Poll about foundations of QM: "experts" disagree on everything

The physics arXiv blog (and, after your humble correspondent, John Preskill) was intrigued by a new preprint by Schlosshauer, Kofler, and Zeilinger:

A Snapshot of Foundational Attitudes Toward Quantum Mechanics

They kind of repeated a 1997 poll organized by Max Tegmark (among 48 participants of a conference at that time) but among 33 participants of a recent quantum-foundations conference.



Off-topic. Greatest snowfall in Jerusalem since 1992. President Peres teaches the Israeli how to keep snowmen from getting cold.

The main result is that there is no consensus on anything. I was actually pleased because I was expecting that there would be a consensus on the wrong answers because that "subdiscipline" of physics is completely screwed; instead, the correct answers were mostly the strongest ones. What did they ask?




Randomness of quantum processes (e.g. decay of nuclei) is:

• 64%: fundamental 
• 48%: irreducible
• 9%: only apparent
• 0%: masking a hidden determinism

The right answers are highlighted by bold fonts. I don't quite understand how "fundamental randomness" may fail to be irreducible – what's the difference – but the difference between the two scores may be due to people's misunderstanding what the subtle word "irreducible" means.

At any rate, in politics, 64% for "fundamental randomness" would be a solid majority.

Do objects have well-defined properties before measurements?

• 52%: yes, in some cases
• 48%: no
• 9%: undecided
• 3%: always

In this case, the right answer has slightly-below-majority of votes. But the "strongest" answer may also be correct – classical properties or properties determined by quantum mechanics to be 100% certain are well-defined before the measurement. Of course, whether you would check "yes, in some cases" as a result depends on what you're ready to include behind "in some cases", namely whether these "some cases" are supposed to differ by the character of the observables or they may depend on the precise values.

At any rate, at least roughly 1/2 of the folks has an idea about this important point which is not too bad.

Einstein's view on quantum mechanics is:

• 64%: wrong
• 12%: will be shown wrong
• 12%: we don't know
• 6%: will be shown right
• 0%: is right

Again, you see a nearly constitutional majority behind the right answer while no one endorsed the "extreme opposite" answer. That looked rather clear. However, what about this one:

Bohr's view on quantum mechanics is:

• 30%: we have to wait
• 27%: wrong
• 21%: correct
• 9%: will be shown right
• 3%: will be shown wrong

The respondents are as split as you can get. I would answer "right" but it's a sufficiently vague question so that other answers seem tolerable to me, too. Bohr's pronouncement often lacked the rigor and accuracy to be completely certain that he meant the right thing. But if I were inclined to vote for a more "neutral" answer, it wouldn't be because we need time to settle the question whether Bohr was right. Time won't help. We already know everything we need to know. What makes the answer a bit fuzzy is that Bohr wasn't always crystal clear. But this won't improve with time.

A similar split appears when it comes to the measurement problem:

• 39%: solved (now or later) in a different way
• 27%: a pseudoproblem
• 27%: none of the above
• 24%: a severe difficulty threatening QM
• 15%: solved by decoherence

The separation of the respondents to groups is almost compatible with their decision to choose the answer randomly! ;-) I've marked two answers as right. Decoherence is an emergent mechanism or calculational framework to determine the boundary between the regimes in which classical physics is a good approximation (but quantum mechanics is still the right underlying description!) and those in which quantum subtleties (especially interference) are important and no classical approximation is acceptable.

But if you don't care where exactly this boundary lies, you may simply assume that the boundary is somewhere. The microscopic world clearly needs the full quantum mechanics; and for some large objects, the classical logic if not physics becomes acceptable. Bohr et al. knew that so they pretty much postulated this dichotomy – one that we may derive more clearly by decoherence today. If you don't care about the location of the boundary and you're OK with the previous answer "no objective reality prior to the measurement", I think that you must conclude that the measurement problem is a pseudoproblem.

What is the message of the violation of Bell's inequalities?

• 64%: local realism is untenable
• 52%: unperformed experiments have no results
• 36%: some notion of nonlocality
• 12%: action at a distance in the physical world
• 6%: let's not jump the gun, take loopholes seriously

It's true that unperformed experiments have no results and it is a part of the explanation why Bell's inequalities are violated in Nature but it is less accurate a description of the reason than the simple and accurate "local realism is untenable" (which was chosen by a large majority). Too bad that "realism" without adjectives apparently wasn't asked about.

Quantum information is:

• 76%: fresh air in quantum foundations
• 27%: we need to wait
• 6%: useful for applications but of no relevance to foundations
• 6%: neither useful nor relevant

This was a close call but I picked that they're useful for applications but of no relevance for foundations. Indeed, (hypothetical) quantum computers only utilize the laws of physics and mechanisms that are well-known from non-computer research of quantum physics. As their functionality depends on the conventional laws of quantum mechanics, they can't be a game-changer.

The answer "fresh air" could also be fine in the sense that the quantum-foundation people may be stuck with rubbish and crackpot non-quantum theories trying to "explain" quantum mechanics – so if they do something that isn't wrong, e.g. quantum algorithms, it's a breath of fresh air. But I am not sure whether this was what was meant by the "fresh air".

We must also wait and see to decide whether they will be constructed and whether it will be soon etc. If something will stop us for a very long time, we could also say that they're not "useful". So all answers have some potential to be OK. Much of it depends on the next question:

When will we have a working and useful quantum computer?

• 9%: within 10 years
• 42%: 10-25 years
• 30%: 25-50 years
• 0%: 50-100 years
• 15%: never

I chose no answer because without a crystal ball and tarot cards, I have no clue. It's conceivable that a gadget of this sort will be ready in 3 years. It may also take 80 or 800 years or people may lose it and never construct one. I am of course convinced that quantum computers are possible in principle and the improvement in the coherence and precision of the components that we need isn't "exponentially severe".

Some unusual complaints against the quantum computation were recently discussed by Scott Aaronson: response to Dyakonov, Zork's blogorhythm

Right interpretation of state vectors:

• 27%: epistemic/informational
• 24%: ontic
• 33%: a mix of epistemic and ontic
• 3%: purely statistical as in ensemble interpretation
• 12%: other

You see that the respondents were split once again but it's partly due to the fact that the answers are vaguely defined and not quite mutually exclusive.

I believe that all the people who answer "ontic" really mean that the wave function is conceptually a set of classical degrees of freedom. That's why this answer is just wrong. All other answers may be partly OK. Epistemic/informational is OK as a "negation" of the wrong "ontic" answer". However, "epistemic" could also lead one to believe that there exist other hidden variables not included in the wave function – i.e. that the wave function is an incomplete description. That's wrong as well. The wave function isn't "ontic" in the classical sense but it's as complete – and, in this sense, as close to "ontic" – as you can get. So you could vote for some "mix" or for "other" which means that you're not quite satisfied with any answer that was given.

I chose not to label the "ensemble interpretation" as correct because the ensemble interpretation makes the claim that only the statistics of the huge repetition of the very same experiment may be predicted by quantum mechanics. This is a very "restricted" or "modest" claim about the powers of quantum mechanics and this modesty is actually wrong. Even if I make 1 million completely different experiments, quantum physics may predict things with a great accuracy.

Imagine that you have 1 million different unstable nuclei (OK, I know that there are not this many isotopes: think about molecules if it's a problem for you) with the lifetime of 10 seconds (for each of them). You observe them for 1 second. Quantum mechanics predicts that 905,000 plus minus 1,000 or so nuclei will remain undecayed (it's not exactly 900,000 because the decrease is exponential, not linear). The relatively small error margin is possible despite the fact that no pair of the nuclei consisted of the same species!

So it's just wrong to say that you need to repeat exactly the same experiment many times. If you want to construct a "nearly certain" proposition – e.g. the proposition that the number of undecayed nuclei in the experiment above is between 900,000 and 910,000 – you may combine the probabilistically known propositions in many creative ways. That's why one shouldn't reduce the probabilistic knowledge just to some particular non-probabilistic one. You could think it's a "safe thing to do". However, you implicitly make statements that quantum mechanics can't achieve certain things – even though it can.

The observer is:

• 39%: a complex quantum system
• 21%: should play no fundamental role whatsoever
• 55%: plays a fundamental role in the application of the formalism but plays no distinguished physical role
• 6%: plays a distinct physical role (soul collapses wave function...)

I think that the first three answers are kind of correct. An observer is certainly just another complex physical system. It's pretty shocking that a majority of the participants of a quantum-foundations conference tries to deny this self-evident fact. Well, some of them may do so because they love some vitalist or spiritist approach similar to the "collapse of waves by the souls".

While the observer is clearly just another complex physical system and plays no distinguished physical role (so the third answer is also OK), it may play a role in the application of the formalism. However, in synergy e.g. with the consistent-histories approach, we may attribute the "subjective choices" to the consistent histories themselves (a framework listing the questions) rather than the observer as an object. For this reason, it looks legitimate to me if someone says that the observer plays no fundamental role whatsoever.

The denial of the "complex quantum system" by 61% of the participants is the most shocking feature of the answers here.

Reconstruction of quantum theory:

• 15%: gives useful insights and has/will supersede the interpretation program
• 45%: gives useful insights but we still need an interpretation
• 30%: cannot solve the quantum foundations
• 27%: will lead to a deeper theory than QM
• 12%: don't know

Reconstruction of quantum theory is a new minor fad that doesn't make any sense. While we may agree with its spirit – similar to "shut up"; "interpretation of quantum mechanics" is a problematic term by itself – everything else it says is some philosophical flapdoodle. The reconstruction program mainly asks "why is it true?" and it always answers "because we derived it". So far so good. But it never cares too much about what we have actually derived! ;-) The degree of support from the participants for this bogus wisdom is stunning. Incidentally, Zeilinger et al. say the same thing.

I also think that the very hypothetical strategy of "reconstruction" is a misunderstanding of the scientific method in general. The right wisdom about Nature can't be directly "reconstructed" by any well-defined procedure. In science, one has to formulate hypotheses at the beginning, and then test them. The "guesswork" (which can't be mechanical) is a necessary part of the process; the creativity and ingenuity of the physicists matters exactly because the "guesswork" matters. This is related to various logical arrows: the evolution of the Universe is a consequence of the laws of physics, not vice versa, so to determine the laws of physics from the observations of the evolution is an "inverse problem" that simply can't have a straightforward solution. It has to be "inferred" by Bayesian inference. That's why the answers always depend on some priors, too, although the dependence may become weak enough once a sufficient amount of evidence is collected and processed.

Favorite interpretation:

• 0%: consistent histories
• 42%: Copenhagen
• 0%: de Broglie-Bohm pilot wave
• 18%: Everett many worlds/minds
• 24%: information-based
• 0%: modal
• 9%: objective collapse, GRW or Penrose
• 6%: quantum Bayesianism
• 6%: relational quantum mechanics
• 0%: ensemble interpretation
• 0%: transactional interpretation
• 12%: other
• 12%: no preferred one

The most correct interpretation, consistent histories, was picked by 0 percent of the participants. What a pack of assholes, politely speaking. ;-) Thank God, at least Copenhagen was picked by respectable 42% (beating many worlds: so Tegmark's claims about the "dominance" of MWI in similar circles have been superseded) and many of the totally silly answers were at 0% or near 0%, too.

How often have you switched interpretation?

• 33%: never
• 21%: once
• 21%: several times
• 21%: no preferred interpretation

I didn't highlight any right answer because this isn't an objective question. It's a question about the events in different individuals' lives. I haven't switched the interpretation in a real sense. At some moment, I didn't quite understand everything so I didn't "claim" anything. Since the times I have an opinion, it's the same opinion.

Does the choice of interpretation depend on philosophical prejudices?

• 58%: a lot
• 27%: a little
• 15%: not at all

Of course, it's mostly about philosophical prejudices. Especially for the believers in the wrong interpretations, it's a matter of quasireligious beliefs they're just not ready to abandon. Zeilinger also say that the influence of the prejudices isn't necessarily a reflection of physicists' being dogmatic; it's due to the absence of experiments that clearly distinguish the different approaches. Maybe. I am not so sure about it because most of the wrong attitudes to QM are quite explicitly incompatible with some experiments or they at least prevent one from writing a theory, a set of rules, that may explain all of them in a unified way.

Superpositions of macro- different states are:

• 67%: possible in principle
• 36%: will eventually be realized
• 12%: in principle impossible
• 6%: impossible because of collapse theory

It's of course possible in principle – linearity is a universal postulate of QM that applies to any states, any objects. For some "small macroscopic" things, it's been realized but the degrees of freedom that are in superposition are very restricted even though they may be delocalized in a material. For completely general and "warm" objects, the superpositions will never be realized in practice. The "collapse theory" (they probably mean GRW/Penrose) is wrong.

In 50 years, conferences on quantum foundations:

• 48%: will still be organized
• 15%: probably no
• 24%: who knows
• 12%: I organize one no matter what

Crystal balls again... It's plausible that all the participants will already be dead so even the last answer may be wrong. They may also change their mind. ;-) I have no problem with such conferences to take place or not to take place. What I have a problem with are the idiotic answers that many of the self-described "experts" offer to many elementary questions. Will it still be so bad – or worse – in 50 years?

The authors also discuss some correlations between the answers, probably kind of obvious ones... TRF readers voted overwhelmingly "NO", just like I did.

Read More

Gustáv Husák: 100 years

Today, the last communist president of Czechoslovakia and Slovak communist Gustáv Husák would celebrate his 100th birthday. When I was a kid, this birthday – January 10th, 1913 – would be the most frequently celebrated one. It would be written down in all the calenders, too.



Click the image for various pictures of Husák. YouTube offers tons of videos. New Year Address in which he said the year was 1895 so they returned the clock by 5 minutes and started again. Various parodies in which Husák says jokes, and so on. It's easy to find his pictures and videos with all the fellow communist leaders, with Gaddaffi, and lots of characters of this sort.

I want to shock you with the size of this image so that you appreciate how omnipresent this image has been during the first 10 years I spent at schools. I am pretty sure that Husák has spent more time in front of my eyes than any of my parents. ;-)




He was born as "Augustin" to a working-class family in Pozsonyhidegkút (Kingdom of Hungary) near Pressburg (today, Dúbravka, as the P-word is called in Slovak today, is a part of Pressburg and Pressburg is known as Bratislava; incidentally, I live in Doubravka in Pilsen, it's a word for a forest) and became involved with the local communist party rather soon. During the Second World War, he was already one of the main organizers of the Slovak National Uprising (1944) against the Slovak clerofascist state.

After the war, he would already hold lots of important communist jobs. That's why I find it really bizarre that during Stalinist purges in 1950, he was sentenced to a life in prison as a supporter of "nationalist bourgeoisie". His six years in the Leopoldov prison were pretty tough but he didn't have any bad feelings. It was just some misunderstanding, he repeatedly stressed.

Needless to say, I agree with him that it was a misunderstanding. He was a kind of a hardcore communists that communists had no reason to arrest. Still, I find it amazing if someone is terrorized by his fellow demagogues for 6 years in a harsh prison and he still can't figure out what disgraceful assholes all these people (including himself) are. ;-)

In 1968, he was alarmed by the pro-freedom "socialism with a human face" organized by another Slovak guy, Alexander Dubček (the boss of the communist party during the Prague Spring), and others. So it's unsurprising that Husák was picked as the new general secretary of the communist party after the Soviet-led 1968 occupation (since 1971) and replaced the ill Czech war hero Ludvík Svoboda as the president (in 1975).

Throughout my childhood, he was the symbol of the new Stalinism and our "friendship with the Soviet Union", too. Nevertheless, later I found out that he wasn't really one of the most hardcore commies, one of those who invited the Soviet troops to "help us in a friendly way", and his own record indicates that he had some character.

In fact, people born in the 1970s including your humble correspondent are known as Husák Children (our Generation X, roughly speaking). Pro-population-growth policies (including various special gifts for birth, and so on) have been invented since the 1960s but they waited for Husák's tenure to be realized. The people born in 1974 (de facto my year, if you ignore one month that I was ahead by) are the strongest class in the demographic composition of Czechia and Slovakia.

Husák wouldn't be the guy who would be heard as saying tough totalitarian proclamations and nasty things about the dissidents such as Havel. This job was done by others – including Husák's successor at the helm of the communist party (since 1997), the funny Milouš Jakeš. Nevertheless, it's clear that Husák couldn't have been innocent. He must have received tons of requests to give pardons for various political prisoners but he has never done so.

Husák was also replaced by Havel as the Czechoslovak president at the end of 1989. It had to be humiliating him because due to various kinds of pressures, it was actually a mostly communist Parliament that still managed to elect Havel (a guy who was in jail just 2 months earlier) as the new president. The vote was actually unanimous. ;-) I am sure that the pro-democratic Civic Forum (OF) movement had to harass the communist deputies rather intensely. A Slovak historian claimed today that Husák actually lobbied for Havel to be elected – he hated Dubček much more. A non-socialism was more acceptable for him than the return to the socialism with a human face.

He died forgotten in 1991.

To summarize, Husák has been a key symbol of the occupation and all the bad communist things in Czechoslovakia during the last 2 decades of communism. Nevertheless, his "bad character" image was probably less black-and-white than what you could expect from similar Stalin-like leading figures of an authoritarian regime.

Read More

RSS AMSU: 2012 was 11th warmest year

Focus moved to the contiguous U.S. states: new warm record

As the preliminary data published two months ago indicated, the satellite temperature record RSS AMSU has indeed concluded that the year 2012 was the 11th warmest year on their 34-year-long record, rather close to the median.



That's not a good starting point for a hype about global warming – something that hasn't been seen for 15+ years at this point – so the climate fearmongers use a different strategy. Before I get to that strategy, let me post the complete table of the RSS AMSU years.





The ranking looks like this:

1. {1998, 0.549},
2. {2010, 0.475},
3. {2005, 0.33},
4. {2003, 0.321},
5. {2002, 0.314},
6. {2007, 0.258},
7. {2001, 0.247},
8. {2006, 0.23},
9. {2009, 0.225},
10. {2004, 0.203},
11. {2012, 0.192},  [LAST YEAR]
12. {1995, 0.158},
13. {2011, 0.147},
14. {1999, 0.103},
15. {1997, 0.103},
16. {1987, 0.098},
17. {2000, 0.092},
18. {1991, 0.081},
19. {1990, 0.075},
20. {1988, 0.067},
21. {1983, 0.066},
22. {2008, 0.049},
23. {1996, 0.046},
24. {1994, 0.029},
25. {1981, 0.021},
26. {1980, 0.015},
27. {1979, -0.094},
28. {1993, -0.117},
29. {1989, -0.119},
30. {1986, -0.139},
31. {1982, -0.173},
32. {1992, -0.179},
33. {1984, -0.224},
34. {1985, -0.261}.

According to their satellite competitors/friends at UAH AMSU, John Christy, Roy Spencer, and others, 2012 was the 9th warmest year. If you know the final figures from the weather stations – HadCRUT3,4, GISS etc. – let me know. Update: For NOAA, 2012 was 10th, 0.57 °C above average.

Because the global mean temperature in 2012 (and most of the previous years) looked so unspectacular, the media focused on a different quantity. See this example at CBS (via Gene):

2012 was warmest year in U.S. on record

For years, the same people would be telling us that you should never look at America only which is only 1.6% of the globe, or only on Europe. All the inconvenient data from the regions (such as the warm 1930s in the U.S.) are just regional flukes. But when the global flukes refuse to collaborate, even regional flukes may be helpful.



Picture from NASA, 1999. Counting the whole U.S. territory, the year 1998 seemed 4th warmest, after 3 dust bowl era years.

The CBS writers quote some weather events, suggesting that they were unprecedented – they were surely not – but the number that is supposed to be well-defined and solid is that the lower 48 states of the U.S. saw the warmest year for 2012. The average was 55.3 °F i.e. 12.9 °C. Incidentally, it's pretty cold! Ten Fahrenheit degrees of extra warming would surely be helpful for the U.S. I will assume that these statements and numbers are right although I can't verify them by any algorithm that could be called independent.

Moreover, the previous 1998 record was beaten by one degree. (Recall that the hegemony of the "sort of recent" year 1998 in the U.S. temperature record was itself a result of suspicious a posteriori adjustments; chances are high that the year 1934 was warmer. Thanks to MM for reminding me.) The strange units used in the U.S. make this edge twice more spectacular than it is. They really mean by 0.55 °C.

Now, if your record is approximately 110 years long, even if the temperature were white noise (each year independent of the previous ones), and it is not, the probability of a new record would be 1/110 per year. If you admit that the noise is "somewhat red" i.e. temperatures tend to be a bit more continuous and they have inertia, the probability per year is much higher, up to 1/2 in models with a huge inertia (which doesn't have to have anything to do with humans!).

It is very unlikely to beat the previous record for the region as large as the 48 U.S. states by 0.55 °C on a given year. Because this temperature difference is close to one sigma (well, depending on your model of the noise), it's a jump by a "whole category" which is rare and should become even rarer.

On the other hand, if you realize that we have waited for 14 years for this new record and there were many (\(N\)) other regions aside from the lower 48 states of the U.S. that could make a similarly catchy story on CBS or elsewhere, you will realize that the relevant probability of the truly interesting statement – namely that "data anywhere in the world on any year give a justification to write a similar story" – is actually approximately \(14N\cdot p_0\) where \(p_0\) was the probability for a single year and the lower states only. This multiplication (which has to be reduced once the probability approaches one!) is known as the look-elsewhere effect.

With the look-elsewhere correction included, you will conclude that it is unspectacular that such a record was finally found somewhere after 14 years: the overall probability isn't far from numbers of order one, if you allow me a bit vague. I have to be vague. This probability can't really be canonically calculated because it depends on your model of what the temperatures are going.

In the jargon of particle physics, the report about the warm 2012 in the U.S. is just another piece of hype about "roughly two-sigma bumps" in some graphs. But you know, if there really were a global warming that would start to matter in some near future, it should be comparably easy to find a five-sigma evidence of some CO2-induced changes or at least "clearly unprecedented changes" with an unknown driver. To increase a 2-sigma bump to a 5-sigma bump (the latter is enough to claim a "discovery" in particle physics, with risks of a false positive comparable to 1 in 3 million), you only need to multiply your dataset by a factor of six. Because there should be lots of data out there, it should mean just to look a bit more carefully and accurately.

But no such genuine evidence exists. What the journalists – and, sadly, some self-described climate scientists – keep on doing is to play with the emotions behind "two-sigma bumps" or, equivalently, small signals from God or Nature that may be combined to see God of global warming out there. Well, I, for one, can't combine them because it's not there.

Look at other regions such as Europe or Asia or Australia or... even the notorious Arctic... and you will see that 2012 wasn't spectacular as far as its temperature went.

Read More

Nonsensical hype on negative temperatures

Off-topic cinema: I've seen my first 3D movie in a cinema today, The Life of Pi about a sensitive Indian teenager whose family moves to Canada with the whole zoo but the boy (believer in all the world's major religions) is the only one who survives on a boat, together with their tiger named Richard Parker. Top Russian actor Gérard Depardieu of Saransk starred as a racist cook on the ship. :-) It turned out that the glasses were some kind of color anaglyphs. The question how it's possible that I can see all RGB channels in both eyes despite the filters replaced my analogous question for circular polarization glasses. ;-)

Fox News and tons of other sources proudly announced that physicists in Munich have finally realized temperatures colder than the absolute zero, –273.15 °C. Their article has ignited a storm in the Jan 4th issue of Science.



When you combine objects with people or worlds that are upside down, like in this 2012 Canadian-French romantic movie "Upside Down" about the love between Adam and Eve from two co-existing worlds, things may get confusing or, more often, downright inconsistent. One has to be careful. ;-)

Needless to say, I completely agree with David Berenstein:

Bad science reporting versus good science reporting

David picked Ars Technica as his example of the most acceptable reporting about this story.

What's going on?




First, we must ask: What does it mean to have a well-defined temperature \(T\) in kelvins (which we call the "absolute temperature")? Recall that the temperature \(t\) in Celsius degrees is linked to the absolute temperature \(T\) by an additive shift,\[

T = t+273.15 \,{\rm K}, \quad t=T-273.15\,{}^\circ {\rm C}

\] As a unit of the temperature difference, one kelvin and one Celsius degree are the same thing.

Roughly speaking, having a well-defined temperature means that the system carries the energy \(kT/2\) per degree of freedom (e.g. a coordinate of a spherically symmetric atom). Because one can't just "count" the relevant degrees of freedom in the most general situation (they're picked from an infinite bath of candidates but one should only pick those that have a chance to be excited, e.g. those with \(kT\geq \hbar \omega\), and things get hard when the formula for the energy is highly non-linear), we need a better, more universal definition.

The most universal definition of temperature is due to Boltzmann. The system has temperature \(T\) if the probability of the arrangement (microstate) \(n\) of the physical system is given by\[

p_n = C \cdot \exp\zav{ -\frac{E_n}{kT} }.

\] Here, and I should have already told you, \(k=1.38\times 10^{-23}\,{\rm J/K}\) is the Boltzmann constant. The coefficient \(C\) must be independent of \(n\) and it is chosen so that the total probability of all microstates is \[

\sum_n p_n = 1.

\] You see that if you have some temperature, the probability of states with a higher energy (imagine the kinetic energy of molecules of gas) exponentially decreases with the energy. The lower temperature \(T\) you have, the larger \(\beta\equiv 1/kT\) is, and the faster the decrease with the energy \(\sim \exp(-\beta E_n)\) is. In the extreme limit \(T=0\), the probabilities decrease "exponentially quickly" with the energy of the state which means that only the state with the lowest possible energy, the ground state, is allowed with the probability \(p_0=1\) (certainty).

Now, the condition \(\sum_n p_n=1\) may be easily satisfied – without encountering a divergence in the sum – because the number of available states isn't increasing exponentially with the energy so the exponential suppression cures any conceivable divergence for high energies. For low energies where the exponential is exponentially growing, we're saved by the fact that the energy is bounded from below. There exist no states with \(E\lt E_0\). For a fundamental enough theory (that can produce particles etc.) such as quantum field theory or string theory, \(E_0\) is the energy of the vacuum. There can't be any states whose energy is lower than the energy of the vacuum.

Things change if the temperature is negative. In that case, \(\exp(-\beta E)\) is exponentially increasing with \(E\) because \(-\beta\gt 0\) now. If there are states with arbitrarily high energies \(E_n\), it's clear that the sum of \(\exp(-\beta E_n)\) will diverge: the terms that you add are growing larger with \(E_n\) and arbitrarily large terms exist.

So the negative temperatures can't exist for a sufficiently general system. The condition that the "total probability of all alternatives equals one" can't be satisfied because the sum of the exponentially increasing probabilities inevitably diverges. It just can't be one.

However, one may find "negative temperature configurations", \(T\lt 0\), in restricted systems that effectively only have states for which the energy is bounded from below as well as from above. In that case (in which you have to manually prohibit changes to almost all the degrees of freedom and only allow e.g. one electron per atom to be excited or unexcited), the sum is convergent – in most cases, it's a sum of a finite number of terms, after all. There's still something interesting about the probabilities\[

p_n = C \cdot \exp\zav{ -\frac{E_n}{kT} }

\] if \(kT\lt 0\): these probabilities actually increase with \(E_n\). In other words, it's more likely that the physical system will be found in a state with a higher energy than it is that it will be found in a state with a lower energy. Well-behaved physical systems have positive temperature and they try to "save energy". They don't try to donate a gas molecule too much energy, for example. However, systems with negative energy exhibit the so-called population inversion. Much like the governments, they simply love to waste money (I mean energy). The more they can waste, the more likely it is that they will. ;-)

Now, it's been known for quite some time that lasers and masers are examples of population inversion. The materials that are expected to emit the nice laser light (or maser radiation) have to be brought to the state in which the excited atoms are more numerous than the unexcited ones. That's why they're ready to emit lots light quanta (and almost no one can absorb them) and why you ultimately get the coherent laser/maser light (you must understand the Bose-Einstein statistics for photons, too).

These negative-temperature materials can't be brought into thermal equilibrium with a general enough system because for a general enough system, the partition sum doesn't converge at negative temperatures because there are states with arbitrarily high energies, as I have mentioned. Instead, what happens to these negative-temperature systems when they're in touch with ordinary positive-temperature matter is described in textbooks on lasers, including the Wikipedia article above.

The lasers and masers have been known for quite some time – and awarded by a Nobel prize 49 years ago – so they're not new inventions. The realization that the population inversion indicates a negative absolute temperature has been known pretty much since the beginning, too. (For technical reasons, the negative temperature was first measured in masers, not lasers.)

So whatever the folks in Munich discovered, it is not a new and revolutionary breakthrough that brings us below the absolute zero for the first time. What they did was some incremental research of phenomena that may be described by the problematic yet catchy term "negative temperatures" but it's simply wrong if this "sexy X factor" is being overhyped in this revolutionary way. Their work simply isn't revolutionary. It is about "just another system" – the Bose Hubbard model – where the population inversion was achieved for new effective degrees of freedom, some motional ones (the momentum is effectively bounded/periodic because the model is defined on a lattice; that's why the negative-temperature construction isn't spoiled by an unlimited kinetic energy). But the thermodynamic essence isn't really different than in the case of lasers and masers.

(Needless to say, this overhyping of catchy terms is being done in many disciplines and I would say that high-energy physics is no exception. The laymen – including most of the sponsors – just can't follow the actual contemporary research so this research is being constantly justified by catchwords that have already existed for 50 years. But for some reasons, these concepts are still being claimed to be hot and new and exciting.)

While the possibility to obtain negative-temperature systems is, with all the necessary disclaimers, demonstrably real, the speculations that the negative-temperature systems are relevant as a description of dark energy is insanely speculative and, as far as I can say, it is wrong and won't be accepted by competent physicists.

To summarize, these stories combine some wrong speculative research about dark energy with "apparent oxymorons" that can be partly realized in practice but that have been realized for half a century so they shouldn't be described with these sensational "new and revolutionary labels". As far as I know, Ars Technica is the only source whose reporting of this story is tolerable – I am still not quite satisfied with it – and everyone else has failed miserably. If you realize that the reporting of this research has pretty much nothing to do with the truth and out of 3 fundamental mistakes about the interpretations, almost all the media pick all 3, you should feel at least as frustrated about the quality of the science-focused inkspillers as I do.

And that's the memo.

Read More

Dine-Haber symposium in Santa Cruz

Between Friday and Sunday, particle physicists organized a spectacular symposium in Santa Cruz to celebrate the 60th birthdays of Michael Dine (left) and Howard Haber (right).



The website of the symposium shows that the program was impressive and included speakers such as Gross, Seiberg, Witten, Arkani-Hamed, Kane, Susskind, Allanach, Grossman, and others.




I spent the first half of the year 2000 in this department inside the UCSC campus – with lots of redwoods around – so I know these two great physicists.



Santa Cruz Sentinel wrote a few words about the event.

Congratulations to Michael and Howard!

Read More

Irrational hysteria about Klaus' amnesty

At the end of his last New Year address as the Czech president, Václav Klaus offered a "shocker" and declared a partial amnesty that has freed about 1/3 of the prisoners. A wave of hysterical criticism has emerged and it is still strengthening. I conjecture that the passionate critics (a group that unfortunately includes almost all people around me who care one way or another; and among the famous people, only the Archbishop of Prague, ex-boss of National Gallery Knížák, several Klaus' aides, and your humble correspondent have defended the decision) don't have a clue about the background – for example, they don't have a clue about most of the facts below. They don't understand why amnesties exist at all.



One of the legal traditions in the Czech lands that have survived since the feudal era is the president's right to declare amnesty and to release prisoners. Amnesties are acts by which the king and/or the emperor could have shown his or her mercy and magnanimity – and the job of the Czech president emulates the emperor in various formal and informal ways and amnesty is one of them. Franz Joseph I of Austria declared the most famous general amnesty in 1857 (as famous one as Napoleon's 1815 amnesty and a few others).

During the imperial era, amnesties repeatedly took place and they had consequences that were not negligible at all. For example, on January 5th, 1917, almost exactly 95 years ago, Charles I of Austria, our last "kaiser" and the last Czech king, declared an amnesty that have changed the lives of many people. Amnesties were never vacuous formalities.



The Bory prison in Pilsen is famous – and quite a good piece of architecture, I would say. The first inmates moved in in 1878.

Among them were Mr Karel Kramář who would become Czechoslovakia's first prime minister on the following year, 1918, and Dr Alois Rašín, our coming first ingenious finance minister (also from 1918) who managed to organize the currency split and other key procedures, almost by himself. They had received nothing less than death penalties.

Just to be sure, Kramář and Rašín were convicted for spying and high treason. They would organize various pan-Slavic conferences and similar things. The death penalties were first reduced to 20 years before they were released altogether. For Rašín, the 1916 death penalty (also for his activities in the Czech independence movement during the First World War, "Maffie", which had about 200 members) wasn't his first contact with prisons and punishments. In 1894, as a politically active student of law (and a fresh holder of the degree), he received 2 years for his work for "Omladina" and the related Czech Young Party. He was jailed here in Pilsen (Bory) but was released during the 1895 amnesty.




Amnesties continued when Czechoslovakia was created. This institute played a special role during communism, too. And be sure that it has affected the lives of the most powerful folks including future communist presidents, too. For example, a young Slovak communist named Dr Gustáv Husák was sentenced (by his fellow but not friendly communists) for spying and high treason in a 1954 process with "burgeois nationalists" running since the early 1950s. He was arguably the most defiant "felon" so a death penalty was rather likely instead of the life in prison he had finally gotten. He may have been lucky that both Stalin and Gottwald died in 1953, shortly before the verdict, so the latter was softened.

Husák was freed by the comprehensive 1960 amnesty by communist president Mr Antonín Novotný. In 1963, he was fully rehabilitated. Ironically enough, he would become the boss of the communist party in 1969, a year after the "not too nationalist" Soviet occupation, and the president of Czechoslovakia since 1975. He kept this job until the 1989 Velvet Revolution so Czechoslovakia spent the last 25 years under a president who would be jailed for the whole life (or executed) if amnesties didn't exist much like it has spent the first decade or two with prime ministers and finance ministers whose death penalty was canceled by an earlier amnesty.

Needless to say, on December 29th, 1989 (I remember the day very well), he was replaced by another chap, Mr Václav Havel, who had been jailed just two months earlier (most often, Havel was arrested here in Pilsen-Bory, too; at some point, he was arrested – and playing chess – here together with the current Archbishop of Prague Dominik Duka whom I mentioned as a Klaus defender at the top). Of course, his own sentences were rather quickly canceled, together with those of other political prisoners.

Just a week later, in early January 1990, Havel made one of his first political decisions as the Czechoslovak president. We've talked about all these amnesties and their impact on the Czechoslovak presidents and you could already be bored by this stuff. You may guess what was Havel's first major decision. Yes, it was a major amnesty again. ;-)

About 1/2 of the 30,000+ Czechoslovak prisoners as of early 1990 were freed! Be sure that those extra 15,000 or so criminals that could suddenly run on the street did make some difference (these 15,000 people were only responsible for 9% of the crime in 1990). Some of them returned to the prison soon; most of them didn't. Havel was criticized by various people. But the gesture has improved the life of many people who sort of deserved it, too.

What I need to emphasize is that a vast majority of the prisoners who were released during various amnesties had been arrested for various "economic crimes". Of course that the political prisoners (but even the murderers etc.) were rather rare – they are just the most interesting tip of an iceberg to write about. But of course that most prisoners serve their time for some "more ordinary" crimes.

Czechoslovakia split exactly 20 years ago, in January 1993, and Havel quickly became the Czech president. During the ten years of his tenure as a Czech president, 1993-2003, Havel granted about 2,000 individual pardons (not to speak about two later amnesties which were negligible relatively to that of 1990: only hundreds of prisoners). Klaus hadn't liked this excessive activity too much and you may see this fact in the numbers, too. Klaus has only granted about 400 pardons during his 10 years. Quite a difference.

Klaus would never declare an amnesty but he always kept this option open, suggesting that an amnesty could take place at the end of his tenure. And that's what we're seeing these days. The amnesty was officially a celebration of the 20th anniversary of the separate Czech Republic (I don't claim that most Czechs would celebrate that we "lost" Slovakia in 1993).

Klaus' amnesty has freed about 7,000 people, between 1/3 and 1/4 of the 25,000- prisoners as of early 2013. So the prisons won't be this overcrowded. The amnesty also saved some people from "forced work" – let's say 20,000 folks won't have to clean the sidewalks. Some celebrities whose struggles with the law are always covered by media – e.g. the Slovak/Czech singer Dara Rolins, a perpetrator of a bad fatal car accident – were freed, too. Some trials were canceled, especially those that take more than 8 years or something like that. I think it's sensible because these super-slow trials cease to be about justice, the memory of the relevant folks is decaying so an accurate judgement is getting less likely. Also, lots of innocent people may be harassed by courts for 8 years which is just bad. Moreover, all such super-slow trials are symptoms as well as partial causes of the inefficiency of our judicial system. (We've been criticized for these "infinite trials" by the European Court of Justice, too.)

Klaus' rules identifying who is freed are very general. A condition is defined on a few general quantities such as the date of the verdict, the total sentence, and a few others. It was his very goal to describe the amnesty "macroscopically" and to avoid intrusion into special and individual cases – Klaus insists he hasn't studied any and hasn't thought about any.

Nevertheless, we see tons of speculations whom Klaus may have wanted to help. I am tired of it because there's no credible evidence – there's even no suggestive evidence of anything like that. People spreading these speculations only show that they are malicious and they have negative prejudices about Klaus (or all politicians?).

There is this special focus of the critics on the economic crime and "big corruption scandals", something they would never forgive (we hear). First of all, I don't think that the perpetrators of "economic crimes" in the most inclusive sense represent the most dangerous or most distasteful group of prisoners. Second of all, the linking of the amnesty to "big corruption scandals" is preposterous because the perpetrators of "big corruption crimes" were sentenced to so long sentences in prison that they're clearly omitted from the amnesty.

I am extremely far from believing that it's a "good thing" for every prisoner who was released that he or she was released. We're talking about 7,000, quite a large group of folks. It's likely that the number of folks for which I would say that the overall sign is "plus" is comparably large to the group of those for which I would say that it is "minus". The victims of some crimes whose culprits were just freed – and whose prosecution may have been stopped altogether – may be angry and they may suffer (usually financially).

But I see no reason to be sure about the overall negative sign of the whole event.

The amnesty has unquestionably been one thing: a somewhat surprising event. I think that it's a good thing. For amnesties to be sufficiently unpredictable (so that criminals can't plan the timing of their crimes), amnesties have to be somewhat surprising, uncertain, and their extent must be unknown in advance, of course. All these basic conditions were satisfied. If you agree that it's the right thing, much of the "excitement" comes from the "surprise factor". But I think it's just bad if someone hysterically reacts to any surprise.

I just don't understand any of the "big picture" criticisms of this amnesty. They don't make any sense to me whatsoever. It's good that Klaus hasn't tried to cherry-pick the crimes. And he has the right to grant pardons and declare amnesties. In fact, about 2/3 of Czechs in recent polls claimed that they want to preserve the president's right to declare amnesties. So the people who ultimately admit that they criticize the institute of amnesties itself really belong to a loud minority.

One may claim – and one is allowed to say – that amnesties are an obsolete institute that doesn't belong to a modern state. Fine. Think whatever you want. But the reality is that they're still a part of our laws and traditions. We have various traces of the feudal era and at least some of them make our nation's life better, at least sometimes.

Also, quite generally, I think that the critics don't understand the "division of labor and responsibilities". It's really none of their business. There are certain decisions that are made or may be made by the government; other decisions that may be made by the president. It's clear that when it comes to any decision, e.g. a decision by the president, you may find people who would disagree with that decision. They wouldn't decide in this way if they were the president themselves. But the matter of fact is that they are not the president. They were not able to win the relevant election etc. So why don't they just get used to the idea that it's up to someone else to decide about similar things?

The right to declare amnesties is really a "business as usual" part of our judicial and constitutional system – and one that has saved the lives of numerous future leaders of our nation in the past, as I have mentioned. So it's nonsensical to suggest that Klaus violated the law or morality by declaring an amnesty. It is exactly as nonsensical as if you say that a baker is a jerk or criminal because he bakes bread in his bakery. Bakers usually produce more than 1 bread per 10 years but that's just a quantitative difference – one that shows that the presidents' job operates with longer timescales than the bakers' job.

Needless to say, this anti-amnesty hysteria isn't an isolated phenomenon. It is a part of the "bad mood" and "anti-politicians bias" that started to spread in our society once again (if it has ever been suppressed at all). Quite generally, I think that all these moods are powered by demagogues and Hitler wannabes; they are intrinsically nothing else than an anti-democratic propaganda. All these opinions that politicians are morally worse people than the "good ordinary people" are just piles of rubbish, an artifact of decades of populism that flattered the "ordinary people" with many kinds of lies. A huge fraction of "ordinary people" just sucks. They are assholes, criminals, liars, hypocrites, but this very proposition has become politically incorrect because one is supposed to pretend that being "ordinary" means the same thing as being Jesus Christ (minus all His own defects, but let me omit the discussion about those).

But it surely doesn't. Politicians in a democratic country reflect the values of the population. They don't reflect it accurately – but if there is a systematic difference, I believe that the average politicians are less egotist and they care about the well-being of others (and the nation as an abstract concept) more than the average people do. So could the folks please stop hyping the idiotic separation to "us" and "them" and to stop waiting for new messiahs?

I won't thank because I know this is clearly too much to ask.

Read More

LHC: discovering grand unification

...aside from supersymmetry...

Apologies if the title was too dramatic. Supersymmetry and its possible looming discovery at the LHC has been discussed many times. But let's look at a different portion of modern model building in particle physics, Grand Unification. Grand Unified Theories (GUTs) are those that embed the Standard Model group\[

SU(3)_c\times SU(2)_W\times U(1)_Y

\] into a larger group, typically "simpler" (having fewer factors), ideally "simple" group in the technical sense (one factor). If it is possible, and it possible, the advantage is that the quarks and leptons may arise in a smaller number of multiplets (representations of the gauge group) and the lower number of factors in the gauge group implies a smaller number of adjustable coupling constants. So the GUTs are more constrained.

If they're verifiably right, they're more beautiful. But because they're more predictive, one may also be worried that they're less flexible and therefore less resilient towards falsification – a characteristic you may consider good or bad. However, the flexibility may be restored by adding various stuff and potentials at the GUT scale so the "qualitative difference" is somewhat debatable. At any rate, from a purely theoretical or aesthetic top-down perspective, it's rather natural to expect that Nature may want to unify the forces near the fundamental scale if She can.

And yes, She can. Many grand unified theories are naturally compatible with everything we may observe at low energies of doable experiments.




Grand unification has been discussed many times on this blog. In this text, I want to be somewhat more specific about the possible choices of the gauge groups and representations and possible particles that could show up at the accelerators (which is generally unlikely as the GUTs are associated with an insanely high energy scale, the GUT scale, which is not far from the Planck scale linked to quantum gravity).

\(SU(5)\): Georgi-Glashow model

The simplest gauge group we may pick is \(SU(5)\). Note that the rank – the maximum number of mutually commuting independent \(U(1)\) subgroups – is equal to four, much like for the Standard Model group. The Georgi-Glashow gauge group has dimension equal to \(d=5^2-1=24\). The adjoint representation, which is therefore 24-dimensional, may be decomposed into representations of the Standard Model subgroup:\[

24\rightarrow (8,1)_0\oplus (1,3)_0\oplus (1,1)_0\oplus (3,2)_{-\frac{5}{6}}\oplus (\bar{3},2)_{\frac{5}{6}}

\] In the parentheses, the first number represents the representation in which the piece transforms under the \(SU(3)_c\) colorful group of QCD. It may be a singlet (doesn't transform at all), a triplet (like quarks), antitriplet (like antiquarks), or octet (like gluons, the adjoint representation). More complicated representations may appear, too.

The second number in the parentheses is the representation under the \(SU(2)_W\) electroweak group. Note that the doublet \({\bf 2}\) is equivalent to its complex conjugate representation in this case – because the representation is pseudoreal (there's only one inequivalent spinor representation in 3 dimensions). The adjoint representation is 3-dimensional. The subscripts indicate the hypercharge i.e. charge under the \(U(1)_Y\) factor of the Standard Model gauge group.

You see that on the right hand side of the equation above, you find the adjoint representations of \(SU(3)_c\), \(SU(2)_W\), and \(U(1)_Y\). There are two new pieces that are complex conjugate to each other – they come with new gauge bosons that should however be insanely heavy (not accessible at the LHC) if the proton is supposed to preserve its longevity we know and love. The new bosons transform as color triplets as well as electroweak doublets. The latter fact implies that they have charges like an exotic quark doublet. We sometimes talk about new X-bosons and Y-bosons.

It's equally interesting to find out whether the leptons and quarks may be rearranged into representations of \(SU(5)\). The answer is YES and this fact is nontrivial. Let's look at all left-handed two-component complex spinor fields that are associated with a single generation of quarks and leptons (the whole field content or particle content is tripled at the end because there are three generations; and the Hermitian conjugate fields are added as well).

We find 15 such spinor fields in total: 2 (up, down: organized as an electroweak doublet) left-handed quarks, each in three colors (6 in total), 2 left-handed antiquarks (separate electroweak singlets), each in 3 colors (their Hermitian conjugates are right-handed quarks; again 6), left-handed electron and left-handed neutrino (they form a doublet), and a left-handed positron (an electroweak singlet). In total, \(6+6+2+1=15\). We may also add the left-handed antineutrino (so far unobserved and insanely feebly interacting if it exists) to raise fifteen to sixteen.

These 15 spinor fields are reorganized as the following representation of \(SU(5)\):\[

\mathbf{\bar{5}}\oplus\mathbf{10}\oplus\mathbf{1}

\] The decomposition of these pieces under the Standard Model group is\[

\eq{
\bar{5}&\rightarrow (\bar{3},1)_{\frac{1}{3}}\oplus (1,2)_{-\frac{1}{2}}\\
10&\rightarrow (3,2)_{\frac{1}{6}}\oplus (\bar{3},1)_{-\frac{2}{3}}\oplus (1,1)_1\\
1&\rightarrow (1,1)_0
}

\] The last line, the left-handed antineutrino (whose Hermitian conjugate is the right-handed neutrino), is optional or uncertain, as we have mentioned. The first line contains the lepton doublet and the \(d\)-antiquark singlet (\(d^c\) and \(\ell\), to use some symbols) on the right hand side. The second line has \(q\), \(u^c\), and \(e^c\). The \(c\) superscript refers to the antiparticles (it stands for "charge conjugation"). Let me emphasize in advance that the clumping of the particles into these larger representations is inequivalent in flipped \(SU(5)\) models.

The \(SU(5)\) grand unified group may be broken down to the Standard Model if you realize that the Standard Model group is exactly the subgroup that commutes with the generator \(U(1)_Y\), the hypercharge. Up to an overall normalization (that sometimes omits the factor of \(1/2\)), it is given by the following traceless \(5\times 5\) matrix:\[

\frac{Y}{2} = \left(\begin{array}{rrr}
-\frac 13&0&0&0&0\\
0&-\frac 13&0&0&0\\
0&0&-\frac 13&0&0\\
0&0&0&+\frac 12&0\\
0&0&0&0&+\frac 12
\end{array}\right)

\] Equivalently, it is the subgroup that keeps a \(Y\)-like vev of a new GUT Higgs field transforming in \({\bf 24}\), the adjoint of \(SU(5)\), invariant. One may also achieve the breaking by Wilson lines (monodromies around non-contractible loops, to be more accurate) in stringy models with extra dimensions and by other means.

The minimum grand unified model predicted a rather slow but not too slow proton decay. Within a year or so, the prediction was ruled out. The simplest grand unified theory has been falsified. The broader concept hasn't been falsified and it has way too many positive features so that we shouldn't think we will kill it too quickly.

Flipped \(SU(5)\) i.e. \(SU(5)\times U(1)\)

The flipped \(SU(5)\) models are the "most comparable ones" to the Georgi-Glashow model. They're associated with the names Dimitri Nanopoulos, Stephen Barr, Ignatios Antoniadis, John Ellis, and John Hagelin and their research in the early 1980s. The realization of this previously overlooked possibility was linked to some string theory research in the 1980s and the 1990s: string theory arguably makes the flipped \(SU(5)\) models more natural than the Georgi-Glashow model.

Note that Sheldon Glashow had already omitted a \(U(1)\) factor once when he tried to construct a purely \(SU(2)\) theory of the electroweak force so it wouldn't be shocking if he has displayed the same excessive fanaticism for minimalism together with Howard Georgi again. ;-)

You could think that that \(SU(5)\times U(1)\) must be just a complicated extension of the original \(SU(5)\) in which we add possibilities and allow things to be deformed. You could think that the Georgi-Glashow model is a special case of the flipped \(SU(5)\) models. But you would be wrong. The flipped \(SU(5)\) models are qualitatively different from their unflipped cousins – and they're "equally robust", in some sense. Their arrangement of quarks and leptons into the \(SU(5)\) multiplets is permuted – therefore "flipped" – relatively to the Georgi-Glashow model.

To mention a visible example of the differences, note that the right-handed neutrino \(SU(5)\) singlet was optional in the Georgi-Glashow model. In the flipped \(SU(5)\) models you also have to use \(\bar{5}\oplus 10 \oplus 1\) but the last, singlet piece isn't optional at all. For a simple reason: it is not a neutrino. It is actually the left-handed positron! We surely need it. So the actual fermionic content we have to add in the flipped \(SU(5)\) models comes in the representation\[

\bar{5}_{-3}+10_{1}+1_{5}

\] where the subscripts indicate the charges under the \(U(1)\) factor of the flipped \(SU(5)\) gauge group. These subscripts are extremely natural from the viewpoint of an \(SO(10)\) or \(Spin(10)\) group in which \(SU(5)\times U(1)\) may be embedded. In that group, the three pieces combine to a 16-dimensional complex spinor representation; the \(U(1)\) charge is proportional to the sum of all the five weights. It is fair to say that the flipped \(SU(5)\) models become more natural than the ordinary Georgi-Glashow \(SU(5)\) if you look "beyond \(SU(5)\)" e.g. at the \(SO(10)\) models.

The decomposition of the relevant flipped \(SU(5)\) representations under the Standard Model group is\[

\eq{
\bar{5}_{-3}&\rightarrow (\bar{3},1)_{-\frac{2}{3}}\oplus (1,2)_{-\frac{1}{2}}\\
10_{1}&\rightarrow (3,2)_{\frac{1}{6}}\oplus (\bar{3},1)_{\frac{1}{3}}\oplus (1,1)_0\\
1_{5}&\rightarrow (1,1)_1\\
24_0&\rightarrow (8,1)_0\oplus (1,3)_0\oplus (1,1)_0\oplus (3,2)_{\frac{1}{6}}\oplus (\bar{3},2)_{-\frac{1}{6}}
}

\] The subscripts on the right hand side are the values of the hypercharge. The last line is the adjoint representation again; there is an extra generator of the \(U(1)\) aside from this line, too. The first line describes the up-antiquark left-handed singlet and the lepton left-handed doublet. The second line describes the quark left-handed doublet, the down-antiquark left-handed singlet; and the left-handed antineutrino (unobserved). The third line is the left-handed positron singlet and can't be omitted.

Not too grand unified groups

Let me mention that there are other GUT-like gauge groups that are far from simple and that have been proposed with various justifications. The electroweak gauge group only treats the left-handed particles as doublets. One may add another \(SU(2)\) under which the right-handed particles are doublets. These left-right models have the gauge group \(SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}\).

The Pati-Salam model has the gauge group \(SU(4)\times SU(2)\times SU(2)\). The two \(SU(2)\) factors are analogous to those in the previous paragraph. However, \(SU(3)_c\) is embedded into an \(SU(4)\) where the "quark of the fourth color" is identified with a lepton.

Also, \(SO(10)\) models may be flipped to \(SO(10)\times U(1)\). The electroweak \(SU(2)_W\) may be extended to another \(SU(3)\) in the 331 models (Paul Frampton was a pioneer). \(SU(6)\) models have been constructed, too.

Trinification has a gauge group composed of three equal pieces, \(SU(3)\times SU(3)\times SU(3)\).

Truly large and simple GUT groups

However, the truly motivated "master gauge groups" are \(SO(10)\) and \(E_6\), an exceptional group. Note that the \(E_6\) group is the only exceptional group that has complex representations at all – something we need to treat left-handed and right-handed fermions separately.

This \(E_6\) is naturally embedded into the \(E_8\) that arises in the heterotic string and heterotic M-theory and it contains pretty much all the GUT groups above as a subgroup, including the group of trinification. The decompositions of all the representations under various subgroups are interesting and you should try to find all of them if you haven't done so. Also, \(SO(10)\times U(1)\) – where the \(U(1)\) may participate or not, depending on whether we have flipped models – may be embedded into \(E_6\).

The fermionic content of \(SO(10)\) models combines into the 16-dimensional spinor representation of \(Spin(10)\) I have already mentioned. But it's even more interesting to see what happens for \(E_6\) because the minimum nontrivial representation is the 27-dimensional fundamental representation, \({\bf 27}\). This inevitably contains some new spinor fields aside from the quark and leptons we know (and different from the right-handed neutrino, too)!

The decomposition of this representation under \(SO(10)\times U(1)\) is\[

27\rightarrow 16_{1}+10_{-2}+1_4.

\] Note that the trace of this \(U(1)\) in this 27-dimensional representation is \(16\times 1-10\times 2+ 1\times 4 = 0\). It has to vanish because it's the trace of a generic generator of a non-Abelian group, \(E_6\).

Now, the \(U(1)\) labels are funny. You may notice that only the 16-dimensional spinor of quarks and leptons has an odd label. If you correlated this \(U(1)\) charge with the R-parity in supersymmetric models (instead of using \(B-L\), and this is my idea), you could say that we will easily observe fermions from the 16-dimensional representation (we do) but bosons from the remaining, 10- and 1-dimensional representations!

So it's funny to ask what are the Standard Model charges of the additional representations. If you use the flipped \(SU(5)\) models, you will find out that \({\bf 10}\) decomposes into \({\bf 5}\oplus \bar{\bf 5}\) and these pieces contain both Higgs doublets of the MSSM (but this field content is tripled because there's a pair of Higgs doublets in each of the three generations!) plus a new electroweak singlet squark with the charges of the down-squark.

Symmetry has been a powerful tool in our successful efforts to understand Nature at least for a century. Supersymmetry tells us that we may expect superpartners of all known particles – although some of them may be much less accessible than others. But we could actually find traces of another, ordinary "bosonic" symmetry, by finding the (broken) symmetry partners of the known quarks and leptons.

For example, if the LHC ultimately started to find the new Higgs doublets predicted above as well as an exotic quark or three, it would be a huge hint of an underlying greater symmetry operating in Nature. Many of these models are heavily constrained and virtually all models with new light charged particles destroy the simplest "intriguing accident" of gauge coupling unification. But I view the simplest match for the MSSM gauge coupling unification to be just a 2-sigma intriguing bump. It may still be a misleading guide and there may be many more fascinating things we may discover if we sacrifice this one. Of course, it's up to us what we believe but on a sunny day in the future, Nature may very well force us to sacrifice the belief in the simplest scenario of gauge coupling unification.

So far, no official discovery of physics beyond the Standard Model has been announced by the LHC; just to be sure, the Higgs boson is almost as old physics as Peter Higgs himself. But this situation isn't guaranteed to last forever. It isn't even guaranteed to survive the Moriond 2013 conference in early March.

Stay tuned.

Read More