Luboš Motl’s Reference Frame

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Schellekens & anthropic principle

4 小时 9 分钟
Albert N. Schellekens wrote a popular 87-page preprint,
The emperor's last clothes?
It is clearly a popular text but yes, indeed, it is way more technical than some books that are considered by their authors to be more-than-popular. ;-)



Wordle...

Schellekens, together with Dieter Lüst and Wolfgang Lerche, wrote a paper or two in the 1980s that argued that the number of vacua in string theory was huge, comparable to 10^{1500}. So if this insight is a discovery or a "paradigm shift", they should surely be included among the fathers of this idea. Well, I am not among those who would think that these "fathers" should be excessively proud about something or even fight for priority! :-) They just wrote a high number (an upper bound) whose derivation was not quite correct and whose philosophical consequences seem irrational to me (and at any rate, they were proposed centuries ago).

At the beginning, Schellekens criticizes the people who now say that they always knew that the number was huge but they didn't find it important enough to talk about it. ;-) Well, I think that his criticism is legitimate and I am not among the people criticized by Schellekens because I never thought that the number was that huge - even though now I think it is probably true - and I do think that this question is somewhat important: those who "knew" it shouldn't have been silent. But I also think that the large number of the vacua itself doesn't imply the anthropic reasoning.

So while there is a sense in which the anthropic principle is a very old story and no contemporary scientist should sell it as his discovery, it is also true that only the stringy flux compactifications that were found in this decade have made the possible anthropic picture of physics "complete". Even though string theory doesn't really imply that the anthropic reasoning is correct, it is also the only framework we know where the numerous vacua may be classified and co-exist in a huge multiverse. String theory offers the only satisfactory incarnation of the anthropic reasoning. As many other important keys, string theory is able to open the gates to the Heaven as well as the Hell.

Is uniqueness the same thing as anthropocentrism?

But as you can guess, I disagree with Schellekens' main theses. The anthropic principle is neither something we should be happy about (Schellekens views it as a victory of string theory and related breakthroughs) nor something we should feel certain about. However, this debate is not just about one-sentence "opinions" and even in his popular text, he has written 87 pages of somewhat insightful arguments. I won't offer you 87 pages but we will look at many of them, anyway.

First, there exist two full propaganda machines justifying the anthropic principle or, on the contrary, the possibility to find the full, unique, and complete laws governing the Universe (monovacuism, if you wish). Schellekens also dedicates a few pages to this propaganda - and various funny and subtle kinds of criticism invented by the physicists in both groups.

The anthropic people including Schellekens and Susskind claim that the "landscape revolution" is analogous to the Copernican revolution and other revolutions in science: stupid people used to think that they were terribly important (they believed in anthropocentrism) but brave scientists have shown that the humans were not so special, after all. The Earth is not a center of the Universe, and neither is our Sun or the Milky Way. The human DNA is not qualitatively different from the DNA of other animals. And perhaps, our Universe is just one among zillions of universes in the multiverse. The properties of elementary particles can't possibly be unique, can they? The Universe is a mess and it has always been one. :-)

Well, that's one story. But I also see a completely different story involving more recent breakthroughs in theoretical physics that are arguably more relevant for the question of predictability of the particle masses than Copernicus' adventures. During the last century or so, we have seen an incredible unification of concepts and observations that eventually allowed us to describe all of chemistry, engineering, and biology (thousands of materials, objects, and their diverse interactions) in terms of a single theory (QED) with one dimensionless parameter, the fine structure constant (and perhaps the proton-electron mass ratio), and even if you're interested in the other physical effects that are pretty much irrelevant for life (such as nuclear physics), we can describe everything by a similar theory with 28 parameters (the Standard Model; plus add General Relativity in a sloppy way to separately describe the gravitational phenomena). It is natural to expect that the missing step to complete the picture is analogous e.g. to the electroweak unification and it will make the remaining parameters calculable, much like the spectral frequencies of all atoms became calculable 80 years ago, and we seem to be damn close to completing this step. The Universe is elegant and it has been elegant even before the first moment when people noticed. ;-)

These are stories about two scientific "trends". These trends seem to have the opposite "signs". They are "derived" from our experience at different time scales. They are "derived" by selectively focusing on some stories while neglecting and humiliating others. I think that every rational person realizes that the answer to the question whether the anthropic explanation of the Standard Model or its unique derivation from a fundamental theory is the right approach doesn't necessarily have to mimic the answers to "similar" questions answered by Copernicus. It doesn't have to "reproduce" the uniqueness of QED, either. We are simply asking different questions than the previous generations and different questions sometimes have the same answers but they often have different answers. For example, the world has been increasing in size in Copernicus' and Hubble's time but so far it has never increased behind the boundaries where we can actually see anything. Many quantities - such as temperature - were shown to depend on the environment (distance from the Sun etc.) but it still seems that the particle masses and couplings we want to calculate are universal across those 14 billion light years of the visible Cosmos.

And the uniqueness has worked in fundamental physics but there are many stories close to fundamental physics where it didn't work and where we believe that historical coincidences played a critical role in determining some parameters.

I say that all sane people must be aware of the fact that we can't "derive" the answer to this completely new question by extrapolating the previous experience. But at the same moment, it seems that many people try to pretend that they believe that such an extrapolation is possible. Sorry but as long as you focus on rational arguments, such an extrapolation is impossible. There's no way to be sure. The "uniqueness" answer hasn't been proven; it is probably necessary to actually find the correct unique answer before we will know that the answer is unique. ;-) And the "anthropic principle" hasn't been proven, either. Whoever thinks that he has a simple philosophical proof of his attitude is sloppy. And whoever thinks that his answer must be correct because all other answers can be defined "not to be science" is an imbecile. And Nature doesn't give a damn how imbeciles define science: Not Even Woit.

When we discuss these anthropic questions, there exist various technical differences between field theory and string theory: string theory actually allows us to define the measure on moduli spaces, count the discrete vacua, and connect them to a unified cosmology via the eternal inflation and tunneling. Because the stringy realistic vacua are discrete, they are more specific and, in principle, completely localizable (even though one of the points of the anthropic approach is that you shouldn't even try to do it). Nevertheless, the deep essence of the anthropic argument seems to be identical in field theory and string theory. So we can ask:

Can the Standard Model parameters be derived from a fundamental theory?

We don't know the answer. Once people actually derive them, the answer will clearly be "Yes". The anthropic people say that the answer is almost certainly "No" and the rest of us says that their conclusion is premature.

Schellekens describes the reactions of the anthropic infidels as disgust (or even religion!) :-), denial, and derision but he also mentions that Burton Richter considers the anthropic people to be creationists. By the way, it is actually very subtle which group is closer to creationism: it depends on your optics.

Schellekens recalls some of the anthropic coincidences that seem to be necessary for life and offers us an anthropic checklist - four steps that help a careless reader to wash his brain and become an anthropic person, too. ;-) The checklist is rather clever, so let us look at it:
  1. The Standard Model may not be the unique mathematical solution of any fundamental theory.
  2. Not all alternative solutions allow observers.
  3. The total number of solutions should be sufficiently large to make the existence of a solution with observers plausible.
  4. We live in the most probable Universe which allows observers.
Why is it clever? Because he is "gradually" making the propositions "more anthropic" and the last one is nothing else than the hardcore anthropic assumption that people like myself clearly want to reject. However, I kind of accept the first statement. So where should I say "No" for the first time? It is actually hard to find the place. But I will find it in the middle of the point (3), anyway. ;-)

First, I tend to agree with (1). I find it unlikely that a fundamental theory - or even string theory with a selection mechanism - would make the rather messy Standard Model (with its parameters) a completely unique solution. After all, we know many other solutions to string theory and I am convinced that many (or most) of them will survive the test of time.

The statement (2) is almost clearly correct, too. For example, some stringy vacua with unbroken supersymmetry can be almost proven not to have any observers or intelligent observers. We don't have a full proof of it - because we can't really define observers and classify all conceivable "types of life" - but it is plausible that we could construct such an argument. One of Schellekens' powerful tools is to emphasize that we don't have to prove that "our island" in the parameter space is the only place that admits life (which seems extremely hard to argue because there can be discretely many "types of life"). It is enough to show that there are many generic places outside that almost certainly don't admit life.

Now, because I have accepted the points (1) and (2), Schellekens says that I have already adopted "some kind of anthropic reasoning" because there are places (different universes) where we don't live. Well, fair enough. It is "some kind" but I still haven't accepted (4), have I? :-) Just the fact that I don't live in the middle of ocean doesn't mean that I can't exactly calculate the the number of protons in the atoms dominating our atmosphere (nitrogen).

I kind of agree with the binary content of the point (3), too, but the precise explanation why I agree could be highly disappointing for Schellekens. If we make an estimate of the probability (or plausibility) that life is born somewhere in the multiverse allowed by the fundamental theory, the probability shouldn't be much smaller than one. The life shouldn't be a completely unexpected accident according to science.

However, one must be very careful how this probability of having life somewhere is calculated. Schellekens is now slowly trying to convert the readers to the irrational anthropic reasoning, in order for them to accept (4), too. Why? Because he wants you to believe that the probability that the life exists somewhere - among N universes - is essentially equal to N times P where P is the probability that the life is created in one "typical" universe (the formula gets corrected if N times P would be close to one or greater than one).

This could be a good order-of-magnitude estimate in an "egalitarian" multiverse where all universes have the same chance to host observers. But I think that this "egalitarianism" is simply incorrect and it is very important for this whole anthropic debate that this principle is incorrect. In fact, I can make the accurate calculation of the probability that a correct fundamental theory allows for observers somewhere on its landscape: the probability is not N times P but rather 100%. It's that simple.

We know that life exists, so if the theory is correct, it must predict life inside one of its solutions. The only problem could occur if no fundamental theory existed at all, but I choose to discard this possibility. If we only want to know whether it predicts life or not, it doesn't matter how many classical solutions it has and what is the distribution of the probabilities that each of them allows intelligent observers. What matters is that it contains at least one universe - ours - that admits life.

This "N times P" calculation is sloppy, ideological, and this ideology - the egalitarianism between vacua that are clearly different, non-equal, and hierarchical in many respects - is the essence of the anthropic fallacy. In my calculation, I didn't even have to multiply two numbers: you might think that it makes my calculation less mathematical. However, my result is actually exact, unlike the results of Schellekens' implicit formula.

It is interesting to look at Schellekens' calculation of the probability in (3) from one more viewpoint. He seems to require that the density of the stringy vacua in the vicinity of our region of the Standard Model parameter space should be huge, otherwise it is awkward to believe that any vacuum of string theory matches reality. I fundamentally disagree with this proposition. Here is my checklist to see why this proposition is irrational:
  • The density of the stringy vacua near our locus in the SM parameter space is not infinite because the number of semirealistic stringy vacua is finite: so Schellekens can never be "completely satisfied".
  • When you try to find out a "natural lower bound" for the density, you won't find an acceptable answer. For example, you might require that the small region that describes our Standard Model with the error margins of parameters as extracted from the 2008 measurements should contain at least one stringy vacuum, if calculated by the densities. But this "falsification" would clearly be irrational because such major decisions about the validity of a theory cannot depend on the number "2008" or some random coincidences about our present world.
  • Moreover (and the following argument is related to the previous one), sometimes in the future, the measurements of the SM parameters will be more accurate, the error margins (and therefore the relevant region) will be smaller, and the number of vacua calculated in the "ball" around our point through the densities could drop well below one. In the future, the "test of sufficient density" is likely to fail even if it passes today. Sometimes in the future, this "density" test will fail. If you know so, shouldn't you agree that the test is failing already today?
  • Once you agree that there exists no "sensible" lower bound on the density of stringy vacua near our locus, you will realize that it should have been completely expected that this criterion was nonsensical from the very beginning. When the density of stringy vacua near our point is (much) lower, it simply means that string theory will be (much) more predictive when it comes to the Standard Model parameters. There is nothing wrong with a theory that is more predictive. We have always believed that we were looking for predictive theories and if the supposed "paradigm shift" is that we must require the theories to be unpredictive, I simply disagree. Schellekens seems to believe otherwise: he thinks that every theory that is predictive is excluded and only theories that can be adjusted in any way to match the observations by chance are allowed. I beg to differ.
  • To summarize, the only sensible "phenomenological" way to falsify string theory (or another hypothetical theory with many vacua) is to show that the number of vacua in the vicinity of our locus in the SM parameter space, plus minus the known error margins, is strictly equal zero. Any other "falsification" claiming that the density seems "too low" is a fallacy based on the (ludicrous) assumption that theories are never allowed to predict anything.
While in (3) this fallacy was incorporated "silently" - the point (3) was written so that you make the "N times P" error yourself - it is written explicitly in point (4) which is nothing else than a logically and scientifically unjustifiable left-wing propaganda.

Let me say one more comment. The anthropic selection could be "partially correct" etc. but even if it is so, the interesting observations are the aspects in which the anthropic reasoning is incorrect. This is where the new patterns and new scientific insights are located. So it would be highly counterproductive to assume that the anthropic assumptions of genericity are "nearly universal".

And one more observation about the point (3). I calculated the probability that a viable universe is somewhere in the landscape of the fundamental theory. That was equal to 100%. But if I give you a Hartle-Hawking-like cosmological selection criterion, it secretly assumes that only one universe gets materialized, not all of them simultaneously, and the formula can produce a different probability for the realization of a (any) universe - and a different formula for the probability that life emerges. The result could be much smaller than 100%. That's true. But what is not true is the implicit assumption of the anthropic people that if I require the probability to be calculated in this way and if I want the result to be close to 100%, I must allow (almost) all vacua on the landscape to contribute. The final section of this essay describes a very dramatic scenario how the probability could be high even if the vast majority of the landscape had a highly suppressed weight in the probabilistic measure. But even if you find the scenario unlikely, there exist less dramatic possibilities where only a tiny fraction of the landscape contributes.

So the answers are
  1. Yes.
  2. Yes.
  3. Yes, but the answer is trivial and the very question tries to make you accept a wrong formula.
  4. No.
The proponents of the anthropic fallacy, including Schellekens, are just not ready or not willing to admit that various calculations they make are just order-of-magnitude estimates that incorrectly assume that certain functions are constants in vast sets of vacua (or in cubed or hypercubed miles of the multiverse). But these quantities and densities of life etc. are not constant. The more we know about the theory, the more we know about the non-constancy and the more accurate calculations we can make. The more we know, the further we are from the fuzzy anthropic ideas about the location of our vacuum in the landscape. It is the very goal of scientific progress to get as far from these fuzzy pictures as we can.

In order to show how political, vague, and socially dependent the anthropic methods are, let me consider the following gedanken experiment. Imagine that you establish a new country and you invite 100 million settlers. Now, the question is: What is the expected number of Fields medal winners? The anthropic people would divide the population by the world population, multiply it by the total number of the Fields medal winners who are alive, and they would get something like 1 Fields medal winner.

But what if I tell you that 99 million settlers are female? Now, it will be an inconvenient question for the left-wing anthropic people. Some of them will say that the probability hasn't changed at all because the sex doesn't matter. The more reasonable ones will make a new calculation and their estimate will decrease by a factor of 100 because there are no female Fields medal winners which is why only the male ones contribute to the expectation value: their total expected number of Fields medal winners will be smaller than one, essentially zero.

Eventually, someone manages to look at the people and among the 1 million of the male settlers, they find Witten, Tao, and Connes. So the correct answer is 3, after all. But the previous estimates turn out to be useless.

The procedures to quantify the phenomenological viability of the multiverse and its subsets are completely analogous. The more we know, the more irrelevant the initial estimates become. And they often turn out to be completely wrong. The anthropic people usually assume that certain quantities, densities, and probabilities are constant for all members of vast sets. But it matters how finely you divide the set into subsets: will you allow your grad students to count the F-theoretical flux vacua and heterotic vacua (or males and females) separately? If you want to get the accurate result, you should divide it to the individual members and do the exact calculation.

Let me mention another, more physical example explaining why we often need to know the exact (or almost exact) answers. The fusion in the Sun is important for our lives but it can only work well if the mass of the helium nucleus is slightly lower than the mass of two protons and two neutrons in the two deuterium nuclei (apologies for oversimplifications, this example is easy to talk about). But you might think that these nuclei are generic states of QCD and by dimensional analysis, the difference of their masses is comparable to the QCD scale. That would generate too high temperatures and maybe other problems. However, the argument is wrong. The energy generated by fusion is comparable to 1% of E=mc^2 only.

And I don't need to assume life to find the 1% figure: a better calculation rooted in QCD or nuclear physics is enough. Some "deeper" patterns that go beyond order-of-magnitude estimates are often damn important for figuring out whether a physical system allows life, among other things. Assuming that all vacua in the landscape have the same probability to host life is analogous to the assumption above that all energy differences in nuclear physics are comparable to the QCD scale. They're not and in many cases, there is a very good scientific reason (not just chance or the requirement of life) why some of them are much smaller.

The very program of the anthropic approach is to forget and deny all deeper patterns and all more accurate and more detailed calculations, to replace our sharp picture of the world by a permanent colorless uniform fog of ignorance. The very goal of this ideology is to convince physicists not to improve their understanding of Nature and to replace exact calculations by low-brow order-of-magnitude estimates. The anthropic reasoning hasn't worked in previous scientific revolutions because more specific explanations were always found and the idea that it is exactly around 2008 when the sharp answers disappear and the anthropic fog becomes relevant for all open questions is a form of fine-tuning. There is no reason for the number 2008 to play such a special role in the scheme of the Universe. ;-)

The assumption that all vacua in the landscape have the same probabilities etc. and we must live in a vacuum in the class that dominates the "total number", whatever the artificial boundaries of the class should be, seems obviously false to me. There exist all kinds of hierarchies, including hierarchies that have neither an anthropic explanation nor a universally acceptable scientific explanation (such as the QCD theta-angle), that show that our vacuum is not completely generic. We kind of know that we have three generations (or the Euler character of a Calabi-Yau) and with further high-energy experiments, it is plausible that we will be able to "measure" other invariants describing the correct compactification, its topology, the numerical values of fluxes, the number of branes, and the shape of the throats. The idea that there can't ever be progress in science is also ludicrous and it's been falsified zillions of times. The only question is how fast the progress will be. We're not guaranteed anything.

The idea that we must live in the "gray" zone of the "most generic" and "uninteresting" vacua could be a great theory for insect in China because it may be the most numerous group of living objects, classified by their country and their class in the Linnaean taxonomy. But this theory simply doesn't look good enough for certain mammals in the Czech Republic.

Schellekens and other anthropic people say that they would be worried if some feature of our world were not "generic" in the stringy vacua - a point analogous to their requirement of a "high density" near our locus. I would not be worried because there exists no law that we would have to be generic. After all, the exact properties of our life and our nationality require the exact vacuum we live in, despite the low density of vacua around (or despite the low population of the nation). But even if someone convinced me that our vacuum should be generic (in "most aspects"), I don't think that anyone knows what the right measure to determine the genericity should be: the "each vacuum has the same vote" measure is surely not good enough because of many reasons, for example because the total number of all vacua (including the AdS5 x S5 vacua) is infinite and the uniform probability measure can't be normalized. It is even wrong to use the counting based on volumes of the Standard Model parameter space because the Standard Model is clearly neither the first nor the last effective field theory that can be written down: it only corresponds to the state of our experimental knowledge of particle physics as of 1973-2008. The QED used to have a smaller parameter space and the MSSM or other future effective theories will require different, possibly larger parameter spaces.

Because the anthropic people rely on so many concepts that are only relevant in 2008, what they're doing is a statistical interpretation of the history of physics, with a focus on the present era, not physics itself. Note that I am in no way saying the "same thing" as Peter Woit. I am actually finding particular material flaws in various arguments while the obnoxious repetitive crackpot only says (731 times) that none of these things is science and he doesn't even have to think about any of the arguments - which is just an arrogant propagandistic nonsense and surely not a contribution to the scientific debate.

We may not be the most special creatures (and universe) in the multiverse (even though Leibniz used to say that our world/life is the best possible world/life) but we are not the most generic (or messy) ones, either. Both of these assumptions are irrational philosophical prejudices and unjustified extrapolations from cases where they happened to work. Now, we can pretty much sit at a reasonably generic point of a statistical distribution but you can't ever be sure how close to the central or most likely values you are. For different quantities, the distance from the "genericity" may be very different. There is clearly no universal answer.

Sometimes you are very generic, and then the insight about your genericity is not too interesting because it carries low information. Sometimes you are special. The information clarifying why you are so special is higher (if a theory predicts a very special feature, it is very predictive) but such cases are less likely. There is a trade-off going on here and whoever thinks that the very anthropic assumptions can lead to a high-information conclusion that is nevertheless very likely to be true, without finding non-anthropic arguments and mechanisms, is clearly making a logical error.

There is no rational reason to think that individual vacua should carry the same "weight" in the anthropic distribution. And if you use the very existence of life to deduce something about the low-energy parameters, you won't get too much interesting information because we know much more than the fact that life exists in our Universe. We also know the values of all low-energy parameters that make this life (and many other things) possible. Anything that can be derived about our compactification from the existence of life can clearly be derived from the known values of the parameters, too (because the life itself can be derived from them). Physicists should finally appreciate that it is legal for them to use all the known experimental data (including those found in the near future) in their search for the correct theory (and its vacuum). It used to be legal in the past, too. ;-)

Why would you ever use the incomplete information about the existence of life only rather than the full information you can have? It looks like a children's game where a kid has to determine something without looking somewhere. But scientists are allowed to look, aren't they? Note that it is still the same complaint against the "selection fallacy" that I have already raised many times. When the anthropic people calculated a probability as "N times P" (Schellekens in his point (3)), they were also using an incomplete information, representing every vacuum by a "generic representative" for some class even though more accurate calculations are clearly possible as long as people keep on improving and sharpening their knowledge about particular vacua and abilities to deal with them.

Laws that maximize life naturally

Finally, I want to say that the ultimate laws governing the vacuum selection can be "naturally" compatible with the existence of life in the preferred Universes.

A universe that admits life has to satisfy all kinds of features and many of them have a quantitative character: various parameters and ratios have to be small. You have to have a lot of hierarchies of scales (a small cosmological constant, an electroweak-Planck gap, fermionic mass hierarchies), a lot of different long-lived states (nuclei, molecules) in the spectrum that have sufficiently different geometries, and so on. Imagine that you create a similar "index of life magic" I_{LM} as a function of various "healthy gaps" in such a way that the vacua with a higher value of the index can reasonably be expected to admit life "more easily" than the vacua with a low value of the index.

This index is an artificial human invention but it is completely plausible that there exists a natural formula - e.g. one derivable from a generalization of a Hartle-Hawking wave function - that has similar consequences and that naturally makes it more likely for life to appear in the universe that is also predicted to be more likely by a cosmological HH-like selection formula.

Do you think that such a hypothesis is a form of a conspiracy theory? Feel free to believe it is. But the objects that make life extremely unlikely in certain environments are just continuous numbers: discrete conditions only reduce the number of viable vacua by a factor comparable to one (such as two). And continuous numbers often like to enter formulae. When you have a Hartle-Hawking formula dictating the probability of different vacua (or low-energy parameters) after an early era of cosmology, it usually depends on these numbers: recall the dependence on the cosmological constant (with the problematic sign). The dependence can be strong, it is almost guaranteed that there is a bias, and the probability that the bias is in the direction that favors the "viable" vacua is significant, maybe even higher than 50% (a priori). When you actually fill in the details of this theory, you will be able to say that the probability is 100%. ;-)

If this picture is correct, there can exist an old-fashioned scientific, non-anthropic explanation why we live in a universe where life looks a priori easy. I find this picture speculative but from the viewpoint of eternity, it is very plausible. Viability can be imprinted to our world through the basic laws of early cosmology. Every "theorem" that tried to prove that similar calculations must be impossible has been circular so far: all of them had to assume that our Universe belongs to the gray zone and it has no theoretical or phenomenological "fingerprints" or special features that could identify it - and they proudly proved that one can't ever identify such a vacuum by its fingerprints in a polynomial time (sorry, Frederik and Michael, but that's what you're doing).

I wouldn't make a bet that someone will actually find such a non-anthropic explanation of the viability of our Universe in a few years but many key events in the history of science have been unexpected. Moreover, the belief that the anthropic fog won't be falsified in a near future (a belief I share) is something different than a belief that it is the correct answer (which I don't share). People naturally focus on research directions where they can make progress, so I am certainly not afraid that every talented physicist is going to work on a hopeless project. But even if some project loses man-hours, it doesn't mean that there can't ever be a new breakthrough in this project. But even if you don't believe that such new insights about the vacuum selection problem will be found in the future, it is probably more fruitful for the physicists to focus on attempts to find new patterns and laws rather than self-fulfilling attempts to prove that science is over. ;-)

Because the arguments that our Universe must be generic (and there is no extra information we can ever learn about it) seem to be circular and seem to contradict the whole history of science which has always seen some additional progress, I think it is reasonable for a physicist to expect that every "generic" description of a system we don't understand is a temporary state of affairs. The more we will know, the more the fuzzy anthropic fog is going to be replaced by a sharper picture full of fascinating insights, important patterns, illuminating relationships, exact numbers, and specific links to previous theories as well as observations, insights that are similar to hundreds of those that have already been found.

And that's the memo.

Roy Spencer in the U.S. Senate

7 小时 16 分钟


(See also Anthony Watts' comments.)

I think his testimony was extremely good. You can see the anonymous faces around who don't want to hear any rational things about the climate, its sensitivity, the natural effects, and the sensible strategies to organize the scientific research in order to find the correct and important insights about the climate.

When Spencer was finished, the only thing that Barbara Boxer was able to say was to congratulate that Spencer was jokingly named Rush Limbaugh's official climatologist. She just wanted to "point it out for people to understand". She apparently thinks that this comment should settle the debate. Well, among the idiots who vote for her, it probably does.



I have great news for you, Ms Boxer. You have been named the official clown of Rush Limbaugh's show which is a higher rank than the official climatologist. Congratulations! I hope that the next time, you won't be hiding your own title, either.

150 minutes of video

A more complete video from the hearings is here. At the beginning, Boxer enumerates millions of catastrophes that are caused by warming, an effect that hasn't existed at least for ten years. As her following comments reveal, her support for this fashionable nonsense is clearly motivated by her desire to spit on Bush's administration. Mr Lautenberg blames global warming and George Bush for a disease of his grandkid: quite incredible. Testimonies and questions follow. You may also go to 1:01:40 where Frank Trautenberg or Lautenberg or what is the name of the old man (D - New Jersey) asks some questions to Spencer.

I must say that these arrogant political fools drive me up the wall and I must pause the video every 10 seconds to avoid overdosing. They don't know 1% of Spencer's knowledge about the climate but they still indicate that they don't have to listen.

Spencer says a lot of key things, for example that the humans obviously have some impact on the climate - for example, they influence the area of forests - which doesn't mean that they can stop using fossil fuels. Whether the carbon technologies can be replaced by something else in the future will depend on technological breakthroughs and you can't legislate new technologies into the existence. In fact, billions have already been spent and nothing that could be called a breakthrough has emerged.

But those political faces simply don't want to hear anything that makes sense. Instead, they want to tell Spencer and real scientists in general that they are putting children at risk. And they want to listen to bought scientists such as Kevin Trenberth to say things that the politicians pay them for saying. In his speech, Spencer recalls that Robert Watson, the 1997-2002 chairman of the IPCC, told Spencer 20 years ago that CO2 should be regulated (much like freons), years before a scientific "justification" was on the table.

It's a very sad tragicomedy - a great example how the active morons such as Boxer and Lautenberg "naturally" get to the top of political affairs in every country that suddenly allows its government to decide about things that should only be decided by the free individuals. At this point, science is completely irrelevant. Science was only good in its manipulated, corrupt form to help the morons to get to their chairs and gain the power.

Frankly speaking, I found even comments by some Republicans, such as Larry Craig (around 56:00), who is a semi-skeptic, insulting, e.g. when he called Spencer "outsider" in the climate science. What the [intercourse] does it mean? By all objective criteria, Spencer is an achieved scientist at the center of his discipline.

Incidentally, Antarctica was about 17 °C warmer 14 million years ago than it is today: ostracods have spoken.

Monckton, APS, and Medusa

周二, 2008-07-22 21:18
The Register published an entertaining article about the funny story involving Christopher Monckton and the American Physical Society.

Recall that Jeff Marque, an APS editor, wrote in their recent newsletter addressed to a small subgroup of the APS called "Forum on Physics & Society" an obvious truism, namely that a considerable fraction of the scientific community are climate skeptics. They opened a rare arena for scientific arguments about this issue.

Needless to say, that was already way too much for the true believers. In an article proudly called Physicists forced to reaffirm that human-caused global warming is “incontrovertible”, Joe Romm of Climate Progress initiated an e-mail campaign and encouraged hundreds of readers of his website to do the following:
So this editor who single-handedly smeared the good name of the American Physical Society and the 50,000 physicists it represents is one “Jeff Marque, Senior Staff Physicist at Beckman Coulter Corporation, 1050 Page Mill Rd., MSY-14, Palo Alto, CA 94304, jjmarque@sbcglobal.net.” Please do email him and his bosses (whose names and e-mails I will provide below) to let them know your thoughts.

What Marque has does [sic] is so beyond the realm of real scientific debate that he should be fired from his editorial position.
So you should imagine those hundreds of incoherent yet angry e-mails that the AGW zealots sent to Marque and his bosses (including Lawrence Krauss, the former FPS chair). Because of his blasphemy, they try to "fire" Jeff Marque - who is not even paid for this minor "job" of an editor. ;-) That's an example how the activist foam of the society starts to influence what's going on in the world. They can even fire people from jobs that don't exist! ;-)

(Recall how easy it was for Jo Abbess, an activist chick, to completely change an article written by the BBC.)

Nevertheless, the APS has published an article by Lord Monckton, Climate Sensitivity Reconsidered, which not only summarizes some of the well-known inconsistencies (such as the wrong fingerprint) in the greenhouse model of the climate but also offers the readers an insightful review of the IPCC methodology.

Among many other things, Monckton explains that the key (and high) IPCC's figure for the climate sensitivity is based on one (1) scientific paper that uses another number "kappa" from two other papers - one of which was written by a person who has promoted his or her own paper through the IPCC. It doesn't exactly look like 2,500 people calculating the sensitivity.



The AGW mujahideens have eventually convinced the APS to add the following disclaimer above Monckton's invited contribution. The health warning (don't look at Medusa!) was written in red ink:
The following article has not undergone any scientific peer review. Its conclusions are in disagreement with the overwhelming opinion of the world scientific community. The Council of the American Physical Society disagrees with this article's conclusions.
Some secret sources of mine indicate that this disclaimer was added by Lawrence Krauss, a well-known far-left critic of physics, who also recently claimed that the cosmologists are destroying the Universe by making observations.

Of course, Lord Monckton and many members of the scientific community have complained because his contribution was an invited one and the insulting fundamentalist disclaimer above was not a part of their agreement.

Moreover, the disclaimer is completely illogical, at least from a scientist's viewpoint. If the paper were not scientifically peer-reviewed in any way, how could they know whether its conclusions agree with the opinion of the "scientific community" or not? ;-) Only the people who don't read the bulk of any scientific papers could know whether they agree with a paper or not without reading it. They're supporting the AGW God regardless of the bulk of all papers and they seem to be particularly proud about their pure belief uncontaminatable by any arguments!

After some additional battles, the red ink comment was replaced by the following remark written in ordinary black ink (the same paragraph was also added above the consensus scientists' contribution):
The following article has not undergone any scientific peer review, since that is not normal procedure for American Physical Society newsletters. The American Physical Society reaffirms the following position on climate change, adopted by its governing body, the APS Council, on November 18, 2007: "Emissions of greenhouse gases from human activities are changing the atmosphere in ways that affect the Earth's climate."
You have heard the holy word again and you will hear it infinitely many times in the future. Amen. That's all very funny. Imagine that a similar comment would be written about an issue that is so far remaining a subject to the scientific method. For example: "The APS reaffirms its official collective position that the cosmological evolution follows the Big Bang theory with dark energy and cold dark matter and particle physics beyond the Standard Model obeys the laws of string theory." ;-) That would be funny, right?

And I am probably being too optimistic here. The APS could also adopt the official position of the PI and announce that "the members of our society are certain the world follows the laws of ekpyrotic loop quantum cosmology with a variable speed of light, two metric tensors, and 30+ braided octopi swimming in the spin foam." :-)

At any rate, the American physicists are no longer treated as sui iuris. They must be protected from Lord Monckton's blasphemy much like little kids must be protected from beer. And frankly speaking, many of them fail to be sui iuris, indeed. There are just so many of them who have been so easily manipulated by the activist foam that I can no longer respect them as honest scientists even though many of them have contributed to high-energy physics and other disciplines.

And that's the memo.

Bonus

A TV regulating institution (Ofcom) in the U.K. decided that The Great Global Warming Swindle didn't materially mislead the viewers to cause harm or offense (i.e. Ofcom agreed that every single complaint by Myles Allen, Phil Jones, and "37 professors" was unjustifiable) but it did misinterpret some climate alarmists' words: see the full verdict and Steve McIntyre's comments. It could be the case but most of the specific accusations by the censor seem manifestly untrue to me.

For example, Fred Singer said in the program that David King argued that Antarctica would become the only habitable place on Earth by the end of the century. The censor argued that it was not true. I can tell you Fred's comment was true and we even know where King said exactly this thing. It was in the Independent on Sunday, May 2, 2004. See this Spiked article or make a Google search. The exact quote was:
Antarctica is likely to be the world's only habitable continent by the end of this century if global warming remains unchecked.
King was said to announce this far-reaching conclusion in a talk to a climate group. Now, the Independent on Sunday could have been inaccurate (although the quotation has never been challenged!). But if it is the case, it is the Independent on Sunday, and not Channel 4 or Fred Singer, who should be chastised! The alarmists are saying tons of similar mad things every day, so even if this particular quote were inaccurate, the big message, namely that the alarmists are lunatics, is accurate.

Oceans, not CO2, drove continental warming

周二, 2008-07-22 02:53
Roger Pielke Sr discusses a new peer-reviewed skeptical climatological paper by G.P. Compo and P.D. Sardeshmukh,
Oceanic influences on recent continental warming (full text; abstract is here)
in Climate Dynamics (2008). They treat the known profiles of the ocean temperature as a possible driver and argue that this function of time is enough to reproduce the observed continental temperatures almost accurately.



This remark means that the greenhouse effect above the land is not among the most important effects while the temperature change of the oceans is primary. However, they can't say why the temperature of the oceans was changing. And of course, the greenhouse effect (mostly above the oceans) can still play a significant role for this question. But it doesn't have to.

The very statement that the ocean temperature is sufficient as a "driver" to explain the continental temperature sounds good and plausible (because of the high heat capacity of the oceans) but I am afraid that it is another example of the logical fallacy emphasized by Roy Spencer. They haven't really proven it. Correlation is not causation and even in the cases where it is, you can't quite know the direction of the causal relationship...

One of the messages of the paper is that the ocean temperature should be studied more carefully and the climate should be investigated in the regional context, not just through the global averages that completely overlook many of the essential phenomena: the paper actually shows that the regional patterns were predicted completely incorrectly by two popular classes of climate models.

Sunday: Questioning the science of climate change

周二, 2008-07-22 00:42
An Australian TV program (playlist, 3 parts, 22 minutes in total, click)
Jennifer Marohasy is among the global warming infidels who are interviewed and she says a couple of wise things, too.

Incidentally, Hospodářské noviny, the Czech counterpart of the Wall Street Journal, informed about NASA's data showing H1 of 2008 as the coolest half-year in 12 years.

They have also included a poll: whom do you consider closer to the truth concerning global warming? Václav Klaus defeated Al Gore 70% vs 30%. It seems that among educated and affluent Czech readers, there is pretty much a consensus. ;-)

The article interviews Ladislav Metelka, the only Czech professional alarmist, who argues that the Sun is behind the cooling. Milan Šálek, another weather scientist, warns that we haven't seen a volcano eruption for quite some time. Its (cooling) effect would be much more significant than the greenhouse effect, he says.

Graph of the day

Gapminder: income per capita vs CO2 emissions per capita (see also PDF for 2003).

You can see that virtually all countries are very close to a particular straight line. ;-) The countries above the line are the oil-rich places that can waste oil; the countries below the line are small islands where they don't have to travel much and places with a lot of nuclear power plants.

In fact, this line doesn't even change much if you push the button and return a few decades into the past (or press "Play"). You may also see where you end up if you reduce your emissions by 80% as certain mentally unstable people - such as a former U.S. vice-president - propose.

Global warming pseudoscientific parasites and their flatulent cows in Wales have sucked additional USD 100 million of taxpayers' money: BBC.

Black holes are politically incorrect

周二, 2008-07-22 00:23
Benjamin has brought my attention to a hilarious story.
John Wiley Price defends his opinion that "black hole" is a racist term.
See Google News. This black commissioner is the sort of folks who are as dumb as a hoe handle and who recently began to influence the public life.



An interview...

John Wiley Price thinks that "that type of language is unacceptable". We are apparently approaching the point at which black aßholes like him will prevent us from using scientific terms such as the "black hole". (If needed, I am ready to call him a "white aßhole" because the focus is on the word "aßhole", not the word "black"!)

In fact, I predicted this story years ago which is why I have often used the term "African American hole" instead. ;-)

He asks why wasn't the term "white hole" used for such a nasty object instead of the "black hole". Well,
  1. the "black hole" was chosen for a good reason that will be explained below
  2. there is nothing nasty about black holes
  3. the term "white hole" is also used, for a similar object, and the relations with black holes will also be explained in detail.
The last, third portion of my explanation will be (relatively speaking) the deepest one and I don't expect people of John Wiley Price's caliber to understand more than 5% of the ideas.

Let me start with a simple comment. "Black" is the (non)color of objects that absorb (nearly) all incoming radiation in the visible part of the spectrum. It just happens that the skin of the people of African descent is closer to black, as defined in the previous sentence, than the skin of the people of European descent.

That has a very good reason. The stronger pigmentation has evolved to protect the deeper layers of the skin from the damaging ultraviolet rays - and this protection is more important in Africa where the solar radiation is more intense. Well, these are the reasons why the people of African descent are called by words related to "black" in most languages. There exist similar rational reasons why "blackberries" and other objects have names incorporating the same adjective.

The history of the term

In 1967, John Wheeler coined the term "black hole" to describe objects that were kind of believed to exist from the 1916 paper about Einstein's general relativity written by Karl Schwarzschild and especially the 1939 paper by Robert Oppenheimer. Their gravitational field is so strong that if you fall into them, it is like if you fall into a hole and you will never escape again. In fact, not even light is fast enough to escape from their powerful gravitational grip. Because light cannot escape, the objects don't emit any radiation and they are black.
Commercial: Spiked: The rise and rise of climate blasphemy
The term "black hole" is therefore exactly what we need. It sounds good, too. And a warning for ill-informed FoxNews journalists: a singularity is surely not the same thing as a black hole! ;-)

Yes, the black holes have the same adjective "black" in them as African Americans, for a good reason. They absorb most of the incoming radiation and don't reflect (or emit) it. If John Wiley Price doesn't want to share this feature with the black holes, he should ask Michael Jackson how to proceed.

Stephen Hawking realized in 1974 that black holes emit some radiation, after all, but it is extremely weak, especially if the black holes are large. I will be mostly neglecting the Hawking radiation in the rest of this note.

There is nothing bad about black holes

Black holes in physics are vaguely analogous to various situations in reality - for example, bureaucracy has become a black hole for lost paperwork (and wasted time of humans). But in pure physics, objects such as black holes or stars don't carry any moral characteristics. There is nothing (morally) good and nothing (morally) bad about the black holes.

In fact, black holes are beautiful and important from a scientific viewpoint. Unlike certain Texan black commissioners, black holes carry the maximum information (or entropy) that one can in principle store in a given volume of space. Their properties completely govern the very high-energy, trans-Planckian scattering of other particles. They are the most natural objects that can be used to verify the consistency of theories of quantum gravity. They became one of the huge success stories of string theory.



Valleyfair attacks: a stunning story how the media have been dishonestly hiding a nasty double hate crime because the racist criminals were black, not white

Black holes and white holes

OK, so why didn't scientists use the term "white holes"? Well, white holes should be objects that tend to emit a lot of light, much like the skin of the Caucasian people, but they don't absorb it. Do they exist? In the real world, they don't. The reason is the second law of thermodynamics, the basic law of macroscopic physics that Sean Carroll completely misunderstands.

There is an inherent difference between the past and the future. If we're thinking about a thought experiment, we may begin with pretty much arbitrary initial conditions in the past. But we are not allowed to decide about the future. The future is, and has to be, whatever follows from the past by the laws of physics. There may exist objects that are "black": they are expected to emit no radiation. But there can't exist objects that are "white" in the sense that there is no radiation coming to their surface. Why? You are simply not allowed to prevent radiation from going anywhere. Some photons are always free to travel in certain directions and hit an object that you wanted to become a "white hole".

This may sound confusing to you. Can't we just apply the time reversal and switch the role of the past and the future? Well, you can do it with spacetime diagrams but it doesn't mean that such reverted histories may occur in reality. In fact, if a plausible history involves an increasing entropy, the time reverted history makes the entropy decrease which is not physically allowed.

Black holes are the highest-entropy objects we can have so this restriction should be the most important in their context: the more entropy a system produces, the more dramatic difference between the past and the future it creates. OK, so how do the rules of thermodynamics work in the presence of black holes?

Black holes and increasing entropy

Let me assume that the reader believes me that the entropy of a large black hole is proportional to the event horizon area, namely "A/4" in Planck units. Jacob Bekenstein was able to guess this relationship by general arguments applying thermodynamics to black holes; Stephen Hawking calculated it by the methods of thermodynamics from the known temperature of the Hawking radiation. Moreover, the relationship can now be calculated and confirmed directly - by counting the microstates in string theory.

Because the total entropy should never decrease, the total area of event horizons should never decrease either.

Indeed, that's correct. And in fact, this law of "increasing event horizon areas" can be derived (and was derived, by Stephen Hawking in 1970) from Einstein's equations of general relativity themselves. Imagine a typical situation. Start with two neutral black holes whose masses are M and M. The radii of the event horizons are R=2M in Planck units so the total event horizon area is twice 4.pi.(2M)^2, i.e. 32.pi.M^2.

These two black holes may merge into one object, one black hole. After some time, it stabilizes. Its mass will be 2M, the radius will be 4M, and the horizon area is 4.pi.(4M)^2 = 64.pi.M^2, more than the initial total area of the event horizons. Indeed, the total area has increased. The important thing is that this process can never occur in reverse: a neutral black hole cannot spontaneously decay into two black holes.

More precisely, such a process is possible in the context of the Hawking radiation but such "huge Hawking particles" are extremely (exponentially) unlikely. For practical purposes, it is impossible for a black hole to split into two.

The important message here is that the classical general relativity including black holes gives a geometric interpretation to the concept of entropy. And the law of increasing entropy can be proved from Einstein's equations. The reason why we can prove this law and not the inverse law is the assumption that the black hole interiors and singularities always occur in the future light cones of normal observers, not in the past light cones.

Do the white holes exist in the Hilbert space?

When you imagine a causal diagram for a star that is collapsing into a black hole and you time-revert it, to obtain a new "object" (really, it's a history) that is naturally called the "white hole", it looks completely different: the singularity is in the past while the star is in the future. The black hole is associated with some microstates in the Hilbert space. Because the causal diagram of a white hole is so different, you might think that the white hole will have to be represented by completely different microstates - because it is so "macroscopically" different.

But this conclusion is incorrect. If you try to find the time-reverted states that are associated with a white hole, you will find the very same states as those that you linked to a black hole. There are simply no other massive microstates and all massive microstates can be used as black hole microstates. It is enough for one slice through the spacetime to look similar in the black hole and white hole case to see that the microstates are "shared". We are led to a clear conclusion first articulated by Stephen Hawking in 1974:
Quantum mechanically, black holes and white holes are the same thing.
When they're the same thing, John Wiley Price could wake up and ask his question "why don't we call them white holes?" again. ;-)

Well, they correspond to the same microstates but if you actually study how they evolve in time, their history includes objects that absorb a lot of radiation but don't emit much. There is indeed an asymmetry between black holes and white holes as long as we define them by the classical causal diagrams. Black holes can exist but white holes can't. The entropy is always increasing because the past is always given by some data carrying finite information while the future is always "derived" and thus more chaotic.

In the context of black holes, this law means that the black hole singularities appear in the future, not in the past, large black holes merge and eat objects around, but they don't decay or emit objects, and this comment applies to light, too. That's why the white/black hole microstates always manifest themselves as black holes in the real world. After all, if they were white holes instead, black morons would also think it is a matter of discrimination because the famous white holes would be everywhere, they would be the key part of the Second Superstring Revolution, and black holes would be underrepresented. ;-)

Because I am not sure that this explanation will convince anyone in this crazy world, Mike Lazaridis should better rename his "BlackBerry" before it is too late. What about a "StrawBerry"? It's not perfect either. While BlackBerry is a nasty attack on a black man, StrawBerry could be an attack on a straw man. ;-)

Meanwhile, "black sheep of the family" should be renamed to a "white wolf of the family" and the "black swan" should become the "white blackbird". A subtle problem with this new notation is that the mostly black wolves are aggressive while the mostly white sheep are peaceful. (The color of devils and angels was simply copied from wolves and sheep.) It seems that Nature is racist Herself. Is it the time to destroy Her? Or is it enough to ban any talk about the color of sheep and wolves in public? :-)

Well, let's not joking about these matters too much because they are pretty serious. I agree with Mr Mayfield that anyone who is offended by the term "black hole" needs a serious psychiatric treatment. Poor Andy Strominger and Cumrun Vafa. They've been voting for junk left-wing politicians like Gore and Kerry throughout their lives and after decades, they find out that 90% of their famous papers are racist crap! ;-)

Bimetric pseudoscience and ghosts

周一, 2008-07-21 19:57
This month, at least two preprints about "bimetric" theories of gravity have been submitted to the arXiv: one of them came from the Imperial College (IC) and the other one was written at the Perimeter Institute (PI).

Here, I want to explain why this kind of writing is ridiculously bad and lethally flawed if understood as science. I claim that the authors of these papers - and dozens of previous papers about the same subject - must be unaware of virtually all elementary facts about physics to be explained below and they should have been failed in their field theory courses.



Two geometries, two gravities, two Newtons? It may sound attractive :-) but it is physically unacceptable.

The IC paper talks about "two metric tensors" - as an example of the Variable Speed of Light misapproach - but there is really one metric tensor only (supplemented by a scalar with unusual interactions): the only thing that is "doubled" are the frames. You can define different frames - different conventions what you mean by a metric tensor and by distances.

Normally, frames (e.g. Einstein frame and string frame in string theory) are related to each other by scaling. In the IC case, they differ by additive terms - such as "∂_μ φ ∂_ν φ" - which means that they generally induce different causal structures but there is still one independent light spin-2 field so the adjective "bimetric" is a misnomer.

It is also wrong to call it a "Variable Speed of Light" theory because the unique metric tensor still defines a unique and fixed value of "c". Whether the IC paper defines a consistent theory depends on details but it is surely not an attractive or a well-motivated theory.

The IP paper is even more seriously flawed because it literally wants to have two metric tensors, "g" and "h", that can be used to measure distances on a manifold. We will explain that it is a physically inconsistent setup because
  1. there can only be one general covariance to remove ghosts
  2. if one introduces new non-local symmetries to get rid of the remaining ghosts, the second metric tensor becomes massive and disappears from long-distance physics
  3. consistent theories of quantum gravity automatically imply that there can only be one independent metric tensor
Ghosts in theories including fields with spin

So let me begin with an explanation what ghosts are. In physics, this concept has a somewhat more specific and abstract meaning than e.g. ghosts from the Ghostbusters movie. ;-) Physicists use the term for two related but different objects:
  1. bad ghosts: states in the Hilbert space whose (squared) norm is negative i.e. that have a negative probability to exist
  2. good ghosts: Faddeev-Popov ghost fields that are very convenient to deal with local (gauge) symmetries
The relationship between bad ghosts and good ghosts is that the refinement of a theory that employs good ghosts replaces the original Hilbert space with the physical Hilbert space of cohomologies of the BRST operator, Q, and if the theory is consistent, this (reduced) physical Hilbert space is free of bad ghosts. That's necessary for a theory to have a physical meaning because negative probabilities can't occur in reality. For example, no one has ever won -30% of elections, as long as he participated at least in one. :-)



Below, I will talk about bad ghosts only. In the first place, we should ask:

Why there should be any bad ghosts?

Well, the reason is simple. Consider a (non-gravitational) theory with a field whose spin is one or higher (spin-0 and spin-1/2 fields won't generate any ghosts: recall that the psi-dagger-psi Dirac inner product, measuring the probability density, is positively definite), for example QCD with spin-one Yang-Mills fields. When you draw the "t=0" slice and try to quantize it - which you eventually have to do because our world is a quantum world - you will have operators A_μ whose Fourier modes give you creation and annihilation operators for particles with certain momenta.

What is the norm of the one-particle states created by these operators? You may see that the inner product of the state created by A_μ with the state created by A_ν is actually proportional to g_μν, the metric tensor. This fact is pretty much required by the Lorentz invariance - the metric tensor is the only "universal" tensor with these indices - but you can derive it explicitly from the action, too. (A priori, you might think that the inner product can also depend on the timelike vector associated with the t=0 slice, but the set of 1-particle states is actually Lorentz-covariant and the inner product doesn't depend on the slicing, after all.)

Now, the metric tensor g_μν is indefinite: when you write it in a diagonal basis, some of its entries must be negative (because the space and time have opposite signature). Most of the entries of vectors and tensors are the purely spatial ones, and these have to generate the positively definite one-particle states in the Hilbert space leading to positive probabilities (regardless of your sign convention for the metric).

The negative-normed entries correspond to quanta - particles - that would lead to negative probabilities. Whenever you would create a final state with such a particle, its probability would be negative (a negative multiple of the squared complex |amplitude|), leading to logically unacceptable predictions - an inconsistent theory. The only way how such a theory could possibly survive is that such ghosts are never produced if you don't have them in the initial state.

Decoupling the ghosts

So if you want to save your theory, you must assume that there are no ghosts to start with. More importantly, the theory must also imply that if there are no ghosts to start with, they are never produced by the evolution. The probability amplitude (for a scattering etc.) including one bad ghost or more ghosts (in the final state) and many ordinary particles (in the final and initial state) must be zero. We say that the ghosts must be decoupled.

(In a theory treated with good, Faddeev-Popov ghosts, it is no longer true that the probability with all kinds of ghosts in the final state must vanish. Instead, the amplitudes with BRST-exact states must vanish, and they automatically do if the BRST axioms such as Q^2=0 are satisfied. Let us follow the old treatment without the good ghosts below.)

Now, it is a very nontrivial requirement that the ghosts must be decoupled from an arbitrary combination of ordinary particles. When you have a "generic" theory where ghosts (which are just "some" parts of your tensorial fields, after all) interact with the normal matter, you may be sure that most of the probability amplitudes will be nonzero. How can you possibly make all of them zero?

The answer is a "gauge invariance". You must "pay" gauge invariance for each potential ghost, and because it is so hard to find a lot of gauge invariance in your theory, you normally have enough gauge invariance to kill the timelike components only. That's why the timelike components must be those associated with the negative-normed one-particle states (regardless of your metric sign conventions).

At every point of spacetime, there must exist a parameter of gauge invariance for each component of bad ghost fields. This is enough. Why? Because the scattering amplitudes are encoded in the correlators of various operators - i.e. in Green's functions - and the operator corresponding to a bad ghost may be expressed, up to a momentum-dependent rescaling, as "∂_μ j^μ" which vanishes because the corresponding current "j" is conserved. It is conserved because of Noether's theorem applied to the global part of the corresponding gauge symmetry.

You can see that the very condition that a quantum version of your theory exists severely constrains how the theory can look like. In classical physics, you might think that any kind of field theory is just fine. You might write any field equations controlling any fields you like. However, most of them would lead to quantum theories that predict negative probabilities and they're not allowed. It follows that fields with spin can't be added arbitrarily: you need a gauge symmetry for each time-like (negative-normed) component of such fields!

That's great. So let us look whether we have enough gauge symmetry to kill the ghosts. Yes, we do. For example, in QCD whose gauge group is SU(3), there are eight Lorentz vectors "A_μ": the 1...8 index is the adjoint index of the 8-dimensional SU(3) Lie algebra. But we also have 8 currents "j_μ" and 8 corresponding parameters of SU(3) transformations at every point. If you think about it, this counting obviously works for every gauge group in every Yang-Mills theory.

Modification for spin-3/2 and spin-2

We will begin with the most difficult case, the spin-3/2 fields.

If the spin is 3/2 (i.e. 1.5), you deal with Rarita-Schwinger fields that effectively carry one spinor index and one vector index. The spinor index would generate a positively definite (=ghost-free) Hilbert space, like the Weyl or Dirac field, but the vector index can go timelike again. Once again, you are threatened by ghosts and negative probabilities. And once again, you need a local symmetry - and the corresponding current - that saves your theory.

How many parameters such a local symmetry should have? Well, if the vector index is "0" (time), you obtain ghosts. But the spinor index can still be anything: the ghosts have many components. There is a whole spinor of ghosts and the corresponding gauge symmetry to kill these ghosts must therefore be a spinor, too. Now, gauge symmetries (and conservation laws) whose parameters carry a spin are heavily constrained by the Coleman-Mandula theorem and its modern refinements. If you wanted a conservation law for too difficult an object (with a high spin), pretty much every momentum of every particle would have to be conserved and the interactions would vanish: too bad even for a remotely realistic theory.

For spin 1/2 conserved quantities, there exists one possibility, and it is called supersymmetry: the conserved charges are called supercharges and they transform as a spinor or spinors. If you want a consistent, ghost-free quantum theory with spin-3/2 fields, it must respect (local) supersymmetry! By pure algebra, you can argue that the anticommutator of two supersymmetries includes a (local) spacetime translation, so the coordinate reparametrizations must automatically be a part of the story. With spin-3/2 fields and nonzero interactions, you must inevitably deal with supergravity, a theory that includes both gravitinos and gravitons.

The spin 1/2 of the supercharge is already pretty high and the conservation law for the supercharges - which is equivalent to the symmetry called supersymmetry - is very constraining. The maximum number of supercharges that a physical theory can possibly have is 32 real components which is equivalent to one real chiral spinor in 11 dimensions or N=8 (complex chiral) Weyl spinors in four dimensions. This "N=8 supergravity" is extremely constrained: its low-energy interactions are fully determined by the required supersymmetry. The less supersymmetry you require, the more free and unconstrained your model building becomes. For N smaller or equal to 4, you can get non-gravitational yet supersymmetric theories but because they're non-gravitational, the supersymmetry must only be global, not local!

Now the main point: spin two

But spinors and supersymmetry might be too complex for some readers, so let's return to an integer spin, namely spin-2. Nevertheless, I will still have to assume that the reader knows why gravity must be carried by spin-2 particles i.e. that the arrogant and mostly anonymous imbeciles from Not Even Wrong and similar dumping grounds of the Internet no longer visit this blog. ;-)

Imagine that you deal with a spin-2 field h_μν - such as the metric tensor - that contains something like the normal kinetic term in the Lagrangian. Again, the Fourier modes of this quantum field will give you creation and annihilation operators. The inner product of the states created by h_μν and by h_μ'ν' will be proportional to something like g_μμ' g_νν'. Or another product of two metric tensors with these four indices or one of their linear combinations. If exactly two of these four indices are timelike (i.e. 0), you may obtain a negative result. For example, "g_00 g_33" is negative.

It follows that the h_01, h_02, h_03 components of the tensor field create ghosts. There are D-1=3 of them and you need roughly D-1 of the gauge parameters, too. Essentially a whole spacetime vector. If you carefully analyze the index structure, you will find out that the conserved currents must be components of a tensor that you may call the stress-energy tensor T_μν. This tensor must be conserved and because its divergence "∂^μ T_μν" must be related to the bad components of the tensor "h" you started with, you may see that the corresponding transformation of "h" must coincide with the standard transformation rule of the metric tensor under the coordinate transformations.

In fact, coordinate reparametrizations are the only local transformations of fields whose infinitesimal parameters naturally transform as vectors.

In other words, the only way how a spin-2 field can be nontrivially interacting with the world, while generating no bad ghosts, is to identify the field with the metric tensor in a generally covariant theory. Because gauge invariance may be viewed as a "fundamental concept", you may derive general relativity from this alternative starting point. See also Gravity from spin-2 gauge invariance.

Fine: so can you have two metric tensors?

You would need "two independent reparameterization invariances". That's not possible in a physically acceptable and interesting theory. When you consider one manifold, there only exists one set of coordinates, after all. So there are only D functions that determine the relationship between two choices of the coordinate system: D parameters of a local symmetry. (Let me not discuss the difference between D-1 and D, it's too subtle.)

In fact, there exists a loophole - a method to have two or more metric tensors; see Arkani-Hamed, Georgi, Schwartz (AGS) based on generalized deconstruction (a phenomenologist's toy model for extra dimensions). However, when you follow their analysis of the physics that follows from their approach, you will find out that only one metric tensor - the "real one" - remains massless. The other one acquires a mass and disappears from the long-distance physics. In fact, their approach is the most natural method to analyze massive spin-2 fields.

Morally speaking, the other spin-2 field in the AGS picture has a similar character as the massive Kaluza-Klein modes of the graviton (or even the massive spin-2 fields in string-theoretical tower of states): in all cases, there are very manifest reasons why the new spin-2 field cannot be massless. You shouldn't view the AGS theory as a very low-energy theory because the theory breaks down as an effective theory above the energy scale (cutoff) that goes to zero (=the theory breaks down everywhere) if the mass of the other graviton itself goes to zero, even though the cutoff goes to zero more slowly than the mass (it is a kind of weighted geometric average of the mass of the massive graviton and the Planck scale).

So if you want to consider theories similar to one envisioned by the IP paper and others - where you can literally measure distances on a large manifold by two independent metric tensors - you are inevitably led to an inconsistent theory with ghosts. A good student should be able to comprehend - and even re-discover - all these facts in a few hours as a part of one homework exercise. People like Magueijo and Hossenfelder couldn't get them at least since 2001 when the wrong bimetric theories first appeared in the literature.

One metric tensor in string theory

Every good field theorist knows why these bimetric papers, and many similar papers, are just wrong. You don't really need to know string theory to make such analyses. Nevertheless, string theory gives us a particularly clear picture why there can't be several massless spin-2 tensors.

You may often hear the crackpots saying that string theory makes no predictions about the reality. Well, it makes tons of predictions. For example, it implies that virtually every paper that the critics' friends have ever written must be completely wrong. It predicts that none of their predictions can ever materialize. Isn't this a powerful prediction, too?

In string theory, you don't have to work hard to derive similar qualitative facts - e.g. that the number of gravitons equals one and not two: they automatically follow from it, from its own technical tools that we're going to look at. I would be skeptical about any theory that doesn't naturally imply any of these general facts about quantum fields. Of course, no theory besides string theory does such things which is one of dozens of reasons why I am skeptical about any non-stringy way to go beyond quantum field theory, to say the very least.

Why is there one metric tensor in any background of string theory, including every single vacuum from the proverbial landscape of 10^{500} solutions? Well, it just seems to be true in every vacuum we have ever seen - perturbatively or nonperturbatively. However, perturbative string theory makes the answer exceptionally transparent and let's look at it.

We will begin with bosonic string theory. The ground state of one string is a tachyon. And you may add the alpha-oscillator excitations. Already the first excitation brings you to the massless level. Two excitations already create a massive particle. So if you're only interested in the massless spectrum, you can only add one excitation in the open string case - generating a spin-1 field - or two excitations (left-moving and right-moving) in the closed string case - generating a spin-2 field.

The open strings can carry additional labels - the Chan-Paton factors (colors associated with the endpoints) - so you can have many components of a spin-1 field. In fact, the Chan-Paton factors become two indices and that's how you generate the whole "square matrix" of the gauge fields, transforming in the adjoint representation.

However, the closed strings don't carry any additional labels similar to the Chan-Paton factors. For example, closed strings don't have any endpoints or other special places that could support additional degrees of freedom. Consequently, the spin-2 massless graviton is inevitably unique. Nothing changes about this conclusion even if you compactify some of the dimensions. Any excitation of the compactified degrees of freedom increases the squared mass. So if you don't want to surpass the massless level, you cannot combine the compactified excitations with the excitations of the noncompact dimensions (that define the "ordinary" spin).

An analogous counting applies to the NS-NS sector of the superstring. Its ground state is a tachyon, too. (This particular tachyon becomes unphysical due to the GSO projections.) The only difference is that the squared mass is 1/2 of the bosonic one and you can work with half-integer-moded fermionic oscillators, too.

The vertex operator - a conformal field theory operator whose correlators are used to calculate the scattering amplitudes for a particular particle in string theory - corresponding to the graviton is proportional to "∂ X_μ(z) ∂* X_ν(z*)". By looking at this object, you can also see that there is only "one type" of the graviton that you can construct. There is only one worldsheet, with one set of coordinates, z and z*, and its embedding into the conventional spacetime is only described by one set of the fields X_μ(z,z*).

There is just no way to ever get two gravitons (or two metric tensors) with indices along the large spacetime coordinates. The only, uninteresting exception is when you imagine that the two metric tensors belong to two "subtheories" that don't interact with one another at all. In this case, you can even have two independent coordinate reparametrizations. Operationally speaking, the other "segment" of the Universe besides your own doesn't really exist. Andrei Linde used this vision - that there can exist completely decoupled worlds on top of ours - to motivate some ideas about the multiverse. The IP paper cited Linde's paper but Linde has clearly nothing to do with the crackpot enterprise of writing theories with several interacting metric tensors!

By the way, string theory has its own, completely new technical way to prove that the ghosts decouple: you don't have to talk about the currents "j" in spacetime. In fact, you can prove that the decoupled unphysical components of fields - such as ghost gluons and ghost gravitons - have vertex operators that can be written as a total derivative of another operator with respect to one or two worldsheet coordinates. Consequently, the integrated vertex operator (over the effectively compact worldsheet) vanishes, and so does the scattering amplitude.

In the BRST treatment including the good ghosts, the arguments would be slightly more sophisticated but they would be equally powerful to derive the conclusions we need.

Related facts about the stringy spectrum

Similar arguments lead to many other, related general conclusions or general predictions of string theory, if you wish. There can't exist massless fields with spin higher than 2 - not even 5/2! ;-) The fields with spin-3/2 must be gravitinos and their number is related to the number of supersymmetries.

The spin-1 fields in string theory may come in many flavors. I have already mentioned the gauge fields produced by open strings with Chan-Paton factors (colors attached to the end points). But there are many other ways how string theory produces spin-1 fields. These pictures may be shown to transform into each other under various dualities and transitions.

But let's look at one more classical way how spin-1 fields may emerge from perturbative string theory: the Kaluza-Klein way. You only need a field whose one vector index is parallel to the large dimensions, to get spin-1: this index can arise from the right-moving side of a closed string. The other index, taken from the left-moving side, may be parallel to a compact dimension. That's equivalent to getting a gauge field, A_μ, from components of a higher-dimensional metric tensor, g_μ5, where 5 is a compact direction. That's nothing else than the Kaluza-Klein theory.

Instead of 5, you may also use e.g. the index 25 on the bosonic, left-moving side of the heterotic string. That also generates a Yang-Mills field. But it turns out that the gauge group in the heterotic string is neither a power of the U(1) nor the isometry of an ordinary manifold you could think about in a classical Kaluza-Klein theory. Instead, it is one of the two 496-dimensional groups, SO(32) or E8 x E8. This larger group is the extended, quantum, or "stringy" isometry of a particular chiral 16-dimensional torus used for the compactification of the 16 "redundant" dimensions on the bosonic side. Still, you can view the emergence of the gauge group in the heterotic string as a generalization of the Kaluza-Klein theory.

There are other ways how the spin-1 fields may come into existence - for example, through lower-dimensional D-branes (related to the open string's Chan-Paton factors discussed above by T-duality) or through F-theoretical singularities (related to and generalizing D7-branes). String theory includes and links all physically consistent ways how fields - including higher-spin fields - can be interacting with each other and how you can generalize this picture.

Whether we already know "everything" about this world is a different question. Of course, we don't yet know everything. But we already know something and the insights of string theory collected so far, much like the laws of mathematics themselves, are a crucial and inseparable part of it. Unfortunately, the physicists who don't know this crucial part are usually ignorant about many other, much more elementary parts of the modern physics cannon, too.

And that's the memo.

Carl Icahn, now on Yahoo's board, will help Microsoft

周一, 2008-07-21 19:54


Carl Icahn, the 46th richest person in the world, won his proxy contest and was named a member of Yahoo's board. He considers Yahoo's refusal to be bought by Microsoft irrational, and so does your humble correspondent. We will see whether his new chair will be enough for the deal.

McCain, computers, and Czechoslovakia

周一, 2008-07-21 00:23


It's at least the third time when John McCain publicly talks about recent events in Czechoslovakia, a country that was dissolved more than 15 years ago.

The hosts pedagogically explain their wise and curious viewers that the split was analogous to the separation of Bennifer who must currently be called Jenn and Ben. ;-) Tomkat and Brangelina are doing just fine.

(By the way, Sam Nunn, a possible running mate of Obama, also thinks that there is a lot of things going on in Czechoslovakia.)
Comedians make fun out of McCain (click)
Incidentally, the Russian oil company now claims that they deliver the missing oil for Czechia (not electricity! We surely don't need it, being exporters of energy, and planning to triple our nuclear sources in 1 decade, to produce 100% of our needs by fission and to export the rest) to Turkey because of financial reasons: the radar is not the reason, they say.

Barack Obama is of course among the last ones who could criticize John McCain. For example, one year ago, Obama was loudly planning to call the president of Canada (to screw NAFTA). Even more entertainingly, he has visited 57 states of the United States of America.
That couldn't stop his fans from recording Obamian rhapsody.
A lot has been recently written about McCain's computer illiteracy, too. Well, I guess that both of these things are justifiable, related to McCain's age, and won't pose immediate problems because he should have a lot of staff that compensates for these holes.

But still, one could feel a bit awkward about McCain's reduced ability to learn new things. Reagan was also old but his hair was black. What do you think about these two (and related) manifestations of McCain's incomplete knowledge about the contemporary world?


Phun: physics fun

周六, 2008-07-19 04:06


This is a demo of an amazing program simulating mechanics that was created as a part of a master thesis. You should have it, too!
Phun home page
Phun download (Windows, Linux, Mac)
Phun YouTube group with many videos
Phunbox: sharing phunlets
Engineering hearts should be pleased.

EUR-CZK: Black swan No 23 goes mainstream

周五, 2008-07-18 21:35


The graph above shows a function of time - between July 2007 and July 2008. Yes, it is an almost perfect decreasing linear function that may be predicted to hit zero in 2012. :-) If you look carefully in April 2008, the function includes a negative multiple of the delta function, besides a smooth component. The function suddenly dropped from 25.00 to 23.00 for a few hours (in Asian trading).

The event was labeled a black swan, a very unlikely and hard-to-predict event that sometimes influences the markets. (The name was chosen because black swans were unknown to the Europeans until they saw them in Australia of the 17th century.) It looked so crazy for a smooth quantity to suddenly jump to as unreasonably low a number as 23.



However, black swans may become pretty ordinary. In three months, namely 1 hour ago, the function dropped below 23 without any delta functions involved. Yes, it is an exchange rate - namely the number of Czech crowns per euro. If you think of the euro as a strengthening currency, you should look at the picture above to realize that your conclusion depends on the reference frame.

The euro went from CZK 29 to CZK 23 in one year which is a 20% or 25% drop, depending on what you consider 100%. The most recent 2.5-month drop of the euro from 25.2 to 23.0 is by more than 9%, corresponding to a 40% annual rate.

The dollar's motion has been more brutal. Because my reference frame was almost fully associated with the U.S. dollar until very recently, I can't tell you any details of my collapsing assets if you want to avoid a heart attack. ;-) But yes, I can tell you that USD went from CZK 44.5 sometimes in 2001 to 14.5 today - a decrease nearly by a factor of pi. Yes, it sucks. That's another reason to like the supernatural units where pi=1.

The Czech koruna has been the world's fastest strengthening currency for quite some time and indeed, there are some very good reasons behind this dynamics. The Big Mac index (assuming that McDonald's Big Mac should cost the same money everywhere, when converted by current rates) indicates that CZK is already slightly overpriced relatively to the U.S. dollar but it is still about 30% undervalued relatively to the euro - which is the main counterpart that CZK should be compared with (because it is the main currency exchanged for CZK) - so there is probably still a lot of room to go, especially if the fresh Czech GDP growth continues.

The Czech currency has also become the new ultimate safe haven currency, replacing USD and CHF.

Hendrik Lorentz: 155th birthday

周五, 2008-07-18 16:41
Yesterday, Terence Tao and Henri Poincaré celebrated their birthdays, Congratulations, especially to the former mathematician.

Hendrik Antoon Lorentz, one of the key physicists of the end of the 19th century and the beginning of the 20th century, was born in Arnhem, the Netherlands on July 18th, 1853.

As a kid, his teachers were annoying him with classical languages. However, he was influenced by his astronomy professor, Frederik Kaiser, and became interested in maths and physics soon.

Because of this success, Hendrik later married Kaiser's niece Aletta, i.e. the daughter of the author of the first Dutch postage stamp, Johann Wilhelm Kaiser. Hendrik's and Aletta's daughter, Geertruida Luberta, became the first Dutch female physicist.

His PhD thesis was about the reflection and refraction of light. When he was 24, he became the physics department chair in Leiden. Although he was writing about mechanics, hydrodynamics (numerical calculations about dams and flood control!), thermodynamics, and solid state theory, his most important contributions were concerned with electromagnetism and light.

Lorentz was a widely admired physicist. For example, Einstein wrote the following sentence about him, among others: "For me personally he meant more than all the others I have met on my life's journey."

In 1902, he shared the Nobel prize with Pieter Zeeman for the discovery and theoretical interpretation of the Zeeman effect (the splitting of spectral lines in the magnetic field). That was a rather cheap Nobel prize for Lorentz. The correct explanation clearly requires one to understand the quantized nature of the angular momentum (and magnetic moments) that Lorentz couldn't have understood: it was decades before quantum mechanics.

Today, his classical hand-waving would be "so-so" (grade: E) as a solution to an undergraduate homework problem. In 1902, it was enough for a Nobel prize for this quantum effect and the recipient was a guy who didn't quite accept quantum mechanics until the end of his life. ;-)

There are many things named after Lorentz. One of the things that are not named after Lorentz is the Lorenz gauge - "∂_mu A^mu = 0" - which is named after Denmark's Ludvig Lorenz even though 90% of scientific papers think otherwise. Lorentz and Lorenz together discovered the Lorentz-Lorenz equation for the index of refraction as a function of molar refractivity, pressure, and temperature.

The Lorentz force is the net electromagnetic force exerted upon a charged particle, q (E+v x B), and it was first formulated outside relativity. The Lorentz distribution, associated with the function similar to 1/(1+x^2), describes the reaction of a (damped) physical system to different frequencies near a resonance. Other effects named after Lorentz, such as the Lorentz transformation or the Lorentz contraction, are related to special relativity and I will discuss them in detail.

Lorentz and relativity

Hendrik Lorentz was one of the physicists who were closest to finding special relativity but he was simply unable to crack the "complete big picture" and abandon the absolute character of simultaneity, the most regressive among the classical, pre-relativistic prejudices, even though he was already writing about "local time" as early as in 1895 and 1899.

Lorentz himself believed in "some kind of an aether" but together with Einstein, he was actually the most important physicist who helped the world to get rid of that ludicrous concept. What did he do so important? Well, he wrote "vacuum" Maxwell's equations that only included one electric vector and one magnetic vector at each point (unlike E,D,H,B of the "material" Maxwell's equations) which showed that if the aether existed, it had to be as simple as the vacuum was after 1905. ;-)

This discovery due to Lorentz was arguably the most important "recent" scientific insight that helped Einstein to discover special relativity. Recall that Einstein wasn't actively aware of the Morley-Michelson experiments: the only way to argue that he may have been passively aware of them was that Einstein referred to a paper by Lorentz where the experiments were mentioned.

And indeed, they were mentioned all over the place because Lorentz cared about these experiments a lot. In order to agree with the newest experiments, Lorentz kept on revising his edition of the "aether". For example, its length had to contract as a function of velocity and, following the early suggestions by George Francis FitzGerald, Lorentz was even able to deduce the right Lorentz factor: that's why we can call the effect Lorentz contraction even though Lorentz didn't have a crisp and modern justification of this effect (including the four-dimensional metric, for example).

Lorentz was also able to figure out that Maxwell's equations were invariant under a change of spacetime coordinates, i.e. the Lorentz transformations. Entertainingly enough, we currently use the term Lorentz group even though one of the main things Lorentz was unable to realize was that the coordinate redefinitions generated a group. Also, he couldn't figure out that these redefinitions had anything to do with the inertial reference frames in mechanics as discussed by Galileo - and that two observers in relative motion should be interpreted "democratically". Of course, any of these two realizations could (and did) abruptly lead to special relativity.

Anyway, he kept on adding seemingly bizarre but necessary effects associated with his "progressive aether" in order to avoid contradictions with the new experiments. At the very end, after a finite number of improvements, he had arguably something that was equivalent to special relativity in one particular inertial frame. But he was unable to realize that the theory was also valid in all other reference frames, even though he also knew the required Lorentz transformations that are known to be able to do the job. That also meant that he didn't have the tools to derive many other conclusions of special relativity such as the mass-energy equivalence.

This story may sound confusing and I have certain problems to understand how a leading physicist of Lorentz's caliber could have been unable to put these pieces together. And an even more puzzling fact is that after 1905, Lorentz temporarily became one of the most distinguished skeptics concerning special relativity (see a quote in the first fast comment).

But nevertheless, he was unable to do these things himself and they had to wait for Einstein who fully cracked the puzzle many years after Lorentz's aether musings. My guess is that without Einstein, special relativity would be found in less than one decade after 1905 and there would be a 50% probability that the discoverer would be from the list {Minkowski, Lorentz, Poincaré}.

Einstein chose a better strategy than Lorentz's permanent interaction with the experimenters who are often clever about minor things but intellectually limited about major issues (and who try to impose not only their hard data but also misleading interpretations upon the theorists): just sit down, go carefully through the available knowledge, and write down the correct theory of space and time from the scratch.

With Einstein's fresh mind, his approach turned out to be more successful but if you don't want to rely on such fresh minds around, I would agree that Lorentz's iterative approach was the most sensible strategy people could have followed to comprehend space and time. Still, whenever a physicist seems to be lost in a chaotic pile of seemingly unrelated laws and observations, it's good to try to return to the basics, see what insights are important and well-established, and reformulate them in new ways.

Indiana Jones IV: very good

周四, 2008-07-17 16:43
Last night, we went to a movie theater and saw
Indiana Jones and the Kingdom of the Crystal Skull
and I think it was very good.
Warning: Spoilers are found below.
In fact, I think it was better than some previous parts of Indiana Jones - I wasn't able to finish one of them because it looked boring to me.

Different people enjoy different kinds of movies. Many people like movies that mimic the reality. Well, I, for one, hate socialist realism. I also hate soap operas that are full of average characters who damage the lives of others in hundreds of random and average ways. I don't need to watch a movie to see these things in a movie theater (or TV) again.

Your humble correspondent prefers movies (the typical