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Random for whom?

At the turn of the year, I have to admit that I have not used this blog very often; but I just wrote a post for another one, so just as well link it here:

I am preparing another text on randomness, of a more unusual kind… more soon ūüôā In the mean time, Merry Christmas and Happy New Year!


Free will, the quantum and the cosmos

The scientific media have recently reported a proposal aimed at closing the “free-will loophole” in Bell experiments with light coming from distant quasars. Wow: free will, quantum mysteries and the cosmos in a single paper! This could only make headlines!

Let me take you on a tour to understand what this is about. The idea that some form of “free will” (in precise jargon, “measurement independence”) is required for a Bell test to be meaningful is not new: John Bell himself stressed it. But I dare say that Francis Bacon and Galileo, and probably even Aristotle, had understood measurement independence — not as applied to Bell tests, for sure, but more modestly as a cornerstone of the scientific method. If you measure the position of a star, you assume that the star is not changing its behavior just because it is being observed. If you drop a stone from different heights, you assume that the stone does not adapt its motion to the height you dropped it from. Think what would be left of physics and chemistry, if matter could look around, guess which experiment it is going to be submitted to, and rapidly cook up an adaptive strategy. And why do you think biologists try not to be seen when they observe the behavior of animals who, contrary to stones, might indeed adapt to the observers’ presence? Well, you got the point.

Still, when it comes to quantum physics, some results are so counter-intuitive that some people are ready to doubt of everything. Would it be possible that the famous two entangled photons, at the moment of leaving the source, are aware of the measurement they are going to be submitted to? Or reversing the roles, is it conceivable that the photons actively influence the random number generators that choose the measurements, in order to bias the choice towards a favorable one? Are photons closer to zebras than to stones? Raise this kind of concern with electric trains and robots, and you get rightly classified in the paranormal category. Raise it with entangled photons, and it becomes respectable science (yes, I ride on it too).

Anyway, let’s continue playing the game. I play the guy who is strongly suspicious of a conspiracy between the thing you call “a source of entangled photons” and the things you call “random number generators” (RNGs). Can you do something to convince me that my suspicions are not founded? If I am absolutely paranoid, you can’t: super-determinism or Matrix-like simulations cannot be falsified by observation. But suppose I am willing to concede something. Specifically, I concede that the RNGs are really initially uncorrelated from the source. Then, measurement independence can only be violated if some signal propagates from the RNGs to the source. Haha, here you catch me: every signal must propagate at the speed of light (OK, OK, I concede you also that one). So, if the suitable space-like separation is guaranteed, the signal will never arrive to the source on time: the photons have left the source without knowing which measurements await them. Measurement independence is guaranteed. This reasoning was first explicitly made (to my knowledge) in a paper by Zeilinger’s group. It is nice science: state assumptions and derive falsifiable consequences.

But now… hmmm… maybe I want to come a little bit back on my concession: maybe you can try and convince me that the random number generators are really independent of the source, at least up to some degree of confidence. You think and… I SAID YOU THINK: pause and think how you would try to convince me, before continuing!

Got it? OK, let’s compare our answers.

What I would like to see is a SIMPLE random number generator, something I can reasonably trust. A resistor directly connected to an oscilloscope, showing a trace that behaves like thermal noise, maybe would do it; or a visible light beam sent on a bulky beam-splitter before reaching some detectors. Or, if I don’t trust electronics (maybe the conspirators use the power network of your city), I may be happy with a grain of pollen performing brownian motion. Or maybe you are so kind that you go all the way and ask two human beings to act as random number generators (although, as well known, we humans are not great at generating randomness). I know well that all these options are questionable, but again, if I don’t concede that there can be randomness somewhere, you won’t be able to convince me of the opposite.

What probably would NOT convince me is to be shown a set of two telescopes pointing at some distant points of the universe, connected with all kind of filters and electronics, accompanied only by your plead of “trust that the only signal that is detected at the end of the measurement chain is that of some very distant quasars, who have not talked to each other nor to any matter here on Earth since billions of years”.

Still, who can resist at the charm of having free will, quantum mysteries and the cosmos in a single paper?

Pope & media: basic guide

This time, I decided to post about something that is not related to science: the resignation of the Pope. After all, it’s public knowledge that I am a practicing Catholic. I know pretty well that most of those who browse this blog are not, and many just don’t care about religion: take this post as an exercise in critical spirit. I am not going to give you “my opinion”, because I am really nobody to have an opinion on such things. But I want to give you a guide to read the media, in case you follow the developments in the coming weeks.

Let us start with an obvious fact: journalists can’t be experts of everything and have to produce stories that attract attention. Also, they have to craft the story in the way the reader expects it.¬†When it comes to scientific topics, we know pretty well how a piece of news should be cast in order to make in the mass media: it will have to sound either like¬†science fiction (faster-than-light communication, parallel universes, time travel…) or like an answer to our ultimate concerns (the existence of God, free will, faster computers and flatter screens).

Now, how do the media craft a story about the Catholic church? Since the 1960s, it has been customary to use the bi-partite categorization “conservatives versus liberals” (at the beginning, the terms used to be “reactionaries versus progressives”, but the ideology that used that language has become less fashionable in the past decades). From afar, this may seem like as suitable a scheme as any other. In reality, this scheme is as wrong as the wave-particle duality in quantum physics: by describing the truth as tension between two extremes, it misses… well, the truth.¬†I am going to propose you an alternative scheme: it’s three-partite, but I guess you can handle the complication.

At one extreme you have those that we scientists tend not to like very much. They think that the church has gone astray in the last 50 years or so, by speaking in favor of religious freedom, by daring to hold prayer sessions with members of other religions, and by accepting the claims of science. To be fair, you won’t find many Catholics thinking this way: they are minorities, to be found essentially in those nations in which Evangelical Fundamentalism is strong (osmosis happens), in some Alpine valleys, and maybe in some particularly stuffy sacristies (but I have not visited the latter).

At the other extreme, you have those who, in the words of a famous author, want to “reduce the Catholic church to yet another liberal Protestant denomination”. The media have a lot of sympathy for those, and maybe my readers too. But my readers are supposed also to understand (rationally, if not emotionally) why myself and many other Catholics don’t want to go that way either.

So far, we have the bipartite scheme. Notice how all those who don’t fit exactly in any of the above categories will be treated by the media as torn between the two, “conservative here, liberal there”. Have you not found this tension in most of the recent media portraits of Pope Benedict? Whatever your opinion on this Pope, he is certainly not a torn, tormented soul: the serenity of the intellectual is one of the traits unanimously noticed. Have you not found the same tension in most of the portraits of the cardinals that are presented as possible successors? “Cardinal X will be liberal on this topic and conservative in this other”. And if you ask me, you will find out that, in what I consider my personal coherence, I am very “liberal” in some topics and very ¬†“conservative” in others (I keep these discussions off my blog, so you have to ask me personally).

In reality, Pope Benedict and most Catholics including myself (and, you can bet it, including the next Pope) belong to a third category: those who know that Ecclesia semper reformanda (“the Church is always in need of change”: I wrote it in Latin to show that it’s quite an old idea, we did not need the pressure of the media to realize it) but who believe in the promise of Jesus that his message will always be preserved in that Church. Of course, this category does not define a monolithic bloc: there are differences of opinion, at times significant ones. Does discord grow? Sadly, at times it does: just as in science, among specialists, we have different opinions on how to make the field progress and we often forget that we have a common goal, the progress of the field.¬†Anyway, whether the Catholics in this category manage to recall that, beyond our differences, we have a common goal, is probably no longer the concern of my reader. So I stop here: just keep in mind this third category, if you want to understand a bit better the media reports in the coming weeks.

It will not backfire

Yesterday I was talking with a colleague about some sloppy papers published in the (supposedly) best journals — don’t try to find out which papers: you won’t guess, the sample is too big. At some point, my friend said about the authors: “It will backfire on them”. He said it with a point of sadness, because he has sincere concern for those people. I have thought it myself many times. But… will it really?

How many people are prisoners of their lust and commit horrible crimes! Many, probably most, go unpunished, even by their own conscience that they have managed to silence. Why should anything happen to people who are just prisoners of their mathematics, whose only mistake consists in not noticing that their definitions do not describe reality?

How many people commit financial crimes and injustices that ruin lives, and live without worries other than that of being one day stolen of their riches by poor fellows who will be called “criminals”! Why should some scientists, very decent fellows, be the victims of unfailing divine wrath just because they embellish (I am not speaking of faking) their results in order to get additional 5k$ per year of travel money?

No, I don’t think it will backfire: I don’t think we will see those sloppy works denounced and their authors forced to make amends. When the lobbying that keeps them going comes to an end, they will probably just be forgotten… but so will most of the works that one can consider “serious”: time is quite blind in erasing stuff.

If you want to uphold supposedly high standards, you must find other motives than the mere fear of being criticized one day.

Determinism and the speed of light

How do we know that no signal can travel faster than the speed of light? There cannot be a direct evidence of this fact. The indisputable fact is that the speed of light is the same in all reference frames.

In my knowledge, augmented with the browsing capability of my students, the only answer lies in the following deduction:

(1) The speed of light being the same in all reference frames and the principle of relativity lead, as well known, to the Lorentz transformation.

(2) Armed with the Lorentz transformation, one can rather easily show that a signal propagating faster than light could allow me to send a message to myself from the future to the past. Einstein himself was well aware of this (I don’t know if he was even the first to notice it).

Now, why is it a problem, that I can send a message to myself from the future to the past? Normally, the answer lists all kind of crazy things I could do, like winning all my bets and analog stuff. For me, the most dramatic consequence is all that I, and many others, can no longer do. First of all, when I receive a message at time t0 sent at time t1, I know that for sure I’ll have to send the message at time t1: it’s unavoidable. Moreover, all the events happened between t0 and t1 that the message informs me about have also become unavoidable. For instance, the message may inform me that a friend who is walking alongside me at t0 will be killed by a car, and even if this is going to happen one hour later, all I can do is to inform him that his life is about to end. Isn’t this absurd enough?

Well, I definitely find it is… but not necessarily someone who believes in full determinism! For such a person, all the information about what is going to happen in the future is already fully contained in the universe now, and always has been. There is nothing wrong in the physical universe that some existing piece of information gets stored in the neurons that call themselves “I” before the corresponding fact can be observed by all the brains: after all, that is what happens when we predict something with the laws of physics (say, the passing of an asteroid close to the earth).

The deduction made above is absolutely conclusive only if one believes in the possibility of creation of information that was previously not available. It is not such an outlandish belief: people believing in human free will have uphold it for centuries, and within physics, quite a few interpretations of quantum physics also uphold it. But it is funny to find it appearing in a topic usually supposed to derive from special relativity alone.

Two disclaimers. First,¬†I am NOT claiming that I believe something can go faster than light — indeed, since I believe in free will, I do find the deduction above perfectly convincing. Second,¬†I am also aware that, if anything would go faster than light, it should be massless: for massive objects, the Lorentz transformation predicts infinite inertia at a speed approaching that of light, independently of any argument about signaling to the past.

P.S.¬†Within a few hours from the first post, I noticed another important assumption in the deduction above: the assumption that any physical phenomenon can be harnessed to send a signal — even more specifically, that it can be harnessed to implement the protocol that allows sending messages to the past (which implies sending the superluminal signal to an observer in relative motion and having it reflected back to myself).