September 16, 2011

Uncertainly yours, the cat

My new math/science effort for Mint is in the paper today: Uncertainly Yours, The Cat.

It's about Lajwanti the cat, errant electrons and a mirror too. I tried my usual -- work in the gratuitous mention of Lady Gaga -- but yet again, I wasn't able to manage it. So the count of Gaga mentions in my columns remains stuck at one, more's the pity.

And as usual, in case the link doesn't work, the text is below.

Your thoughts always welcome.

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Postscript: Please read Rahul Siddharthan's debunking of my article, here. Live and learn.

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With two cats at home, it's always a delight when they compete to rub themselves against my shin. So I sometimes wonder, why would anyone dream up a cat? "DD's lost it", you're thinking. But I would submit that the world's best-known cat, at least among physicists, is an imaginary one.

And get this: she never lived, but people say she's both dead and alive.

This feline was the creation of the great German physicist Erwin Schrödinger, who died 50 years ago. Seeking to understand Heisenberg's Uncertainty Principle, fundamental to modern physics, he thought of a cat. I mean, the last thing I expected to hear about in college was a purely hypothetical cat. Yet generations of students the world over know this one well.

Absent mathematical jargon, the Uncertainty Principle says something simple: the act of measuring something affects that measurement. For example, it is impossible to determine both the location of an electron and the speed at which it moves. If you measure its speed accurately, this process of measurement itself makes its location hard to pin down, and vice versa. The uncertainty in one measurement, Heisenberg tells us, depends on the uncertainty in the other.

Looked at another way, measurement decides the state of the electron.

This is not such a mysterious idea. Imagine an anthropologist visiting a tribal village to study its inhabitants. His very presence will disturb the state of the village: we all behave differently when strangers come visiting. By observing, the anthropologist affects what he wants to observe. He never gets a "true" picture of the village.

Sure, but why is this important? Traditionally, physics nurtured the idea that nature's laws tell us the past and future. If we can fully describe the state of the universe right now, for example, we can deduce its state at any other time. Heisenberg shattered this romantic notion. Not only is there uncertainty in the properties of things, the act of measuring properties itself increases uncertainty. You cannot determine the state of the universe at a given time; life is not predictable.

Now this is fine with tiny particles like electrons that nobody can see anyway. What about ordinary objects?

What about, say, cats?

That very question occured to Schrödinger. His famous thought experiment went something like this. Put Lajwanti the cat into a box. Also put in a device that, when turned on, might or might not emit a single electron. That is, over a minute, the chances are exactly 50-50 that it emits an electron. If it does, it also releases a poisonous spray, goodbye Lajwanti. If it doesn't, she lives to fight another minute.

Seal the box and put it far enough away that you can't tell what's going on inside. Turn on the device for exactly one minute. What happens to the cat?

Trivial question, right? The answer: we don't know. The Uncertainty Principle reminds us that we can't predict the behaviour of the device: even if we pinpoint the location of its every electron, we have no idea about their motions, no way to determine their behaviour during that minute, no way to tell if one will be emitted. Thus we don't know if Lajwanti is alive or dead.

Until, of course, we walk over to the box and open it to hear -- let's hope -- the loud miaow of a bewildered cat. Only then do we actually know that she survived her uncertain ordeal.

With the box sealed, we know only that Lajwanti is either alive or dead. This must seem blindingly mundane. But it is entirely consistent with the laws of physics to think of her, before opening the box, as simultaneously alive and dead. Here's the crucial idea: the act of opening the box and looking in on Lajwanti -- taking a measurement, in other words -- is what puts her definitely into one of those two states: alive, we hope.

What's the point? What's so profound about a cat shut into a box?

Well, there's the effect of measurement, the idea of uncertainty, and more. But perhaps the deepest yet simplest point is this: reality takes shape only when we observe it.

We know an electron is emitted only when we detect it. The anthropologist learns something about tribal customs only when he actually observes a tribe, even if that affects their behaviour. We find out poor Lajwanti's fate only when we open Schrödinger's box.

Haven't we all wondered on these lines before? If I turn my back to the mirror, is my image really there? If there's nobody to hear, does a tree that falls in a forest make a sound?

Is there reality without observation, existence without consciousness?

Schrödinger's cat shows that the laws of physics might answer those questions with "no". That may be too extreme for people who believe reality surrounds them without needing to be looked at.

Then again, Lajwanti herself isn't real.

16 comments:

Rajarshi said...

Dear Sir,

This is one of the best explanations of Heisenberg's Uncertainity Principle I have come across. Recently, I watched the award winning docu-drama 'What the bleep do we know'. This article echoes many of those ideas but then it's difficult for lay people to visualize such concepts.

Regards,
Rajarshi

Anonymous said...

Can you explain this also while you are about it. http://www.nytimes.com/2011/09/15/nyregion/willow-lost-cat-from-colorado-resurfaces-in-manhattan.html?ref=nyregion

Boskoe said...

In other words, sab kuch Maya hai!!

rsidd said...

Dilip -- we did exchange some e-mails but here's my reaction to it.

Anonymous said...

Quantum mechanics is a model that works to explain many many things. Let's not give it a deeper meaning beyond that. Particles don't exist in states, it is how we choose to model our understanding.

Perhaps after this public debunking by rsidd you can submit all your physics articles to him for review. Try "time dilation" for your next popular work.

Anonymous said...

I would also like to invite RSIDD to explain to all of us the "A watched pot never boils" quantum experiment - and a summary of the following . article . Thank you.

rsidd said...

anon -- the "observer" in the quantum Zeno effect (and in quantum experiments generally) may be a machine. The nature of the observer was mysterious in von Neumann's time, but even at that time, it was widely accepted that a "classical" (macroscopic) system is adequate. Today I doubt any serious physicist would claim that the human mind is necessary. Don't believe something just because it has Springer's stamp on it.

By the way, just yesterday I heard a nice talk on the quantum Zeno effect (originally proposed theoretically by Misra and Sudarshan in the late 1970s), by Anu Venugopalan on the occasion of ECG Sudarshan's 80th birthday.

Dilip D'Souza said...

This article came out of some amount of idle reading and idle thinking I did a long time ago, in order to get the cat experiment (and the uncertainty principle) to make sense to me. (Which they didn't when I first ever heard of them).

I am no physicist, but this reasoning put it in some perspective for me. I thought the same perspective might be approachable and interesting for readers of this Mint column. That's why I wrote it.

rsidd said...

There is in fact a hard question that I did not really address above: the "collapse of the wavefunction", i.e. what happens when it is observed. The traditional view is that it collapses probabilistically into one of the allowed eigenstates of the quantity being observed. I argued above that it doesn't matter whether the observer is a human or a cat or a machine. But the vexing question to a physicist is, how to describe this process? Is it in fact governed by Schroedinger's equation, or does it need to be added on in an ad-hoc manner (as in the traditional interpretation)?

The current most popular view seems to be that it happens by decoherence. To me it looks quite convincing but there is no rigorous demonstration that this is in fact what happens.

Stapp seems to want to exploit this gap by saying the human mind is responsible for the collapse, but to me that is not a satisfying answer. On the other hand, he is not stupid.

But there is another motivation for those who want to link the mind to the foundations of quantum mechanics: the question of free will. We all like to think we have free will. But Newtonian mechanics is totally deterministic. Schroedinger's equation is deterministic too, but the observation/collapse thing introduces a probabilistic element -- which is still not the same as free will. But could free will emerge somehow as a way of controlling the collapse of the wavefunction? On the other hand, there are lots of psychological experiments suggesting that free will is an illusion -- our bodies respond to situations before we are consciously aware of them, but we still think we are controlling our bodies.

My feeling is that there is something fundamental that we don't understand, in terms of the origin of free will (or even the illusion of free will, if it is an illusion), and the nature of consciousness. But the answers are not to be found in quantum mechanics.

Anonymous said...

Free will? No such thing otherwise marketing and propaganda would never be successful. That aside, thanks to RSIDD for his notes about decoherence. As for the absence of DDD coherence about that cat ... it is rare to find a journalist so honest as to confess to it and in this case we observers interact with him and collapse ourselves into the desired final state.

Ludwig said...

The final words on Schrodinger's feline may be found here, here, and here. :)

Ankur Kulkarni said...

DD - don't you think it is your responsibility to have your work read by a physicist, just to ensure that you are not writing something factually incorrect, and possibly misleading? Or at least to introduce a disclaimer clarifying your ignorance on certain matters?

rsidd said...

@ankur -- I did suggest in private mail that he should have run it by a physicist first. But I also agree with anon (Sept18 4:44) that it is rare to find a journalist who links to a rebuttal of his article above the article itself. Dilip also linked freely to critical reviews of his book, I remember. That is why I take his writings seriously, always.

Haja Peer Mohamed H said...

And Yes... Uncertainly, the cat. Good Post to share!

km said...

Dilip,

This is another fine reminder of why your blog (and articles) are always worth reading (as are Rahul's ideas...)

Dilip D'Souza said...

Thanks km. I wish I can find the mental bandwidth to resuscitate this blog, though. Just a few too many things going on of late. But the comments like yours encourage me.