CPT symmetry and quantum frameness

I just finished a paper with Barry Sanders (the quantum guy, not the football guy) that develops a quantum resource for overcoming a superselection rule created by a matter–anti-matter dissimilarity.  (OK, whose head just exploded?)  Maybe I should just post the abstract:

Due to Lorentz invariance and locality, physical laws are invariant under simultaneous Charge-Parity-Time (CPT) inversion, which makes this symmetry one of the most fundamental in the universe. We show that CPT symmetry leads to superselection, which can be circumvented with CPT frameness resources. Our frameness resource is applicable to quantum communication between superselection sectors of the universe that can be identical or inverted under CPT inversion. Whether the sectors are identical or inverted need not be known.

Here’s the problem in a nutshell: suppose Alice lives in a part of the universe that is entirely made of normal matter and Bob lives in a part of the universe that is made entirely of anti-matter (yes, I know there is an imbalance of matter and anti-matter in the universe, but bear with me).  Can Alice and Bob communicate with one another?  If so, can they tell if they are in different sectors of the universe or not?

It turns out this is a trickier question than it might first appear.  First of all, it does rely a bit on the nature of what it means for something to be a “particle” versus an “anti-particle.”  For most particles, their corresponding anti-particles have the opposite sign for all internal symmetries: electric charge, baryon number, lepton number, strangeness, charm, bottomness (beauty), topness (truth).  Neutrinos and anti0neutrinos, which have opposite lepton number, also happen to have opposite parity - neutrinos are all left-handed while anti-neutrinos are all right-handed (see, also, chirality and helicity).  It also turns out that certain meson decay processes suggest that we must adhere to the Feynman-Stueckelberg interpretation of anti-particles as particles moving backward in time.  Thus to switch from a particle state to an anti-particle state, we need to apply the full CPT operator and swap the internal symmetries, parity, and time.

Suppose Alice sent Bob a message encoded in, say, electrons, to be measured with some Stern-Gerlach-type device.  The electrons actually look like “positrons” to Bob (Bob’s “electrons” would be Alice’s positrons).  In other words, he’ll measure them (assuming he doesn’t annihilate them in the process) as having the opposite spin from what Alice encoded them with, i.e. a |0> state to Alice looks like a |1> state to Bob.  Now, if Bob knows he’s in a different sector of the universe, all he has to do is flip each qubit state he gets and he’ll be able to decode the message.  But what if he doesn’t know?

Ah, there’s the rub.  What Alice and Bob need is a common reference frame.  Something that is invariant under the CPT transformation should look the same to Alice and Bob.  As it turns out, circularly polarized photon states are invariant under the CPT operation.  To understand why, consider a particle spinning on its axis that is moving away from you and further suppose its direction of motion is parallel to its axis of spin.  Suppose it moves in a “right-handed” manner, i.e. it is spinning clockwise as seen from your viewpoint.  Now suppose you hop onto something that is moving faster than this particle.  Once you pass it, if you now look back on the particle (which is behind you), it will appear to be spinning counter-clockwise (it’s just like looking at a clock from behind).  The “rotation” of photons corresponds to circular polarization. The thing about photons, however, is that you can’t move faster than light so you can never get into a frame that makes the rotation look different!

In the paper, we show that you can implement that BB84 protocol with this concept (in addition to the usual straightforward communication).  In the process, it also turns out that Alice and Bob can use this information to figure out if they are in the same or in different sectors (i.e. whether they are both made of matter, for example, or one is matter and the other anti-matter).  They can’t, of course, tell which is which.  In fact the only way to tell is for them to communicate with all other sectors of the universe and look for an imbalance.

Did they or didn’t they find the Higgs boson?

By now I’m sure anyone who reads this blog has heard that CERN made an announcement concerning the Higgs boson this morning.  The results hint strongly that the Higgs – or something – is there.  There are two detectors that are involved in the search – CMS and ATLAS.  The statistical confidence (don’t even get me started on that one) of CMS is between 2 and 2.5 sigma while it is between 3 and 3.5 for ATLAS.  The FQXi Facebook page (which I presume is being handled by Zeeya Merali this morning) noted that, apparently, biologists are mocking us (i.e. physicists) for not taking a sigma of less than 3 as definitive proof.  Zeeya (er, whomever is tweeting/Facebooking this morning) notes, however, that roughly 50% of particle physics experiments with a sigma of less than 3 are false positives.  Such is the life of a physicist.

FQXi video on language and truth

My own brief (and somewhat unplanned) talk at the FQXi conference has finally been uploaded to the site.  It’s not quite as embarrassing as it felt at the time, though I say “uuhhh” a lot (which I hate doing and try not to do in my presentations).  Kudos to Shevaun on making the videos look nice.

UPDATE: I fixed the link.  Doh!

The internal ideological threat to science

Perhaps certain segments of science feel threatened by the growing anti-science rhetoric one seems to encounter each day in the media and elsewhere.  Perhaps it is just another example of the sense of absolute surety that people nowadays have about their own ideas and convictions.  Regardless, there is a growing trend in science of absolutism – that certain ideas are sacred and infallible.  Unfortunately, this not only goes against the core principles of science (it is inherently “updatable”) but has the potential to hinder progress.

The latest example I have stumbled on is an ongoing discussion on LinkedIn about the nature of mass.  One individual declares that mass is just energy.  It’s a perfectly valid argument, but one I happen to disagree with for a number of reasons.  In declaring my disagreement, however, I incurred a great deal of wrathful assertions that I was simply wrong and that there was no real debate about this point anymore (which is not true since plenty of peer-reviewed journals still publish articles on this topic).  It was accompanied by the usual vitriol that is seen in online discussions (why do I let myself get sucked into these things?).

So what is there that can be done about it?  I have no idea.  I try very hard to educate my students not to do things like this.  It’s a start, I guess.  I’m also thinking of suggesting an article that confronts this topic to some of my acquaintances at various journals and magazines.  Otherwise I’m at a loss.  For all our pomposity about our superior methods of thinking, scientists are just as ideological and stupid as everyone else.

I want MY money back

I’ve just gotten a little fed up with the people in charge, from the administrators at my college to the people on Wall Street.  And I’m equally pissed at the people who think all these protestors are whining liberals.  So:

Dear 53%, 1%, 100%, Santa Claus, Wall Street, etc.

I work multiple jobs to make ends meet. I give way more to the government than I get. I don’t like giving money to the government. On the other hand, the top 1% paid $318 billion in taxes in 2009 but indirectly got it back via the $700 billion bailout of Wall Street. So Wall Street not only got the 1%’s money (i.e. their own), but they also got MY money and YOUR money and they’re not doing anything with it other than hoarding it while the economy tanks. And THAT’S why I’m pissed. I want MY fukcin’ money back, a$$holes.

Guest blogging at FQXi

I have a guest blog post over at FQXi that talks about some of the same things I talked about in a few of my recent posts over here.  Nevertheless, for interested readers, here’s the link.

Geoffrey West on complexity (and a sad goodbye to Steve Jobs)

As I was sitting down after dinner this evening news came through the interwebs that Steve Jobs had passed away.  Given that he had lived seven years with a form of pancreatic cancer, it’s pretty amazing he made it this far.  As cantankerous as he was – and whether you love or hate Apple products – you can’t deny that he changed the world of personal electronics.  He was a true visionary.

Anyway, on to other matters.  At the recent FQXi conference on time I had the pleasure of sharing a Zodiac with Geoffrey West while bouncing around Åbyfjorden, Sweden (the patch under my ear in the picture below is what kept me from vomiting all over Geoffrey).  Anyhow, he gave what I think was my favorite talk at the conference.  I’ve linked to it below the picture (and note that if you catch site of me around 34 minutes or so, I am not sleeping!).  It is worth a watch.  In fact I think it ought to be required watching for just about anyone.  It’s solidified my intention to start doing more research in complexity theory.  I think physics provides the perfect means by which complexity can be studied, meaning that its reductionist methods tend to be ideal for solving complex problems – take it apart and put it back together again, piece by piece.  Anyway, watch the video.

Here’s the video:

Faster-than-light (FTL) particles detected: implications for physics

Physicists at CERN have reported what they believe to be evidence of neutrinos traveling faster than the speed of light.  Of course this is usually considered a big “no-no.”  So, on the one hand you have people saying that one of the fundamental pillars of physics is close to crumbling (NEWSFLASH!! Call the press!!).  On the other hand you have people saying the results are flawed because it’s just too ridiculous to be true (those people at CERN are idiots!).

Frankly, I hate the modern tendency to hype things to opposite extremes.  The truth of the matter is that a) the idea has been previously suggested and b) possibly even previously detected in Segré’s and Chamberlain’s famous antiproton experiment that garnered them the 1959 Nobel Prize (as pointed out by Cooper in 1982).  In addition, it seems to me that it is becoming clear to a lot of people that both time and gravity are emergent phenomena.  Since even special relativity is based on a metric that inherently assumes the existence of time, it would seem that relativity itself is emergent.  The “cosmic speed limit” (as Tom Moore calls the speed of light) is taken as one of two postulates from which relativity is derived (the other being that the laws of physics are the same in all inertial reference frames).  But that’s all it ever was in the beginning – a good guess.  It turned out that causality followed naturally from this assumption and human beings like causality because we can’t imagine how the world would work without it.  But maybe causality only applies to macroscopic objects.  It seems quite clear that fundamental particles simply do not follow the rules of classical physics (and relativity is a classical theory) so who’s to say they have to be causal?  In fact, there are lots of kluge’s in quantum field theory (QFT) that allow for all sorts of bizarre behavior (with all sorts of ad hoc arguments added to assuage our feelings about causality).

So does this all mean we toss relativity out the window entirely (not to mention the Standard Model and most of QFT)?  Well, no, not exactly.  Look, engineers (and by extension anyone who owns any GPS-based device) rely on relativity every day to make the GPS system work.  Likewise quantum electrodynamics (QED), which is inherently relativistic, is the single most accurate scientific theory known (it agrees with experiment to some insane number of decimal places).  So what it means is that we are merely pinning down the limitations on the theory.  All theories are really nothing more than models – they’re simply the most self-consistent way we have to describe the reality we see until we find something better.  For example, the discovery of relativity didn’t stop people from using Newtonian mechanics – again, engineers use it every day to make sure buildings stand up and cars drive properly.

So, in short, don’t believe the hype – either way.  It’s not the end of physics as we know it.  But it is wicked cool and very exciting because it means we’ve just discovered another “layer of the onion” we call the universe.

The nature of time: FQXi, Scandanavia, and the end of a hiatus

I suppose it is appropriate that the post ending my nearly three-month-long hiatus is about the nature of time. I just recently returned from the absolutely fantastic FQXi conference Setting Time Aright that took place first onboard the National Geographic Explorer sailing the coasts of Norway and Sweden starting in Bergen, and then in Copenhagen.  It was eight days of intellectual bliss – interdisciplinary, cutting edge, and small enough that we could really all interact in some way. I met and/or hung out with some amazing people including Jaan Tallinn, Nick Pritzker, David Eagleman, Jesse Dylan, and Julian Barbour, among many others (see the conference website for a complete list). At some point soon the full conference will be available to watch on the Net. For now you’ll have to contend yourself with my pithy comments.

On the surface, it would seem that there was little agreement about the nature of time, i.e. what it is. Certainly the neuroscientists and psychologists have a very different take on it than the physicists. But I don’t think anyone would deny that what physics tells us time ‘is’ must be what time really is. The question is, then, does physics tell us specifically what time actually is?

Yes and no. Anyone who really studies physics will (or at least should) know that relativity has quite a bit to say about time (I recommend, by the way, the superb book Six Ideas That Shaped Physics, Unit R: The Laws of Physics Are Frame-Independent by Tom Moore for learning basic, non-tensor special relativity). In fact there are several kinds of time: coordinate time, proper time, and the spacetime interval (which is the kind of “time” measured by a photon).

That’s all very well and good for someone who doesn’t care about the fundamental nature of time and who only needs an operational definition. But physics didn’t get where it is today by remaining content with operational solutions to problems. Physics is, ideally, like a child that doesn’t stop asking why? So physics should ask where time comes from to begin with. Is it something that is fundamental to the universe or does it arise from something else? If it arises from something else we should seek to know how and why. One never knows the interesting doors this might open for further research (or even technology).

While there seemed to be a great deal of disagreement about the nature of time at this conference (e.g. Julian Barbour is convinced it doesn’t even exist), there very clearly was an underlying commonality to all of the views – even those of the psychologists and neuroscientists.

First let me say that one of the most striking things I found was that everyone’s work – absolutely every last one including the psychologists’ – involved either quantum mechanics or probability & statistics (including statistical mechanics and information theory, i.e. anything Edwin Jaynes would have written about – actually he wrote a bit about quantum stuff too). Ironically these are not the topics we emphasize in basic science and mathematics education (surprisingly few people have a good understanding of probability and statistics and most people are never even exposed to quantum mechanics!).

So given that commonality that seemed to cross disciplines, it is no surprise that pretty much everyone agreed that time has something to do with entropy. In fact many of the presenters and attendees probably think this is simply a trivial truth. So perhaps we should have been debating entropy, which is something that is still not entirely well understood as a concept. What is clear, however, is that it is some kind of statistical phenomenon. This is true for every single definition of entropy in every field (including instances in which the word is completely abused). Thus it would seem that there’s an underlying consensus – whether it is realized or not – that time must be some sort of statistical phenomenon.

This is actually quite remarkable. First, it points to the likelihood that time is not fundamental in the universe and so, in some sense, Julian Barbour is correct in that it doesn’t exist as a fundamental entity. In other words it would seem to be an emergent phenomenon. Second, if it is emergent, then due to the fact that it is at the heart of relativity, perhaps relativity is an emergent phenomenon as well (actually it is not difficult to argue this on a philosophical level). Following this line of reasoning would suggest that gravity would then have to be an emergent phenomenon (which actually makes some sense).

Now before everyone starts talking about these observations as being indicative of what was discussed at the conference, please know they represent my extrapolation from the commonalities I saw in all of the talks. Precisely how much of this any given attendee would agree with would likely vary greatly. Nevertheless, it is an intriguing line of reasoning to take and it certainly not unique (gravity has been proposed as being an emergent and/or thermodynamic phenomenon before).

What all of this means for your daily life is … well, nothing really. However, there were a number of talks that had some very interesting and useful insights into certain aspects of daily life. Keep an eye peeled for the conference videos (and a possible documentary). Nevertheless, they are fascinating and intriguing ideas to contemplate. Perhaps this sign from Bergen was a bit of a foreshadowing of the rest of the conference…

Women in Science

You can tell by the lack of posts that I haven’t been terribly inspired to write anything. It’s been a tough 12 months or so. But I don’t want to abandon the blog entirely, so, at least for now, I’ll post some interesting article links.

This one caught my eye this morning. Written by two women in science, it suggests that perhaps one reason women are underrepresented in the sciences is a result of a conscious choice on their parts. Not being a woman, I can’t really comment either way. Nevertheless, I think it is interesting. Perhaps if I still have readers out there and haven’t lost them all over the past few months, someone will actually comment.