Monday, November 19, 2012

Quantum interpretations are scientific

Quantum Mechanics is famous for having multiple interpretations.  Among them, the two most common interpretations are the Many Worlds Interpretation (MWI) and the Copenhagen interpretation.

According to the Copenhagen interpretation, when you measure a system that is in a mixed quantum state, then the system "collapses" into a definite state (that is, a state that gives you only a single result for your measurement).  There are different probabilities for the system to collapse into different states, but it will always be a definite state.

In contrast, MWI says that there is no collapse.  Rather, when you measure a system in a mixed quantum state, now you are in a mixed quantum state.  One component of your state consists of you having measured one outcome; another component consists of you having measured the other outcome.  These different components don't interact with each other, and evolve independently.  The ultimate consequence is that the entire universe is in a mixed state with many components that don't interact with one another.  Thus the name "many worlds".

MWI and the Copenhagen interpretation give identical predictions in all experiments.  So it's impossible to falsify one in favor of the other.  That's why some contend that the interpretation question is non-scientific.  I do not agree, for two reasons:

1. Different interpretations suggest different directions for future theories.
2. Experiments might have something to say about Copenhagen vs MWI after all.

1. Directions for future theories

I want to quote something Richard Feynman said.  Not because Feynman said it, therefore it was right, but because Feynman put the idea into my head.  This occurred in a lecture series Feynman gave at Cornell (specifically, the second lecture, section 8).  Feynman explained that there are three different ways to state the law of gravitation:
  1. Each object senses where all the other objects are, and feels a force towards each object of magnitude GmM/R^2.
  2. There is a gravitational potential in every point of space, governed by laws that only look at its surrounding neighborhood, without looking at far away objects.  The gravitational force is determined by this potential.
  3. Given a start and end point, an object travels by the path that minimizes a particular quantity.
So the question is, which of these theories is correct?  Is this a scientific question?  Feynman said:
They are equivalent, scientifically; it is impossible to make a decision, because there's no experimental way to distinguish if all the consequences are the same.

Psychologically, they're very different in two ways.  First, philosophically, you like them or don't like them--training is the only thing you can do to beat that disease.  Second, psychologically they're different because they're completely unequivalent when you go to guess at a new law.

As long as physics is incomplete, and we're trying to find out the other laws, and to understand the other laws, then the different possible formulations give clues as to what might happen in another circumstance.  And they become not equivalent in psychologically suggesting to us to guess as to what the laws might look like in a wider situation.
Physics has developed a lot since we discovered the law of gravitation, so we know for a fact that the different interpretations have different uses.  The second theory has helped us understand some of the fundamental character of quantum field theory.  But the third theory gave us Feynman path integrals, which are related to Feynman diagrams, an easy way to represent fundamental particle interactions.  The first theory has not been very useful, and that's that.

MWI and the Copenhagen interpretation are in the same situation as the law of gravity.  They're equivalent in terms of predictions, but they lead to different ways of thinking which suggest different directions for expanding physical theories.  The first thing that comes to mind is that MWI is deterministic and unitary (meaning it is deterministic if time plays backwards too).  That's useful because it suggests that we can continue coming up with fundamental laws that obey time-symmetry.  There may be other uses too.

As I argued in "Multiverses are scientific", scientific ideas can serve many roles.  There are observations, hypotheses, experiments, theories, predictions, and so forth. Quantum interpretations also fulfill a role in science--they suggest different directions for future theories.  They do not fulfill the role of hypotheses which can be tested.  And that is okay, because not all scientific ideas need to fulfill every single role at once.  A hypothesis doesn't also need to be a theory, and an interpretation doesn't also need to be a hypothesis.  So the fact that the interpretations are not falsifiable doesn't necessarily mean it is unscientific.

2. How to (possibly) verify MWI

First, I need to explain how the Copenhagen interpretation and MWI, despite their differences, vary continuously into one another.  Consider a thought experiment where a mechanical device detects whether a radioactive atom decays within a half-life.  If it does, then it turns on a laser pointer, which provokes a cat to run through a hallway.  At the other end of the hallway, I can see if the cat appears or not.  Whatever I see, I publish my results for other scientists to see.

The question is, when does the collapse occur?  Does it collapse when radioactive atom observes itself decaying?  Does it collapse when the mechanical device observes the radioactive atom?  Do the mechanical device and radioactive atom both collapse when the cat sees the laser pointer?  Do the cat, device, and atom collapse when I see the cat (or not)?  Do the cat, device, atom, and I all collapse when other scientists see my results? Etc. etc.

If you answer "no" ad infinitum, you are taking the MWI.  But if you eventually answer "yes", you are taking the Copenhagen interpretation.  To make the Copenhagen interpretation similar to the MWI, all you have to do is say "no" lots of times before eventually saying "yes".

We don't know the answer to all those questions, and cannot know.  But we do know the answer to the first few is "no".  We can verify that small systems are in mixed states because we can measure interference effects.  With more complex systems, it's harder because of the sheer randomness that occurs when you have lots of particles at a non-zero temperature.  In my knowledge, the largest quantum system created was 40 microns in length, and needed to be cooled down to 0.1 K.

It will be hard to push that limit, but we definitely could, in very small steps.  We could push the Copenhagen interpretation closer and closer to MWI, though we will never quite reach it.  Alternatively, MWI could be falsified if it's found that mixed states do not exist past a certain point (ie if no interference is found where it is expected).


People sometimes say that MWI is unscientific, because it posits parallel worlds that cannot be observed.  This is mistaken because it assumes that every single idea in science needs to be verifiable.  Scientific ideas may also serve other roles, such as suggesting future directions for theories which themselves would be experimentally verifiable.  Secondly, it so happens that MWI is partially verifiable in very small increments.


schrodingasdawg said...

I think you've misunderstood the Copenhagen interpretation, and confused it with an objective collapse theory. von Neumann's interpretation, for instance, asserts that the wave-function is a real thing, and that it is consciousness that causes the collapse.

The Copenhagen interpretation (and I'd recommend reading what Bohr and Heisenberg wrote on this), on the other hand, is radically anti-realist. It claims that the wave-function is not actually a real, physical property of the system being studied; instead, it is a subjective thing, assigned to the physical system by someone on the basis of what this someone knows about the system. When a measurement is performed, our knowledge changes, so we assign a different wave-function to it. That's all collapse is. It's not a dynamical process, as an objective collapse theory would suggest.

The Copenhagen interpretation would also have it that "wave-function collapse," then, happens at different points for different people. In the Wigner's friend thought experiment, it happens for Wigner's friend when the friend opens the box with the cat. For Wigner, it doesn't happen until Wigner goes into the lab.

You should probably see from this that you can put of "collapse" indefinitely in Copenhagen by further removing the person assigning the wave-function from the system. You can't experimentally distinguish it from MWI after all. It's only objective collapse theories that you can distinguish from either CI or MWI, which make the same predictions.

miller said...

Yes, I failed to make a distinction between an objective collapse interpretation and a subjective collapse interpretation. My impression is that this reflects the way the Copenhagen interpretation is typically taught. That is to say, the distinction is not taught, and no one particularly cares about it.

But you're correct that my second section just doesn't apply to a subjective collapse interpretation.