How to unify general relativity and quantum mechanics

Unifying quantum mechanics and general relativity has been a problem for decades. I believe that I have cracked that nut.

Special relativity:

Philosophical principle: Laws of physics should not depend on observer’s speed.

Math: Lorentz transform, new way to “add” speeds.

Issues it solved: Maxwell’s equations predict a value for the speed of light that does not depend on your own speed.

Physical observations: The speed of light is indeed independent on observers’ speed (Michelson and Morley’s experiment).

Counter-intuitive aspects: There is no absolute simultaneity and no absolute time. There’s an absolute speed limit for physical objects in the universe.

New requirements: Physicists must now pay attention to the “observer” or “referential”.

Thought experiment: Alice is in a train, while Bob is on the ground watching the train pass him by. What happens if Bob sees a flash hit the train “simultaneously” at both ends? Hint: what happens “at the same time” for Bob is not happening “at the same time” for Alice. That explains why we cannot consider simultaneity as absolute.

General relativity:

Philosophical principle: Laws of physics should not depend on observer’s state of motion, including acceleration.

Math: Non-euclidean geometry, tensor and metrics.

Issues it solved: Discrepancies in the trajectory of Mercury.

Physical observations: Gravitation has an impact on light rays and clocks.

Counter-intuitive aspects: Light has no mass, but is still subject to gravity. The presence of a mass “bends” space-time.

New requirement: Physicists must pay attention to the metric (including curvature) of a given region of space-time.

Typical thought experiment: Alice is in a box on Earth, Bob is in a similar box dragged by a rocket at 1 g. The similarity between their experience explains why we can treat gravitation as a curvature of space-time.

Quantum mechanics:

Philosophical principle: Several, “Shut up and calculate” being the top dog today (meaning: if math flies against your intuition, trust the math).

Math: Hilbert spaces, Hamiltonian.

Issues it solved: Black body radiation, structure of matter.

Physical observations: Quantization of light, wave-particle duality, Young’s slits experiment.

Counter-intuitive aspects: Observing something changes it. There are quantities we can’t know at the same time with arbitrary precision, e.g. speed and position of a particle.

New requirement: Physicists must pay attention to what they observe and in which order, as observation may change the outcome of the experiment.

Typical thought experiment: Schrödinger puts his cat in a box where a system built on radioactive decays can kill it at an unknown time in the future. From a quantum mechanical point of view, before you open the box, the cat is in a superposition of two states, alive and dead.

Theory of incomplete measurements:

Philosophical principle: Everything we know about the world, we know from measurements. Laws of physics should be independent from the measurements we chose.

Math: “Meta-math” notation to describe physical experiments independently from the mathematical or symbolical representation of the measurement results. The math of quantum mechanics and general relativity applies only to measurement results, the “meta-math” describes the experiments, including what you measure and what physical section of the universe you use to measure it.

Issues it solved: Unifying quantum mechanics and general relativity. Quantum measurement problem. Why is the wave function complex-valued. Why doesn’t quantum mechanics apply at macroscopic scale (the answer being that it does). Why are there infinities appearing during renormalization, and why is it correct to replace them with observed values?

Physical observations: Room-scale experiments with quantum-like properties. How to transition the definition of the “meter” from a solid rod of matter to a laser beam. Physically different clocks and space measurements diverge at infinity. How can we talk about the probability of a photon being “in the Andromeda galaxy” during a lab experiment? Every measurement of space and time is related to properties of photons. Space-time interpreted as “echolocation with photons”.

Counter-intuitive aspects: Quantum mechanics is the necessary form of physics when we deal with probabilistic knowledge of the world. In most cases, our knowledge of the world is probabilistic. All measurements are not equivalent, and a “better” measurement (i.e. higher resolution) is not universally better (i.e. it may not correctly extend a lower-resolution but wider scale measurement). Space-time (and all measurements) are quantized. There is no pre-existing “continuum”, the continuum is a mathematical simplification we introduce to unify physically different measurements of the same thing (e.g. distance measurements by our eye and by pocket rulers).

New requirement: Physicists must specify which measurement they use and how two measurements of the “same thing” (e.g. mass) are calibrated to match one another.

Typical thought experiment: Measure the earth surface with the reference palladium rod, and then with a laser. Both methods were at some point used to define the “meter” (i.e. distance). Why don’t they bend the same way under gravitational influence? In that case, the Einstein tensors and metrics would be different based on which measurement “technology” you used.

More details: IntroductionShort paper.

So how does the unification happen?

To illustrate how the unification happens without too much math, imagine a biologist trying to describe the movement of ants on the floor.

The “quantum mechanical” way to do it to compute the probability of having an ant at each location. The further away from the ants’ nest, the lower the probability. Also, the probability to find an ant somewhere is related to the probability of finding it someplace near a short time before. When you try to setup the “boundary conditions” for these probabilities, you will say something like: the ant has to be somewhere, so the probability summed over all of space is one; and the probability becomes vanishingly small “at infinity”.

The general-relativistic way to do it will consider the trajectories of the ants on the 2D surface. But to be very precise, it will need to take into account the fact that ants are on a large-scale sphere, and deduce that the 2D surface they walk on is not flat (euclidean) but curved. For example, if an ant travelled along the edges of a 1000km square (from its point of view), it would not return exactly where it left off, therefore proving that the 2D surface is not flat.

At a relatively small scale, the two approaches can be made to coincide almost exactly. But they diverge in their interpretation of “at infinity”. Actually, assuming observed ants stay within a radius R of the nest, there are an infinite number of coordinate systems that are equal on that radius R, but diverge beyond R. Of course, the probabilities you compute depend on the coordinate system.

In particular, if you take a “curved” coordinate systems that loops around the earth to match the “general relativistic” view of the world, the physically observed probability does not match the original idea we have that probability becomes vanishingly small at infinity and that the sum is one. In that physical coordinates system, the probability to see ants is periodically non-zero (every earth circumference, you see the same ant “again”). So your integral and probability computation is no longer valid. It shows false infinities that are not observed in the physical world. You need to “renormalize” it.

In the theory of incomplete measurements, you focus on probabilities like in quantum mechanics, but only on the possible measurement results of your specific physical measurement system. If your measurement system follows the curvature of earth (e.g. you use solid rods of matter), then the probabilities will be formally different from a measurement system that does not follow it (e.g. you use laser beams). Key topological or metric properties therefore depend on the measurement apparatus being chosen. There is no “x” in the equations that assumes some underlying space-time with specific topology or metric. Instead, there is a “x as measured by this apparatus”, with the topology and metric that derives from the given apparatus.

Furthermore, all the probabilities will be computed using finite sums, because all known measurement instruments give only finite measurement results. There may be a “measurement not valid” probability bin. But if you are measuring the position of a photon in a lab, there cannot be a “photon was found in the Andromeda galaxy” probability bin (unlike in quantum mechanics), because your measurement apparatus simply cannot detect your photon in the Andromeda galaxy. Such a probability is non-sensical from a physical point of view, so we build the math to exclude it.

So in the theory of incomplete measurements, you only have finite sums that cannot diverge, and renormalisation is the mathematical equivalent of calibrating physically different measurement instruments to match one another.

The analogy is not perfect, but in my opinion, it explains relatively well what happens with as little math as possible.

La SNCF en flagrant délit d’IP-tracking

La SNCF augmente son prix de 41% en deux minutes

La SNCF augmente son prix de 41% en deux minutes

La SNCF affirme ne pas pratiquer l’IP tracking, J’ai du mal à y croire.

Il y a quelques minutes, ma femme va sur le site Voyages SNCF, et demande un billet Paris-Antibes. Prix du billet: 80€. “Attention, dernières places à ce prix”, bien sûr. Mais à un moment, elle fait une erreur, et décide de refaire une recherche sur le même site. Le même billet passe soudainement à 113€.

Je fais un essai depuis un autre navigateur, puis depuis une autre machine dans la même maison (donc même adresse IP depuis l’extérieur). Le billet reste coincé à 113€.

Mais, histoire de vérifier si les billets à 80€ ont vraiment été épuisés (la théorie du blog de la SNCF ci-dessus), je décide de passer par mon smartphone en 3G. Du coup, forcément, changement d’adresse IP. Et là, surprise (pas vraiment, en fait), je retrouve le billet à 80€. Que j’achète.

Le billet acheté: 80€ seulement !

Le billet acheté: 80€

Alor, si la SNCF ne fait pas d’IP tracking, pourquoi ce que je viens de décrire se passe à chaque fois? Ce phénomène ne peut pas s’expliquer par l’épuisement des billets à un certain palier de tarif; parce que les prix affichés sur un même ordinateur dépendent de l’IP utilisée !

Paul Graham recommends doing things that don’t scale

As usual, Paul Graham writes an interesting piece about startups. He recommends doing things that don’t scale. Thinking like a big company is a sure way to fail. It’s a reassuring piece for the startup creator that I am, because at Taodyne, we are indeed in this phase where you do everything yourself and you’d need 48 hours a day to do the basics. Good to know that the solution to this problem is to keep working.

Connect this to the survivor bias. This is a very serious cognitive bias, which makes us look only at the survivors, at the planes who return from combat, at the successful entrepreneurs. Because we don’t look at the dead startups or planes that were shot down, we build our statistics on a biased sample. As a result, we make incorrect assumptions. For example, if the planes that return have mostly been shot in the tail and wings, you might deduce that this is where planes are being shot at, so that’s the parts you need to protect, when in reality what this proves is that these are the parts that don’t prevent a plane from returning when shot. Very useful.

Last interesting link of the day is the discussion about bullying on the Linux Kernel Mailing List (LKML). Sarah Sharp, a female Intel engineer, stands up to Linus Torvalds and asks him to stop verbal abuse. It’s an interesting conflict between very smart people. To me, there’s a lot of cultural difference at play here (one of the main topics of Grenouille Bouillie). For example, I learned from Torvalds what Management by Perkele means. On one side, it’s legitimate for Sarah to explain that she is offended by Linus’ behavior. On the other hand, it’s legitimate for Linus to keep doing what works.

Sarah reminds me of a very good friend of mine and former colleague, Karen Noel, a very sharp engineer who joined me on the HPVM project and taught me everything I forgot about VMS. Like Sarah, Karen was willing to stand up her ground while remaining very polite.

Everything is broken and no one cares

Everything is broken and no one cares

This post from Dear Apple is just so true, and so clearly on topic for Grenouille Bouillie!

Have we reached the point in complexity where we can’t make good quality products anymore? Or is that some kind of strategic choice?

The original post is mostly about Apple products, but the same is true with Linux, with Android, with Windows.

Here is my own list of additional bugs, focusing on those that can easily be reproduced:

  1. Open a file named X in any of the new Apple applications, those without Save As. Open another file named Y. Save Y as X. Beachball. For every application. Worse yet, since applications often remember which windows were open, you get the beachball again when you reopen the application. It takes another force quit for the application to (fortunately) offer to not reopen the windows.
  2. A relatively well known one now: Type F i l e : / / / in practically any OSX application. Without the spaces. Hang or assert depending on your luck.
  3. Use a stereoscopic application like Tao Presentations ( Activate stereoscopy. Switch spaces or unplug an external monitor. Kernel panic or hang to be expected. Go tell to your customers that the kernel panic is Apple’s fault, not ours…
  4. If you backup over the network, set your computer to sleep after say 1 hour while on power. Change your disk enough that the backup takes more than one hour. Backup disk will come up as corrupt after a couple of days, and OSX will suggest you start a new one (and the cycle will repeat).
  5. Use the “Share” button. It takes forever to show up the window (like 2-3 seconds in general on my 2.6GHz quad-core i7 with 8GB of RAM). Since what I type generally begins with an uppercase letter, I usually prepare myself by having the finger on the shift key. But to that stupid animation framework, “shift” means “slow animation down so that Steve can demo it”. Steve is dead, but the “shift” behavior is still there.

I’ll keep updating this list as more come to mind. Add your own favorite bugs in the comments.

First update (Feb 13, 2013):

  1. Safari often fails to refresh various portions of the screen. Visible in particular when used in combination with Redmine. This used to be very annoying, but it has gotten much better in more recent updates of Safari.
  2. iTunes 11 no longer has Coverflow. It was a neat way to navigate in your music, which wasn’t even the default, why remove it?
  3. Valgrind on OSX 10.8 is completely broken. I have no idea what’s wrong, but it’s a pretty useful tool for developers, and Apple has nothing in its own development tools that is even remotely close.
  4. “Detect displays” is gone, both from the Monitors control panel and from the Monitors menu icon. Combine that with the fact that OSX 10.8, unlike its predecessors, sometimes totally fails to detect that you unplug a monitor. And you find yourself with windows stuck on a screen that is no longer there…
  5. That little Monitor menu icon used to be quite handy, e.g. to select the right resolution when connecting to an external projector for the first time. Now, it’s entirely useless. It only offers mirroring, fails to show up 90% of the time when there is a possibility to do mirroring, shows up when mirroring is impossible (e.g. after you disconnected the projector). It used to be working and useful, it’s now broken and useless. What’s not to love?
  6. Contacts used to have a way for me to format phone numbers the way I like. That’s gone. Now I have to accept the (broken) way it formats all phone numbers for me.
  7. I used to be able to sync between iPhone and Contacts relatively reliably. Now, if there’s a way to remove a phone number, I’ve not found it. Old numbers I removed keep reappearing at the next sync, ensuring that I never know which of the 2, 3 or 4 phone numbers I have is the not dead one.
  8. Still in Contacts, putting Facebook e-mail addresses as the first choice for my contacts? No thanks, it was heinous enough that Facebook replaced all genuine email addresses with aliases. But having that as the first one that pops up is really annoying.
  9. Now fixed, but in the early 10.8, connecting a wired network when I also had Wifi on the same network would not give me higher speed. It would just drop all network connectivity.

Updated February 28th after restoring a machine following a serious problem:

  1. Time machine restores are only good if your target disk is at least as big. But with Apple’s recent move to SSD, this may no longer be affordable to you. In my case, I’d like to squeeze 1TB of data into 512G. Time machine does not give me the level of fine-grained control I’d need to restore what I really need. So I need to try and do it manually, which is a real pain.
  2. Calendar sync is a real mess. Restoring calendars from a backup is worse.
  3. Spaces? Where are my good old spaces? Why is it I had spaces on the original machine, no longer have them, and find myself unable to say “I want 6 spaces” or to setup keyboard shortcuts for them as they used to be.

When Google oversteps its authority

Recently, a user of Tao Presentations informed us that Google Chrome displayed a dire warning after he downloaded our software: “Tao Presentations may be malicious software”. Uh oh, for the average Joe, that’s a big no-no.

Google locks out “unapproved” programs

It’s not just us. Recently, I tried to download some of the amazing demos created by Iñigo Quilez. Same thing. Seriously, a 4K exe that manages to display a complete mountain? And Google Chrome would have me believe that there’s room in there for “malicious software”? Get real.

Now, it took me quite a while to find a solution to this problem. Apparently, you just need to record your site in Google’s Webmaster tools, and after scanning your site and ensuring (I assume) that there’s no known virus signature in the files, things should improve.

I still find this really annoying that a browser vendor would, by default, tag unknown files as “malicious”. Who are they to make this judgment call?

Why didn’t Google implement a real solution?

Shouldn’t they instead have something a little more sophisticated, that actually detects malicious signatures? You know, like a real anti-virus? Don’t tell me that Google doesn’t have smart enough engineers to write an in-browser anti-virus that doesn’t completely suck.

Nah, instead they went the easy route: anything that we don’t know is malicious. And we tell your users so.

I used to be a big fan of Chrome. Not anymore. Because of this single issue. I think this demonstrate an incredibly stupid arrogance and lack of technical diligence on Google’s part.

Google overstepped its authority and took advantage of their weight. Let’s not get used to it.

Moi Président de PME

Quel “président” j’aimerais être?

Un président de PME qui, d’abord, respecte la France, qui l’aime. Je suis le président d’une petite société, je ne peux être que président de pratiquement rien, chef de rien, mais en définitive responsable de tout.

Moi, président de PME, je ne suis même pas le chef d’une minorité. Je n’ai pas le temps de recevoir qui que ce soit parce que je travaille soir et week-ends.

Moi, président de PME, j’ai à traiter avec des investisseurs, pas à polémiquer de savoir si on les appelle associés ou collaborateurs.

Moi, président de PME, je participe à toutes sortes de collectes de fond parce que que je n’ai pas l’option du déficit budgétaire.

Moi, président de PME, je fais fonctionner la boîte de façon indépendante, mais j’ai des compte à rendre si j’agis contre l’avis de mon “conseil d’administration” (ou ce qui en tient lieu dans une SAS).

Moi, président de PME, je n’ai pas la prétention de nommer des directeurs, je sais très bien que c’est par leur indépendance d’esprit et leur initiative qu’ils ont mérité ce titre

Moi, président de PME, je fais en sorte que mon comportement soit à chaque instant exemplaire, tout en ayant une conscience plus aigue que jamais de mes propres limites.

Moi, président de PME, ce n’est pas de gaité de coeur que j’ai un statut très peu protégé, sachant très bien que si mes actions venaient à être contestées, aucun magistrat n’hésiterait jamais à me convoquer.

Moi, président de PME, j’ai constitué une équipe paritaire, avec autant de femmes que d’hommes dans la mesure où on peut le faire dans une équipe de cinq. Et alors?

Moi, président de PME, je suis soumis tout comme mes investisseurs à un code de déontologie qui interdit tout conflit d’intérêts. Là encore, et alors?

Moi, président de PME, je constate que mes associés ne cumulent rien, sinon les heures de travail mal payées, car on peut considérer qu’à partir de 70h par semaine, on se consacre plus que pleinement à sa tâche.

Moi, président de PME, j’aimerais bien voir un peu de décentralisation, j’aimerais bien qu’on donne aux forces vives locales que sont les PMEs un nouveau souffle, qu’on tire parti de leurs compétences, qu’on leur accorde un peu de liberté.

Moi, président de PME, j’aimerais bien grossir assez pour avoir des partenaires sociaux ou consacrer du temps aux associations professionnelles. Je préférerais quelques discussions régulières à des lois imposées sans négociation.

Moi, président de PME, je me contenterais bien d’un petit débat. On a évoqué la taxation du capital, et il est légitime qu’il puisse y avoir sur ces questions là un débat citoyen.

Moi, président de PME, je suis soumis à la proportionnelle face à mes actionnaires, et ce n’est pas en 2017, c’est dès maintenant que l’ensemble de leurs sensibilités est représentée.

Moi, président de PME, je suis la tête dans le guidon, avec toute la hauteur de vue qui va avec. J’aimerais bien fixer de grandes orientations, de grandes impulsions, mais en même temps, je dois m’occuper de tout et je dois avoir toujours le souci de la proximité avec les clients.

J’aurais bien aimé une vie un peu plus normale, mais rien n’est normal quand on est président de PME. Etre président, c’est pas si facile. Notre monde traverse une crise majeure, en tous cas la France. Mais on peut encore réussir à se fâcher avec l’Europe. On peut encore créer plein de conflits en se montant les uns contre les autres ou en se disputant sur l’environnement Bien sûr qu’un président doit avoir une réponse toute prête qui prenne de haut ses sujets: “je n’aime pas les riches“, ça suffit largement à montrer qu’on est proche du peuple, qu’on est capable de comprendre toute la complexité de réalité économique et sociale en France.

Cela dit, moi, président de PME, j’aimerais bien qu’on laisse nos investisseurs tranquilles. Ca serait déjà pas mal comme changement tout de suite.

Et si vous ne comprenez pas pourquoi je dis ça:

(Mis à jour pour utiliser le terme de PME, plus général que SAS)