If you’re a regular reader of ReducedMass then you’ll remember an article from a week ago on quantum cryptography, and hopefully it wasn’t mind numbingly boring and you actually read it as well. Before that, i had written an article trying to explain some of the quantum weirdness using Bells inequality. Now, this time (as promised in the last article) I’ll tie these two together into one ultra-safe and delicious quantum cryptography protocol that involves Bells inequality!

I know it’s a mean thing to do, but I’m afraid i’ll have to assume you’ve read the two previous articles here. I’ll try and make my explanations clear and sum up the main points from the old articles before using them, so hopefully you can gain something from this without having read them, but truthfully, it’ll be hard. But enough with the sobering forewords, lets dive right in!

Now if you’ll remember, two entangled photon will break the so-called Bell inequality, while un-entangled (completely unconnected) photons would not. A way to measure the bell inequality would be to have a source of entangled photons, have it send one photon towards Alice, one towards Bob and have them measure their polarization in different basis (for example Bob in +-45° and Alice in the horizontal/vertical). Now imagine that someone (lets call her Eve) intercepts the photon coming over to Bob, measures it, and resends it. It is impossible for Eve to measure the entangled photon, and send another one on-to Bob that is also entangled with Alice. So if Eve intercepts the photons, Alice and Bob will see that the Bell inequality is NOT broken, and therefore they will know that someone was listening in!

So in essence what they do, without going too deeply into it, is combine the encryption protocol we discussed in the previous article with this property of entangled photons. So you have a source sending out entangled photons to Alice and Bob, they will measure it in a random basis, and get either 0 or 1 as an outcome. Alice calls Bob and tells him what basis she measured in, and if he measured in the same one, they will know they measured the same thing, and they’ll keep that bit for their one-time-pad. BUT! and here’s the kicker, if they did NOT have the same basis, that is the equivilant of testing the Bell inequality! So they will use those results to see if it (the inequality) is broken or not. If it IS broken, then they know the photons were entangled and no-one was listening, and if it’s NOT broken they know the code has been compromised and they throw it away.

I came across this story today, a good original article from what i can tell, telling about the implementation of a high temperature superconductor into the grid (over in Long Island). Now i could’ve sworn that my professors told me about another place that did this, but i can’t for the life of me find it, so I’ll assume that the article is right.

Using superconductors is of course nothing new. They are already implemented in MANY places outside the lab, like in MRI’s that use liquid nitrogen cooled coils to create magnetic fields. Also, although i guess that counts as “in the lab”, CERN has HUGE superconducting coils to create magnetic fields (see picture) that will bend particles in the monster of a particle accelerator. But as you can imagine, because you have to cool all these things using liquid nitrogen, it is not in widespread use, so I’m always happy to read about new applications like this.

We here at ReducedMass are no strangers to superconductors, only a few months back there were claims that there had been a breakthrough and a room temperature superconductor had been made! This would obviously revolutionize the whole field, because now you no longer need liquid nitrogen, so widespread use of superconductors becomes MUCH more feasible. However, as we showed, it was all a misunderstanding and although it was promising research, there was no room-temp superconductor made.

I’m very excited about the field though, it seems like every week i read an article about a new group of researchers that say they are getting closer and closer to understanding how high temperature superconductors work (there is no complete theory describing this phenomena), and once that happens, i would imagine the field will make huge strides towards the holy grail, a room temperature superconductor.

Well i promised when i wrote about quantum entanglement a few weeks ago, that i would write another article in the same field soon(ish), so here i am to deliver on my word.

To start off with, lets quickly discuss normal cryptography. The only 100% safe method of sending data between two persons is a so called “one time pad protocol“, in which two persons, Alice and Bob, each have the same sequence of 0’s and 1’s (their one-time pad), lets say it’s 01110110. Alice now has an 8bit message she wants to send to Bob (lets say 10101010), then she simply adds her two numbers together (without carrying the terms), and the outcome from that is COMPLETELY random, however! if Bob takes this random number, and again adds the one-time pad to it, he’ll get the original message! This is 100% secure and if a 3rd person (Eve) is listening, she can only intercept the random message and gets no information. Check out the picture on top to see how Alice adds the one time pad to the message, gets a random message out, and then Bob adds the code again to retain the original message.

However! The big problem is, how the hell do you get the one-time pad to Alice and Bob without someone intercepting it? There is no 100% secure way to do this! And this is actually where the quantum stuff comes in, so in a sense, it’s not really quantum cryptography, but more like quantum key distribution.

So here is the basic idea, Alice wants to send a random sequence of 0’s and 1’s to Bob, and be 100% sure that Eve did not listen in on them. To do this, she sends a single photon (particle of light) that can be in one of two basis (0 and 1, so one photon=one bit), and Bob can only measure in one of them. To get slightly technical, the polarization of the light is either in the + basis (horizontal/vertical) or the x basis (+ or - 45 degrees). You can think of the lightwave as a rope being shaken in only one direction, say it’s being shaken up and down, then it would be vertically polarized (we’ll use the | sign for that), shaken left right would be horizontal (-), and then you can imagine you can shake it + and - 45° ( / and \ )as well. Check out the picture for a visual depiction of it, you can see the horizontal/vertical and one of the 45° angle ones too.

So lets see at what happens in some different situations. If Alice sends through either | or - polarized light, and Bob measures in that basis (the + basis), he will measure the exact same polarization as Alice sent out. If however he measures in the wrong basis, the +-45° (x basis), then the outcome is random! There is 50% chance of him measuring +45 and 50% measuring -45.

Ok now that all those things are out of the way! Lets get down to business, here is the protocol Alice and Bob would use to send a one-time pad between each other (called BB84):

1) Alice prepares a random polarization (-, |, \ or /) and sends it off to Bob.
2) Bob chooses a basis to measure the photon in at random (Alice has not told him anything about the photon she sent!).
3) Repeat the process however many times you want (remember, one photon=one bit).
4) Bob calls Alice and tells her which basis he measured in, and she tells him if it was wrong or right, and they both get rid of all the wrong bits (~50%).

So now all they need to do is assign numerical values to each polarization, say Horizontal=0, Vertical=1, and +45°=0,-45°=1. Then they both have a long number of 0’s and 1’s that are identical. Ok so this shows how they could transfer the code between themselves, but how could they possibly know if they’ve been eavesdropped? The easiest way to explain it is to look at a table explaining how each step of the way, assuming Eve is indeed listening. I could’ve made one myself, but the first google image result is actually perfect, so I’m kind of jacking that one (taken from this article).

So as you can see, Alice sends out in some polarization, and Bob measures either in the + basis (R in the picture) or x basis (D in the picture), this time however! Eve is right in the middle, measuring the photon before Bob gets it, and resending whatever she measured on to Bob (in order to avoid detection). So in #1,2 and 5, Alice and Bob agree that they used the same basis, but #3 and #4 they didn’t, so those two are thrown away. In #1 and #5, Eve was lucky! She measured in the correct basis, so she simply sends the same message along for Bob to detect, and they have no idea she did this. However! In #2 Eve measured in the wrong basis! So she’ll measure it and send it along to Bob, in the wrong basis (not knowing if she measured in the right basis or not), so now if you remember our discussion from before, there is now a 50% chance of Bob measuring the wrong result (compared to Alice) at his end! So now there is an error in the code, and if Alice and Bob simply compare a small percentage of their code, they can see if there are any errors (that is, if someone was listening).

I will be making a smaller followup post on this in the coming days, where i will discuss how you can enhance the security of this key distribution protocol, using the weirdness of quantum entanglement, which i talked about a few weeks ago.

Well i was all prepared to make a post tonight but turns out it’s taking a good bit longer to write then i had anticipated! So it’s not coming until tomorrow. Teaser: It’ll be an article about how quantum cryptography works.

Until then! I came across this rather awesome commercial for lab equipment. When you hear the words “Commercial for lab equipment” awesome is not exactly the first word that comes to mind, which is what makes this video rather mindblowing. Maybe it’s just because i’m a huge geek, but i enjoyed it anyway! Check out their website here.

First off! Sorry for the delay in posts, miraculously it was not caused by drinking this time around, but because i moved everything i owned and went back to Iceland for the summer (and started a new job at an engineering firm as a summer intern). But just because i’m out of the cozy life of academia for a few months does not mean i’ll put reducedmass on the backburner, there will be updates throughout the summer.

Which brings me to the subject of this post! I actually found this one quite a while ago but somehow completely forgot to write about it, so you may have seen this as well at some social networking sites. It is a video from the History Channel, talking about a gravity express railway. The basic idea is easy to understand, you dig a hole straight through the earth, say from New York to Sidney, and jump in, how long would it take to travel from one end to the other?

The answer? 42 minutes, but what if it’s from New York to Los Angeles? Still 42 minutes! Any two points you’d connect would take 42 minutes. The video actually does a great job at explaining it, and has some cool CGI to illustrate.

However! You shouldn’t hold your breath waiting for this to kick in, seeing as how we humans have been unable to dig any further down than around 12km, and a straight line through the earth would be a bit more than 12.000km.

Now i know that every last news source online has done this story already, hell it’s on the Drudgereport frontpage as i write this, but if for some reason you refuse to read anything but our humble blog here’s the story (plus it’s hard to not write a headline about watermelon viagra).

Without really going into much details (which would be hard too seeing as how this is more biology/medicine and I’m a physics student), they have found out that watermelons contain large quantities of a substance called citrulline, which has the benefit of increasing blood flow in your body, which is of course the same thing that Viagra does. It’s however not the exact same, as Viagra is organ specific, while watermelons would target the entire vascular system. The basic message is: fruit is good for you!

This is of course also a perfect time to bring in one of the most controversial XKCD comics ever made, the infamous fruit chart.

As you can plainly see, the watermelon is not a top contender in the fruit wars (in fact i’d have it even lower on the tasty bar, it’s bland as hell!). If for some miracle you don’t know XKCD, i can HIGHLY recommend reading it. It’s a comic with a bunch of nerdy humor and science jokes, but also bunches of quirky stuff, easily one of my top3 favorite places online.

P.S. Some practical advice to everyone, don’t get drunk the day before you have to move out of an apartment, spending a day hung over in cleaning supply fumes is far from optimal.

Well to be honest, huge is not the first word that springs into mind when you say one millimeter (that’s 0.0393700787 inches for you metrically challenged), but when it comes to atoms it’s a behemoth. The usual diameter of an atom is of the order of one Angstrom, which is 0.00000000001 meters, so we’re talking about an atom approximately seven orders of magnitudes bigger!

One of the first theories put forth to explain the behavior of atoms, was the so-called Bohr model, named after one of the greatest physicists ever to live, the Danish Niels Bohr. The basic premise of the model was that electrons orbit around a core of protons and neutrons, much like the moon orbits the earth. He used classical physics to calculate several properties of atoms based on this model, but it was ultimately wrong and the correct theory of atoms was found with quantum mechanics (which he had a big hand in founding). You can check out this explanation of it (also linked in the press-release), it looks kind of childish with the cartoons and everything, but it actually does a pretty good job of explaining it in a simple way.

The story does not end there though! As it often happens, once you scale things up from the very tiny, to the somewhat large, things stop exhibiting the weird effects of quantum mechanics, and start behaving more like classical systems we know and love from our every day life. This holds true for atoms as well, so atoms that are at a sufficiently large scale actually DO behave like the Bohr model predicts!

The scientists over at Rice University managed to make one of these very large Bohr atoms and observe it’s circular path around the nucleus. Like i said before, the size of the atom was close to one millimeter, a far cry from the one angstrom they usually are. The large size was achieved using lasers to excite the atom and electric fields to manipulate it into the configuration they wanted.

You can check out their press-release here, it’s quite short actually and to the point, and also discusses in a little more detail how they actually managed to make the potassium atoms so large, so i recommend reading it.

As a followup to my last post about Bells inequality, i figured i’d give you a quick link to an article written about a very recent test of it, confirming that indeed, quantum mechanics does not obey the Bell inequality. The next two paragraphs will quickly sum up my last article in case you didn’t read it. Those who did can feel free to skip it.

In “real life” we are used to be able to precisely predict the outcome of results. Say you throw a baseball to your friend, if you were to measure it’s direction and velocity, you could accurately predict exactly where it will land and when, plus how much energy it has etc, this is what is called “deterministic”, since we can accurately determine outcomes. On the quantum scale however,q things are quite different and outcomes of measurements can not be perfectly predicted, in fact different outcomes will be measured with a certain probability, and you have no way of predicting exactly what you’ll get.

Many people did not like this at all, such as Einstein, who proposed that quantum mechanics was simply an incomplete theory, and if only we had the full picture, quantum mechanics would be deterministic as well. In order for this to be true, quantum mechanics would have to fulfill the so-called Bell inquality, and in short, it does not (you can read the older article for a more in-depth view of it, this is just a quick sum-up for those that didn’t feel like reading the whole article).

Like i explained in the article, there have been numerous experimental tests of the Bell inequality at the quantum level, and they agree, it is indeed broken. I figured you might be interested in reading about the largest test of the Bell inequality so far, which spanned two laboratories across two different towns! They had it at this distance so they could make sure that there was no way that the two particles could have exchanged any information before they were measured, and once again, it has been confirmed that quantum mechanics are weird.

As this is not a press-release like most their news, but an actual article written by PhysOrg, i will simply point you towards it rather then recite it here.

Since i just finished a course in Quantum Information, which studies quantum cryptography, quantum computers and other such things, i thought i might write a few articles about these things as they are interesting, highly useful and seem to have captured the interest of the general public fairly well. I hope i can manage to explain this in a way that a lay-person could read this and get the gist of it, if i fail for some reason, feel free to leave a comment and i’ll try to elaborate on points i was unclear on.

To start with, i wanted to do a short article on something called Bells inequality, which shows us that the fact that outcomes of measurements in quantum systems occur with a certain probability (as opposed to being able to precisely predict the outcome of an experiment in classical physics) can not be explained away by simply saying that the theory of quantum mechanics is incomplete and if only we knew about those factors we have not found yet, we could perfectly predict everything.

To begin with, i’ll have to introduce one of the weirdest results of quantum mechanics, quantum entanglement. It more or less means that it is possible to have two quantum systems (for example single photons (particles of light) or single atoms), that are somehow connected (entangled) with each-other, so there is no way to describe one particle without including the other. So for example lets say we have two atoms that have their spin entangled. A simplified way of imagining what the spin of an atom is, is that it’s the equivalent of the earth rotating about it’s axis. The two possible spins that the atom can have is spin-up, or spin-down, and using the analogy from before about the earths rotation, you can imagine spin-up being a clockwise rotation and spin-down being a counter-clockwise rotation. So what does it mean that they are entangled? Well it means that if you were to take atom #1 and measure it’s spin along the x-axis and get some result, then you know for certain, that atom #2 has the exact opposite spin. So say #1 measures spin-up, then you know that #2 has spin-down. This holds true even if the two particles are at the opposite ends of the galaxy!

Now if you think this is weird, don’t feel stupid, great minds were (and are) boggled by this as well, and in fact Einstein was sure that this could not be true. He argued that if you have two systems, A and B, that are completely separated by space, then the measurement of A must not modify the description of B. But when doing the math in quantum mechanics, this is exactly what you get! So Einstein maintained that the theory of quantum mechanics was incomplete, and that if you DID have the complete theory then the results of a measurement of a quantum system would not depend on probabilities, but you should be able to completely predict your results (like you can in classical everyday physics).

Phew! Ok that was a lot of backstory and explaining in order to get to what i really wanted to talk about, Bells inequality. So on one hand we have a theory giving us some very unintuitive answers, and on the other we have Einstein saying that this is only because the theory is incomplete, and if we had the full picture then all the weird things in quantum mechanics would make sense to us. But how can we test which one is true? This is where Bells inequality comes into play!

What it basically states, is that if you have three coins, and throw them all into the air at once, then you are 100% sure that at least two of them will be identical (heads/heads or tails/tails). So of P(1,2) is the probability of coin 1 and coin 2 being the same, then

P(1,2)+P(2,3)+P(1,3) >= 1

So the sum of all the probabilities should be equal to or more than 1 (100% probability). Seems pretty straight forward and obvious yes? Obviously 3 coins will have a 100% certainty to have 2 outcomes be the same, at least in the classical world we live in, and that’s where the catch is. If Einstein was to be right, and quantum mechanics was indeed deterministic like the classical world we know (that is to say, the current model of quantum mechanics is wrong), then this inequality HAS to be fulfilled for quantum mechanics.

So lets see what happens in the quantum picture. We’ll return to our entangled atoms from before, where Alice has one of them, and Bob has the other. The coins in this picture, are the spins of the atoms along different axis, so for example the spin along the x-axis can be either up or down, and each one has a 50% probability of being measured (remember that they can only do one measurement on each atom). So lets say that Alice measures the spin in the x-direction, and gets spin-up, she calls Bob and tells him the good news, so now Bob KNOWS that if he measures in the x-direction as well, he’ll get spin-down with 100% certainty (because they are entangled). So what happens now if Bob measures the spin along the y-axis? What is the probability of him getting the same result as he would have got along the x-axis (the equivalent of getting heads/heads, tails/tails)? Well without going into the math of quantum mechanics, i can tell you that it is 1/4. So looking back at the equation from Bells inequality, P(1,2)=1/4, and in fact P(2,3) and P(1,3) is also 1/4 (it doesn’t matter which axis you measure, it’s always the same math), so you see that

P(1,2)+P(2,3)+P(1,3)=3/4

which is obviously less then 1, and Bells inequality is therefore NOT fulfilled, and Einsteins explanation was wrong. This is also heavily backed by experiments done to test the Bells inequality, so it would seem that the current theory of quantum mechanics lives to see another day!

Now if you think about it, it’s not really that surprising that these things are completely counter-intuitive. After all, we humans never experience any quantum mechanical effects (they can only be observed at extremely small levels, like single atoms or single photons), so our brains have simply not evolved to be able to comprehend these things intuitively.

Lastly! Phil Plait over at the Bad Astronomy blog actually did a similar article a few weeks ago, where he discusses quantum cryptography (which also heavily depends on entanglement), i might write an article on that as well, assuming people didn’t fall sleep over this one and are interested in hearing more, but until then, you can check out his article.

Well, exams are over (and passed), so now i won’t have to take an exam or be at a lecture again … ever. As promised the rate of articles will pick up somewhat now, so here goes.

It seems like every other story we do somehow involves MIT doing something revolutionary, those guys are really at the forefront of science/engineering. This time around they claim to have made the worlds most power-efficient solar power solution.

The contraption is basically a cleverly designed mirror that focuses the sunlight it reflects onto a small area that absorbs the heat from the light quite efficiently into copper wires, that then transfer the heat to water surrounding them. The water then heats up and eventually produces steam, that could be used to power turbines, creating electricity. I could babble on here about the design and such, but MIT’s news service is actually quite good, and they have a video with the lead-designer explaining everything quite well, and he even demonstrates how the light beam is powrful enough to quickly make a plank of wood go up in flames. So check out this video here. I can also recommend reading their press-release on the matter.