The bogus “interpretations” of quantum mechanics

I’ve not written on this blog for a long time. A talk in Mouans-Sartoux yesterday prompted me to write this rant about what I will (demonstrably) call bogus interpretations of quantum mechanics. Specifically the “dead and alive cat” myth.

Schrödinger’s cat

One of the most iconic thought experiments used to explain quantum mechanics is called Schrödinger’s cat. And it is usually illustrated the way Wikipedia illustrates it, with a superposition of cats, one dead and one alive:

1995px-schrodingers_cat-svg

The article of Wikipedia on the topic is quite clear that the cat may be simultaneously both alive and dead (emphasis mine):

The scenario presents a cat that may be simultaneously both alive and dead,[2][3][4][5][6][7][8] a state known as a quantum superposition, as a result of being linked to a random subatomic event that may or may not occur.

In other words, in this way of presenting the experiment, the entangled state of the cat is ontological. It is reality. In that interpretation, the cat is both alive and dead before you open the box.

This is wrong. And I can prove it.

Schrödinger’s cat experiment doesn’t change if the box is made of glass

I can’t possibly be the first person to notice that Schrödinger’s cat experiment does not change a bit if the box in which the cat resides is made of glass.

Let me illustrate. Let’s say that the radioactive particle killing the cat has a half-life of one hour. In other words, in one hour, half of the particles disintegrate, the other half does not.

Let’s start by doing the original experiment, with a sealed metal box. After one hour, we don’t know if the cat is dead. It has a 50% chance of being dead, 50% chance of being alive. This is the now famous entangled state of the cat, the cat being “simultaneously both alive and dead”. When we open the box, the traditional phraseology is that the wave function “collapses” and we have a cat that is either dead or alive.

But if we instead use a glass box, we can then observe the cat along the way. We see a dead cat, or a live cat, never an entangled state. Yet the outcome of the experiment is exactly the same. After one hour, we have 50% chances of the cat being dead, and 50% of chances of the cat being alive.

If you don’t trust me, simply imagine that you have 1000 boxes with a cat inside. After one hour, you will have roughly 500 dead cats, and 500 cats that are still alive. Yet you can observe any cat at any time in this experiment, and I am pretty positive that it will never be a “cat cloud”, a bizarro superposition of a live cat and a dead one. The “simultaneously both alive and dead” cat is a myth.

Quantum mechanics is what physics become when you build it on statistics

What this tells us is that quantum mechanics does not describe what is. It describes what we know. Since you don’t know when individual particles will disintegrate, you cannot predict ahead of time which cats will be alive, which ones will be dead. What you can predict however is the statistical distribution.

And that’s what quantum mechanics does. It helps us rephrase all of physics with statistical distributions. It is a better way to model a world where everything is not as predictable as the trajectory of planets, but where we can still observe and count events.

The collapse of the wave function is nothing mysterious. It is simply the way our knowledge evolves, the way statistical distributions change as we perform experiments and get results. Before you open the box, you have 50% chances of a dead cat, and 50% of a live cat. That’s the “state” not of the universe, but of your knowledge. After you open the box, you have either a dead cat, or a live cat, and your knowledge of the world has “collapsed” onto one of these two statistical distributions.

There is a large number of widespread quantum myths

Presenting quantum mechanics as mysterious, even bizarre, is appealing since it makes the story interesting to tell. It attracts attention. And it also puts physicists who understand these things above mere mortals who can’t.

But the result is the multiplication of widespread quantum myths. Like the idea that quantum mechanics only applies at a small scale (emphasis mine):

Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics.

Another example is the question “why is the wave function complex?” Clearly, this seem problematic to many. But if you see quantum mechanics as a statistical description of what we know, the problem goes away.

The (Lost) Art of Presentation

A slide from "It's time to fix HTTPS"

Reviewing my daily feed of tweets this morning, I ran across a presentation called “It’s time to fix HTTPS“. The topic itself is of interest to all of us, since it concerns the security of e-commerce transactions, among other things.

Yet the slide deck lacks basic appeal:

  • Only text (or busy screen snapshots)
  • No obvious organization or story
  • Three boring slides of disclaimers and acknowledgments at the beginning,
  • Acronyms, jargon,
  • Long sentences, broken apparently at random

This kind of presentation is not an infrequent occurrence, unfortunately. For some reason, many scientists and computer scientists seem to take pride in showing horrible slides. I resisted the urge to make a catalog.

So let me state something that should be obvious, but obviously is not: Just because you are smart doesn’t mean your presentations have to suck. Or put it another way: Your time is not so precious that you shouldn’t help your readers get your point.

Sharing an idea

The whole point of a presentation is to share an idea, to convince someone. This requires some work at two distinct levels, form and contents. Let’s assume that you have the contents, what can you do about the form?

Here are three simple things to keep in mind to build a presentation that is useful for you and for your readers:

  • Tell a story
  • Keep their attention
  • Be a guide

Remember above everything else that your objective is to share your idea, not rehash it to yourself. Therefore, if the idea does not contaminate your audience, the presentation failed its objective.

Storytelling

The “storytelling” word has been used and abused. The gist of storytelling is that sharing an idea is not just about sharing facts, it’s about making your audience take ownership of your idea, make it their own.

This is often hard to accept for the scientific minds. Aren’t facts enough? In reality, all facts can be disputed. All opinions have to be defended, explained, elaborated. Even if the idea is obvious to you, it may still be wrong, or dangerous, or you may need to explain the basics to avoid losing half of you audience.

Storytelling is not about what you say, but about how you say it. Don’t write “It’s time to fix HTTPS“. Prefer “Do you know it’s really your bank talking to your browser?” Instead of “Global PKI, as currently implemented in browsers, does not work“, what about “The browser chain of trust hangs to weak links“? (assuming I understood the core argument correctly)

What am I doing with this simple rephrasing? I’m trying to deliver the same facts, the same core idea, but in a way that the audience may relate to. Not everybody knows what HTTPS means, but anybody (reading Google Docs) knows what a browser is or that security matters when it talks to a bank.

Even the best facts need a good story for people to get interested or remember them.

Keep their attention

The slide deck about HTTPS is on a topic that interests me, but I had some trouble following it to the end.

In these days of soundbites when wisdom has to fit in 140 characters, sometimes you need all the help you can get from fancy visuals, animations, speaker charism simply to keep the audience awake. And if you don’t have a speaker (e.g. for an on-line presentation), you may need other tricks.

Google Docs is clearly not the best tool when it comes to delivering fancy presentations. It’s not a limitation of on-line tools, though. Actually, some of the most convincing innovation in that spaces comes from on-line tools. SlideRocket delivers really nice presentations, arguably much better than the average PowerPoint. And what’s the best reason to use Prezi, if not fancy visuals?

Still, do not go overboard. Beware that a movie does not replace a presentation. Who has not seen one too many on-line video like this one?

It certainly took a lot of work. But in my option, it’s the exact opposite of the HTTPS slide, i.e. it’s all about showing off effect after effect. It doesn’t keep my attention either, it smites it to bits.

So how could the HTTPS slide deck retain my attention better? There needs to be some level of organization, some key message, some way for me to understand “Ah, that’s what they are talking about now”. We don’t want raw data, we are already over-fed with data. So whatever we pay attention to needs to be structured.

Fancy visuals do not replace the presentation. But, utilized well, they make it live.

Be a guide

Sharing innovation is even more difficult. To paraphrase A.C. Clarkeany sufficiently advanced idea is indistinguishable from gibberish.

It takes a fair amount of marketing and communication to correctly explain the value and benefits of some new technology. I remember being very happy that VMware was doing all the work of educating our customers about the value of server virtualization, which meant we didn’t have to do that work when talking about HPVM.

Innovation is about telling others what to do. And nobody wants to follow directions, so you need to do it not with brute force, but by getting the audience to actually follow you. One way to do that is by showing a better way. Another is by inducing fear of the current situation.

The HTTPS presentation tries both approaches, but without much conviction. The fear is too implicit, you really need to understand the technology. The better way, the greener pasture just over the fence is a little bit too vague. So it’s not entirely convincing. The technical arguments could be made into a much more appealing proposal, however.

To be a guide, you need to already know where you are going.

Futurism

IEEE Spectrum pokes fun at Ray Kurzweil’s predictions about the future:

Therein lie the frustrations of Kurzweil’s brand of tech punditry. On close examination, his clearest and most successful predictions often lack originality or profundity. And most of his predictions come with so many loopholes that they border on the unfalsifiable. Yet he continues to be taken seriously enough as an oracle of technology

Ray Kurzweil is, among other things, a founder of the Singularity University (link currently down, maybe they can’t take the load).

Well, my reader may remember that I already wrote about the Singularity. And my conclusion was this: the Singularity as commonly defined has already happened. And in any case, chances are that any real singularity is something you can only observe from the outside, but that you will barely notice, if at all, while you are in the middle of it.

Alan Kay is famous among other things for his quote: “The best way to predict the future is to invent it“. I talked to Alan Kay on several occasions while we were both at HP, and after these discussions, I was rather tempted to rewrite his great word of wisdom as follows: “The best way to secure one’s future is to rewrite history.” Ironically, IEEE Spectrum seems to have reached the same conclusion about Ray Kurzweil.

P versus NP

A researcher from HP Labs named Vinay Deolalikar announced a new proof that complexity classes P and NP are different. The paper made it to the Slashdot front-page (more on this below).

What constitutes a “proof”?

This is far from being the first claimed proof. There are about as many proofs that P is the same as NP than proofs of the opposite. With, for good measure, a few papers claiming that this is really undecidable… This just shows that the problem is not solved just because of one more paper. Indeed, the new “proof” takes more than 60 pages to explain, and it references a number of equally complex theorems and proofs.

This is interesting, because it means that very few, except some of the most advanced specialists in the field, will be able to understand the proof by themselves. Instead, the vast majority (including the vast majority of scientists) will accept the conclusion of a very small number of people regarding the validity of the proof. And since understanding the proof is so difficult, it may very well be that even the most experience mathematicians will be reluctant to draw very clear-cut conclusions.

Sometimes, clear-cut conclusions can be drawn. When I was a student, another student made the local news by announcing he had a proof of Fermat’s last theorem. We managed to get a copy of the paper, and shared that with our math teacher. He looked at it for about five minutes, and commented: “This is somewhat ridiculously wrong”.

However, In most cases, reaching such a definite conclusion is difficult. This puts us in the difficult position of having to trust someone else with better understanding than ours.

Understanding things by yourself

That being said, it’s always interesting to try and understand things by yourself. So I tried to read the summary of the proof. I don’t understand a tenth of it. However, the little I understood seemed really interesting.

If I can venture into totally bogus analogies, it looks to me like what Deolalikar did is build the mathematical equivalent of ice cube melting, and drew conclusions from it. Specifically, when ice freezes, phase change happens not globally, but in local clusters. You can infer some things about the cluster configuration (e.g. crystal structure) that were not there in the liquid configuration. In other words, the ice cube is “simpler” than water.

Now, replace atoms with mathematical variables, forces between atoms with some well-chosen Markov properties that happen to be local (like forces between atoms). The frozen cube corresponds to a P-class problem where you have some kind of strong proximity binding, so that you can deduce things locally. By contrast, liquid water corresponds to NP-class problems where you can’t deduce anything about a remote atom from what you learn about any number of atoms. Roughly speaking, Deolalikar’s proof is that if you can tell water from ice, then P and NP classes are distinct.

Of course, this is only an analogy, and it is very limited like any analogy, and I apologize in advance for totally misrepresenting Deolalikar’s subtle work. Nevertheless, I found the approach fascinating.

Crowds are stupid

Now, an alternative to personal understanding is to trust the crowd. Democracy. Unfortunately, if Slashdot is any indication, this doesn’t work at all.

Slashdot has a moderation system, where people vote for comments they find “Interesting” or “Insightful” or “Funny”. You’d think that this would let good comments rise to the top. But what really happens is that people with “moderation points” apparently feel an urge to moderate as quickly as they can. So the very first comments get moderated up very quickly, and drown any later comments in the noise.

Here are some of the comments on the P vs. NP announcement that Slashdot thought were “good”:

  • P is not NP when N is not 1 (“Funny”)
  • A random series of totally uninformed opinions on the cryptography impact (“Interesting” and “Funny”)

There are a few relevant gems in there, like the opinion of a professor at MIT that the proof is not valid. That leads to another more serious analysis. But there are a few redeeming gems even on Slashdot. Still, it’s too bad you have to sift through mud to find them.

Really bad math in a sci-fi book…

I have just been reading Alien Embassy by Ian Watson (in the French translation published by Presses Pocket). This is a somewhat esoteric book, and I can’t say that I’m really fond of that genre. But it is an interesting story, it’s well written, and I enjoyed it.

Howewer, something really puzzled me, and it has to do with what seems to be the deep (mis)understanding of relatively fundamental mathematics, namely irrational or imaginary numbers, somewhere in the first third of the book.

Irrational numbers

Unfortunately, I can’t quote the original text, only back-translate from French, which may be hard to map on the original text. It reads something like that (I’d appreciate if some reader could give me the actual original text):

– He’s talking about mathematics, whispered the voice of Klimt. Irrational numbers are numbers like pi, the constant ratio between the circumference and the diameter of a circle, you must know that.

– That’s about twenty two seventh, I added; I knew at least that!

– It’s a very important number. Without it, geometry could not exist, Klimt commented. It represents a true geometrical relation. Pi appears as soon as you draw a circle. Yet it is totally irrational. There is no explanation to the sum “tweny two seventh”. You can divide twenty two by seventh as long as you want, you will never get a really definitive answer. […]

This is bogus twice.

  • First, the author reasons about 22/7 instead of reasoning about pi. The two numbers are really not that close. To the fourth decimal, 22/7 is 3.1428 whereas pi is 3.1415. It’s really bizarre to talk about the irrational nature of pi by using the different number 22/7 that just happens to share 3 digits with it…
  • But second, and more importantly, irrational in mathematics means precisely that the number cannot be identified to the ratio of any two integers. That seems to have eluded the author entirely, as he seems to think that 22/7 itself is irrational, and that “irrational” denotes a number with an infinite number of decimals, like 1/3 = 0.33333…

Imaginary numbers

There is a similar issue a couple of pages later:

– From what I know, our scientists consider mathematics as imaginary dimensions, said Klimt
Imaginary dimensions? the Azuran fluttered. Imaginary? Ah, but that’s where you got it wrong. These other dimensions are all but imaginary. They really exist. […]

Here, multiple layers of a very strange understanding of mathematics and physics mix up. I don’t think any scientist ever considered mathematics as a whole to be imaginary dimensions. Mathematics use symbols and relations between symbols, and I think that most mathematicians would consider the mathematics we can ever talk about as a countable set. There are imaginary numbers, a terminology that refers to a class of complex numbers like i that have a negative square (e.g. i2=-1).

Where imaginary dimensions show up is for example in some explanations of Einstein’s special relativity, where time is considered as an imaginary dimension, as opposed to three real spatial dimensions. This is a mathematical trick to account for the form of distance in space-time, which has three squares with the same sign and one with a different sign (ds2 = − (dt2) + dx2 + dy2 + dz2).

Why does it matter?

Why bother about two little errors in what is, after all, simply intended to be entertainment? Well, it shows the limits of terminology when we cross domain boundaries. What seems to have confused the author in both cases is that a terminology in mathematics has a very precise meaning that happens to be really far from the everyday meaning of the same word.

The problem is that this gave the author, and possibly his readers, a false sense of understanding. Curiously, this echoes in my mind a number of issues I had with popular science books, some of which were written by well known names in physics. And it is also a problem with the operating systems people use on computers all the time: we tend to forget that a “desktop” or a “window” has nothing to do with the common acceptation of the term, which may confuse beginners quite a bit.

I’m not sure there is much to do about it, though, but to gently correct the mistakes when you see them. After all, short of inventing new terminology all the time (like “quarks” or “widgets”), we just have to proceed by analogy (e.g. “mouse”, “complex numbers”) and then stick with that wording. We consciously forget that the word is the same, the concepts end up being quite different in our brain.

But this has implication in another area I am interested in, concept programming. We give names to concepts, but these names overlap. Our brains know very well how to sort it out, but only after we have been trained. As a result, the big simplification I was expecting from concept programming might not happen, after all…

The woes of the "One laptop per child" project

Ivan Krstić writes in Sic Transit Gloria Laptopi about the woes of the One Laptop Per Child (OLPC) project.

The whole essay is a bit long, but definitely worth reading. It goes through the history of the OLPC project (including its roots in early experiments), through musings about the best choice of operating system, to suggestions on how to move the project forward successfully, after what appears to have been a severe crisis.

No matter what, Krstić is right that the whole experience will not have been in vain. But it’s too bad that a project like this can die for purely political reasons. On one hand, OLPC could not have seen the light of day without the efficient support of someone like Nicholas Negroponte. On the other hand, if we are to trust Krstić earlier essay, Things to remember when reading news about OLPC, he’s now almost a liability to the project:

To those on the outside and looking in: remember that, though he takes the liberty of speaking in its name, Nicholas is not OLPC. OLPC is Walter Bender, Scott Ananian, Chris Ball, Mitch Bradley, Mark Foster, Marco Pesenti Gritti, Mary Lou Jepsen, Andres Salomon, Richard Smith, Michael Stone, Tomeu Vizoso, John Watlington, Dan Williams, Dave Woodhouse, and the community, and the rest of the people who worked days, nights, and weekends without end, fighting like warrior poets to make this project work. Nicholas wasn’t the one who built the hardware, or wrote the software, or deployed the machines. Nicholas talks, but these people’s work walks.

Makes you wonder who really “invented” the OLPC… Two earlier posts may be relevant to this topic:

How To Teach Special Relativity

How to Teach Special Relativity is a famous article by John Bell where he advocates that the way we teach relativity does not give good results. He describes an experiment now known as Bell’s spaceship paradox (even if Bell did not invent it):




In Bell’s version of the thought experiment, two spaceships, which are initially at rest in some common inertial reference frame are connected by a taut string. At time zero in the common inertial frame, both spaceships start to accelerate, with a constant proper acceleration g as measured by an on-board accelerometer. Question: does the string break – i.e. does the distance between the two spaceships increase?

Considered a difficult problem

The correct answer is that the string does break, even if the spaceships appear to always be at the same distance from one another as seen from an observer who did not accelerate with the spaceships. Yet, according to Wikipedia:

Bell reported that he encountered much skepticism from “a distinguished experimentalist” when he presented the paradox. To attempt to resolve the dispute, an informal and non-systematic canvas was made of the CERN theory division. According to Bell, a “clear consensus” of the CERN theory division arrived at the answer that the string would not break.

In other words, this problem was considered hard by a majority of serious physicists at the time Bell raised the question in 1976. I would venture to say that this remains the case today, except that this particular paradox is probably well known now. But the teaching of special relativity has not changed. This is how we explain the paradox today. I have a lot of admiration for John Baez in general, his “blog” is even in the sidebar of this one. But with all due respect, the explanation of the paradox posted on his web site is utterly complicated (I know he gives credit to someone else for it, but by hosting it on his web site, I would say that he condones it).

It should be easy

This particular formulation of the paradox was not known to me until someone recently asked me if the string would break. Using my little technique, it took me less than one minute to have the correct answer, without looking it up, obviously, but also without any computation or complicated diagram. Here is the mental diagram I used (click to see it in high resolution):

On this diagram, time is represented horizontally, and the two space ships are represented by the green and red curves, which are identical but separated by a distance along the vertical “spatial” axis. The distance at rest is represented by the blue arrow. The distance as measured between the two ships after they started moving is measured by the green and red arrows. The distance as measured “from the ground” is along the vertical axis, and remains constant.

Remember the only trick is that a “cosine” contraction on this diagram corresponds to a dilatation in relativity and conversely. On the diagram, the red and green arrows are obviously shorter than the blue arrow. The contraction factor is the cosine of the angle between these arrows and the vertical (space) axis, which is the same as the angle between the red or green curve and the horizontal axis. Therefore, relativity predicts that the distance between the two ships, as seen from the ship, will increase. Specifically, it increases by a factor usually denoted “gamma” (but which I prefer writing as the cosine of an angle myself), which can also be seen as a hyperbolic cosine, and which plays in Minkowski geometry the exact same role as the cosine in the Euclidean diagram above. You can find the precise mathematical relationship here.

Consequently, the string will break.

Accelerated solids in relativity

Another interesting observation one can make from the diagram is that you cannot draw a straight line that is perpendicular to both curves. What is “space” for one ship is not just “space” for the other. You need to draw a curved line between the two rockets if you want to always be perpendicular to the local “time” direction. In other words, the “time” direction for the string is not constant along the way, so all parts are not moving at the same speed. Someone sitting anywhere on the string will see other parts of the string move relative to him. That’s another way to explain why the string will break.

You can easily verify that this problem exists for any kind of accelerated solid. All parts of an accelerated solid in special relativity do not move at the same speed.

My own puzzle

Here is the interesting other thing that I realized within this short moment of reflection: there is a way for the two ships to accelerate “identically” (for a suitable definition of identically which remains to be given) so that the string will not break. Can you find it?

C’est tout de même dur à avaler.
Comment voulez vous qu’on enseigne cela à des élèves de Terminale?

Jean-Claude Carrière, in Entretiens sur la multitude du monde with Thibault Damour