# Yet another cat question

1. Feb 12, 2006

### jhe1984

Okay, I've been reading up on this Schrondinger's cat thought-experiment and I'm not really seeing what the big deal is (which according to everything I've read on QM so far is a big red flag - confusion is key). So please help/correct me as I walk through the thing.

Basically, there is a cat that is inside a mechanism that is triggered (by the decay of a radioactive substance) to either kill - if the substance decays - or not kill - if the substance does not decay - the cat.

And according to ...(? - don't know what, but I'm not sure it's crucial), there is a 50% chance that the substance decays in a given time period - let's say an hour.

So going into the box, there is a 50% chance that the cat will live and a 50% chance that the cat will die.

And, after that hour's up, the box is opened and the cat is either alive or dead.

If this general description is correct, I don't see what's the problem?

In some cases, the cat dies; in others, it lives. It's random, yeah, but I don't see how it's spawned the perplexity that it has. But I am not a scientist, so most likely there is an important contradiction that I am overlooking.

Please explain. (With minimal math, if possible. )

2. Feb 13, 2006

### zekise

The metaphor is - when you open the box - you will see both a dead cat and a live cat simultaneously (essentially 1 cat appearing in 2 contradictory dead-and-alive states). And not a dead cat with 50% chance and a live cat with 50% chance, which is a single either-dead-or-alive state. Yes, this is hard to imagine. But this has been demonstrated in quantum mechanics with tiny objects.

However note - in practice you will not see a dead and alive cat simultaneously. This has to do with quantum to classic transition - and decoherence theory explains why for MACRO objects that interact with their environment, the 2 states (dead and alive) will decohere into a single state (either dead or alive). However, for MICRO objects, this 2 (superposed) states continues to remain an empirical fact.

Set up a double slit experiment, and shoot a single photon at the slits. You will see an interference pattern on the screen. If the photon had gone through slit 1, you would get a bell. If it went through slit 2, you would also get a bell. The only way you can see an interference pattern is if the photon, which is indivisable, had gone throught BOTH slits simultaneously - namely it had 2 states at the same time. Otherwise, there is no other way to explain the IP.

I hope this helps.

3. Feb 13, 2006

### ZapperZ

Staff Emeritus
I think your explanation here isn't correct.

The metaphor is that before you open the box, the state of the cat is in a superposition of both alive anddead. This metaphor is an illustration of the superposition of orthorgonal states of a wavefunction, such as

$$\Psi = a|u> + b|v>$$

The difference between this and our classical world is that, in our classical universe, the cat is either dead or alive. It cannot exist in a superposition of two very distinct states.

The act of opening the box "collapses" (if you buy the Copenhagen Interpretation) the state (i.e. you now make a measurement) so that now, the cat is unambiguously determined to be dead or alive. You now have either a |u> or a |v> state and no longer the superposition of the two.

Zz.

4. Feb 13, 2006

### DaveC426913

What has always fascinated me is the following concept:

The act of opening and observing the cat in the box doesn't collapse the superposed state *in* the box, it collapses *our* existence into a state where we either open a box with a dead cat in it, or open a box with a live cat in it. Really, we are in a larger box - which, until observed by an external observer to us exists in its own superposed state.

But then again, that's not the Copenhagen Interpretation, is it? Is that the Many Worlds interpretation?

5. Feb 13, 2006

### ZapperZ

Staff Emeritus
I think that's CI. I remember the same scenario being mentioned by John Gribbin in "In Search of the Schrodinger Cat". (Yes, I DO read pop-sci books now and then.)

However, one can only carry this picture for so long before it becomes absurd (at least, in my opinion). The chained wavefunction picture is one aspect of CI that I really don't like, as much as the "collapse" word being used here.

Zz.

6. Feb 13, 2006

### caribou

Yeah, it's all about quantum theory predicting two physically mixed realities and yet we experience one physical reality which isn't mixed with another one and asking why that is.

7. Feb 13, 2006

### ZapperZ

Staff Emeritus
Actually, while we experience only "one" of the realities, keep in mind that the whole idea of non-commuting operators is that making a measurement represented by one operator does not completely collapse the superposition on the other. For example, if you measure the z-component (not one of PF members) of the angular momentum, i.e. Lz, then while you have "collapsed" any superposition of that angular momentum state, Lx and Ly are still undetermined and still in superposition. This is because, as any undergrad physics student taking a QM course would know, Lx and Ly do not commute with Lz.

Why would this be relevant here? It means that we can detect the effects of such superposition indirectly. This is what is being done with all the Schrodinger Cat-type experiments. The Delft and Stony Brook experiments that I have often referred to are just a few of the examples.

So yes, we can observe the consequences of such superposition.

Zz.

8. Feb 13, 2006

### vanesch

Staff Emeritus
Well, that's to me indeed the many worlds view, if you replace "collapse" by "is observed to be", no ?

A better name, especially in the context here, is the relative state interpretation.

Because if the superposition exists when someone opens the bigger box to see US, he also has the option of having us in the state 1) cat is dead + we saw dead cat OR 2) cat is live + we saw cat live.
As such, to that bigger-box-observer, we are STILL in a superposition of states (in "parallel worlds") of which WE only experienced one branch.

The Copenhagen interpretation is different. It says that there is a clear (well...) separation between a TRUE MACROSCOPIC world, which is ruled STRICTLY by classical mechanics, and an imaginary MICROSCOPIC WORLD, and that the imaginary microscopic world is the imaginary item which influences the macroscopic world through the measurement process. So in the CI, there is a barrier between the microworld (which is not really supposed to exist in a precise way) of which we have a description through quantum theory, and the truely existing macroscopic world, which suffers the influence of the microworld.

This means that there is NO relativity between observer and observed, but between microworld and macroworld. As such, because the cat is a macroscopic, classical object, the quantum description does not apply to it. The transition quantum-> classical took place at some definite point when the particle was detected and the bottle of poison shattered.

It is a quite schizophrenic viewpoint, if you ask me!

Last edited: Feb 13, 2006
9. Feb 13, 2006

### jhe1984

Okay but - unless you'd see both an alive and dead cat - I don't see how or why this uncertainty about the cat's life before we open the box is such an issue.

Perhaps it is because I am not familiar with the prevailing thought before this - like determinism - and am used to random events or probability?

But if I am understanding you, the situation's really no different than a game of Russian roulette with 3 bullets in and 3 empty spaces (in a six-shooter). If you couldn't see the bullets, both the statements "oh, he's a dead man" and "dont worry, he's fine" make the same amount of sense. So for that instance (technically, I guess) he's both alive and dead. Is this an accurate approximation and if so what's the big deal scientifically - since this sort of thing undoubtedly preceded quantum puzzles?

10. Feb 13, 2006

### ZapperZ

Staff Emeritus
But what you are describing here is just semantics. You are using human description that can be rather vague or "culture-specific" in terms of its meaning.

What the Schrodinger Cat-type experiment tries to do is show that this superposition is in terms of physical reality, and that it has definite consequences that can be measured.

Zz.

11. Feb 13, 2006

### jhe1984

Hmm. I understand what you're saying about the semantics, but unfortunately I'm just not getting it.

Any advice - or is their a better approximation or physical paradox?

If the box was transparent, would we be able to see the cat die (or not die)?

12. Feb 13, 2006

### ZapperZ

Staff Emeritus
If the box is transparent, there's no superposition. You have absolute knowledge of the state of the cat being either dead or alive. This is the same as having only ONE state function, being either |u> or |v> with 100% certainty. There's no superposition here.

Whenever we deal with something like this, it is always useful to know what exactly is the physical principle that is being illustrated here. The physical principle is superposition of orthorgonal states. If each of these states represent a physical outcome of a measurement, such as the position of the object, then you will notice that before a measurement, the object has several different location simultaneously. So what you need to keep in mind is the physical principle being described by the mathematics. The Cat is simply an attempt to illustrate this principle in ways most people might be able to understand.

Zz.

13. Feb 13, 2006

### zekise

Well, there are two unrelated issues. First is the superposed state. The other is the act of measurement. For the purpose of answering the original pedagogic question, conflating the first with the second will mislead the questioner IMO.

So by "opening the box" I really meant that if we could somehow ideally observe the cat without measurement. (maybe a quantum Zeno measurement?) Sorry if that was not clear.

In reality, the superposition collapses as soon as the Beta particle (or lack thereof!) hits the detector consisting of many degrees of freedom and superselection occurs. This is way before the cat is affected in any manner. The cat never enters a superposed state, and opening the box or observing the cat makes no difference. Thus the cat being in a superposed state is simply metaphoric. At least this is what I understand from decoherence theory.

14. Feb 13, 2006

### jhe1984

Okay, so the paradox is that we know the state must be one or the other (either |u> or |v> ), but that since we are unable to know which it is until it is measured, the object is said to be in a superimposed state?

Or, are physicists saying that it actually IS both before measurement and that the act of measuring itself causes it to "choose" one state or the other - basically, if we could somehow "see" it before measurement, there really would be two alternate (and eventually mutually exclusive) states at once?

And if it's the latter, how does that differ philosophically from the former?

And isn't either just speculation (whether it is superimposed or is a random one or the other) since we can never prove that it's one or the other?

Yikes, this is confusing.

15. Feb 13, 2006

### jhe1984

And one more question: isn't physics creeping into philosophy here?

"To exist is to be perceived" and "is there a reality apart from our perception of reality?", sort of things.

Is it looking to mathematically prove one and not the other - I'm kinda skeptical on this point.

16. Feb 13, 2006

### Edgardo

Hi jhe1984,

you are right, there doesn't seem to be anything strange BUT... only in the classical sense. With classical I mean that the cat really HAS a property, either dead or alive.

However, in quantum mechanics, things do not necessarily possess a definite property. Think of the cat as being simultaneously dead AND alive, a picture showing both the dead and alive cat, somehow BLURRY or SMEARED:

http://www.d-f-g.net/fun/pic.php?pic=schroedingers-cat [Broken]
http://universe-review.ca/I12-21-cat.jpg
http://www.math.sunysb.edu/~scott/Quantum/schrodinger.png

So the cat, in its blurry/smeared state, walks through the streets. Then you meet it and decide to "ask it" whether it's alive or not. It will suddenly stop to exist in that blurry state and will become "sharp", for example sharp-alive. But it can also happen that it will become sharp-dead. And it was your "question" that made him sharp.

(Maybe that is why Schrödinger cats hide in the dark alleys? ;))

Here's an article that with further information:
http://www.phys.washington.edu/users/dbkaplan/325_02/Schrodinger.jpg

It's interesting to note that Schrödinger didn't like the concept of "blurry properties". So he invented that cat-thought experiment because he wanted to show what silly consequences that "blurry-concept" actually would have for our daily life, namely such blurry cats walking through the streets. Of course nobody has ever observed such a cat.

Last edited by a moderator: May 2, 2017
17. Feb 13, 2006

### zekise

If you mean that the cat (or some other macro objects) does not exist, or does not exist in a (non-quantum) classical state, until they are observed (by a conscious or unconscious observer) - I am not sure how you arrived at this conclusion based on the discussion we have had here.

For a superposition to collapse on a preferred basis, all it has to do is interact with a system with many degrees of freedoms (as I understand decoherence theory - please correct me if I am wrong). There are no observation involved, no measurement, no perception, no feelings, no monads, no selfs, no consciousness. You may wish to interpret the verb "interact" to be synonymous to "observe" etc. That would be an exercise in semantics.

So no - if you put all of conscious humanity on freeze, the universe is not going to go away. You will still be able to defreeze humanity!

18. Feb 13, 2006

### ttn

Schroedinger himself certainly didn't intend the cat thought experiment as a mere illustration of the superposition principle. It was, rather, an illustration of the measurement problem: QM says that the alpha particle is in a superposition of positions (say, still in the parent nucleus and over near the geiger counter), but because of the linearity of the quantum dynamics this superposition can be "magnified" into a superposition that is macroscopic and (he and Einstein would have said) preposterous.

Schroedinger did *not* think that the cat would end up in a superposition of alive and dead, to be resolved only when a human opened the box and looked. He thought (and assumed others would also think) that it is insane to think that a cat can be in a superposition of alive and dead, and equally insane to think that the mere act of opening the box and looking can have this dramatic physical effect on the state of the cat.

This all highlights the "measurement problem" from which orthodox QM suffers. Is it the act of observation (literal conscious awareness) that constitutes the "measurements" which resolve superpositions into definite outcomes? That seems crazy, as illustrated by the cat. So then maybe the cat "measures" the state of the vial of poison? Or maybe the vial "measures" the state of the hammer? Or maybe the relay "measures" the output of the geiger counter? etc. The problem is: we start out with a superposition at the level of the alpha particle, and definitely end up with a state that is *not* a superposition; orthodox QM says the transition happens when a "measurement" occurs. But what the heck is a measurement exactly? Where along this continuous chain from micro to macro do the normal dynamics defer to the collapse postulate? Schroedinger was using this cat thought experiment in this way to argue against the completeness doctrine -- i.e., to argue for "hidden variables" at the original micro-level. Such variables would resolve the "fuzziness" at the very beginning, and the whole ambiguous chain would never get going. (For example, Bohm's theory does not suffer from the measurement problem because it attributes a definite position to the alpha particle from the very beginning, whether or not it is "measured.")

Let me repeat one last time what "the measurement problem" is, because I think it's not sufficiently well understood. Orthodox QM says that there are two different rules according to which wave functions evolve: Schroedinger's equation, and the collapse postulate. The first law applies when no measurement is being made; the second applies when a measurement is being made. But the theory never tells us what exact sort of physical process constitutes a "measurement." The theory is, to use Bell's apt description, "unprofessionally vague and ambiguous." *This* is what is supposed to be brought out by the infamous cat.

19. Feb 13, 2006

### zekise

My amateur understanding of Decoherence Theory is that the act of measurement (sans collapse) is satisfactorily explained by superselection and emergence of a stable preferred basis upon the interaction of the measured object with a system containing large degrees of freedom resulting in redundancy of the information obtained.

20. Feb 13, 2006

### ZapperZ

Staff Emeritus
But if we are going to over-extend such a scenario, I would also ask why you are ignoring Bob Laughlin's presentation that this whole "measurement problem" isn't really a problem. Rather, a "measurement" is really an emergent quantity because such an observation is an interaction with a many-body system (refer to his book). It explained why our measurement produces "newtonlike" quantities.

I did not wish to overcomplicate the matter since from the OP, it is obvious that there needed to be a clarification of what is supposed to be represented by this thought experiment.

Zz.