vttoth — September 3rd, 2010
Electroweak theory has several coupling constants: there is g, there is g‘, there is e, and then there is the Weinberg angle θW and its sine and cosine, and I am always worried about making mistakes.
Well, here’s a neat way to remember: the three constants and the Weinberg angle have a nice geometrical relationship (as it should be evident from the fact that the Weinberg angle is just a measure of the abstract rotation that is used to break the symmetry of a massless theory).
This diagram also makes it clear that so long as you keep the triangle a right triangle, all it takes is two numbers (e.g., e and θW) and the triangle is fully determined. This is true even when the coupling constants are running.
Categories: Physics |
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vttoth — September 2nd, 2010
Our monster Living Review about the Pioneer anomaly is now officially published. There were times when I thought we’d never get to this point.
Categories: Physics |
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vttoth — July 24th, 2010
I have been reading the celebrated biography of Albert Einstein by Walter Isaacson, and in it, the chapter about Einstein’s beliefs and faith. In particular, the question of free will.
In Einstein’s deterministic universe, according to Isaacson, there is no room for free will. In contrast, physicists who accepted quantum mechanics as a fundamental description of nature could point at quantum uncertainty as proof that non-deterministic systems exist and thus free will is possible.
I boldly disagree with both views.
First, I look out my window at a nearby intersection where there is a set of traffic lights. This set is a deterministic machine. To determine its state, the machine responds to inputs such the reading of an internal clock, the presence of a car in a left turning lane or the pressing of a button by a pedestrian who wishes the cross the street. Now suppose I incorporate into the system a truly random element, such as a relay that closes depending on whether an atomic decay process takes place or not. So now the light set is not deterministic anymore: sometimes it provides a green light allowing a vehicle to turn left, sometimes not, sometimes it responds to a pedestrian pressing the crossing button, sometimes not. So… does this mean that my set of traffic lights suddenly acquired free will? Of course not. A pair of dice does not have free will either.
On the other hand, suppose I build a machine with true artificial intelligence. It has not happened yet but I have no doubt that it is going to happen. Such a machine would acquire information about its environment (i.e., “learn”) while it executes its core program (its “instincts”) to perform its intended function. Often, its decisions would be quite unpredictable, but not because of any quantum randomness. They are unpredictable because even if you knew the machine’s initial state in full detail, you’d need another machine even more complex than this one to model it and accurately predict its behavior. Furthermore, the machine’s decisions will be influenced by many things, possibly involving an attempt to comply with accepted norms of behavior (i.e., “ethics”) if it helps the machine accomplish the goals of its core programming. Does this machine have free will? I’d argue that it does, at least insofar as the term has any meaning.
And that, of course, is the problem. We all think we know what “free will” means, but is that true? Can we actually define a “decision making system with free will”? Perhaps not. Think about an operational definition: given an internal state I and external inputs E, a free will machine will make decision D. Of course the moment you have this operational definition, the machine ceases to have what we usually think of as free will, its behavior being entirely deterministic. And no, a random number generator does not help in this case either. It may change the operational definition to something like, given internal state I and external inputs E, the machine will make decision Di with probability Pi, the sum of all Pi-s being 1. But it cannot be this randomization of decisions that bestows a machine with free will; otherwise, our traffic lights here at the corner could have free will, too.
So perhaps the question about free will fails for the simple reason that free will is an ill-defined and possibly self-contradictory concept. Perhaps it’s just another grammatically correct phrase that has no more actual meaning than, say, “true falsehood” or “a number that is odd and even” or “the fourth side of a triangle”.
Categories: Physics, Programming |
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vttoth — July 20th, 2010
It’s been 41 years since Armstrong’s first “one small step” on the surface of the Moon.
Year after year, I express my hope that it won’t take another, well, 41 years before the next step is taken.
Categories: Space |
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vttoth — June 30th, 2010
Can both climate alarmists and climate deniers be right (or wrong) at the same time? Perhaps so. At least that’s my understanding after reading about a new study that was designed to evaluate the judgment of climate experts.
The way I see it, yes, there is consensus that the planet is warming. Yes, there is consensus that human activity contributes to the warming. Yes, there is consensus that the warming can have disastrous consequences.
However, there is no consensus regarding the magnitude of future warming. There is no consensus regarding the extent to which human activity vs. natural causes are responsible for the warming. And I don’t think a consensus exist that the consequences of the warming are uniformly bad for humanity, or even that the bad consequences outweigh the potentially good ones.
In any case, consensus is irrelevant. Science is not supposed to be a democracy of scientists, but a tyranny of facts.What makes a scientific theory right is not consensus but logical consistency and good agreement with observation.
Scientists are, however, responsible to communicate not only what they know but also what they don’t understand (this is what defines the line between a climate change advocate and a climate change alarmist, I guess.) Conversely, scientists are supposed to be able to express their doubts without questioning or withholding facts (this, perhaps, is what distinguishes a climate change skeptic from a climate change denier.)
Unfortunately when the debate becomes political, such nuances are often lost or ignored. Politics, especially populist politics, abhors uncertainties and prefers to paint everything in black and white. If uncertainties are mentioned at all, they are merely used as “proof” that the other side is wrong, therefore our side must be right, with no room in the middle. You either believe Al Gore’s Inconvenient Truth like the gospel, or you accuse Al Gore of being a fraud artist out to get rich on phony carbon credits.
Categories: Weather and Climate |
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vttoth — June 23rd, 2010
Ouch! That was quite the rumble. Enough to freak out all the cats. This is the third significant earthquake I experienced here in Ottawa; it may not have been the strongest as measured by instruments, but it certainly felt the most, hmmm, “hostile” sounds like the right word.
Categories: Canada, Geology |
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vttoth — June 14th, 2010
Hayabusa, or at least the part of it that was meant to survive atmospheric re-entry, has returned. Hayabusa, also known as MUSES-C, is a Japanese spacecraft, the first ever asteroid sample return mission. Unfortunately it is not yet clear if it has actually managed to collect any samples. Even so, it’s been one impressive mission.
Categories: Space |
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vttoth — May 28th, 2010
This Homer Simpson is one smart fellow. While he was trying to compete with Edison as an inventor, he accidentally managed to discover the mass of the Higgs boson, disprove Fermat’s theorem, discover that we live in a closed universe, and he was doing a bit of topology, too.
His Higgs mass estimate is a tad off, though. Whether or not the Higgs exists, the jury is still out, but its mass is definitely not around 775 GeV.
Categories: Mathematics, Physics, Television |
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vttoth — May 26th, 2010
This is going to remain a memorable picture for some time to come:
It’s not every May, after all, that we measure 35.8 degrees Centigrade in what is supposedly the world’s second coldest capital city.
Categories: Weather and Climate |
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vttoth — May 26th, 2010
Welcome home, Atlantis, for the very last time.
After being in service for a quarter century, her next trip is to a museum somewhere.
Categories: Space |
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