The strange many worlds of quantum mechanics

[KimB]

I just thought I'd start up a little post on something that I've been discussing for a little while in some other places: which interpretation of quantum mechanics is most likely to be accurate?

For the uninitiated, first I'm going to present a basic description of the measurement problem in quantum mechanics. The measurement problem comes about because between measurements, quantum mechanical particles behave like waves. But the moment we actually perform a measurement, they look like particles. The measurement problem deals with exactly how and why this measurement problem exists.

Here's a description of the two-slit experiment that highlights the issue:
http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec13.html

The basic idea here is that the electron acts like a wave, passing through both slits then interfering with itself, until it strikes the screen, at which point it presents a single blip. The blips on the screen from multiple electrons add up to make the interference pattern we expect from each electron being a wave traveling through the pair of slits.

There have been historically three different approaches to attempt to understand this exceedingly weird phenomenon. First, you could close your eyes and ignore any physical mechanism that might be causing the collapse, and just accept that some collapse happens when a measurement is performed. This would be the Copenhagen interpretation. The primary problem with the Copenhagen interpretation is that it doesn't actually describe what's going on at the collapse, and it is amenable to rather absurd interpretations like the idea that whether or not there is an experimenter reading the outcome of an experiment will change its outcome, even though the apparatus remains unchanged.

The second major interpretation is the Bohm interpretation. In this interpretation, it is proposed that there are two sorts of entities: there's wavefunctions, and there's particles. Each particle has a "pilot wave" that interacts like the normal quantum mechanical wavefunction. This interpretation explains the two-slit experiment by stating that the electron itself only passes through one of the slits, but its pilot wave travels through both and impacts the entire screen. The interaction between the pilot wave and the particle provides the probability that the electron will strike any given position on the screen.

The third major interpretation states that there is only one type of thing, the quantum-mechanical wavefunction, and it evolves just like quantum mechanics says it does, with no collapse ever occurring. This is known as the many-worlds interpretation, which will later make sense. It stemmed out of the mind of Hugh Everett III in 1957, who realized that just looking at how quantum mechanical waves interact with one another could easily explain how quantum mechanical waves appear to collapse when measurements are performed. The answer, it seems, has to do with the fact that in order to properly determine what quantum mechanics says about the results of an experiment, we have to not only take into account the quantum mechanical nature of what is being observed, but also the quantum mechanical nature of the apparatus. What he discovered is that when you interact a simple quantum mechanical wavefunction (e.g. an electron that has just passed through a two-slit apparatus) with a complex wavefunction (e.g. the detector apparatus), the wavefunction is split into a group of different components by that interaction, components which are prevented from interfering with one another.

In fact, those different components are prevented from any sort of interaction whatsoever. So, imagine we have a two-slit experiment wherein we're going to measure which slit the electron goes through. When that interaction occurs, the wavefunction of the electron and experimental setup together is split into two parts. One part has the electron traveling through slit 1, with the measurement apparatus observing it going through slit 1. The other part has the electron traveling through slit 2, with the measurement apparatus observing it going through slit 2. The beauty of Everett's picture is that he recognized that this interaction between the apparatus and the electron causes what is known as decoherence: once the two have interacted, the two states are prevented from interfering with one another, due to the complexity of the measurement apparatus.

So, we end up with a wavefunction that is describing two different situations: the apparatus observes the electron going through slit 1, and it observes the electron going through slit 2. Both situations are amplitudes of the wavefunction, but since they can't interact with one another, it will appear to the measurement apparatus as if the wavefunction has collapsed to one state or the other, now that the apparatus can no longer access the state where the other state has been observed.

The discovery of decoherence dramatically changes the playground of quantum mechanics, as it completely does away with any necessity to add new rules to the theory to explain collapse. With the recognition of decoherence, we discover that the appearance of wavefunction collapse was built into the theory to begin with, just by the properties of how wavefunctions interact. Because this theory requires no additional assumptions above simple wavefunction dynamics, it seems exceedingly likely that it is accurate, because any other interpretation is going to require adding new machinery.

And yet, the results of the theory are exceedingly strange. We discover that quantum mechanics predicts that every possible event occurs. It shows that there exist within the wavefunction of the universe a series of approximately classical worlds, each one unable to interact with any of the others. There are literally billions upon billions of alternate versions of you and me, all described by the same wavefunction. Every single event that is actually possible is realized somewhere in this space.

But if science has taught us anything, it's taught us that the fact that something is weird is no reason whatsoever to discard it. So, we should accept the many-worlds interpretation, because the only alternative is to accept a theory that requires more hypothetical and unnecessary entities.

I hope some of you find this interesting

 

[dizietsma]

All three are correct until you pick anyone of them and then that is the one and only correct one.

 

[KimB]

All three are correct until you pick anyone of them and then that is the one and only correct one.

Heh. Occam's Razor disagrees.

 

[MfA]

Many worlds theory ... god doesn't just play dice, he throws a metric fuckton of them ...

I cling to the hope physicists will find some hidden variables.

 

[KimB]

Many worlds theory ... god doesn't just play dice, he throws a metric fuckton of them ...

I cling to the hope physicists will find some hidden variables.

The problem is that any hidden variables theory that doesn't also include the many worlds that Everett predicted can't work due to Bell's theorem. The Bohm interpretation, for instance, which has a non-collapsing "pilot wave" that follows Schroedinger's equation, includes the many worlds within this pilot wave. It just "picks out" a single one of those many worlds to be real by putting particles in one of them. These other components of the pilot wave without particles will still wiggle around, bounce off one another, and otherwise interact. It is still entirely possible within the mathematics of the theory for observers to inhabit these other worlds, even though adherents claim that these other worlds are just illusory.

Thus there is only one possible way for there to not be "many worlds": wave function collapse is real. But there's no way to make wave function collapse a real phenomenon without throwing determinism out the window, or without adding new dynamics to the theory. Thus Occam's Razor will always exclude such theories, unless they can provide definite, measurable predictions that are then verified. So far none has been able to do so, and the experiments are firmly on the side of decoherence theory and Everett's many worlds.

 

[MfA]

It just "picks out" a single one of those many worlds to be real by putting particles in one of them.

It's arbitrary and inelegant, but it proves it can be done without waveform collapse or many worlds ... the fact it can be done at all opens the gates for the possibility of it being done elegantly.

 

[KimB]

It's arbitrary and inelegant, but it proves it can be done without waveform collapse or many worlds ... the fact it can be done at all opens the gates for the possibility of it being done elegantly.

Nope. Experiments prove the reality of the wavefunction. The only way to have an alternative model to the MWI that describes reality is to both have the wavefunction and something else. Therefore the MWI always wins on Occam's Razor grounds, unless evidence comes up to falsify the interpretation.

 

[MfA]

There is no proof outside of mathematics, only evidence.

Also, new observables correlated to the hidden variables are perfectly possible ... and those could allow more accurate predictions than contemporary QM ... better predictions beat all. When I say I hope they find hidden variables I meant in a measureable way ...

 

[KimB]

There is no proof outside of mathematics, only evidence.

While true, at some point the experimental evidence is so strong that it becomes overwhelming. Bell's theorem gave us a window to directly test if the weird results of quantum mechanics were real or not: they are. Other tests such as those of the Aharanov-Bohm effect that demonstrate the reality of the complex phase of the wave function.

Also, new observables correlated to the hidden variables are perfectly possible ... and those could allow more accurate predictions than contemporary QM ... better predictions beat all. When I say I hope they find hidden variables I meant in a measureable way ...

Sure, and you couldn't say that any such theory was accurate without first falsifying the MWI, which I already stated. This requires looking very closely at the boundary between collapse and no collapse, which has been done and so far accords perfectly with MWI.

 

[MfA]

If they find hidden variables which allow predictions of things which QM assumes completely random statements like "the boundary between collapse and no collapse" become nonsensical. (The fact you can measure the standing wave function of "particles" has little to do with the wave function in a pure probabilistic sense ... they might simply be waves in a more classical sense.)

PS. I didn't say my hope was based on any rational thought, I just like the clockwork universe better.

 

[KimB]

If they find hidden variables which allow predictions of things which QM assumes completely random statements like "the boundary between collapse and no collapse" become nonsensical. (The fact you can measure the standing wave function of "particles" has little to do with the wave function in a pure probabilistic sense ... they might simply be waves in a more classical sense.)

PS. I didn't say my hope was based on any rational thought, I just like the clockwork universe better.

Well, the MWI is a clockwork universe. It is fully and completely deterministic. We just can't access the entirety of what's going on within it.

 

[Fred]

I'm more partial to decoherence + the consistent histories approach eg neo Copenhagen.

 

[KimB]

I'm more partial to decoherence + the consistent histories approach eg neo Copenhagen.

It seems to me that that approach is identical to the MWI.

 

[Fred]

They are all essentially equivalent, in the sense that its really hard to find a testable difference between any, even in principle.

There are also a lot of variants within each category, so its relatively difficult to list tangible differences without getting into nitty gritty details. Imo, a lot of it comes down to which mathematical notation you like the most and which nice attribute you are least willing to relax. CH for instance works seemlessly with both the density matrix as well as decoherence, which are both important in my line of work, so consequently I tend to pick that version.

Its also something that I haven't spent much time thinking about since my Grad school days, b/c I personally find the whole subject rather tedious, and am a firm believer in the 'shut up and calculate' approach.

 

[KimB]

They are all essentially equivalent, in the sense that its really hard to find a testable difference between any, even in principle.

No, they aren't essentially equivalent, because most interpretations simply ignore what goes on during the collapse. When I said that it looked to me like Consistent Histories was the same as the MWI, I mean it looked like it was absolutely identical in everything it says about the way the natural world behaves, specifically that there is no wavefunction collapse, just the appearance of it, and that the "bird's eye view" of the universe would show many approximately classical, approximately non-interacting worlds within it. It looks, to me, like basically just another way of looking at the mathematics, not a genuinely different interpretation.

This is contrasted against, for example, the Copenhagen interpretation, which states that observers actually change the universe through the process of observing. The interpretation basically ignores any mechanism of collapse, and so any observation of collapse where the wavefunction was not observed would falsify this interpretation. Turns out this has been done:
http://prola.aps.org/abstract/PRL/v77/i24/p4887_1

But regardless, even where there aren't testable differences, this is where Occam's Razor helps: go for the theory that has the fewest hypothetical entities. This argues strongly for a minimalistic MWI (some MWI variants have added dynamics to quantum mechanics, as is necessary in all other approaches).

Its also something that I haven't spent much time thinking about since my Grad school days, b/c I personally find the whole subject rather tedious, and am a firm believer in the 'shut up and calculate' approach.

Indeed, and this was the attitude of most of my colleagues. I thought it was fascinating, but whatever. The point remains that if you're performing work that is sensitive to wavefunction collapse, such as quantum computing research, then it makes a lot of sense to be aware that the (still, revoltingly) standard Copenhagen interpretation is just plain wrong.

 

[Neeyik]

But regardless, even where there aren't testable differences, this is where Occam's Razor helps: go for the theory that has the fewest hypothetical entities.

Strictly speaking that should be "go for the most complete working theory that has the fewest hypothetical entities" - is it known for certain that following the MWI will eventually produce a more accurate model of nature than, say, CI would?

 

[KimB]

Strictly speaking that should be "go for the most complete working theory that has the fewest hypothetical entities" - is it known for certain that following the MWI will eventually produce a more accurate model of nature than, say, CI would?

Certainly, because decoherence theory actually describes what happens at the boundary between collapse and no collapse. The Copenhagen Interpretation ignores any physical process that may be going on, or at worst assumes it's discrete and collapse only happens when there's an observer (which is flat wrong).

And even if it only said as much as the Copenhagen Interpretation, it'd still be superior due to the smaller number of postulates required to express the theory.

 

[Neeyik]

And even if it only said as much as the Copenhagen Interpretation, it'd still be superior due to the smaller number of postulates required to express the theory.

But if that was the case, why would that automatically make it a better theory? And yes, I do know about Occam's razor, the scientific method and so on - I make the point because there's always the possibility that the clumsiest, most-factor-laden theory ultimate is the right one, even if it sure as hell doesn't look that way right now. Granted this is a bit of a stupid point but as somebody who has to teach/explain QT interpretations on an initial/fundamental level to numerous students each year, I'm reticient to say "this is right, that's wrong" when the jury is still rather out (plus I just don't have the time anymore to really keep up with the latest developments in theoretical physics). Hell, it wasn't that long ago when it was generally expected that we should saying the MWI was billy bonkers and CI was the way to go.

 

[Fred]

I'd say decoherence is pretty much universally accepted nowdays since people use it to actually measure things in the lab.

Otoh just about every interpretation can be made to fit with it (some with more difficulty, but still). Also it essentially pulls the wool over your eyes and sidesteps the key conceptual arguments, which are arguably still there.
As for which interpretation is best. Again, you poll the experts and you'll find people all over the board, and there hasn't been much real unambigous progress for decades on the measurement problem.
One day when im old, maybe i'll look at the problem again, but for now its backburner material and a pretty obvious career faux pas.

 

[Mize]

Chalnoth - isn't there a famous particle-splitting experiment where one can force the spin of one of the particles then measure the other and the first forced measurement will "cause" the other to be the opposite (action at a distance)? So the quantum wave results in coherence at a distance?