Thinking quantum

In quantum physics, every metric is conceived as a vector. But that's where its relation with classical physics ends, makes teaching a pain.

Teaching classical mechanics is easy because we engage with it every day in many ways. Enough successful visualization tools exist to do that.

Just wondering why quantum mechanics has to be so hard. All I need is to find a smart way to make visualizing it easier.

Analogizing quantum physics with classical physics creates more problems than it solves. More than anything, the practice creates a need to nip cognitive inconsistencies in the bud.

If quantum mechanics is the way the world works at its most fundamental levels, why is it taught in continuation of classical physics?

Is or isn’t it easier to teach mathematics and experiments relating to quantum mechanics and then present the classical scenario as an idealized, macroscopic state?

After all, isn't that the real physics of the times? We completely understand classical mechanics; we need more people who can "think quantum" today.

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.

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.

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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]