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)


(*) 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.

interpretations, part 3/4

I recommend that you read the first part of this series first.

The ensemble interpretation goes back to Albert Einstein, who assumed that W does not describe an individual system, but instead an ensemble of equivalent systems or experiments. (Notice that Chad Orzel emphasizes that we need to use many photons to see an interference effect in the Mach-Zehnder interferometer.)

This resolves the mismatch between W and R, without assuming that anything is wrong with either W or R (*).

It seems to me that this minimalist interpretation is actually quite popular with many physicists and especially experimentalists.

Further, I think it is the philosophical basis of the "shut up and calculate" approach and suspect that some physicists use it who are otherwise convinced that Einstein never understood quantum theory.

In stark contrast, the Copenhagen interpretation assumes that W very well describes individual quantum systems, but emphasizes that we necessarily have to use classical concepts to describe the outcome of experiments. Therefore, one needs to change the 'description' during a measurement and the wave function
'collapses' at some point; Nowadays one could refer to decoherence to better determine that point.

In this interview Werner Heisenberg emphasized that W does not describe (fundamental) reality itself...

"That is just the point; I do not know what the words fundamental reality mean.
They are taken from our daily life situation where they have a good meaning,
but when we use such terms we are usually extrapolating from our daily lives
into an area very remote from it, where we cannot expect the words to have a meaning.
This is perhaps one of the fundamental difficulties of philosophy: that our thinking hangs in the language."

... instead he assumed that W does describe what he called 'potentiality'.

'What does a wave function actually describe?' In old physics, the mathematical scheme
described a system as it was, there in space and time.
One could call this an objective description of the system.
But in quantum theory the wave function cannot be called a description of an objective system,
but rather a description of observational situations.

The explanations of Niels Bohr were usually even more profound, with complementarity playing
a prominent role in his philosophy; But it seems that they were indeed so profound that nobody actually read them (x).

Let me finally mention some results which emphasize that
the problem to understand the measurement process results from the impossibility of self-measurement.
The observer of an experiment can therefore not use W to describe herself and her own experience.
In my opinion one could either use these results as further argument in support of the 'collapse' of the
Copenhagen interpretation or as the starting point for a new 'relational interpretation'.


(*) Notice that in many cases a Wick rotation translates between quantum and statistical mechanics.

(x) "In a widely used compendium of papers on quantum theory [...], the pages of Bohr's reprinted article are out of order.
This paper (Bohr's response to the famous 1935 Einstein-Podolsky-Rosen critique of the standard Copenhagen interpretation)
is widely cited in contemporary literature by physicists and philosophers of science.
Yet I have never heard anybody complain that something is wrong with Bohr's text in this volume."

Mara Beller about the philosophical pronouncements of Bohr, Born, Heisenberg and Pauli.

continue to part 4.

la statistique bayƩsienne

Andrew Gelman and Cosma Shalizi wrote something about the real philosophical foundations of Bayesian data analysis. Very interesting.

Unfortunately, it is all French to me...

interpretations, part 2/4

I recommend that you read the first part of this series first.

The idea that the wave function W is only an incomplete description of the
reality R is as old as quantum theory itself.
Already at the Solvay conference of 1927 Louis deBroglie suggested to add
'hidden variables' with W being only a 'pilot wave'.

During the 1930s Albert Einstein published several thought experiments
(the most famous being the EPR paper) to demonstrate that W was obviously incomplete.

Consider the following 1-dimensional thought experiment.

A particle enters a detector of (great) length L at time tI and we determine its momentum p = mv
with high precision, knowing that this will lead to large uncertainty dx in its position x.
At a later time tF we turn the detector on, which will now determine the position x of the particle
with high precision and leave dp large. But although we assume that Heisenberg's uncertainty relation
holds for each measurement, we can now reconstruct the path of the particle between tI and tF,
knowing v(tI) and x(tF) with high precision and assuming conservation of momentum (just as we can
reconstruct the path which the photon must have taken in the Mach-Zehnder interferometer, once we know which
detector clicked).

But this reconstructed path R(t) for tF > t > tI is not described at all by the wave function W(t); This suggests
that W provides for an incomplete description of reality only.

A consistent theory of hidden variables for non-relativistic quantum theory was later formulated by David Bohm
and attempts have been made to generalize it to relativistic field theories (1, 2).

By the way, notice that the 'hidden variables' are actually the particle and pointer positions
we observe in a measurement (while we never experience the
wave function directly).


An even more elegant way to introduce hidden variables is to refer to (human) consciousness as selection
principle. This works especially well, because on one hand one cannot deny the reality
of our conscious experience, on the other hand it never directly shows up in physics.

John v. Neumann was the first to mention it, Wigner and his
made the idea popular and Henry Stapp worked out some concrete proposals.
Actual experiments, using EEGs to test the influence of consciousness on quantum experiments, have been proposed, as described in this paper.

Of course, in a section about quantum theory and consciousness I have to mention Roger Penrose. He does not only think that W is incomplete, but assumes that current quantum theory is actually wrong, because
it ignores the effects of (quantum) gravitation. He also proposed an actual experiment to test his idea.

There are many other proposals to modify quantum theory and I only mention the Ghirardi-Rimini-Weber theory,
which assumes real sporadic collapse of the wave function.

continue to part 3.

interpretations, part 1/4

It is time to write about something truly exciting, in other words it is time to write
about the interpretation problem of quantum theory. This is the 1st of 4 posts about it, the introduction if you will.

Some time ago, Chad Orzel wrote a blog post explaining decoherence and it shall be the starting point for us (he later wrote a more detailed explanation as response to a comment).

Consider a single photon in a Mach-Zehnder interferometer, which will end up at one of the two detecors D1 and D2.

If the interferometer is properly set up, the wave function W of the photon will be something like |1> + |2> (normalization coefficients are absorbed in the state vectors). Notice that W is symmetric in the two possible outcomes 1 and 2.

However, we know that when we do the experiment, only one of the detectors will click, either D1 or D2.

And so we have already all the ingredients together for the interpretation problem.

W: The wave function |1> + |2> is symmetric and prefers neither 1 or 2.

R: In reality, only one detector will click, either D1 or D2, and obviously one is preferred over the other.

As Chad explains, decoherence will eliminate to some extent the quantum interference between |1> and |2> and in this sense 'classical behavior' emerges; But this does not really solve our problem.

Even if the product between |1> and |2> or |D1> and |D2> is nearly zero, this does not elimiate the fact that W is symmetric and R is not. (Notice also, that decoherence will in general bring the product between |D1> and |D2> close to zero but not exactly zero and there is no sharp cut-off between quantum interference and classical behavior. But this is really not that important to our problem.)

By the way, please notice that the interpretation problem is a real problem (W does not match R); We are not talking about an 'interpretation problem' in the sense an art critic or a philosopher might use that phrase.

It is evident that every attempt to solve the interpretation problem must fall into one of three categories.

i) The problem is with W. The wave function is not a complete description of R. We will encounter this approach in part 2 of this series as hidden variables, etc.

ii) While W is complete, the problem is about what we mean with 'W describes R'. The Copenhagen interpretation, the ensemble interpretation and others belong here. I will discuss them in part 3.

iii) The most radical proposal is to assume that W is fine and our problem is with R; Reality is just not what we think it is. The many-worlds interpretation is the most important example and I will discuss it in the final part 4 of this series.

One more remark about the upcoming parts; While similar reviews often point to a favored interpretation and describe all others in a negative light, I will try something new and describe all interpretations as convincing and favorable as I can. I hope that this will increase the entertainment value.

continue to part 2.