Schrödinger's Cat: A Thought Experiment on Quantum Mechanics

[tokajak]

FADE IN:
SCENE 1 – A WAITING ROOM - SOMETIME IN 1935
A young man is seated alone in a small, sparsely furnished room. There are three wooden chairs, a hat stand and a door on each side of the scene. The man is intently reading a book. At his side on the floor is a large wooden box which has a carry-handle on the top and a hinged door at the front.
As the door on one side of the room opens, a man and a woman appear. The elderly matron is carrying a small dog. As she leaves via the other door, the seated man’s attention does not move from his book.
MATRON
Thank you Dr. Nielsen. I will see you again next week.
NIELSEN
Yes, see you then and make sure she takes those pills every day.
Dr. Nielsen is dressed in a wool suit with a vest and a tie in the manner of a 1930’s physician. He retrieves a black notebook from the inside pocket of his jacket, turns the pages then reads.
NIELSEN
Hello. Dr. Schrödinger, I presume. I am Dr. Nielsen.
They move towards each other to shake hands but the younger man drops his book on the floor, fumbles to retrieve it then eventually shakes the offered hand nervously.

SCHRÖDINGER
Hello. Yes, I am Dr. Schrödinger. Thank you very much for agreeing to see me at such short notice.

NIELSEN
You are fortunate that a client canceled his appointment this morning. Please come into my consultation room.

SCENE 2 – THE CONSULTATION ROOM

The young man lifts the wooden box then carries it through the door where the scene changes to a room that contains a large desk, 2 chairs and a table in the middle of the room. There are few books on the shelf above the desk but the decorations are minimal, giving the appearance of a clinical room. Nielsen takes his seat at the desk and the young man places the box on the table.
NIELSEN
Now, Dr. Schrödinger, this is your first visit, is that correct? Are you a medical doctor?
SCHRÖDINGER
No, no. I am an academic at the University where I do research in Theoretical Physics and this is indeed my first visit.
NIELSEN
Very well, so how may I help you? Is that your dog or your cat in the box?
SCHRÖDINGER
It’s my cat but I must explain that the situation is somewhat complicated and unusual.
NIELSEN
Well why don’t you take your cat out of the box so that I can examine it while you tell me more about the problem?

SCHRÖDINGER
That is actually the problem. I can’t take the cat out of the box.
NIELSEN
I don’t understand. Is there something wrong with the door? Why can’t I see your cat?

Nielsen has a puzzled look on his face as he shifts his gaze from the box to Schrödinger and back again several times.

SCHRÖDINGER
I am afraid that if I open the box, the cat may be dead.

Nielsen is visibly shocked and considerably more perplexed by this strange statement.

NIELSEN
I see. Can you tell me what symptoms the cat had before you put it in the box?
SCHRÖDINGER
Oh, the cat was perfectly healthy when I put it in the box.
NIELSEN
Sorry, this does not make sense. Perhaps you could explain why you would bring a healthy cat to a vet. Does it need a vaccination? What makes you think that it may be dead?

SCHRÖDINGER
I think it could be dead because I also put a small bottle of cyanide gas in the box.

Nielsen is astounded and begins to show signs of agitation. He then decides that this must be some form of a joke so he responds sternly.


NIELSEN
My dear fellow, if you put cyanide in the box with the cat then it will most certainly be dead.

SCHRÖDINGER
No, not at all. The bottle was sealed.
NIELSEN
Then, in that case, the cat will obviously be alive. Why, may I ask, did you put the cyanide in the box? Are you trying to kill your cat?
SCHRÖDINGER
I have no intention of killing the cat. It could still be alive but I am not certain.
NIELSEN
Naturally, if the cyanide bottle is sealed then the cat will still be alive. Dr. Schrödinger, I must admit that I don’t understand why you are here. If you intend to play these strange, cruel games with your cat, why bring it here to me?

SCHRÖDINGER
Well, the fact is that I put the cat in the box as part of an experiment. It is a test of a hypothesis that I have recently developed.

NIELSEN
You have completely confused me, Dr. Schrödinger. You just told me that you are a physicist so why are you conducting these odd medical experiments on your cat? Don’t you usually use mice for that?
SCHRÖDINGER
I have been working in a very new field of physics known as Quantum Mechanics which is a theory that describes how sub-atomic particles interact.
NIELSEN
This does not explain anything. Why, in God’s name would sub-atomic particles have anything to do with your cat?
SCHRÖDINGER
The purpose of the experiment is to demonstrate that uncertainty in Quantum Mechanics is not just a theory but can actually have an effect on the real world that we can observe. I have been attempting to translate a quantum event into something observable.

NIELSEN
I fail to see how you have managed to involve your cat in your work and why would you want to involve me?

SCHRÖDINGER
Let me explain. In addition to the cyanide bottle and the cat, I have also included some mildly radioactive material and a radiation detector. This detector is connected to the bottle in such a way that the device will open the bottle if a radioactive emission is detected.
NIELSEN
But why are you doing these very odd experiments with your cat? Surely you could use instruments to measure the radiation levels. It seems very cruel and unreasonable to threaten the life of your cat just to help you prove some esoteric idea.
SCHRÖDINGER
That is the whole point of the experiment. A random event at the sub-atomic level can actually influence the life or death of the cat. The unknown state of a quantum event can be directly linked to its health.
NIELSEN
This is ridiculous. If you have set up this experiment then why don’t you just open the damn door to find out what has happened to the cat and, I repeat, why bring this to me? There is no cure for cyanide poisoning so I can’t do anything if the gas bottle has already been broken. I think you should leave now. I don’t understand what you are trying to prove and I refuse to participate in your cruel plan to kill an otherwise healthy cat just to demonstrate some crazy, abstract theory.
SCHRÖDINGER
But you can’t accuse me of murder when you don’t know if the cat is alive or dead. Cats sleep 20 hours per day so, just because there is no movement in the box, does not mean that the cat is dead. I brought it here because I am curious to know whether there is some way to determine whether the cat is alive or dead without opening the box.
NIELSEN
Well, of course it is possible to listen carefully for the sound of breathing or a heartbeat but that does not make sense when all you need to do is open the box. You are confusing me even further.
SCHRÖDINGER
I have already thought about that. Listening for a heartbeat is just another form of observation which is the same as opening the box. The point I am trying to illustrate is that I can’t know if the cat is alive or dead unless I open the box or listen for breathing or a heartbeat. The real question is what condition the cat is in now before I make an observation.
NIELSEN
Dr. Schrödinger, I am not a magician and definitely don’t want to be part of some kind of circus act because this seems like a very odd and pointless way to prove a theory. I must ask you to remove the cyanide from the box before it does any harm, unless, of course, the cat is already dead.
SCHRÖDINGER
You don’t seem to appreciate that because there is no way to know whether the cat is alive or dead without making some observation, the fundamental uncertainty that is characteristic of the sub-atomic world is not simply a theoretical concept. It has a direct effect on the cat’s fate. Until I open the box, the cat is therefore both alive and dead at the same time. There is no proof that I have harmed it.
NIELSEN
Now it is clear that you are quite insane. Any reasonable person knows perfectly well that it is not possible to be both alive and dead. It is an either/or situation. I think that you are the one who needs some help if you believe you can play these stupid philosophical games with the life of a cat.
SCHRÖDINGER
Dr. Nielsen, you fail to see that is precisely the objective of the experiment. I am attempting to demonstrate that concepts which appear absurd to our normal thought processes actually make sense at the quantum mechanical level. Although that uncertainty is fundamental to the theory, it cannot be explained in any way that we can comprehend.
NIELSEN
That is quite enough. Here is the basic reality, I am a vet. If your cat is sick then I can try to help but if it is already dead then there is nothing I can do. Similarly, if it is alive, there is also nothing that needs to be done. I don’t find practical jokes funny if that is what you are trying to do. On the other hand, if you want to play God then I suggest that you don’t involve me, your cat, or any other animal.
SCHRÖDINGER
Dr. Nielsen. You have not been very helpful. I simply came here to ask you if there is some way to determine whether a cat is alive or dead but you don’t seem to understand. Then you accuse me of both insanity and cruelty when you have no information about whether a cat is alive or dead. I would have thought that such knowledge is a fundamental requirement of your profession.
NIELSEN
This is far too much. I refuse to be accused of professional incompetence by a man who has clearly lost contact with any form of reality. I demand that you leave this room immediately before I call the authorities. Furthermore, I suggest that you find another field of study. If the only result of your research is killing harmless animals then I don’t believe it is any use to mankind.
Good Day, Sir

Schrodinger stands, moves to the table, then opens the door of the box to reveal that it is entirely empty.

SCHRÖDINGER
This is a thought experiment. I don’t actually own a cat.
NIELSEN
Get out of here! Now! The only thing you have proven is that you are a complete fool. There is no uncertainty about that.


FADE OUT:
THE END

 

[bhobba]

You don’t seem to appreciate that because there is no way to know whether the cat is alive or dead without making some observation, the fundamental uncertainty that is characteristic of the sub-atomic world is not simply a theoretical concept. It has a direct effect on the cat’s fate. Until I open the box, the cat is therefore both alive and dead at the same time. There is no proof that I have harmed it.

Amusing

But the situation is actually quite simple.

The cat is never in some kind of weird superposition.

It is alive or dead - period.

According to QM the observation takes place at the particle detector - not when the box is opened. Everything is classical from that point on.

Schroedinger knew this - and wouldn't actually claim what was said above because he knows its wrong. The purpose of the thought experiment was to highlight an issue with QM - namely, while in any actual set-up its trivial to determine where the quantum classical cut occurred the theory doesn't say where that is. Yet it relies on such a cut. He would claim something along those lines.

What is required is a fully quantum theory of measurement without this arbitrary cut.

A lot of work since Schroedinger's time has been put into doing just that and much progress made - but a few issues (most think they are minor - including me - but opinions vary) still remain without going into the detail of what they are.

Also, while a genuine issue, its really only a minor blemish within the usual Copenhagen interpretation which many I suspect don't actually fully understand:
http://motls.blogspot.com.au/2011/05/copenhagen-interpretation-of-quantum.html

Thanks
Bill

 

[tokajak]

The story is simply a bit of fun, speculating about a hypothetical scenario.

As to the Copenhagen Interpretation, as the name implies, it is an attempt at finding some physical meaning for the mathematics rather than a comprehensive theory. The concept of wave-particle duality is an acceptance that QM is an incomplete but useful abstraction that matches some but not all observable behaviour.

 

[bhobba]

The concept of wave-particle duality is an acceptance that QM is an incomplete but useful abstraction that matches some but not all observable behaviour.

Indeed it is a simple bit of fun - my comment was just to set the record straight so to speak about the actual issues raised.

But I also want to add the wave particle duality is just something students are taught at the beginning levels of QM. Since Dirac came up with his transformation theory, about 1927, which is basically QM as we know it today, it has been consigned to the dustbin of history - simply something students are told about in the semi-historical way the subject is usually taught to motivate the full theory.

To see what the real explanation for stuff like the double slit experiment, the wave particle duality is usually used, see the following:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

I think its better to start with its conceptual core:
http://www.scottaaronson.com/democritus/lec9.html

Thanks
Bill

 

[tokajak]

In common with many people who are not involved in QM as their 'day job', my understanding of the subject developed through the classical route of following the historical developments from the early days of debates which focused on determination of a physical meaning for the mathematics. Popular explanations of QM typically involve attempts to explain difficult mathematical extractions in terms of simple ideas such as cats and multi-dimensional existences. Scott Aaronson has an interesting perspective that I would like to explore in more detail. Many thanks for the pointers.

 

[bhobba]

In common with many people who are not involved in QM as their 'day job', my understanding of the subject developed through the classical route of following the historical developments from the early days of debates which focused on determination of a physical meaning for the mathematics.

Sort of.

It actually took a while for the mathematics to develop, but reached its final form when Dirac came up with his transformation theory in 1927 and Von Neumann published his mathematical Foundations of QM which was the first book to provide a rigorous mathematical theory. Dirac's approach had issues with rigour no need to go into here except to say it spurred the mathematicians to rectify it and these days Dirac's approach can be treated with full rigour. But that's just an interesting by the by.

Popular explanations of QM typically involve attempts to explain difficult mathematical extractions in terms of simple ideas such as cats and multi-dimensional existences. Scott Aaronson has an interesting perspective that I would like to explore in more detail. Many thanks for the pointers.

It is indeed a challenge to explain, correctly, QM at the lay level without the aid of advanced math.

In fact I believe its basically impossible - which is why they often resort to half truths like the wave particle duality and parables such as Schroedinger's cat. Whether it actually aids in increasing general understanding is a matter of debate.

Thanks
Bill

 

[Matterwave]

Amusing

But the situation is actually quite simple.

The cat is never in some kind of weird superposition.

It is alive or dead - period.

As this is not a physically verifiable statement, by definition, one can not, in physics, make this statement with such certainty.

According to QM the observation takes place at the particle detector - not when the box is opened. Everything is classical from that point on.

I don' t think QM says this. I could make a detector a series of more and more complicated interactions (e.g. a photo multiplier), at no point will QM say "oh, it's here, collapse all the wavefunctions!".

Schroedinger knew this - and wouldn't actually claim what was said above because he knows its wrong. The purpose of the thought experiment was to highlight an issue with QM - namely, while in any actual set-up its trivial to determine where the quantum classical cut occurred the theory doesn't say where that is. Yet it relies on such a cut. He would claim something along those lines.

I'm pretty sure Schroedinger made his famous cat thought experiment in an attempt to discredit Born's probabilistic interpretation of the wave function. He wanted to interpret it as some sort of electron density function, but was unsuccessful.