April 29, 2005

Cat in a box

I'm not sure why, but I always liked this piece I did some years ago to explain a scientific idea that intrigues me. Never saw print, I believe.

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Who is Schrodinger's cat? Arguably the world's most famous purely hypothetical feline. Never lived, but some say he's both dead and alive. At the same time. Ask your nearest physicist.

Erwin Schrodinger was a Nobel winning German physicist who died in 1961. The cat was part of a thought experiment he devised to explain one of the fundamental ideas of modern physics: Heisenberg's Uncertainty Principle.

Shorn of jargon, the Uncertainty Principle says something very simple: the act of measuring something changes the result of that measurement. Heisenberg showed that simultaneously determining both the position of an electron and the speed at which it is moving is impossible. If you can measure its speed accurately, that measurement will itself make its location wildly uncertain. And vice versa.

Put another way, measurement decides the state of the electron.

This is not such an esoteric idea. Examples abound, and not just among electrons. Imagine an anthropologist visiting a remote tribal village to study its inhabitants. His very presence disturbs the villagers, who will behave differently with this stranger in their midst. So by simply observing, the anthropologist affects what he wants to observe; and thus can never hope to get a true picture of life there.

This is all very well with tiny particles nobody can see anyway, and maybe also with distant tribals. But what about everyday objects around us? What about, say, cats?

Well, that very question occured to Schrodinger. His famous thought experiment goes something like this. Let's say we have a sealed box with a cat in it. Also in the box is a device that can randomly emit marbles. In the course of a minute, the chances are exactly 50-50 that it emits one. If it does, the marble breaks a vial and releases a poisonous gas into the box. Kitty is instantly asphyxiated. Otherwise, nothing happens.

We put the box somewhere far away, where we have no way to tell what's going on inside it. Suppose we turn on the device for exactly one minute. Question: what happens to the cat?

It must seem like a trivial question. The answer is that we don't know. We cannot predict whether a marble was actually emitted. So we don't know if the cat is alive or dead.

But if we walk up to the box and open it to hear -- let's hope -- the loud miaow of a very puzzled cat, only then do we actually know that it has survived its uncertain ordeal.

Before then, the best we can say about the cat is the non-sequitur that it is either alive or dead. But that's not really such a non-sequitur. It is entirely consistent with the laws of physics to think of the cat, before we open its box, as being both alive and dead, with a probability of 50 per cent for each state. Here's the point of the experiment: our act of opening the box and observing the cat -- taking a measurement, in other words -- is what puts the cat definitely into one of those states.

Cat, alive.

So what's the point, you want to know. What's so earth-shaking about this cat shut in a box?

There are many points, actually: the effect of measurement, the idea of uncertainty, the fact of indeterminacy (of that, perhaps another time). But probably the deepest and yet simplest point is this interesting view of the world: reality takes shape only when, precisely when, we sense it. Until then, it's uncertain. That's the Principle.

The anthropologist gets a picture of tribal behaviour only when he actually observes them, even if that changes the way they behave. We really know the fate of that poor cat only when we open Schrodinger's box.

All of us have wondered on these lines. Is my image in a mirror really there if I cannot see the mirror -- if I've turned my back to it, for example? Does a tree falling in a forest make a sound, if nobody is there to hear it?

Is there reality without observation, existence without consciousness?

Schrodinger's cat showed that the laws of physics might answer that last question with "no". That may be too extreme a view for most people's tastes, people who believe reality surrounds them without needing to be looked at. Then again, Schrodinger's cat wasn't real himself.

14 comments:

k.r.a.k.t.i.k said...

Yes,

Schrodinger's Cat ... alongwith the "Twin Paradox" (oftentimes wrongly attributed to Einstein) perhaps one of the more enduring thought experiments in science ... the Twin Paradox has an easy enough explanation ... Schrodinger's Cat, however ... leads one to profound thoughts about physics and eventually metaphysics itself.

Nice to see you do a piece on science Dilip, especially theoretical physics :-D...

Miaow!

-- Kraktik

Anonymous said...

Super to see you tread on a path that might lead to that science column.
Any thoughts on the last chapter of 'The Dilbert Future' by Scott Adams ? if you've read it, that is..
Interesting debates to be had there..

noopsterama said...

I had read this piece a while ago, thanks for refreshing my memory!

Schrodinger's Cat- what a nice name for a fundoo concept! :))

Anonymous said...

Hi Sudhakar. A good one there at rediff.com

Dilip D'Souza said...

Anoop, you read this before? I'm amazed. Do you remember where? I wrote (a version of) it for a syndicated science column I used to do; but the week I sent it in, the column shut down. So I have always thought it never appeared.

Anonymous 4:12 pm: I have one of Adams' books, but I haven't read this one. Tell me more. I presume you are a certain ticket-giver?

And Kraktik, how about an explanation of the Twin Paradox? I'll post an occasional science piece, your thoughts always welcome.

Anonymous said...

"We really know the fate of that poor cat only when we open Schrodinger's box."

I think this is obvious. What is astounding about the concept of a quantum wave function collapse on observation is that the cat itself doesn't know if it is dead or alive until we open the box. This is the point you should emphasize. The twin paradox is not a paradox at all and cannot be compared to Schroedinger's cat in any way at all.

Also there are 2 interpretations of this phenomenon. Copenhagen and Many worlds.

http://en.wikipedia.org/wiki/Schr%F6dinger%27s_cat

k.r.a.k.t.i.k said...

Yes,

As Anonymous (whoever that maybe be) rightly says, the "Twin Paradox" isn't a paradox at all ...

This was something coined in the 1920s/30s (not sure) to explain the consequences of time dilation. The main argument was thus: consider two twins, exactly alike in that they even age in the same fashion. One of them is chosen to go on a space mission in a rocketship reaching nearly the speed of light, while the other remains on Earth.

Due to something known as the "warpage" of space-time due to the immense gravity created by one as one approaches the speed of light (mass increases manifold unto infinity as one approaches light speed, according to the postulates of General Relativity) time in the definition of Earth seems to be slowed down for the space ship.

Thus it will pass that in the same time that the twin travelling aboard the space ship ages a normal 10 years, the twin on earth will have long since died and new generations will be flourishing (the exact difference depends on the speed). The "paradox" of course was that if the twin came back to earth, he would be much older than any other being alive.

The "catch" in this whole "paradox" is the fact that as long as the twin is travelling near light speed, he/she doesn't age as fast as people on Earth, agreed ... but as and when he/she slows down to make that approach, the ageing process must catch up.

I'm sure my explanation isn't up to the mark, but then, on Dilip's request, a humble try!

zap said...

Adams goes off on a strange tangent int he last chapter of The Dilbert Future. Talks about alternate realities and unified theories. It makes you wonder if he is pulling a fast one on the reader.
Tickety-boo then!

wise donkey said...

hmmm:)

a good blog on science btw scithought.blogspot.com

Tanuj said...

dilip and others, i read this interesting book called 'in search of schrodinger's cat' by someone called jogn gribben. worth at least one read, bien sur!

see- http://www.amazon.com/gp/reader/0553342533/ref=sib_dp_pt/104-1515961-2746319#reader-link

Souvik Das said...

Your exposition of the Schrodinger's Cat paradox is almost flawless, though the analogy of random marbles being shot out of a box instead of the decay of a radioactive atom might be misleading.

You see, the decay of a radioactive atom is a process that is known to be fundamentally acausal in the sense we cannot tell in principle when it will decay. The operative term being 'in principle'.

When you speak of a box that shoots off marbles at random, the reader might tend to think that if he / she knew the fine details of its mechanism, it would not in principle be a process of pure chance.

A machine conjures the image of a deterministic mechanism. In case of radioactive decay, the 'mechanism' is fundamentally indeterministic and dependent on measurement. That is the source of the paradox.

I am glad to see a blog that has harped so much on the depressing politics of India suddenly come up with an exposition of one of nature's deepest mysteries. Like Einstein used to say, contemplating nature is often a wonderful way to escape the grit of daily life.

Souvik Das said...

Dilip,

I would like to see your exposition of the twin paradox. Though it is hardly a paradox at all ~ almost any physics undergraduate with a basic understanding of General Relativity will be able to tell you that it has to do with the inability of Special Relativity to account for accelerating reference frames. It isn't of the same class of paradoxes as Schrodinger's Cat.

It often bugs me that such esoteric concepts of physics get the limelight thanks to the wave of pop science authors we have seen over the last decade. Sure, they are very profound, but the public also need to be aware of the delights of contemplating down to earth phenomena like why rivers meander... or why boiled eggs when spun will stand on end!

Catching any glimpse of an understanding of nature at any level is a rare joy that can last a lifetime.

-Souvik

Dilip D'Souza said...

Thanks for your thoughts, Souvik. I may attempt something around the Twin Paradox, but then I have the tough task of topping Kraktik's excellent account!

In my draft of the piece, I had a device shooting electrons -- I only changed it to marbles to make it a little more accessible. I already talk about electrons earlier, and my experience is, there are only so many electrons a reader is willing to be positive about...

And you're right, the down to earth phenomena are fascinating to think about and explore. Food for thought. I'll post an occasional science thing like this, can't tell how often, but every now and then.

Oui oui Tanuj! Je croix que j'ai cette livre, ou I used to have it.

And zap, I shall look for Adams' book. Thx.

row said...

Hi

I'm just writing to let you know that your "cat in a box" piece is featured in BBC Collective's web column this week. You can see it, and link to it if you like, here:

http://www.bbc.co.uk/dna/collective/A14034241

Best wishes

Rowan Kerek

Content Producer
bbc.co.uk/collective