I was wondering what the intuitions of the blog readers are regarding the familiar example of Schrodinger’s cat.
Here are several regarding whether or not the cat is alive or dead.
1) The cat is either alive or dead by metaphysical necessity.
2) It is a meaningless assertion because we can’t assert anything because we have no empirical verification.
3) It is unassertable but still the cat is still necessarily either alive or dead.
4) The cat is alive and not alive.
5) The truth of whether or not the cat is alive or dead is indeterminate, dropping bivalence here.
I think most people would fall under 1, but I’m leaning towards 5.
Readers?
Advertisements
Can you tell us the thought experiment in simple terms?
Is this close?
The cat is in a place that no being can observe except the cat. The cat may or may not be killed by substances in the container. You have to make an assertion of whether or not the cat is dead or alive without opening the box to see.
I missed something, yes? If not, then I lean toward # 2. If you have facts then you might be able to say that there is an 80% probablity that the cat is dead but you can not know for sure.
In the below quote…I am interpreting psi-function as just a way of displaying the probability. Am I way off base?
from your wiki link:
Schrödinger wrote: 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 psi-function 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.
I vote (1).
I find it hard to agree with #1. Is a person in a vegetative state really alive? Is a frozen embryo really alive? Neither is quite dead either. So I’m not sure that something has to be dead or alive by metaphysical necessity. Maybe I am getting confused by the idea of the identity of the cat. When does it seize to be a cat? Is it dead once it is no longer a cat? I’ve been reading a book called ‘Science Fiction and Philosophy.’ It has me thinking about things like that. When does a cat seize to be a cat once you start replacing its parts?
I guess (in this example) the identity of the cat is not in question. But I still (on principle) can’t agree with #1.
from wiki:
If a proposition is metaphysically necessary, there’s no genuine sense of possibility according to which its negation is possible.
Susan,
The thought experiment takes for granted that being alive and being dead are contradictories, i.e. ‘dead’ is synonymous with ‘not alive’. If there are borderline cases due to the vagueness of the concept of life then that is being set to one side.
The thought experiment gets off the ground with the concept of superposition that arises in quantum mechanics.
From wikipedia: ‘The principle of superposition states that if the world can be in any configuration, any possible arrangement of particles or fields, and if the world could also be in another configuration, then the world can also be in a state which is a superposition of the two, where the amount of each configuration that is in the superposition is specified by a complex number.’
This kind of superposition is common at the subatomic level and is only resolved once a particle’s position or momentum is observed, for example. The thought experiment links the decay of radioactive material to the life/death state of the cat because whether or not a particle is emitted by excited atoms (i.e. gives off radiation) is an instance of the quantum uncertainty that is only resolved by observation. Because the radioactive decay kills the cat and whether or not sufficient decay has occurred is a matter of uncertainty, the cat itself is placed in a superposition of both live and dead states, in the same way as the decaying atoms.
On one interpretation, the cat is both alive and not alive. On another, there is a fact of the matter as to whether the cat is alive or dead, but we just cannot know which until we look inside the box…
Thanks for your kind response and the link to more….
http://intentionalobjects.wordpress.com/2011/01/21/non-contradiction/
Perhaps this is related to something I read about the other day….the uncertainty principle….
Food for thought. Thanks.
Now look what you’ve done… You have made me VERY curious about quantum theory.
Here is a quote from a book called ‘Breaking the Time Barrier’ by Jenny Randles:
The team could easily create twin particles……test whether communication between the entangled particles was occurring at faster than light speeds …..If quantum theory was correct, the twin particles would be entangled and act as one. Changes induced by …..would be transmitted to the twin photon, causing it to react in sympathy….Test after test produced the same outcome. The entangled particles were spookily linked and any communication causing them to act this way not only exceeded light speed, it appeared instantaneous. Although experiments like Aspect’s have now proven quantum theory beyond a reasonable doubt, Einstein was by no means alone in denying this version of the nature of reality. Erwin Schrodinger was also highly skeptical. His thought experiment imagined a cat……quantum physics predicts that the pellet fires and the cat dies and at the same time the pellet does not fire and it survives…..These two possibilities are called superpositions and exist until something causes reality to manifest as a live cat or a dead cat…..making the choice between the various possible outcomes…..Every event that happens involves countless possible outcomes…Yet quantum mechanics argues that all these multiple states must form superpositions and all remain real until the wave function collapses into the reality that we experience.
Yep…. I’m sticking with # 2
I would not seek to argue against such a well-founded theory. Yet, one way for the dogged coherentist to deny the conclusions of true contradiction or a failure of bivalence is to deny that superpositioned states are truly contradictory, or even contrary. It may be that our concepts like the momentum and position etc. of ordinary objects do not apply to microscopic entities and we are only able to analogize from the behaviour of medium-sized dry goods to behaviour of “entities” at the quantum level. This would explain why we do not see quantum effects at the macro level, e.g. “undead” cats. Our everyday concepts do apply well enough to everyday objects like cats in everyday states like being alive.
Oh, I just thought of an example.
Most would say that SQUARE CIRCLE is a contradictory concept. Yet, when you take into account non-euclidean geomertries, it turns out that this view asumes a flat space. There are exotic topologies that will allow the above concept to be instantiated. But, our everyday though works in flat space.
Erwin Schrodinger proposed the paradox in order to expose in a more direct manner what he and many others believed was an absurd implication of the Copenhagen Interpretation, viz., if subatomic particles behave indefinitely, then so too must macroscopic objects (that is, insofar as subatomic particles compose macroscopic objects).
In other words, the Copenhagen Interpretation entails that there must exist uncertainty relationships between classical values, such as position and velocity, of macroscopic objects, e.g., emeralds, roses, and cats. However, we may with a very high degree of precision simultaneously assign cats classical values. Thus, Copenhagen indeterminacy is false.
The standard Copenhagen response consists in both biting the proverbial bullet and noting that the implication is not as absurd as one might first suppose. In nuce, the response goes something like this: one may harmonize the determinacy of macroscopic objects with the indeterminacy of microscopic objects by showing that a wave function represents the initial state of a macro-object, and that, due to the mass of the macro-object, the wave function will remain very high over a relatively very long period of time (Schrodinger’s equation is here material).
Schrodinger’s cat paradox, however, circumvents the response (which most parties deem more than plausible) and ties the indeterminacy of subatomic particles to macroscopic objects by introducing the cat as means to measuring a property of a subatomic particle. If, as the Copenhagen Interpretation asserts, the wave function is a complete description of the wave/particle duality, that is, if the wave function establishes completely the possible information available from which to calculate the probability that a measurement procedure will return a given value, then the state of the radioactive atom is indeterminate (in this case, the probability of decay is .50 and non-decay is .50).
If the atom’s state is indeterminate, then whether the cat is alive or dead is indeterminate. However, cats are at any time either alive or not alive; never neither, never both. Thus, difficulties ensue for the Copenhagen Interpretation- or so think critics contend, at least.
Before continuing, I should clarify two things.
First, (2) does not seem at all correct because we have copious amounts of experimental evidence which confirm that the wave function is a complete description (note here the failure of the Einstein-Podolsky-Rosen argument) and that quantum events are probabilistic in nature.
Second, (3) makes no sense at all: an unassertable sentence is either true or false. What?
That aside, on to (1), (4), and (5).
The Copenhagen Interpretation in no way entails the fourth option. Rather, some ontologically bloated and immoderate many-worlds interpretation (MWI) entails (4). However, even if in the end a MWI were to prove acceptable, it would not follow that (4) is a contradiction, let alone a true contradiction, because a contradiction entails that P and not-P are true in the same world at the same time and in the same respect, and this is of course not the case under a MWI: the cat is alive and not alive at two different worlds.
The first option also strikes me as problematic. If the perhaps the most highly confirmed, most successful (measured in terms of accuracy of predictions) scientific theory to date overwhelmingly suggests that quantum events are probabilistic in nature, then for one to assert (1) seems to me to beg the question:
‘The cat must be either alive or not alive.’
‘Why is that?’
‘Because it is metaphysically necessary!’
Moreover, the intuition which most likely engenders the attraction towards (1) may I think find an easy home in (5). That is, most have the intuition that if one were to investigate the box one would observe a live cat or a dead cat. The Copenhagen Interpretation, commonly construed endorses (5), says that when one investigates the box, one *will* observe a live cat or a dead cat. However, before observing the cat one must content oneself with the information one possesses concerning the state of the radioactive atom: the probability of decay and non-decay is .50 and .50, respectively. Therefore, before observing the cat, one’s degree of belief that one will, say, find the cat dead is .50. In other words, one can neither assert nor believe independently of observation whether the cat *is* alive or not alive. For the state of a quantum system *is* its corresponding probability space.
The difficulty which remains for the Copenhagen solution is the measurement problem: When, precisely, does a measurement / observation occur and hence when does the wave function collapse from the probability distribution to the determinate value? The problem is a contentious one and is by no means settled.
In the end, I vote for (5).
Aaron,
So am I correct in taking your indirect question to be whether Schrodinger’s Cat can be legitimately used to attack the principles of bivalence and contradiction? I find that pretty interesting! My knowledge of quantum mechanics is quite poor, but I suppose my answer to your initial post depends on my understanding of how subatomic particles could be called indeterminate if, after being measured, they show a determined state. You said:
“If, as the Copenhagen Interpretation asserts, the wave function is a complete description of the wave/particle duality, that is, if the wave function establishes completely the possible information available from which to calculate the probability that a measurement procedure will return a given value, then the state of the radioactive atom is indeterminate (in this case, the probability of decay is .50 and non-decay is .50).”
Is this, then, the issue?: the probability of decay/non-decay is known to be 50/50 but measurement procedures will only represent one of these two probabilities and so the act of measuring interferes with rather than confirms the state/superposition of said subatomic particle. I have heard of this problem being called the measurement problem, and it too seems to deal with wavefunction collapse. Again, please forgive the poverty of my knowledge and any misunderstanding on my part – my knowledge of quantum mechanics and the behavior of subatomic particles is quite small. However, if I understand it correctly, I suppose my initial question still stands of how we can even determine that subatomic particles possess superpositions and that measurement results in what I would call an unnatural (or a forced) collapse into a single state. Wouldn’t all attempts to ascertain whether the state of subatomic particles is determined or not result in measurement?
@ Aaron—indefinitely<=in your first paragraph, that word is supposed to be indeterminate. Correct? If yes, maybe the editor will fix it and then delete this line. If indefinitely is the correct word, then I'm more confused.
I didn't like the word meaningless in option two but the word bivalence (in option 5) threw me also. Without that additional phrase, you would have swayed me to vote for 5.
It is the timing, yes? At one moment the cat is alive. At another moment the cat might be dead. BUT at the moment in question (in the transition) we don't know.
Is it the case of the excluded middle?
http://www.philosophyprofessor.com/philosophies/excluded-middle-law.php
I'm thinking that we can't drop bivalence if I understand its meaning. The proposition has to be clear. The steps have to be adequate. A proposition can't predict the future. It has to be current. Am I wrong?
If I understand Aaron correctly, the cat is dead in one world and alive in another world. The wave collapses and then we have our current reality.
So where is that option? #6. The cat is alive in one world and dead in another world.
It's string theory. Possible simultaneous worlds. IF you set up the question so that we have to believe that these superpositions are true, then the cat is alive in one world and dead in another world.
Certainly that seems like nonsense. But it also seems like nonsense that photons can communicate instantly which is what quantum theory states. Correct?
Is this the definition of bivalence that you're using:
In logic, the semantic principle of bivalence states that every declarative sentence expressing a proposition (of a theory under inspection) is either true or false.
My point is that if you state that these two statements are true
1. An atom can be in a state of decay and non decay simultaneously until you observe it
2. Once you observe it, it will chose either decay or nondecay
Then the cat is alive until you observe it. And once you observe it, it will be known to you if it is dead or alive.
Here is a quote from a new york times article
http://www.nytimes.com/1996/06/02/weekinreview/on-skinning-schrodinger-s-cat.html?pagewanted=3&src=pm
"Our brains didn't grow up down there so we can probably never really get it."
So….I think …for now….I’m sticking with my vote for #2 if you won't offer me #6
I didn’t offer #6 because I wanted to put pressure on bivalence.
Susan,
I meant ‘indefinitely’ to connote its second definition ‘not clearly define or determined; not precise or exact’ and so used it as a synonym for ‘indeterminate;’ I apologize for the miscommunication.
“It is the timing, yes? At one moment the cat is alive. At another moment the cat might be dead. BUT at the moment in question (in the transition) we don’t know.”
No, not quite. It is not that wave function entails the cat transitions to and fro in the states ‘alive’ and ‘not alive.’ Rather, in the Copenhagen Interpretation, the state of a quantum system is fundamentally indeterminate. That is, the wave function describes completely the possible outcomes (the probability amplitude) of the values (momentum, position, etc.) of a measurement procedure of a subatomic particle. To assert otherwise is to impose determinacy upon an indeterminate event.
“If I understand Aaron correctly, the cat is dead in one world and alive in another world. The wave collapses and then we have our current reality.”
In bringing up multiple world interpretations I meant only to clarify that (4) is a poor option since nobody really asserts that the cat is both alive and not alive in the same sense and in the same way.
“My point is that if you state that these two statements are true
1. An atom can be in a state of decay and non decay simultaneously until you observe it
2. Once you observe it, it will chose either decay or nondecay
Then the cat is alive until you observe it. And once you observe it, it will be known to you if it is dead or alive.”
Again, Susan, to say, ‘Then the cat is alive until you observe it,’ is to miss the initial point: The Copenhagen Interpretation holds that whether the cat is alive or not is indeterminate. In other words, to assert that ‘The cat is now determinately alive’ or ‘The cat is now determinately not alive’ is to impose determinacy upon the quantum system when none is to be found.
The wave function collapses when a measurement occurs. Think of it this way: the probability of all the various outcomes are narrowed down to a definite value when one measures the particle. What exactly constitutes a measurement procedure is a different matter. In Schrodinger’s cat paradox, most who endorse the Copenhagen Interpretation (or some close variant) hold that the Geiger counter measures the particle and so the conscious act of observing is not necessary.
Finally, as an aside, there remain good reasons besides quantum paradoxes why one might want to reject the law of excluded middle (LEM). In fact, the reasons need not entail a rejection of bivalence. For instance, intuitionistic logic, a bivalent logic, rejects LEM and the Logic of Paradox, a three value logic, accepts LEM.
Ok. I change my vote to 5. 🙂
Okay, then my pressure tactic worked!
Ok, this post and the corresponding comments have made me: One, feel a little lost; two, realize I need to go spend some time understanding what you said; and three re-acknowledge the beauty of a community of thinkers. Wow, I love the direct communication of complicated ideas.
You are assuming there is one cat. many Worlder would
say
6) There is an alive cat and a dead cat
Perhaps, but that does not matter to me as I am concerned only about the things going on in one world.
Even though I assume the blog entry was mainly about bivalence, the post and the comments have renewed my interest in string theory. I’m going to watch Brian Green’s documentary called the ‘Elegant Universe’ and I’ve put Stephen Hawking’s book “Grand Design’ on my reading list.
On another note, I have been thinking about the concept “bivalence”. My google search only helps me a little. It seems you could devote an entire course to the concept. It seems in simple terms, bivalence states that every declarative sentence expressing a proposition (of a theory under inspection) is either true or false.
I went to a “philosophy workshop” yesterday. It seemed to me that the exercise parameters offered to us reduced our choices. It seemed we were not allowed the answer “it depends.” It seemed we were only allowed true or false. The more I think about it, the more it seems inadequate.
For instance, is the below statement true or false?
Domestication of cats is bad.
Right, but I could just say that “Domestication of cats is bad.” does not express a claim that has a truth value at all. It is merely an expression of your approval or disapproval of domesticating cats. (All moral claims would go this way as well)
So you’re saying that there are no moral claims that can be deemed objectively true or false? OR…are you saying that by definition bivalence does not include moral claims?
I don’t know the answer to whether moral claims can be objectivity true or false. It was just a way out of your problem.
I love that answer.