standard approach: Hilbert spaces, kets, bras,
Schrodinger equation. Then at the end of that class, mixed states were
introduced as an afterthought, and they were introduced in a misleading way. Suppose
we prepare many copies of a quantum state A, and many copies of a quantum state
B. We can then create a

**mixed state**by the following**preparation process**: randomly choose p% of the time the quantum state A and (1-p)% of the time quantum state B. For example, suppose some photons are vertically polarized (state A), and some photons are horizontally polarized (state B). Then if we randomly select 50% of the time horizontally polarized photons and 50% of the time vertical polarized photons we end up with a random mixture of the two. Big deal I said at that time. Why do we want to do that? To make our lives harder in computing the answers to problems? And in thinking that,__I completely missed the point about mixed states__. Here is how:**The key point of mixed states IN QUANTUM MECHANICS is that**

__the decomposition of MIXED STATES into__

__PURE__**Unlike classical mechanics, an ignorance interpretation of mixed states in not tenable. For example, suppose that in the process above, “A” corresponds instead to photons which are left-circularly polarized, and “B” corresponds to photons which are right-circularly polarized. Mix them up 50%-50% and the end state**

__STATES is not unique__.**as mixing vertical and horizontal polarized photons:**

__is the same__**.**

__no experiment is able to distinguish between the two preparation procedures__
So now back to MWI. MWI asserts that the wavefunction
evolves ONLY unitary, and this means that until observation, Schrodinger’s cat is
both dead

**and**alive. However, experiments reveal only a dead**or**an alive cat, and MWI’s explanation is that the world splits into two copies at the time of measurement: in one branch the cat is dead, while in another the cat is alive. (Isn’t this nice? It means we are all immortals: there is always a branch in which we never die).
But here is the catch: if the quantum state is in a mixed
state, there is an ambiguity on which decomposition is used by the measurement
process. For a photon in the mixed state from above, is the world going to
split into a branch where a photon polarized vertically and a branch where it
is polarized horizontally, or is the universe going to split into two branches
where the photon is left or right circularly polarized?

**Somehow there must be a**Indeed, decoherence solves the basis ambiguity problem, but in the process we miss a__preferred base__for this split. On this MWI is silent, but decoherence comes to the rescue.**fundamental tension between MWI and decoherence**:- On one hand decoherence is trivial and natural because is rooted in unavoidable interaction with the environment.
- On the other hand, the universe splitting process is nothing short of extraordinary: a humble photon can split the entire universe into two branches.

**This is MWI’s big pink elephant in the room: merging two ideas opposite in spirit to solve the measurement problem. MWI without decoherence does not work due to basis ambiguity; decoherence without MWI does not work because the outcome is not unique. Together they work, but it is like mixing fire with water. No wonder some people deride MWI and call it: the Many**

__Why is the split happening only after decoherence? What is so SPECIAL about an un-special, mundane, common-place process like decoherence?__**Words**Interpretation. I fully agree with Zurek when he says MWI has the feeling of a cheap shot in solving a complex problem.

Now onto Causal Sets. I never listened before to a talk about this approach and I was fortunate to hear
Rafael Sorkin’s cogent presentation. To me, my first impression was about the

**unreasonable effectiveness of the approach**. The key result of this approach is the correct order of magnitude prediction for the Cosmological Constant: 10^{-120}.
So how do the competing physical theories stack up to the
challenge of predicting the value of the cosmological constant?

- In quantum field theory, vacuum is a very violent place and if you count vacuum fluctuations as contributing to dark energy then you make a prediction which is wrong by about 120 orders of magnitude!!!
- In supersymmetric field theory, the cosmological constant must be exactly zero!
- String theory predicts a small value, but of the wrong sign, and models of the right sign were called Rube Goldberg models.

Where all the smart and complex solution failed, causal sets
succeeded. Here how the magic happens:

The diameter of the known universe in Plank’s units is 10

^{60 }It’s volume is then approximately ~10^{240}and the cosmological constant Lambda is computed by the model to be = 1/sqrt(Volume)~ 10^{-120}(**applause please**).
This is because a causal set is a set of elements with an
order relation: transitive + acyclicity + local finiteness (discreetness). In
causal sets “

*Geometry =order + number*” and causal set are**uniformly embeddable**in a manifold. Hence**Number=Volume.**
Causal sets can be employed also outside physics, for
example in the growth of the web pages on the internet! But the predictions
become bizarre and obviously wrong in this case: just as the universe can
expand and recollapse in causal set cosmological models, so too the Internet
can vanish one day by pure chance of birth and death of new web pages.

This is why my impression of causal sets is that of
unreasonable effectiveness. I tend to think the approach is incorrect, but
still, I cannot simply discard the correct cosmological value prediction where
no other theory succeeded. Either something is fundamentally right in this
approach, or the model is simply incredibly lucky – don’t know which one is the
correct explanation.

Very engaging explanations, thanks.

ReplyDeleteWas there a pilot-wave talk in this conference?

i would have thought that after Yves Couder's many demonstrations of macroscopic systems exhibiting quantum phenomena, this interpretation would have regained momentum..

No, it was not this time, but there were in prior years. This time the theme of the conference was focused on emergence, but in general Bohmists are well represented at the conference. Yves Couder's demonstrations are not really quantum mechanics but they do look nice.

ReplyDeleteI see. What would it take to convince you that pilot-wave systems akin to Couder's are the best interpretation of quantum mechanics (keeping in mind the drawbacks of other alternatives)?

ReplyDeleteStep one: make your case.

ReplyDeleteStep 1.5 (optional): do you have a preprint/published paper making the case?

Step two: rebut objections (which I'll formulate after steps 1 and 1.5)

Caution: "the *best* interpretation of quantum mechanics" is a very ambitious goal. Since I can argue on behalf of every other available interpretation, I have a lot of ammunition to shoot holes into the argument.