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Information is Physical (?)
If you know anything about computers, then you probably have some idea of the way it stores and processes information. It is all about the 1’s and 0’s right? You write the 1’s and 0’s somewhere, the computer somehow reads it and BAM! It does what you want. Well, that is perhaps oversimplifying things just a little, but life is too short to care for the details. In any case, you have to store those 1’s and 0’s somewhere, perhaps on a microSD card or a hard disk drive or a compact disc or any one of the whole multitude of devices meant to store your digital information. In this sense, you probably already have an intuitive idea that information is physical because you always have to write them down on physical objects.
In 1961, Rolf Landauer took this (admittedly obvious) observation to another level by demonstrating a physical principle using it. It essentially states the following: the erasure of a single bit of information has to cost a minimum amount of energy called the Landauer limit (it has a numerical value of KTln2, see http://en.wikipedia.org/wiki/Landauer%27s_principle). Details aside, the essential argument revolves around a theoretical engine, named the Szilard Engine (Figure 1) after the scientist who studied it. The engine appears to be able to do physical work without actually requiring any input of energy. This violates the 2nd law of thermodynamics, which says that this engine is giving us too good a deal and that a free lunch is impossible. The Szilard engine, however, does require you to make a measurement that gives you a single bit of information about the system in order to do work. Since the information has to be written down somewhere, and the actual writing on information appears to be doable without costing any energy, it should cost energy to erase this bit of information. In this way, there is no free lunch since you will eventually run out of space to write down the measurement and erasure of information has to be performed.
These arguments are fairly convincing, and Landauer’s principle is accepted by many in the scientific community today. However, the issue of its validity is far from completely settled. One may for instance argue that the assumptions underlying the Szilard engine cannot be valid. Using the same set of assumptions, you can actually design a separate engine that does work without even performing a measurement (See Figure 2), also a clear violation of the 2nd Law of Thermodynamics. Is there a flaw in such a design
So this casts some doubt as to whether Landauer’s principle is actually valid or not. Needless to say, this is an issue that is still being debated today, decades after the principle was proposed. Whatever your stand is on the issue, information remains physical, so keep that hard disk drive handy.
Physics is the experimental science
If you think that you can’t be surprised by classical physics any more, you should definitely watch the video I’ve uploaded below.
Here goes the follow-up video but don’t watch it without trying to answer the question posed in the first one. I was pretty much amazed how much attention the relatively simple problem can draw.
These two videos nicely show that physics is the experimental science. It doesn’t matter how great is your theory or how well you think you understand the well established theory, you should always be able to experimentally check your predictions.
Looking Through the Looking Glass
‘Well! I’ve often seen a cat without a grin,’ thought Alice, ‘but a grin without a cat! It’s the most curious thing I ever saw in my life!’ – Alice in Wonderland
Pictured: The infamous Cheshire Cat. Its smile is in the top right but the rest of the cat is elsewhere! How does that work?
The Cheshire Cat may seem like the product of a mind descending into madness, but then so is Quantum Mechanics. It will therefore surprise absolutely no one that a quantum version of the Cheshire Cat story exists. The Quantum Cheshire Cat also continues the ongoing fascination that physicists have with cute fluffy cats (see Schrodinger’s cat for another example). I am a dog person myself, but I digress.
Let us break down the Cheshire cat into its parts. The cat has a large toothy grin, you see, but a cat grinning is not the weirdest part. The weirdness comes along when the body of the Cheshire disappears and then reappears somewhere else, but the grin stays behind, floating suspiciously without a body attached.
Inspired by this, Aharanov et al. presented a way to translate this previously fictional weirdness into Quantum Mechanics. Unable to perform experiments on actual cats, they proposed an experiment using photons instead. Photons have an intrinsic property called polarization, which basically tells you the direction that the electromagnetic waves are oscillating. In Aharanov’s experiment, the photons are set up such that they can move along on 2 possible paths – Left and Right, and the polarizations are along 2 possible directions – Horizontal and Vertical. The polarization is a part of the photon, since it doesn’t make much sense to speak of which direction a photon is oscillating in when the photon is not there.
In Aharanov’s experiment, however, it is possible to have the photon in the left path but the polarization on the right! Suppose we implement Aharanov’s experiment and we prepare the photons in exactly the same manner many times in a row. If we were to make a measurement to see if the photon travelled the left path, the detector will always click, 100% of the time. We will therefore conclude that the photon is travelling the left path, not a difficult conclusion to make. However, if we were to make a polarization measurement on the right path, that detector will start giving us clicks! This means there is photon polarization on the right path! We have previously ascertained, with 100% confidence that a photon prepared in the same manner will always travel the left path, so the photon must have performed a “Cheshire Cat”, by moving in the left path, but having its polarization appear on the right.
The above argument is called counterfactual reasoning. Counterfactual reasoning basically refers to arguments made on the following basis: we didn’t do this, but if we did, this would have happened instead. In the previous paragraph, we are measured the polarization on the right path, but suppose we didn’t and measured the path of the photon instead, then we will conclude that the photon is always on the left, but this somehow contradicts our polarization experiment. The apparent weirdness, or paradox, therefore arises because we employed counterfactual logic, since we didn’t (and couldn’t) measure the path of the photon on the same photon we are measuring the polarization, but made our conclusion supposing that we did.
Aharanov et al. of course realized this, and thinking that may be an avenue for criticism, also devised an alternative reasoning based off of weak measurements that does not rely on counterfactual reasoning. I personally don’t think it is a problem per se, but instead perfectly illustrates how our everyday ‘common sense logic’ simply does not apply to quantum mechanics. In any case, it is fun to ponder why counterfactual reasoning does not work in quantum mechanics.
Link to Aharanov et al.’s paper : [1202.0631] Quantum Cheshire Cats – arXiv.org
On Compression of Non-classically Correlated Bit String
Recently we have worked on a new approach to analyzing correlations. Two parties: Alice and Bob, each generate a binary string (consisting of 1s and 0s). This string may be generated by flipping a coin or by making projective measurements on a quantum state (such as one arm of a Bell pair). Remarkably, we can analyse the bipartite correlations independently of how these strings are generated by looking at how well Alice and Bob’s bit strings can be compressed. Check out the video abstract:
On compression of non-classically correlated bit strings
Is it possible to kill somebody with a table tennis ball?
I’d like to pose the following question for this week’s blog: Can you kill a person with a table tennis ball (without eating the ball and dying from poison in the celluloid)? There Well, with the right physics knowledge you might, but I’ll leave you to decide for yourself:
Here’s what a world-class table tennis player can do (which is still pretty cool):
Recently researchers have successfully accelerated electrons using laser pulses . This achievement is far-reaching and will have immediate practical consequences; including methods for building less expensive and smaller devices for medicine and materials science applications. The new method capitalizes on our ability to implement techniques based on commercial near-infrared laser with greater efficiency then any pre-existing technology.
Behind all of this lies a simple idea. A particle’s velocity can be boosted through the interaction between its charge and the electric field component parallel to the particle beam line. Furthermore optimal acceleration conditions, which are experimentally more challenging to meet, dictate that the phase velocity of the accelerating field should always be tuned to the velocity of the relativistic particle.
In this experiment scientist used a micro-fabricated dielectric structure of two gratings (longitudinal cross-section resembles two opposing combs with some space in-between for the electrons to pass through). By preparing the right period for the gratings it was possible to get the diffraction modes of the incident laser pulse to form inside the structure and match the phase resonance conditions.
First results seem to be very promising. This new kind of accelerator offers electron acceleration of 250 MeV/m whereas the standard linear accelerator works at 30 MeV/m. Discoveries utilizing common tools, which promise better solution for practical applications, are always important.
 E. A. Peralta et al., Nature, 27 Sept 2013 (10.1038/nature12664)
How to cool your (quantum) beer
Everybody has a fridge. Maybe not an Eskimo, but I have heard that Eskimos actually use fridges to make sure that their foodstuffs are not always completely frozen. I have never personally met an Eskimo to verify this, but anyway everybody has a fridge, and everybody enjoys a nice cold beverage every now and then. Including physicists.
Now, as physicists are wont to do, they start to think: What if you have a quantum beer?
Suppose said beer is a qubit. This is the smallest possible beer since a qubit only has 2 discrete energy states. What is the smallest self contained refrigerator that, in principle, can be constructed?
This was a question that was tackled by Linden et. al. (See link). Their answer: a single atom that can occupy at least 3 discrete energy states. Or alternatively, if you construct your fridge out of qubits, then the answer is 2 qubits which collectively occupy a grand total of 4 possible energy states.
How does it work? Well, technicalities aside, it really is pretty simple. Consider the case where the fridge is made out of 2 qubits. Suppose when a qubit is occupying its lowest energy (ground) state, we label the state 0 and say the qubit is in the state 0. If the qubit is occupying its excited state (the only other energy level), then we say it is in state 1.If you have 3 qubits, then we can describe them compactly in the following way: 000 means all 3 qubits are in the lowest energy state, 001 means only the 3rd qubit is excited, and so on.
All you then need to do is to arrange an interaction between the qubits (or in physics nomenclature, introduce an interacting Hamiltonian) which transfers a 3 qubit state from an energy configuration of 101 to 010. If your quantum beer is the first qubit, then if you start at state 1, you will end in state 0. This means basically that the qubit becomes less energetic and therefore cooler. The problem is that such an interaction between 101<–>010 typically go both ways, which causes the state of your beer to go from 1->0 (cooling) and from 0->1 (heating) with equal measure, messing up the cooling process. This is where a little bit of ingenuity becomes necessary. By putting part of the fridge at a different (higher) temperature, and tweaking the energy levels of the qubits appropriately, you can make the beer and fridge system more likely to find itself in the 101 configuration than the 010 configuration. This means that your beer is more likely to go from 1->0 than from 0->1, and wala! you have a 2 qubit fridge and a nice chill qubit beer.
And that’s pretty cool.
If you leave no trace it’s like it never happened…
Everyone has heard about the perfect murder. If you leave no trace, there is nothing that can lead anyone to you. However, if you did something (either bad or good) but no one was watching, is it like you never did it?
However, if you suffered from amnesia, brain damage, or some other unpleasant accident, this information seems to be permanently lost. In this case the question “did it really happened?” seems to be unanswerable.
Recently I rediscovered a paper [PRL 103, 080401 (2009)] (clearly the original event where I first read the paper did exist even if I had forgotten it) that addresses the above question. In particular, it is suggested that events in which entropy is decreasing might actually happen in our universe, but they necessarily leave no trace. Therefore, one cannot observe them and hence we conclude from observable data that entropy can never decrease. Since the job of a physicist is to study things that we do observe, it seems that these strange events are beyond the scope of physics…
Conway’s game of life
One of the cooler things I discovered recently was that when you google search “Conway’s game of life” google automatically begins to play the game of life in the background of the search results page. It is rather mesmerizing,
The game of life is played on a grid of little squares; squares have two configurations “alive” and “dead” which are usually represented by using two different colours. A single game consists of a initial seed or starting configuration and a set of rules which govern how the grid updates:
(1) Any live cell will remain alive if it has 2 or 3 live neighbors; otherwise it will die.
(2) Any dead cell with 3 live neighbors will become alive.
The rules are roughly motivated by physical considerations; if the population density is too low or too high then individual members of a colony will die before reproducing. However three alive cells may reproduce to create a extra adjacent live cell.
The game is extremely popular because the seemingly overly simple rules can generate extremely complicated patterns. Recently it was demonstrated that certain initial conditions of the game of life can give rise to emergent behavior in the sense that we can aggregate large sections of the grid (consisting of multiple cells) and treat this section as an individual “macroscopic cell” which behaves non-trivially. There are no simple set of rules for how these macroscopic cells behave; all update
rules continue to apply to the small indivisible cells which constitute them. Nevertheless it is possible to initialize the game of life so that the macroscopic squares effectively appear to evolve according to conditions (1) and (2). There is quite a spellbinding example of this available here. Check it out as it is unbelievable at first sight.