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Friday, February 17, 2012

Quantum of nonsense Part I - A Crash course in quantum theory

 This is the first part of a two parter, discussing the use of the world 'quantum' by quacks. And rather than just jump into why they're quacks, I thought I'd split the post into two and give a brief history of quantum theory. Believe me, it's far stranger and more enjoyable than anything a purveyor of woo could spin. And I put some cute kittens in for good measure.

Quantum mechanics is weird - Discoveries in this field have been wonderfully counter-intuitive, prompting the legendary Niels Bohr to state "..those who are not shocked when they first come across quantum theory cannot possibly have understood it.". In fact, so profound are some of the questions it raises about reality that the ineffable Richard Feynman once said "I think I can safely say that nobody understands quantum mechanics.". Because the subject is so incredibly jaw-droppingly at odds with what we're used to in our macroscopic world, the fact that the microscopic behaves quite differently dazzles people.

But it is this very dazzling property that has made purveyors of nonsense grasp it, and use it as a stamp to justify their outlandish claims. The field of quantum mysticism and quantum healing is the use of modern physics terms to lend weight to a loose connection of new age and spiritual jargon, totally mangling the beautiful science in the process - Works by Deepak Chopra, Robert Anton Wilson, Gary Zukev et al have offered quantum mechanics as some kind of magical deus ex machina to explain away any gaping holes in their new ages drivel.  Only here's the kicker - invoking quantum mechanics to 'explain' these, or indeed any human experiences is so stupid, it's not even wrong. So I decided to write a post condemning these utter quacks, when I came to the realisation that starting off that way might deny my readers an insight into the utterly crazy world of quantum mechanics. So I decided to split the post into two, with the first part a quick crash course into the brain shaking world of the very small and some other time I shall do a follow up on why new-agers and quacks love the word quantum and how they get it wrong everytime....



Einstein reacts to Deepak Chopra's latest take on Quantum healing...


Lighting the way
Our weird and wonderful story begins in the 17th century with the thoughts of the original action man of physics one Sir Isaac Newton - Newton was thinking about light, as a polymath is wont to do when he's not looking for bible code and inventing cat flaps. How exactly does light travel from one place to another, and what exactly IS light ?


Newton - Would often be found musing over Optics and less often over the hottest trends in wig fashion


Newton thought very hard about this - he knew light had energy and that it travelled. Musing over this, he came up with his Corpuscular theory of light. His idea was that light was made up of little tiny particles called corpuscles. These little bundles travelled at some finite velocity and didn't require any medium in which to move. There was a little sticking point though - Newton's theory didn't account for some phenomena like diffraction, the spreading out of light as it hits an obstacle, in much the same wave a ripple in a pond spreads out when it encounters a rock. His theory wasn't seriously challenged until about 100 years later by Thomas Young. Young was a renaissance man like Einstein, and was famous for discoveries in the field of engineering, medicine and Egyptology in addition to his impressive physics credentials. Show off. Anyway,  Young realised that there was another way for energy to propagate - wave motion. Imagine it like a slinky if you will - if you shake one end, the motions travels down the length of it and imparts energy at the other end, despite the fact the actual slinky has not itself moved location.


Slinky dog - Subtly teaching us about wave mechanics, the crafty informative bugger..

The beauty of Young's idea was that it described light phenomena wonderfully - it predicted diffraction, reflection, refraction and a whole host of other ideas. There was now no doubt that light behaved like a wave and up until the early 20th century there was no reason to think otherwise. The particle theory of light was done and dusted. Going back to our slinky analogy, it's useful to note the one thing waves need that particles don't; a medium to propagate through. The plastic / metal of the slinky is the medium. Sound waves travel through the medium of air and water waves through water. Without these media, they simply cannot travel. For this reason, physicists assumed that there must be a medium between the sun and the earth which allowed light waves to travel through it. They called this hypothetical medium aether when they were feeling verbose, and just "the aether" in hallowed hushed tones when they wanted to be mysterious, probably while wearing cloaks and engaging in some Gregorian chanting.

We are the physicists and we seek the aether!


Just one small problem...

There was just one slight problem - the aether didn't exist. This was shown by the famous Michelson-Morley experiment, the most famous null result in physics. The ramifications of this experiment and a curious derivation from Maxwell's equations led a young patent clerk from Germany named Albert Einstein to a truly wondrous theory called special relativity in 1905, a fascinating area with an intimate relationship to quantum mechanics but at the moment we'll leave it be and jump to the world's most obscure light bulb joke.

Wait for it....


"How many Max Plancks does it take change a light bulb?

Never heard that one before eh?  In 1900 Max Planck was a desperate man - he had been commissioned in 1894 by an electric company to improve the efficiency of their light bulbs. To do so he had to consider a theoretical construct known as a black body, a perfect emitter and absorber of radiation. To reconcile theory with experiment, Planck inadvertently made a radical assumption; rather than allowing the system to have a continuum of energy emitted, he instead assumed the energy could only be emitted in discrete packets called 'quanta'. Planck viewed the solution as a purely formal one and didn't think too much of it. Yet what he had effectively done was show that energy could only be emitted in discrete levels or 'steps', totally overturning the classical idea of energy being a smooth continuous 'ramp'. At the same time, Planck's solution solved a problem in physics known as the ultraviolet catastrophe, where the power emitted by a black body became infinite in the UV range. With Planck's solution, the problem disappeared and his theory matched experiment. Many physics textbooks claim Planck's work on blackbodys was motivated by this problem but in fact his motivation was light bulbs. Seriously, one could not make that up.




From Hand waving to mind blowing...
A "quanta" merely refers to a discrete packet, so it was apparent Planck's solution had 'quantised' energy. At this point no one gave this quantisation of results much notice, including Planck himself. They figured it was some problem with the model. Models, after all, are approximations of reality. But for Einstein, this actually solved a problem he'd been musing on called the photoelectric effect. This effect is observed when high energy light, even at low intensity, causes a metal to eject electrons. But curiously, lower energy light, even at high intensity couldn't dislodge them. This makes no sense in classical physics - if you imagine light like a wave lapping away at a sea cliff; a lot of little waves have the same cumulative effect as a few powerful waves. Yet this wasn't happening - only certain energies were doing it, intensity didn't matter.  Einstein solved the puzzle by deducing that the light was arriving in packets which we know call photons. If one of these packets had enough energy, an electron was emitted. Einstein had used Planck's guess to solve a totally unrelated problem, and had begun to show that light was a particle.

So here was Einstein in 1905 postulating that light was a particle, and making a pretty damn convincing case for it. But this kind of flew in the face of previous experiments and theory - Young had shown light was a wave. Maxwell's equations worked, and relied on light having wave properties. Waves and particles are mutually exclusive, what in the name of Schrodinger's fond regard for animal welfare was going on ?


Is this really the only way to demonstrate the madness of macroscopic observer effect Dr. Schrodinger ?!

The current explanation to this conundrum is one of the most mind-blowing results in all of physics - Light is both a particle and a wave at once, and will display the properties of either / or depending on how you choose to measure it. In essence, light is neither a wave nor a particle but somehow both.

Stop for a second - if that isn't making your logical brain go into convulsions, think about it again - it is something of a paradox of modern physics. What's more, there is a further principle which physicists call complementarity that essentially states something equally weird - while the wave and particle nature co-exist, any attempts to measure the properties of one state destroys all information about the other state. More correctly, the twain properties can never be measured at the exact same time.

This is deeply weird, and equally, deeply wonderful.


Mind: Blown.

This behavior isn't limited to 'just' wave-ticles of light. French aristocrat (queue infamous joke) and physicist Louis De Broglie reasoned that matter should also have wave properties associated with it. This was shown to be the case - that matter itself has wave like properties. The reason we don't observe them is that unless the object is truly very very tiny, they are not visible to us in our macroscopic world. However, this could still be tested with small particles like electrons and even neutrons, even though these are ostensibly particles. The same credo of complementarity held of course; attempts to view the dual properties at once faltered, destroying information about one of the states. This crazy concept is called wave-particle duality, and is a cornerstone of quantum theory. Despite its apparent outlandishness, it has been verified time and time again by experiment. If this is melting your brain slightly, rest assured that is only indication that you are correctly grasping the enormity of that finding. As the inimitable Niels Bohr said..

Niels bore, the third most famous and great Dane after Hans Christian Anderson and Scooby Doo


Einstein takes his quantum ball home


 Now, physics up to this point had been deterministic. If you knew all the variables, you'd be able to always predict the output. But new quantum theory suggested that at the very, very small end of the scale, events were probabilistic. These probabilities were related to the square of the wave function, Ψ, of the system. Werner Heisenberg also showed that there was an inherent uncertainty in some variable pairs, such as position and momentum and energy and time - there would always be an uncertainty in these measurements as they involved the interaction of the system and the measuring device. This relationship was verified and is now known as the uncertainty principle. These ideas taken together for the basis of what is called the Copenhagen interpretation of quantum mechanics, which postulates..

  • A system is completely described by its wave function Ψ
  • Nature is essentially probabilistic
  • It is impossible to know the value of all system properties at once (uncertainty)
  • Matter exhibits wave-particle duality, both cannot be measured at once (complementarity)
  • Quantum mechanical systems will reproduce classical results for large systems / particles

This interpretation of quantum mechanics is the most common, but there are others, differing mainly on the nature of the wavefunction.  Now, a system can be in a superposition of all possible states, but the act of measuring them forces the system to collapse down to a single measured state. This bizarre behaviour is called wavefunction collapse, and is still a hotly contested question. In the Copenhagen interpretation, the measurement 'forces' the system into one state, where as the in the 'Many worlds' interruption, each possible state exists in a different universe. There are dozens of interpretations of Quantum mechanics - note that the the predictive power is beyond dispute, but the philosophical question of what these results imply about nature itself is still a thorny issue.

But ironically, the man who had lead the world into the quantum revolution loathed the new formulations - Einstein did not at all approve of the probabilistic interpretations, preferring a version of the ensemble interpretation which argues the wave function doesn't apply to an individual system but only to groups of them. This is when Einstein famously argued "God does not play dice!". Legend has it that Bohr muttered he should stop telling God what to do.

Bohr and Einstein had a series of debates, and every example he gave Bohr was able to counter. Finally, Einstein along with some colleagues came up with the EPR paradox - a quantum system has a wave function, but if this system is split into two, the system still maintains one wavefunction between them. Then, if you performed a measurement on one of them, even separated by vast distances, the other would be forced into a state too. Einstein and his co-authors argued that there must be a class of 'hidden variables' that told each particle what to do. QED, thought Einstein, as the other idea meant that non-local effects could instantly travel seemed utterly absurd on the face of it.


Smug Einstein - QED, bitches!

Only nature conspired against Einstein when it turned out non-locality was exacted what happened. These particles sharing a wavefunction became known as entangled entities,  and were shown to violate the classical notion of locality. In the Copenhagen interpretation, this would be explained as instant wavefunction collapse. Einstein maintained until his death in 1955 that quantum mechanics was an incomplete theory. Erwin Schrodinger had an equally great misgiving about the Copenhagen interpretation, and highlighted the insanity of trying to apply multiple states to macroscopic objects.

"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The wavefunction of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts."

This is the basis of the infamous Schrodinger's cat experiment, which takes issues with the observer's role in wave function collapse. There are as many interpretations of this thought experiment as there are interpretations of quantum mechanics. 

Nice kitty, GET IN THE DAMN BOX!


Class dismissed - some concluding remarks


The world of the very tiny behaves nothing like the world we know, and at small enough scales quantum effects dominate. What puts the limit on this scale ? The limit is related to a constant of nature we know as Planck's constant. It is given by..

 h = 6.626 x 10^-34 J / s 

To write this out in normal notation, it would look like...

h = 0.0000000000000000000000000000000006626 J / s

Planck's constant is tiny but utterly dominates in quantum realms, and perhaps were it bigger we'd be far more familiar with quantum effects.

Stay tuned for Part II - Quantum Quackery! 
 














6 comments:

  1. Eventhough I understood the Schrodinger's cat experiment only faintly at first and had to read more of it elsewhere to grasp it more.

    Thanks for the article, waiting for the second part -- hope you'll be specific in your criticism of Chopra, Robert Anton Wilson, Zukav etc.

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    Replies
    1. What I meant (above comment) to say was that irrespective of the little difficulty in understanding the cat experiment; I enjoyed your article and please keep up the good work.

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    2. Ah cheers, glad you enjoyed it! Yeah, you're right though - I skimmed on the definition of the Schrondiger cat thought experiment. Basically, because Cophenagen claims quantum states exist in a superposition of states until they're observed, S. pointed out that scaled up to macroscopic sizes this made no sense - you cannot have a half dead / half alive cat!

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  2. Thanks for putting in the time to write that. I thought it was well written and (for a non-physicist like me) a very informative refresher of the salient points. (It's easy to get lost in the terminology in comment threads etc.)

    I have one question, though. What did you mean by: "invoking quantum mechanics to 'explain' these, or indeed any human experiences is so stupid, it's not even wrong" ?

    Surely it *is* wrong if QM is not a (possible) explanation for these things? (Or is it that the things being "explained" do not, themselves, exist in the first place?!)

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    Replies
    1. Hey Cabbage of Doom (awesome user handle by the way) - You've actually kind of pre-empted by part two post, in which I'll look at some of the claims made by Quantum quacks and why they are not possible to analyse through that lens. I'll try to give an outline here but the 'long' but will be the follow up post!

      The kicker for me is the mistake made when scaling up quantum physics to the scale we're used to in everyday lights. All interpretations of QM have the credo that in the limits of large sizes or numbers, the rules should predict classical phenomena! This is why for example we see buses travelling in well defined linear paths, rather than quantum leaping and teleporting in and out of existance (though this may improve the public transport situation in Dublin at any rate) . The route to madness lies in failing to realise this; we do not live in a domain where quantum effects dominate, as we are too massive and composed of too many elements!

      I'll also handle misapplication of the observer effect, entanglement and quantum consciousness so do stay tuned :) Hope that helps!

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