The weakening measurement

Unlike the special theory of relativity that the superluminal-neutrinos fiasco sought to defy, Heisenberg's uncertainty principle presents very few, and equally iffy, measurement techniques to stand verified. While both Einstein's and Heisenberg's foundations are close to fundamental truths, the uncertainty principle has more guided than dictated applications that involved its consequences. Essentially, a defiance of Heisenberg is one for the statisticians.

And I'm pessimistic. Let's face it, who wouldn't be?

Anyway, the parameters involved in the experiment were:

1. The particles being measured


2. Weak measurement


3. The apparatus

The experimenters claim that a value of the photon's original polarization, X, was obtained upon a weak measurement. Then, a "stronger" measurement was made, yielding a value A. However, according to Heisenberg's principle, the observation should have changed the polarization from A to some fixed value A'.

Now, the conclusions they drew:

1. Obtaining X did not change A: X = A


2. A' - A < Limits set by Heisenberg

The terms of the weak measurement are understood with the following formula in mind:



(The bra-ket, or Dirac, notation signifies the dot-product between two vectors or vector-states.)

Here, φ(1,2) denote the pre- and post-selected states, A-hat the observable system, and Aw the value of the weak-measurement. Thus, when the pre-selected state tends toward becoming orthogonal to the post-selected state, the value of the weak measurement increases, becoming large, or "strong", enough to affect the being-measured value of A-hat.

In our case: Aw = A - X; φ(1) = A; φ(2) = A'.

As listed above, the sources of error are:

1. φ(1,2)


2. X

To prove that Heisenberg was miserly all along, Aw would have been increased until φ(1) • φ(2) equaled 0 (through multiple runs of the same experiment), and then φ(2) - φ(1), or A' - A, measured and compared to the different corresponding values of X. After determining the strength of the weak measurement thus, A' - X can be determined.

I am skeptical because X signifies the extent of coupling between the measuring device and the system being measured, and its standard deviation, in the case of this experiment, is dependent on the standard deviation of A' - A, which is in turn dependent on X.

A simple overview of particle physics

(Click on the image for a larger size)

The philosophies in physics

As a big week for physics comes up–a July 4 update by CERN on the search for the Higgs boson followed by ICHEP '12 at Melbourne–I feel really anxious as a small-time proto-journalist and particle-physics-enthusiast. If CERN announces the discovery of evidence that rules out the existence of such a thing as the Higgs particle, not much will be lost apart from years of theoretical groundwork set in place for the post-Higgs universe. Physicists obeying the Standard Model will, to think the snowclone, scramble to their boards and come up with another hypothesis that explains mass-formation in quantum-mechanical terms.

For me... I don't know what it means. Sure, I will have to unlearn the Higgs mechanism, which does make a lot of sense, and scour through the outpouring of scientific literature that will definitely follow to keep track of new directions and, more fascinatingly, new thought. The competing supertheories–loop quantum gravity (LQG) and string theory–will have to have their innards adjusted to make up for the change in the mechanism of mass-formation. Even then, their principle bone of contention will remain unchanged: whether there exists an absolute frame of reference. All this while, the universe, however, will have continued to witness the rise and fall of stars, galaxies and matter.



It is easier to consider the non-existence of the Higgs boson than its proven existence: the post-Higgs world is dark, riddled with problems more complex and, unsurprisingly, more philosophical. The two theories that dominated the first half of the previous century, quantum mechanics and special relativity, will still have to be reconciled. While special relativity holds causality and locality close to its heart, quantum mechanics' tendency to violate the latter made it disagreeable at the philosophical level to A. Einstein (in a humorous and ironical turn, his attempts to illustrate this "anomaly" numerically opened up the field that further made acceptable the implications of quantum mechanics).

The theories' impudent bickering continues with mathematical terms as well. While one prohibits travel at the speed of light, the other allows for the conclusive demonstration of superluminal communication. While one keeps all objects nailed to one place in space and time, the other allows for the occupation of multiple regions of space at a time. While one operates in a universe wherein gods don't play with dice, the other can exist at all only if there are unseen powers that gamble on a secondly basis. If you ask me, I'd prefer one with no gods; I also have a strange feeling that that's not a physics problem.

Speaking of causality, physicists of the Standard Model believe that the four fundamental forces–nuclear, weak, gravitational, and electromagnetic–cause everything that happens in this universe. However, they are at a loss to explain why the weak force is 10³²-times stronger than the gravitational force (even the finding of the Higgs boson won't fix this–assuming the boson exists). An attempt to explain this anomaly exists in the name of supersymmetry (SUSY) or, together with the Standard Model, MSSM. If an entity in the (hypothetical) likeness of the Higgs boson cannot exist, then MSSM will also fall with it.

Taunting physicists everywhere all the way through this mesh of intense speculation, Werner Heisenberg's tragic formulation remains indefatigable. In a universe in which the scale at which physics is born is only hypothetical, in which energy in its fundamental form is thought to be a result of probabilistic fluctuations in a quantum field, determinism plays a dominant role in determining the future as well as, in some ways, contradicting it. The quantum field, counter-intuitively, is antecedent to human intervention: Heisenberg postulated that physical quantities such as position and particle spin come in conjugate quantities, and that making a measurement of one quantity makes the other indeterminable. In other words, one cannot simultaneously know the position and momentum of a particle, or the spins of a particle around two different axes.

To me, this seems like a problem of scale: humans are macroscopic in the sense that they can manipulate objects using the laws of classical mechanics and not the laws of quantum mechanics. However, a sense of scale is rendered incontextualizable when it is known that the dynamics of quantum mechanics affect the entire universe through a principle called the collapse postulate (i.e., collapse of the state vector): if I measure an observable physical property of a system that is in a particular state, I subject the entire system to collapse into a state that is described by the observable's eigenstate. Even further, there exist many eigenstates for collapsing into; which eigenstate is "chosen" depends on its observation (this is an awfully close analogue to the anthropic principle).

[caption id="attachment_23523" align="aligncenter" width="600"] xkcd #45[/caption]

That reminds me. The greatest unsolved question in my opinion is whether the universe houses the brain or if the brain houses the universe. To be honest, I started writing this post without knowing how it would end: there were multiple eigenstates it could "collapse" into. That it would collapse into this particular one was unknown to me, too, and, in hindsight, there was no way I could have known about any aspect of its destiny. Having said that, the nature of the universe–and the brain/universe protogenesis problem–with the knowledge of deterministic causality and mensural antecedence, if the universe conceived the brain, the brain must inherit the characteristics of the universe, and therefore must not allow for freewill.

Now, I'm faintly depressed. And yes, this eigenstate did exist in the possibility-space.

What's allowed and disallowed in the name of SUSY

The International Conference on High Energy Physics (ICHEP) is due to begin on July 7 in Melbourne. This is the 26th episode of the most prestigious scientific conference on particle physics. In keeping with its stature, scientists from the ATLAS and CMS collaborations at the LHC plan to announce the results of preliminary tests conducted to look for the Higgs boson on July 4. Although speculations still will run rife within the high-energy and particle physics communities, they will be subdued; after all, nobody wants to be involved in another OPERAtic fiasco.

Earlier this year, CERN announced that the beam energy at the LHC would be increased from 3.5 TeV/beam to 4 TeV/beam. This means the collision energy will see a jump from 7 TeV to 8 TeV, increasing the chances of recreating the elusive Higgs boson, the "God particle", and confirming if the Standard Model is able to explain the mechanism of mass formation in this universe. While this was the stated goal when the LHC was being constructed, another particle physics hypothesis was taking shape that lent itself to the LHC's purpose.

In 1981, Howard Georgi and Savas Dimopoulos proposed a correction to the Standard Model to solve for what is called the hierarchy problem. Specifically, the question is why the weak force (mediated by the W± and Z bosons) is 10³² times stronger than gravity. Both forces are mediated by natural constants: Fermi's constant for the weak force and for gravity, Newton's constant. However, when operations of the Standard Model are used to quantum-correct for Fermi's constant (a process that involves correcting for errors), its value starts to deviate from closer to Newton's constant to something much, much higher.

[caption id="attachment_23462" align="aligncenter" width="410"] Savas Dimopoulos (L) and Howard Georgi[/caption]

Even by the late 1960s, the propositions of the Standard Model were cemented strongly enough into the psyche of mathematicians and scientists the world over: it had predicted with remarkable accuracy most naturally occurring processes and had predicted the existence of other particles, too, discovered later at detectors such as the Tevatron, ATLAS, CMS, and ZEUS. In other words, it was inviolable. At the same time, there were no provisions to correct for the deviation, indicating that there could be certain entities - particles and forces - that were yet to be discovered and that could solve the hierarchy problem, and perhaps explain the nature of dark matter, too.

So, the 1981 Georgi-Dimopoulos solution was called the Minimal Supersymmetric Standard Model (MSSM), a special formulation of supersymmetry, first proposed in 1966 by Hironari Miyazawa, that paired particles of half-integer spin with those of integer spin and vice versa. (The spin of a particle is the quantum mechanical equivalent of its orbital angular momentum, although one has never been representative of the other. Expressed in multiples of the reduced Planck's constant, particle spin is denoted in natural units as simply an integer or half-integer.)



Particles of half-integer spin are called fermions and include leptons and quarks. Particles with integer spin are called bosons and comprise photons, the W± and Z bosons, eight gluons, and the hypothetical, scalar boson named after co-postulator Peter Higgs. The principle of supersymmetry (SUSY) states that for each fermion, there is a corresponding boson, and for each boson, there is a corresponding fermion. Also, if SUSY is assumed to possess an unbroken symmetry, then a particle and its superpartner will have the same mass. The superpartners are yet to be discovered, and if anyone has a chance of finding them, it has to be at the LHC.

MSSM solved for the hierarchy problem, which could be restated as the mass of the Higgs boson being much lower than the mass at which new physics appears (Planck mass), by exploiting the effects of what is called the spin-statistics theorem (SST). SST implies that the quantum corrections to the Higgs-mass-squared will be positive if from a boson, and negative if from a fermion. Along with MSSM, however, because of the existence of a superpartner to every particle, the contribution to the correction, Δm²_H, is zero. This result leaves the Higgs mass lower than the Planck mass.

[caption id="attachment_23463" align="aligncenter" width="414"] The existence of extra dimensions has been proposed to explain the hierarchy problem. However, the law of parsimony, insofar as SUSY seems validatable, prevents physicists from turning so radical.[/caption]

MSSM didn't just stabilize the weak scale: in turn, it necessitated the existence of more than one Higgs field for mass-coupling since the Higgs boson would have a superpartner, the fermionic Higgsino. For all other particles, though, particulate doubling didn't involve an invocation of special fields or extrinsic parameters and was fairly simple. The presence of a single Higgsino in the existing Higgs field would supply an extra degree of freedom (DoF), leaving the Higgs mechanism theoretically inconsistent. However, the presence of two Higgsinos instead of one doesn't lead to this anomaly (called the gauge anomaly).

The necessity of a second Higgs field was reinforced by another aspect of the Higgs mechanism: mass-coupling. The Higgs boson binds stronger to the heavier particle, which means that there must be a coupling constant to describe the proportionality. This was named after Hideki Yukawa, a Japanese theoretical physicist, and termed λ_f. When a Higgs boson couples with an up-quark, λ_f = +1/2; when it couples with a down-quark, λ_f = -1/2. SUSY, however, prohibits this switch to the value's complex conjugate (a mass-reducing move), and necessitates a second Higgs field to describe the interactions.

[caption id="attachment_23464" align="aligncenter" width="512"] A "quasi-political" explanation of the Higgs mechanism surfaced in 1993 and likened the process to a political leader entering a room full of party members. As she moved through the room, the members moved out of their evenly spaced "slots" and towards her, forming a cluster around her. The speed of the leader was then restricted because there were always a knot of people around her, and she became slowed (like a heavy particle). Finally, as she moved away, the members returned to their original positions in the room.[/caption]

The MSSM-predicted superpartners are thought to have masses 100- to 1,000-times that of the proton, and require extremely large energies to be recreated in a hadronic collision. The sole, unambiguous way to validate the MSSM theory is to spot the particles in a laboratory experiment (such as those conducted at CERN, not in a high-school chemistry lab). Even as the LHC prepares for that, however, there are certain aspects of MSSM that aren't understood even theoretically.

The first is the mu problem (that arises in describing the superpotential, or mass, of the Higgsino). Mu appears in the term μH_uH_d, and in order to perfectly describe the quantum vacuum expectation value of the Higgsino after electroweak symmetry breaking (again, the Higgsino's mass), mu's value must be of that order of magnitude close to the electroweak scale (As an analog of electroweak symmetry breaking, MSSM also introduces a soft SUSY-breaking, the terms of which must also be of the order of magnitude of the electroweak scale). The question is whence these large differences in magnitudes, whether they are natural, and if they are, then how.

The second is the problem of flavour mixing. Neutrinos and quarks exhibit a property called flavours, which they seem to change through a mechanism called flavour-mixing. Since no instances of this phenomenon have been observed outside the ambit of the Standard Model, the new terms introduced by MSSM must not interfere with it. In other words, MSSM must be flavour-invariant, and, by an extension of the same logic, CP-invariant.

Because of its involvement in determining which particle has how much mass, MSSM plays a central role in clarifying our understanding of gravity as well as, it has been theorized, in unifying gravity with special relativity. Even though it exists only in the theoretical realm, even though physicists are attracted to it because its consequences seem like favourable solutions, the mathematics of MSSM does explain many of the anomalies that threaten the Standard Model. To wit, dark matter is hypothesized to be the superpartner of the graviton, the particle that mediates the gravitational force, and is given the name gravitino (Here's a paper from 2007 that attempts to explain the thermal production of gravitinos in the early universe).

While the beam energies were increased in pursuit of the Higgs boson after CERN's landmark December 13, 2011 announcement, let's hope that the folks at ATLAS, CMS, ALICE, and other detectors have something to say about opening the next big chapter in particle physics, the next big chapter that will bring humankind one giant leap closer to understanding the universe and the stuff that we're made of.

On quantum entanglement and teleportation (part II)

(The introductory text can be read here.)

Apparatus

Imagine two devices separated by a large distance (any distance large enough to nullify quantum mechanical effects). These are devices that receive inputs and yield results. There are two modes in which an input may be received: classical and quantum-mechanical. Moreover, the input is generated by the same source and is delivered simultaneously.



Procedure

1. A set of inputs is generated at the source.


2. Each input may instruct the device to yield a result ‘x’ or ‘y’.


3. Device A reads the instructions and yields a result, A’


4. Device B reads the instructions and yields a result, B’

(A’ and B’ are now the states of the instructions after they have been measured by A and B, respectively)

Observations

1. If A’ and B’ are in the same state – i.e., if they are the result {x, x} or {y, y} – then they may be said to be entangled. To have achieved this, A and B must have communicated in some way to yield the same results arising from the input or must be in possession of some information that enabled them to yield the same result.


2. If it so happened that A and B communicated instantaneously – i.e., at faster than the speed of light – then they may be said to be quantum entangled. (Note that, in a quantum mechanical context, the results are found to be identical only upon observation, which means the act of observing the result is also a participant in the measurement process.)

Inferences

[caption id="attachment_23229" align="alignleft" width="115"] John Stewart Bell[/caption]

#1 If we assume the observations are being made on particles instead of some arbitrary “inputs”, then Heisenberg’s uncertainty principle kicks in. When we make the measurement, we are changing the value of some state variable of the particle, and it is the final state that we end up observing. John Stewart Bell, a Scottish physicist, was the first to make this observation, and added that the act of observation was somehow tied in with quantum entanglement (i.e., that the results were quantum-entangled in some way owed itself in part to the act of observing).

#2 The act of observing is a classical phenomenon because the devices A and B that enable the measurement are classical devices. That said, J.S. Bell argued that this is where the line between classical mechanics and quantum mechanics blurred.

Theoretical physicists live in a classical world, looking out into a quantum-mechanical world. The latter we describe only subjectively, in terms of procedures and results in our classical domain. (…) Now nobody knows just where the boundary between the classical and the quantum domain is situated. (…) More plausible to me is that we will find that there is no boundary. The wave functions would prove to be a provisional or incomplete description of the quantum-mechanical part. It is this possibility, of a homogeneous account of the world, which is for me the chief motivation of the study of the so-called "hidden variable" possibility.

- J.S. Bell

#3 The EPR (Einstein-Podolsky-Rosen) paradox is aimed at refuting quantum mechanics by leveling itself against the possibility of quantum entanglement. Since entanglement occurred only on conjugate entities – particles that are somehow but definitely paired – then the measurement of one of the A’-state variables should render indeterminate that state variable in B’ (Heisenberg uncertainty prin.). However, entanglement has already been observed. This means that either the two particles should have communicated or that the information necessary to generate the same outcome was already present in the two particles.

[gallery link="file"]

The physicists preferred the latter explanation, asserting that some “hidden local variable” was responsible for controlling the outcome of the act of observing. Of course, they made two assumptions in reaching this conclusion: locality and realism. (Note that this is a classical explanation of a perceived quantum mechanical effect.)

#4 In 1964, Bell came out with his famous theorem that refuted EPR’s preferred explanation. He observed that any local realist theories are incompatible with quantum mechanics. Essentially, this means that since a great number of experiments agree with the predictions of quantum mechanical theory, and since many of the results are greater than to be explicable by local hidden variables, either locality or realism is in conflict with quantum mechanics.

The principle of locality states that an object is affected directly only by its immediate surroundings, not by an event that is occurring simultaneously a large distance away. Realism, or counterfactual definiteness (CFD), is the ability to assume the existence of objects and parameters even when they have not been observed – or, to believe that constitutionally present particles shape the properties of the object at all levels. Bell posited that locality had been violated, and that superluminal communication was happening.

[caption id="attachment_23242" align="alignleft" width="114"] David Bohm[/caption]

#5 Bell’s hypothesis was based on the de Broglie-Bohm theory, which interpreted quantum mechanical effects as being caused by an encoding function (called the wave function) that did not let the particles that it guided feedback into itself. The interpretation also assumed that the velocities of the particles depended solely on the wave function, and that the wave function depended on the whole configuration of the universe. That's a contradiction of locality right there.

What does this have to do with teleportation?

Teleportation, by definition, is an instance of non-locality because it implies instantaneous communication. If two particles can communicate faster than at the speed of light to replicate quantum mechanical effects, then perhaps complex objects can someday be replicated instantaneously across large distances by simultaneously reproducing the quantum states of the particles associated with the object.

Of course, such a possibility is hinged on Bell’s theorem being true, on the EPR paradox’s implied existence of locality being false. To date, numerous experiments have been conducted that have neither conclusively validated nor invalidated Bell’s theorem. The difficulty lies in what Bell's theorem implied for the real world: it made quantum mechanics and local realism mutually exclusive. Either quantum mechanics fell short of explaining some physical parameters, or superluminal information communication was occurring (see Lorentz covariance).

[youtube http://www.youtube.com/watch?v=V0zQHNmz0gU]

Disentangling quantum entanglement

Very few scientific concepts enjoy the popularity of teleportation: the idea is equally awe-inspiring among scientists and laymen. To the most inspired, so to speak, what is fascinating is not how it’s accomplished as much as the possibility of “leaving” one space and “arriving” at another, but traversing the interim distance instantaneously. The implications of such travel are significant even at first sight. For example, imagine being able to teleport an object from earth into interstellar space, hundreds of thousands of kilometers away, without having to bother with rockets that might take years to span the same distance.

The sole field of physics seemingly capable of tackling the problems associated with such an esoteric and fragile system—quantum mechanics—still has leaps and bounds to go, however, before it can realize the teleportation of objects. For starters, it hasn’t figured out what really happens during the teleportation of a few photons even though it has accomplished just that with an 80-per-cent accuracy over a distance of 97 km.

In a paper submitted to arXiv on May 9, 2012, Jian-Wei Pan, et al, demonstrate how they used an exotic phenomenon called quantum entanglement to achieve teleportation across Qinghai Lake in western China. Using an ultraviolet laser aimed at a barium crystal, Pan’s team generated pairs of quantum-entangled photons. Then, each photon of a pair was transmitted using a telescope to two parties on either sides of the lake, A and B.

[caption id="attachment_23171" align="aligncenter" width="460"] The experimental setup[/caption]

Making a measurement of the photons yields a good description of the “state” the photons are collectively in. Therefore, A’s and B’s goals are to see if a third party interacting with these photons ends up in a state similar to the control group even when separated by 97 km of free-space. Here, the state of the system refers to the values of a few fixed variables: if the variables hold a particular set of values, then the system is said to be in a particular state (states are usually independent of extrinsic properties such as mass, etc).

To measure this change, the researchers at Site A let photons generated at locally to interact with the incoming modified photons. Simply put, the foreigners would leave an imprint on the locals upon interaction. This imprinted state is then measured and compared with the state of the photons at Site B. In Pan’s experiment, the between the two agreement was 8 on 10.

The aspect that makes such an outcome wonderful is that the particles didn’t have to end up with the same state. Further, 80 per cent is a value large enough to rule out any coincidence (but small enough to rule out a complete success). If this long-distance communication between nanoscopic particles is further investigated, it becomes evident that their pre-travel entanglement provided for a form of durability and predictability of state that let the particles behave similarly in two very different measurement experiments. At the same time, it is the nature of this entanglement that baffles most scientists.

The formal definition of entanglement is very fundamental in the sense that quantum mechanics deals with it in terms of probabilities. When two groups of photons are said to be quantum-entangled, it means that the states that the groups are in are related to each other by means of a variable. If the variable changes, then the properties of the photons change, too. However, the groups’ relationship with each other does not, like siblings who remain siblings despite how old they get or when they each die.

The existence of this variable is not as much disputed as it is hoped into existence (Little wonder then that it’s handled as a product of probabilities?). Because it remains outside the realm of human control, experiments with teleportation tend to leave the hidden variable alone and instead focus on how much the measurement sites can be separated by, how efficiently large molecules can be entangled, etc., i.e., testing the limits of its practicability.

In order to do so, the photons are subjected to a simplified treatment—one conceptualised so as to make the fewest assumptions as well as not introduce new sources of error. Instead of groups of photons, two are addressed, and each is “allowed” to exist in one of two states. Schrodinger’s cat takes off here and asserts that the particles may exist in this state, that state, or the counter-intuitive superposition of both, and that revelation can come only with observation.

Let’s say the two particles are ‘a’ and ‘b’, the states ‘0’ and ‘1’. The four possible combinations of states, then, are:

{0, 0}
{0, 1}
{1, 0}
{1, 1}

Entanglement is said to have occurred when b is in a particular state when a is in a particular state. That is, if b is 1 every time a is 0, then a and b are entangled. Since this property is commutative, a will be 0 every time b is 1. Further, the change occurs instantaneously irrespective of the distance between the two particles (giving the impression that they're "communicating" at a speed faster than light's). The presence of such an order coupled with the four possible outcomes makes each outcome a particular state of the system, called a Bell state.

To find out what the Bell state is, a Bell measurement is made. Because of Heisenberg’s uncertainty principle, however, the act of making the measurement changes the state of the system. Even so, this alteration doesn’t matter as long as the pre-measurement state is discovered. In Pan’s experiment, with six initial states, the Bell measurement was made using the imprinting mechanism to reveal that the entangled photons had interacted with other particles to yield a final state that resembled the initial.

[caption id="attachment_23175" align="aligncenter" width="729"] xkcd #824[/caption]

Earlier, another experiment had been conducted that demonstrated the teleportation of quantum information across 16 km. The principal shortcoming of that experiment was that the photons to be teleported—the “locals” —had been specially generated within the lab under careful conditions. Practically, this is a highly ideal condition that can seldom be met: if this blogger is to be teleported, he cannot be carefully “prepared” in a lab. Pan and his colleagues eliminated this necessity by generating local photons with random quantum states.

At the same time, they have failed to discount a possible source of error: the entangled photons and the to-be-teleported photons were generated by the same source. Even though this limitation doesn’t interfere significantly, it is a limitation nonetheless. (What is the confidence with which it may be asserted that the “local” photons are created in a mixed state? If it’s being assumed that this is not a source of error, what were the considerations made? Et cetera.)

I must concede that looking behind the teleportation curtain kills a lot of the fantasy. Even if entanglement continues to elude understanding, simplifying something so enigmatic to probabilistic proportions and then to linear algebra can be a bit of a buzzkill—disregarding that that is the purpose of scientific endeavour, of course. With their paper, Jian-Wei Pan and his team currently sit pretty at the forefront of quantum mechanical teleportation. Even if we still have a long way go, the knowledge of Pan’s experiment gives us the best shot at ultimately achieving the teleportation of complex objects.

Leonard Hofstadter vs. Leslie Winkle: What's at stake

As far as TV shows are concerned, I'm a big fan of The Big Bang Theory. I've always thought nerds were cool, but the show only popularized that opinion - at least in some circles that wouldn't have accepted, to use lingo from the show, the paradigm. My only problem with the show is the character I really like, Dr. Sheldon Cooper, is a string theorist and a character I find annoying, Leslie Winkle, is an LQG-adherent (Loop Quantum Gravity).

[youtube http://www.youtube.com/watch?v=d9YBgqxpaLk]

I haven't received any formal training in particle physics. I believe that understanding the natural philosophy of the universe can happen to perfection just by a lot of reasoned thought with a compatible dose of theories and a few formulae.

On that note: I'm an advocate of LQG, and I'm going to spend the rest of this post on detailing why that is and how it works. Or, if you like, I'm going to try and explain what the squiggles on Sheldon's and Leonard's boards mean and what the squiggles on Leslie's board could mean.

The story must begin the way all histories of physical theories do: with Isaac Newton. In describing the fundamental laws of classical mechanics, Newton needed a frame reference, a fixed entity with reference to which objects could accelerate. Without a frame of reference, we'd never be able to understand how an apple falls from a tree, for example. We know it did because we see it against an unmoving background. Thinking as he was in much more stripped-down terms, Newton conceived of a background space against which all things could be measured.

- Sir Isaac Newton

In the 19th century, there was a breakthrough by Michael Faraday and James Clerk Maxwell. Working with electricity, Faraday imagined that two charges interacted via a mediating electric field. He established that the field lines started and ended with charges, and in a space where there were no charges, the field lines bent around and formed loops. These field lines were called Faraday lines. Maxwell then transcribed Faraday's hypothesis onto paper and birthed the Maxwellian equations, which described the behaviour of electromagnetic fields in much the same way.

- The image shows a point source generating a field. Notice how the field lines are all parts of closed loops.

And then, there was Albert Einstein, whose principle contribution was the idea that gravity is not just a force but an inherent attribute of space-time itself. However, when attempting to work this into his general theory of relativity, he realized that gravitational force also had to be mediated by a field like electricity and magnetism were. This meant that a gravitational field had to exist with loops, lines and everything else.

Einstein also stumbled across one other astounding realization. All those years ago, when Newton had conceptualized a background space to serve as a frame of reference, he'd described acceleration in terms of a gravitational force - a discovery he's the most known for. Einstein found, however, that this Newtonian background space was nothing other than gravitational field itself. Because the field permeated through space-time and gave mass to objects that interacted with the field, it became a frame of reference.

These "stumblings" gave rise to two important conclusions.

1. Loops didn't exist in a background space (as was previously thought) but on another layer of loops. And those loops? On yet another layer of loops. And those loops? You get the idea.


2. Because there was a gravitational field that mediated gravity, low-frequency excitations of the field had to manifest as some particle. Just as the low-frequency manifestation of an electric field are electrons and of an electromagnetic field are photons, the excitations of a gravitational field are called gravitons. (Note: these have nothing to do with the Higgs boson)

This lack of a background space was disturbing to many physicists. At this point, some decided to ignore this outcome of general relativity and proceeded as if there was background space - a region that didn't have any underlying loops. In fact, these theorists went on to postulate that the gravitational field was the resultant when a background space and a quantum field acted together. These are today known as the string theorists.

- xkcd comic #171

The other faction decided to take into account this lack of background space and set about trying to formulate a background-independent theory of the nature of the universe. These are the LQG-advocates. According to them, the universe offers no background space naturally but they are created when the Faraday lines of the gravitational fields are quantum-excited.

Let me explain.

The gravitational field exists on another layer of loops (we don't know what they are). Because the point sources that created the gravitational field - Higgs bosons - quickly decayed long ago, the lines are large closed loops. The gravitational field permeates throughout the space-time continuum, and therefore there are infinitely many such loops.

- One of the decay signatures of a Higgs boson is a tau lepton-antilepton pair, shown above. Tau leptons are extremely hard to detect because they decay too quickly. However, other signatures include quark-antiquark pairs and electron/muon lepton-antilepton pairs, which are relative more long-lived.

When one of these loops is excited to some energy, physical space is created. It is important to understand that the loops are not in that space but that they are the space. Earlier, there was a conundrum: if there are two loops that are separated by a really small distance, then each loop will represent one degree of freedom for the universe, i.e. one avenue of change.

Since there are infinitely many such loops, the universe has to have infinite degrees of freedom. But that is not the case. That was dissolved after physicists realised that all the loops were a part of the same field, and no space could have separated the loops because the loops were space.

- In LQG, the point where two loops intersect is called a node. The region that corresponds to a node is called a cell, the section of a loop joining two nodes is called a link, and the surface of a cell that a link passes through is called a... well, a surface.

So, that is the story of the universe - according to some. The string theorists believe that long, one-dimensional strings exist in a background space, and their vibrations manifest as particles that make up the universe.

I chose to be on the LQG side of things because I see no reason to disregard Einstein's conclusion that there is no background space. Also, string theory has turned up no testable hypotheses because it claims the strings exist at the Planck scale (one-hundred-billion-trillion-trillionth of a metre) whereas the mathematics of LQG has been able to explain the formation of black holes (I'll save that for another post, another day).

- While string theory claims that the universe exists as strings at the Planck scale, LQG claims that at such scales, the granular cells that the space-time continuum is made of should show up. But such claims are yet untested.

In conclusion: when Leonard says he prefers his universe stringy, not loopy, all this is what he means. However, I can sympathise with Leslie when she leaves in a huff after Leonard wants to "let the kids decide" which hypothesis to choose.

Why A Language Resembles Physics So Much

Here's why a language is like physics. It's common knowledge that both of them help us understand the world: physics is a study of the physical word, a methodological inspection of every phenomenon we encounter, every experience we are affected by; language is tool of conveyance, and the passenger borne is meaning, and so by speaking in a language, we are only trapping the meaning of out thoughts in words and setting them afloat in a sea of communication. However, the world of physics is split into two distinct factions: the wave theorists' and the particle theorists' factions. How does this bode for language?

[caption id="" align="alignright" width="300" caption="Particle detection in a cloud chamber"][/caption]

The particle theorists see the world as being composed of discrete packets of energy that are, all of them, bound inexcusably by the law of conservation of energy and all the laws of thermodynamics. The wave theorists see the world as being seated on manifestations of energy being propagated as a continuous wave; in other words, the discretion as particles is discredited even though the law of conservation of energy and the laws of thermodynamics still hold.

Amongst particle theorists, all the energy that is present in this universe is a constitution of a very large number of packets, each of which contains a definite amount of energy that is unchanging over time. If a space contains twice as much energy as another, it does not mean the packets are twice as voluminous, it only means there are twice as many such packets. When we look out into this universe, all that we understand or all that there is to be understood at all can be done so if only there is an "amount" of meaning attached to it. Our interaction with this meaning is possible only through a tool that allows us to exchange meaning in the process - a tool like a word. A word can be said to contain a discrete amount of meaning. Even though different people may see it to be different amounts, the innate value of that meaning does not change over time. The adjective "beautiful" ascribes different amounts of beauty according to different people, and to each person therein, the amount of beauty the word describes is the same. However, "beautiful" never does come to ascribe ugliness to an object - apart from signifying its absence.

Words are discrete, like particles of meaning being strung together to create a large volume of meaning called a sentence. Sentences are then strung together to create a larger concatenation of meaning: it could be multi-dimensional, too, because a paragraph might discuss the properties of different objects through different adjectives and, in the process, create an array of meaning, so to speak. Now, if we were to zoom out to view the bigger picture, what we see is a language: there are grammatical rules that are the thermodynamic tyrants of communication, and then there are various other principles and theories that lay down how meaning is generated as well as understood - the "laws of conservation of meaning".

Even though we have described words to be discrete capsules that contain a set amount of meaning, it doesn't mean that the language as such prevents us from ascribing some amount of meaning to the gaps between these particles. Between one word and another, there is a boundary that prevents the spillage of any semantic entity, a boundary that holds it within a space in the confines of which it exists and can be understood. At the same time, with the combination of words, we create a "wave" of meaning that is present everywhere - even unto where "beautiful" and "pulchritudinous" can't reach, thereunto does "of a winsome exquisiteness surpassing the glow of a young star".