Sunday, June 1, 2014

Superposition, Decoherence, Schrodinger's Cat and other magical lies my professors told me.

For any student of Quantum Mechanics (QM), the interpretation of the QM formalism is at first a puzzling proposal.  Simply put it is 'counter intuitive' and most people "shut up and calculate" essentially bowing to the myth that "QM is very weird".

How can things be in 'several states' at the same time. QM matter must be of a different, slightly magical, nature.  It is perhaps best exemplified by paradox of the Schrodinger cat that is both dead and alive, supposedly at the same.

In this post we will apply the formalism of walkers, an emergent model of QM dynamics that comes about from the association of a particle and a wave and show how it sheds a new light on the fundamental interpretation of QM and show that in this interpretation, the cat is simply always dead.

We will also use this formalism to shed light on the typically QM notion of coherence and decoherence.

We study the walkers by simulations and our little group operates on facebook:


A brief overview of Walkers. 



Walkers are the association of a particle bouncing on a liquid silicon surface and the waves this bouncing creates. Everytime the particle bounces on the surface it creates a standing wave (modeled by a Bessel function in 2D) which in turn drives the particle.  The sum of the history of bouncing informs the future bouncing.  When the particle bounces it picks up an acceleration due to the gradient of the local surface (like a surfer on a wave). This dynamical system, the association of the particle and its wave exhibits interesting self-quantized dynamics.

A strict interpretation of the deBroglie wave/particle duality.

Louis deBroglie, one of the fathers of QM, postulated wave/particle duality.  Observing that sometimes matter behaves as a wave and sometimes as a particle, he postulated a relation between the energy of a particle and it's 'deBroglie' wavelength in his PhD thesis. This earned him the Nobel prize in 1929. The walker are a strict implementation of this idea as we have both a particle and its adjoined wave.

Surfers vs Walkers

This point is a little technical but is worth mentioning.  The walkers 'bounce'.  Each bounce creates a wave.  This is a 'discrete' phenomena as opposed to 'continuous'. We sum a finite number of waves.  A continuous phenomena, requiring integration, would be a 'surfer'.  It is worth mentioning because some of the current formalism for the walkers (most notably the Bush formalism we use in this research) is really a 'surfer' formalism, assuming a continuous wave creation along the path.The surfer creates the waves it surfs on.

Self-excitation, Self quantization. QM behavior

The dynamics of this system is interesting in it's path.  The particle will self-excite and start 'walking' as seen in the video.  More importantly to the QM study, some of the behavior observed mimics QM.  For example if the particle is submitted to an elastic potential (by way of an EM field) it starts orbiting and showing 'quantized' (discrete sets) of possible orbits.  The path cannot be "anything" it is quantized by it's own history, the path creates the path.  The history quantizes (by offering a discrete set of possibilities) the future.

Chaotic Dynamics



To understand the solution, pay close attention to the video above. It is a run captured in matlab by Heligone of dotwave.org. The point is that the orbit goes from trefoils to ovals and (not seen here) sometimes circles.  These are the quantized orbits.  The change between these orbits is called 'intermittence' and is a characteristic signature of chaotic dynamics.  The dynamics will randomly change between these stable, discrete, orbits.

Superposition revisited as intermittence

If one observes these objects over long periods of time, one can compute the 'time' the particle spends in each orbit.  With this mental picture we can revisit QM.  It is a different interpretation than QM.  In QM, the particle is in 'several states' AT ONCE, meaning it would be in the oval and the trefoil at the same time. This is difficult to picture for macro objects such as the cat. In this model, the particle oscillates between those states over time, but NOT AT THE SAME TIME.  There is no superposition, just intermittence, an oscillation between the states with certain transition probabilities.

Weights as probabilities. 

If one computes the times, one can arrive at the probability one would observe the particle in a particular state. These are transition probabilities.  This formalism demystifies the Hilbert space formalism that says that the particle is in all the states with various probabilities.  Here there is a logical and simple interpretation for those 'weights' they are the probabilities to find the particle in the particular quantized states available to the dynamics.  It is simply the time it spends in each quantized orbit.

Schrodinger's cat is always dead

Let's revisit the Schrodinger cat paradox in this picture.   The idea that a cat would be dead and alive has confused generations of students for the past 100 years and while it makes for good magical mythology it is just false logic in this picture.  More importantly, it is the act of observing it that kills the cat. There are several problems with the paradox: a/ we are not in 2 states at the same time.  In this model we either are in orbit A or B but not in both at the same time. We oscillate between those states at different times. We are only in ONE state at a time (even if changing rapidly). b/ the category dead/alive are different than intermitting between orbit a and b. Simply put we cannot 'intermit' between dead and alive like we can jump back and forth from orbit A to B and vice versa.  But ounce you reach "dead", you stay dead.  So essentially the particle would eventually orbit to 'dead' state for the cat, and once it has done it, the cat IS DEAD. End of story.

Observation

In this picture the idea that observation is what killed the cat, which is the usual interpretation, is laughable.  You didn't magically kill the cat with your thoughts, the cat died because the particle decayed. End of story.

But Quid of Decoherence and the measurement problem.

This is technical but is the heart of the issue at hand.  In QM, the act of observation is what creates the 'wave collapse' and 'decoherence'.  The system is classical, not QM after the act of observation.

There is a big difference in the walker system: Essentially in the case of walkers, the observation of the particle (here in silicon and silico) DOES NOT DESTROY THE FIELD.  This is the important part. If the act of measuring interferes with the field (uses tools that are on the order of magnitude of the deBroglie wavelength), which is the case for 'classical QM" (remember the observation of slits in the Young double slit experiments is enough to destroy the QM result) then one loses the chaotic dynamics induced by the field. Observing a QM dynamic induced by a 'field' destroys the field. So the QM dynamics stop the moment we 'observe' them.  The measurement problem is at the heart of our problems with QM.

The notion of 'coherence' and 'decoherence' which is usually magically associated with the existence of 'superposition' and it's disappearance (the mythical wave collapse) is very simply the existence of intermittence due to chaotic dynamics.  "Coherence" in the walker/surfer picture is the existence of the association of the particle and the field and the resulting chaotic/intermittent dynamics.  Destroying the field destroys that dynamic. the dynamic becomes classical dynamics and ceases to be quantum dynamics. Observing a QM system destroys its QM dynamics if one destroys the field. Decoherence is the destruction of the wavefield self-generated by the particle bouncing about and thus the end of the QM dynamic. QM dynamics is a chaotic dynamics brought about by memory of its past via a wavefield that is easy to destroy.

And that is all there is to it.

A brief historical philosophy consideration

In conclusion, the latest Couder work, simply explains many of the QM behaviors and the magical coherence/decoherence and seems very simple in retrospect. Why wasn't this 'particle/wave' duality taken to it's logical conclusion by the founding fathers of QM? One has to project back to the Solvay conference in 1927, where deBroglie proposed these ideas and was shot down by the Copenhagen school. It is not hard to see why.

To make headway with these models (which we do in the 21st century) one needs the formalism of chaotic dynamics (which was developed in the 80's and 90's) and powerful computers to run the integration as there is little headway to be had analytically.  In short, while philosophically satisfying, the wave/particle duality interpretation is difficult from a practical standpoint.  In front of this model there was the straightforward (if magical) interpretation of the Copenhagen school: namely a vectorial superposition of states in a abstract 'hilbert space' that could give practical results in calculation.  The 'shut up and calculate' mentality was justified as it gave us the atom bomb, most the technological advances of the late 20th century (think lasers, computer spin storage etc) and the CERN Higgs. The practical nature of the formalism was justification enough. The interpretation was secondary.

There is no magic.

7 comments:

czARgb said...

What does this suggest in terms of quantum computation? I suspect this would rule out a many worlds interpretation and along with it the possibility for quantum computation, if in fact the many states of superposition do not occur simultaneously, but in time division.

Marc Fleury said...

I am not an expert on quantum computation but those who are are throwing the BS flag gladly, namely that the 'superposition' they thing they observe is not there. I have no idea what this model says about that except that in this picture the field is a very 'fragile' construct and as soon as you interact with the particle and the field you destroy the association and lose the QM dynamics which are nothing more than chaotic dynamics in intermittence.

The Everett many world interpretation has long been considered absolute garbage by most people. What are we to make of energy conservation? if every little QM observation CREATES a separate universe then you need to have double the energy for everything that happens?. But this is the kind of 'non-sense' that doesn't even need to be addressed in this picture. It just doesn't make any sense. The fact that it is still around is just because it makes for good bla bla and cocktail conversation.

czARgb said...

Thanks for the reply Marc. Classical computation is energy consuming and to store a bit of concluded information an entropy increasing process. I think Quantum Computation raises objections quite similar to the ones you mention with Everett's many world interpretation.

Is there a name for an interpretation where the word create in the sentence: "CREATES a separate universe" is replaced by "CONSIDERS a separate universe" (at the risk of opening the discussion to the meaning of considers") ? Quantum computation (if it was in fact true) would require at minimum the latter to be possible. Other than that we would need an alternate description in which unseen degrees of freedom within a single universe take the burden of computation. Could such degrees of freedom exist in the time division phenomena that you have described? I am not sure, although I think probably not. Thanks again!

Marc Fleury said...

Well, the whole 'unseen degrees of freedom" is in fact the name of the game in this study. Einstein used to call it "hidden variables" and the thing with hidden variables is that Bell inequalities strictly differentiate between hidden variables and classical QM. The experiment of Aspect/GHZ rule in favor of classical QM. In this interpretation the 'hidden variable' is the field itself in a way and how it interacts with the particle in a feedback loop. In this interpretation 'making sense' of the classical Copenhaguen imagery becomes superfluous as we are considering different 'object'. Where QM speaks of a 'superposition' in a hilbert space (read: being in several states at once) this approach speaks of intermittence, different time slices where you are in different states and the jumps are due to chaotic dynamics (in the mathematical sense: with the presence of intermittences aka jumping around). Reconciling this interpretation which is fundamentally deterministic (even if chaotic and thus statistical in outlook) with the more abstract objects QM introduces may not be relevant after all.

Marc Fleury said...

In other words, the cat is dead, was always dead and you didn't kill it with your mind.

Anonymous said...

You are quite right that sloppy expositors make it sound like "you killed the cat with your thoughts" but careful ones explain that an "observer" is not necessarily a human or even alive, but could be a detector. I do not have a good physics background but I guess you are criticizing that notion too? It sounds like you are but your later comment "it's not your thoughts that kill the cat" make it sound as if you are *only* criticizing the idea that human thoughts kill the cat.. Maybe you wanted to just use the metaphor :-)

Second, wikipedia under "mary worlds" gives to rebuttals of why it does not violate "conservation of energy" but again I do not have the physics background (I have a PhD in math..and even there it is pure, not applied, so far removed..and more on other projects (education etc) these days anyway)..

Third and last: have you read the expository article "Quantum Mysteries for Anyone"? Anyone with basic Probability 101 math class and some patience can follow this article..it quotes Einstein at beginning, telling a friend why he does not trust QM: "do you really believe that, the moon is 'not there' when you don't look at it?" But as the article shows, and then gives mathematical proof of (assuming you trust the 'if you build this experiment, the results will be such-and-such)" the fact that: "we can now PROVE that the moon really is NOT there when you don't look at it!". Metaphorically: not the moon itself, not the (dead) cat, but on the particle level, the article shows. Interested in a physicist's reaction.

You created JBOSS, you're Marc yes? That's how I found this blog. If not, then your blog is still very interesting (though time limits how often I can return) If you did create it, thanks..I own shares of Red Hat linux, you have helped that company do well :-) and more importantly helpful to the world in middleware etc etc. Regards and respect to you.

Marc Fleury said...

(yes on identity, but that is a past one :))

Onto your points. Yes, the observer doesn't have to be human or anything, just that anything interacting at some point with the system will trigger intermittence. The intermittence happens, this is why we observe statistics. But there cannot be intermittence between dead and alive. It is mostly the notion of 'superposition' that I attack here. That something is in state A and B AT THE SAME TIME is what is non-sensical in retrospect.